From fb6a1fae0a0475a498bba27bd2c906c11f9f2498 Mon Sep 17 00:00:00 2001
From: Matheus Bonavite dos Reis Cardoso
 <36443980+MatheusBonavite@users.noreply.github.com>
Date: Tue, 8 Dec 2020 04:59:32 -0300
Subject: [PATCH 001/264] Add Horner's Method (#575)

* Add Horner's Method

* Update README.md

Co-authored-by: matheus <matheus.cardoso@sydle.com>
---
 src/algorithms/math/horner-method/README.md   | 21 +++++++++++++++++++
 .../__test__/hornerMethod.test.js             | 14 +++++++++++++
 .../math/horner-method/hornerMethod.js        | 17 +++++++++++++++
 3 files changed, 52 insertions(+)
 create mode 100644 src/algorithms/math/horner-method/README.md
 create mode 100644 src/algorithms/math/horner-method/__test__/hornerMethod.test.js
 create mode 100644 src/algorithms/math/horner-method/hornerMethod.js

diff --git a/src/algorithms/math/horner-method/README.md b/src/algorithms/math/horner-method/README.md
new file mode 100644
index 0000000000..719257b330
--- /dev/null
+++ b/src/algorithms/math/horner-method/README.md
@@ -0,0 +1,21 @@
+# Horner's Method
+
+In mathematics, Horner's method (or Horner's scheme) is an algorithm for polynomial evaluation.
+With this method, it is possible to evaluate a polynomial with only n additions and n multiplications.
+Hence, its storage requirements are n times the number of bits of x.
+
+Horner's method can be based on the following identity:
+![](https://wikimedia.org/api/rest_v1/media/math/render/svg/2a576e42d875496f8b0f0dda5ebff7c2415532e4)
+, which is called Horner's rule.
+
+To solve the right part of the identity above, for a given x, we start by iterating through the polynomial from the inside out,
+accumulating each iteration result. After n iterations, with n being the order of the polynomial, the accumulated result gives
+us the polynomial evaluation. 
+
+Using the polynomial:
+![](http://www.sciweavers.org/tex2img.php?eq=%244x%5E4%20%2B%202x%5E3%20%2B%203x%5E2%2B%20x%5E1%20%2B%203%24&bc=White&fc=Black&im=jpg&fs=12&ff=arev&edit=0), a traditional approach to evaluate it at x = 2, could be representing it as an array [3,1,3,2,4] and iterate over it saving each iteration value at an accumulator, such as acc += pow(x=2,index) * array[index]. In essence, each power of a number (pow) operation is n-1 multiplications. So, in this scenario, a total of 15 operations would have happened, composed of 5 additions, 5 multiplications, and 5 pows.
+
+Now, using the same scenario but with Horner's rule, the polynomial can be re-written as ![](http://www.sciweavers.org/tex2img.php?eq=%24x%28x%28x%284x%2B2%29%2B3%29%2B1%29%2B3%24&bc=White&fc=Black&im=jpg&fs=12&ff=arev&edit=0), representing it as [4,2,3,1,3] it is possible to save the first iteration as acc = arr[0]*(x=2) + arr[1], and then finish iterations for acc *= (x=2) + arr[index]. In the same scenario but using Horner's rule, a total of 10 operations would have happened, composed of only 5 additions and 5 multiplications.
+## References
+
+- [Wikipedia](https://en.wikipedia.org/wiki/Horner%27s_method)
diff --git a/src/algorithms/math/horner-method/__test__/hornerMethod.test.js b/src/algorithms/math/horner-method/__test__/hornerMethod.test.js
new file mode 100644
index 0000000000..85d74bbc8d
--- /dev/null
+++ b/src/algorithms/math/horner-method/__test__/hornerMethod.test.js
@@ -0,0 +1,14 @@
+import hornerMethod from '../hornerMethod';
+
+describe('hornerMethod', () => {
+  it('should evaluate the polynomial on the specified point correctly', () => {
+    expect(hornerMethod([8],0.1)).toBe(8);
+    expect(hornerMethod([2,4,2,5],0.555)).toBe(7.68400775);
+    expect(hornerMethod([2,4,2,5],0.75)).toBe(9.59375);
+    expect(hornerMethod([1,1,1,1,1],1.75)).toBe(20.55078125);
+    expect(hornerMethod([15,3.5,0,2,1.42,0.41],0.315)).toBe(1.136730065140625);
+    expect(hornerMethod([0,0,2.77,1.42,0.41],1.35)).toBe(7.375325000000001);
+    expect(hornerMethod([0,0,2.77,1.42,2.3311],1.35)).toBe(9.296425000000001);
+    expect(hornerMethod([2,0,0,5.757,5.31412,12.3213],3.141)).toBe(697.2731167035034);
+  });
+});
\ No newline at end of file
diff --git a/src/algorithms/math/horner-method/hornerMethod.js b/src/algorithms/math/horner-method/hornerMethod.js
new file mode 100644
index 0000000000..11b029f879
--- /dev/null
+++ b/src/algorithms/math/horner-method/hornerMethod.js
@@ -0,0 +1,17 @@
+/**
+ * Returns the evaluation of a polynomial function at a certain point.
+ * Uses Horner's rule.
+ * @param {number[]} numbers
+ * @return {number}
+ */
+export default function hornerMethod(numbers, point) {
+  // polynomial function is just a constant.
+  if (numbers.length === 1) {
+    return numbers[0];
+  }
+  return numbers.reduce((accumulator, currentValue, index) => {
+    return index === 1
+      ? numbers[0] * point + currentValue
+      : accumulator * point + currentValue;
+  });
+}

From 21400e36fc56a8e89ed94a02942bcde06211325c Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Tue, 8 Dec 2020 09:52:37 +0100
Subject: [PATCH 002/264] Simplify Horner's Method code and add the link to it
 in main READMe.

---
 README.md                                     |  1 +
 src/algorithms/math/horner-method/README.md   | 21 +++++++--------
 .../__test__/classicPolynome.test.js          | 14 ++++++++++
 .../__test__/hornerMethod.test.js             | 27 ++++++++++++-------
 .../math/horner-method/classicPolynome.js     | 16 +++++++++++
 .../math/horner-method/hornerMethod.js        | 21 +++++++--------
 6 files changed, 68 insertions(+), 32 deletions(-)
 create mode 100644 src/algorithms/math/horner-method/__test__/classicPolynome.test.js
 create mode 100644 src/algorithms/math/horner-method/classicPolynome.js

diff --git a/README.md b/README.md
index 88d3b7ca89..a8d1b9e7f6 100644
--- a/README.md
+++ b/README.md
@@ -73,6 +73,7 @@ a set of rules that precisely define a sequence of operations.
   * `B` [Complex Number](src/algorithms/math/complex-number) - complex numbers and basic operations with them
   * `B` [Radian & Degree](src/algorithms/math/radian) - radians to degree and backwards conversion
   * `B` [Fast Powering](src/algorithms/math/fast-powering)
+  * `B` [Horner's method](src/algorithms/math/horner-method) - polynomial evaluation
   * `A` [Integer Partition](src/algorithms/math/integer-partition)
   * `A` [Square Root](src/algorithms/math/square-root) - Newton's method
   * `A` [Liu Hui π Algorithm](src/algorithms/math/liu-hui) - approximate π calculations based on N-gons
diff --git a/src/algorithms/math/horner-method/README.md b/src/algorithms/math/horner-method/README.md
index 719257b330..4526e5b167 100644
--- a/src/algorithms/math/horner-method/README.md
+++ b/src/algorithms/math/horner-method/README.md
@@ -1,21 +1,20 @@
 # Horner's Method
 
-In mathematics, Horner's method (or Horner's scheme) is an algorithm for polynomial evaluation.
-With this method, it is possible to evaluate a polynomial with only n additions and n multiplications.
-Hence, its storage requirements are n times the number of bits of x.
+In mathematics, Horner's method (or Horner's scheme) is an algorithm for polynomial evaluation. With this method, it is possible to evaluate a polynomial with only `n` additions and `n` multiplications. Hence, its storage requirements are `n` times the number of bits of `x`.
 
 Horner's method can be based on the following identity:
-![](https://wikimedia.org/api/rest_v1/media/math/render/svg/2a576e42d875496f8b0f0dda5ebff7c2415532e4)
-, which is called Horner's rule.
 
-To solve the right part of the identity above, for a given x, we start by iterating through the polynomial from the inside out,
-accumulating each iteration result. After n iterations, with n being the order of the polynomial, the accumulated result gives
-us the polynomial evaluation. 
+![Horner's rule](https://wikimedia.org/api/rest_v1/media/math/render/svg/2a576e42d875496f8b0f0dda5ebff7c2415532e4)
 
-Using the polynomial:
-![](http://www.sciweavers.org/tex2img.php?eq=%244x%5E4%20%2B%202x%5E3%20%2B%203x%5E2%2B%20x%5E1%20%2B%203%24&bc=White&fc=Black&im=jpg&fs=12&ff=arev&edit=0), a traditional approach to evaluate it at x = 2, could be representing it as an array [3,1,3,2,4] and iterate over it saving each iteration value at an accumulator, such as acc += pow(x=2,index) * array[index]. In essence, each power of a number (pow) operation is n-1 multiplications. So, in this scenario, a total of 15 operations would have happened, composed of 5 additions, 5 multiplications, and 5 pows.
+This identity is called _Horner's rule_.
+
+To solve the right part of the identity above, for a given `x`, we start by iterating through the polynomial from the inside out, accumulating each iteration result. After `n` iterations, with `n` being the order of the polynomial, the accumulated result gives us the polynomial evaluation. 
+
+**Using the polynomial:**
+![Traditional approach](http://www.sciweavers.org/tex2img.php?eq=%244x%5E4%20%2B%202x%5E3%20%2B%203x%5E2%2B%20x%5E1%20%2B%203%24&bc=White&fc=Black&im=jpg&fs=12&ff=arev&edit=0), a traditional approach to evaluate it at `x = 2`, could be representing it as an array `[3, 1, 3, 2, 4]` and iterate over it saving each iteration value at an accumulator, such as `acc += pow(x=2, index) * array[index]`. In essence, each power of a number (`pow`) operation is `n-1` multiplications. So, in this scenario, a total of `14` operations would have happened, composed of `4` additions, `5` multiplications, and `5` pows (we're assuming that each power is calculated by repeated multiplication).
+
+Now, **using the same scenario but with Horner's rule**, the polynomial can be re-written as ![Horner's rule approach](http://www.sciweavers.org/tex2img.php?eq=%24x%28x%28x%284x%2B2%29%2B3%29%2B1%29%2B3%24&bc=White&fc=Black&im=jpg&fs=12&ff=arev&edit=0), representing it as `[4, 2, 3, 1, 3]` it is possible to save the first iteration as `acc = arr[0] * (x=2) + arr[1]`, and then finish iterations for `acc *= (x=2) + arr[index]`. In the same scenario but using Horner's rule, a total of `10` operations would have happened, composed of only `4` additions and `4` multiplications.
 
-Now, using the same scenario but with Horner's rule, the polynomial can be re-written as ![](http://www.sciweavers.org/tex2img.php?eq=%24x%28x%28x%284x%2B2%29%2B3%29%2B1%29%2B3%24&bc=White&fc=Black&im=jpg&fs=12&ff=arev&edit=0), representing it as [4,2,3,1,3] it is possible to save the first iteration as acc = arr[0]*(x=2) + arr[1], and then finish iterations for acc *= (x=2) + arr[index]. In the same scenario but using Horner's rule, a total of 10 operations would have happened, composed of only 5 additions and 5 multiplications.
 ## References
 
 - [Wikipedia](https://en.wikipedia.org/wiki/Horner%27s_method)
diff --git a/src/algorithms/math/horner-method/__test__/classicPolynome.test.js b/src/algorithms/math/horner-method/__test__/classicPolynome.test.js
new file mode 100644
index 0000000000..8cdf950d6e
--- /dev/null
+++ b/src/algorithms/math/horner-method/__test__/classicPolynome.test.js
@@ -0,0 +1,14 @@
+import classicPolynome from '../classicPolynome';
+
+describe('classicPolynome', () => {
+  it('should evaluate the polynomial for the specified value of x correctly', () => {
+    expect(classicPolynome([8], 0.1)).toBe(8);
+    expect(classicPolynome([2, 4, 2, 5], 0.555)).toBe(7.68400775);
+    expect(classicPolynome([2, 4, 2, 5], 0.75)).toBe(9.59375);
+    expect(classicPolynome([1, 1, 1, 1, 1], 1.75)).toBe(20.55078125);
+    expect(classicPolynome([15, 3.5, 0, 2, 1.42, 0.41], 0.315)).toBe(1.1367300651406251);
+    expect(classicPolynome([0, 0, 2.77, 1.42, 0.41], 1.35)).toBe(7.375325000000001);
+    expect(classicPolynome([0, 0, 2.77, 1.42, 2.3311], 1.35)).toBe(9.296425000000001);
+    expect(classicPolynome([2, 0, 0, 5.757, 5.31412, 12.3213], 3.141)).toBe(697.2731167035034);
+  });
+});
diff --git a/src/algorithms/math/horner-method/__test__/hornerMethod.test.js b/src/algorithms/math/horner-method/__test__/hornerMethod.test.js
index 85d74bbc8d..177ceb1aad 100644
--- a/src/algorithms/math/horner-method/__test__/hornerMethod.test.js
+++ b/src/algorithms/math/horner-method/__test__/hornerMethod.test.js
@@ -1,14 +1,21 @@
 import hornerMethod from '../hornerMethod';
+import classicPolynome from '../classicPolynome';
 
 describe('hornerMethod', () => {
-  it('should evaluate the polynomial on the specified point correctly', () => {
-    expect(hornerMethod([8],0.1)).toBe(8);
-    expect(hornerMethod([2,4,2,5],0.555)).toBe(7.68400775);
-    expect(hornerMethod([2,4,2,5],0.75)).toBe(9.59375);
-    expect(hornerMethod([1,1,1,1,1],1.75)).toBe(20.55078125);
-    expect(hornerMethod([15,3.5,0,2,1.42,0.41],0.315)).toBe(1.136730065140625);
-    expect(hornerMethod([0,0,2.77,1.42,0.41],1.35)).toBe(7.375325000000001);
-    expect(hornerMethod([0,0,2.77,1.42,2.3311],1.35)).toBe(9.296425000000001);
-    expect(hornerMethod([2,0,0,5.757,5.31412,12.3213],3.141)).toBe(697.2731167035034);
+  it('should evaluate the polynomial for the specified value of x correctly', () => {
+    expect(hornerMethod([8], 0.1)).toBe(8);
+    expect(hornerMethod([2, 4, 2, 5], 0.555)).toBe(7.68400775);
+    expect(hornerMethod([2, 4, 2, 5], 0.75)).toBe(9.59375);
+    expect(hornerMethod([1, 1, 1, 1, 1], 1.75)).toBe(20.55078125);
+    expect(hornerMethod([15, 3.5, 0, 2, 1.42, 0.41], 0.315)).toBe(1.136730065140625);
+    expect(hornerMethod([0, 0, 2.77, 1.42, 0.41], 1.35)).toBe(7.375325000000001);
+    expect(hornerMethod([0, 0, 2.77, 1.42, 2.3311], 1.35)).toBe(9.296425000000001);
+    expect(hornerMethod([2, 0, 0, 5.757, 5.31412, 12.3213], 3.141)).toBe(697.2731167035034);
   });
-});
\ No newline at end of file
+
+  it('should evaluate the same polynomial value as classical approach', () => {
+    expect(hornerMethod([8], 0.1)).toBe(classicPolynome([8], 0.1));
+    expect(hornerMethod([2, 4, 2, 5], 0.555)).toBe(classicPolynome([2, 4, 2, 5], 0.555));
+    expect(hornerMethod([2, 4, 2, 5], 0.75)).toBe(classicPolynome([2, 4, 2, 5], 0.75));
+  });
+});
diff --git a/src/algorithms/math/horner-method/classicPolynome.js b/src/algorithms/math/horner-method/classicPolynome.js
new file mode 100644
index 0000000000..1f6aa8613c
--- /dev/null
+++ b/src/algorithms/math/horner-method/classicPolynome.js
@@ -0,0 +1,16 @@
+/**
+ * Returns the evaluation of a polynomial function at a certain point.
+ * Uses straightforward approach with powers.
+ *
+ * @param {number[]} coefficients - i.e. [4, 3, 2] for (4 * x^2 + 3 * x + 2)
+ * @param {number} xVal
+ * @return {number}
+ */
+export default function classicPolynome(coefficients, xVal) {
+  return coefficients.reverse().reduce(
+    (accumulator, currentCoefficient, index) => {
+      return accumulator + currentCoefficient * (xVal ** index);
+    },
+    0,
+  );
+}
diff --git a/src/algorithms/math/horner-method/hornerMethod.js b/src/algorithms/math/horner-method/hornerMethod.js
index 11b029f879..2236170ed1 100644
--- a/src/algorithms/math/horner-method/hornerMethod.js
+++ b/src/algorithms/math/horner-method/hornerMethod.js
@@ -1,17 +1,16 @@
 /**
  * Returns the evaluation of a polynomial function at a certain point.
  * Uses Horner's rule.
- * @param {number[]} numbers
+ *
+ * @param {number[]} coefficients - i.e. [4, 3, 2] for (4 * x^2 + 3 * x + 2)
+ * @param {number} xVal
  * @return {number}
  */
-export default function hornerMethod(numbers, point) {
-  // polynomial function is just a constant.
-  if (numbers.length === 1) {
-    return numbers[0];
-  }
-  return numbers.reduce((accumulator, currentValue, index) => {
-    return index === 1
-      ? numbers[0] * point + currentValue
-      : accumulator * point + currentValue;
-  });
+export default function hornerMethod(coefficients, xVal) {
+  return coefficients.reduce(
+    (accumulator, currentCoefficient) => {
+      return accumulator * xVal + currentCoefficient;
+    },
+    0,
+  );
 }

From 9751670a06afb2aab359cb5f5fe78a4be713a023 Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Tue, 8 Dec 2020 09:56:46 +0100
Subject: [PATCH 003/264] Use text formulas instead of images since images a
 not loading sometimes.

---
 src/algorithms/math/horner-method/README.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/src/algorithms/math/horner-method/README.md b/src/algorithms/math/horner-method/README.md
index 4526e5b167..991a674deb 100644
--- a/src/algorithms/math/horner-method/README.md
+++ b/src/algorithms/math/horner-method/README.md
@@ -11,9 +11,9 @@ This identity is called _Horner's rule_.
 To solve the right part of the identity above, for a given `x`, we start by iterating through the polynomial from the inside out, accumulating each iteration result. After `n` iterations, with `n` being the order of the polynomial, the accumulated result gives us the polynomial evaluation. 
 
 **Using the polynomial:**
-![Traditional approach](http://www.sciweavers.org/tex2img.php?eq=%244x%5E4%20%2B%202x%5E3%20%2B%203x%5E2%2B%20x%5E1%20%2B%203%24&bc=White&fc=Black&im=jpg&fs=12&ff=arev&edit=0), a traditional approach to evaluate it at `x = 2`, could be representing it as an array `[3, 1, 3, 2, 4]` and iterate over it saving each iteration value at an accumulator, such as `acc += pow(x=2, index) * array[index]`. In essence, each power of a number (`pow`) operation is `n-1` multiplications. So, in this scenario, a total of `14` operations would have happened, composed of `4` additions, `5` multiplications, and `5` pows (we're assuming that each power is calculated by repeated multiplication).
+`4 * x^4 + 2 * x^3 + 3 * x^2 + x^1 + 3`, a traditional approach to evaluate it at `x = 2`, could be representing it as an array `[3, 1, 3, 2, 4]` and iterate over it saving each iteration value at an accumulator, such as `acc += pow(x=2, index) * array[index]`. In essence, each power of a number (`pow`) operation is `n-1` multiplications. So, in this scenario, a total of `14` operations would have happened, composed of `4` additions, `5` multiplications, and `5` pows (we're assuming that each power is calculated by repeated multiplication).
 
-Now, **using the same scenario but with Horner's rule**, the polynomial can be re-written as ![Horner's rule approach](http://www.sciweavers.org/tex2img.php?eq=%24x%28x%28x%284x%2B2%29%2B3%29%2B1%29%2B3%24&bc=White&fc=Black&im=jpg&fs=12&ff=arev&edit=0), representing it as `[4, 2, 3, 1, 3]` it is possible to save the first iteration as `acc = arr[0] * (x=2) + arr[1]`, and then finish iterations for `acc *= (x=2) + arr[index]`. In the same scenario but using Horner's rule, a total of `10` operations would have happened, composed of only `4` additions and `4` multiplications.
+Now, **using the same scenario but with Horner's rule**, the polynomial can be re-written as `x * (x * (x * (4 * x + 2) + 3) + 1) + 3`, representing it as `[4, 2, 3, 1, 3]` it is possible to save the first iteration as `acc = arr[0] * (x=2) + arr[1]`, and then finish iterations for `acc *= (x=2) + arr[index]`. In the same scenario but using Horner's rule, a total of `10` operations would have happened, composed of only `4` additions and `4` multiplications.
 
 ## References
 

From 2ec7fe2f022d4025545b2068c486c4f5f4100e3c Mon Sep 17 00:00:00 2001
From: Rodrigo Stuani <stuani.developer@gmail.com>
Date: Wed, 9 Dec 2020 04:09:29 -0300
Subject: [PATCH 004/264] set Data Structure to "Estrutura de Dados" (#547)

set Data Structure to "Estrutura de Dados".

Co-authored-by: Oleksii Trekhleb <trehleb@gmail.com>
---
 README.pt-BR.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.pt-BR.md b/README.pt-BR.md
index c4d225e025..a1556c7fc2 100644
--- a/README.pt-BR.md
+++ b/README.pt-BR.md
@@ -21,7 +21,7 @@ _Leia isto em outros idiomas:_
 [_Español_](README.es-ES.md),
 [_Türk_](README.tr-TR.md)
 
-## Data Structures
+## Estrutura de Dados
 
 Uma estrutura de dados é uma maneira particular de organizar e armazenar dados em um computador para que ele possa
 ser acessado e modificado de forma eficiente. Mais precisamente, uma estrutura de dados é uma coleção de dados

From ebd6ffd2c0f3e9d3120dbf61c1961882b26f38e7 Mon Sep 17 00:00:00 2001
From: Brian Tomlin <tendonstrength@gmail.com>
Date: Wed, 9 Dec 2020 01:11:03 -0600
Subject: [PATCH 005/264] Fix typo in tree BFS testcase name (#542)

---
 .../breadth-first-search/__test__/breadthFirstSearch.test.js    | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/algorithms/tree/breadth-first-search/__test__/breadthFirstSearch.test.js b/src/algorithms/tree/breadth-first-search/__test__/breadthFirstSearch.test.js
index 4a77f0f310..2bf653a9cf 100644
--- a/src/algorithms/tree/breadth-first-search/__test__/breadthFirstSearch.test.js
+++ b/src/algorithms/tree/breadth-first-search/__test__/breadthFirstSearch.test.js
@@ -2,7 +2,7 @@ import BinaryTreeNode from '../../../../data-structures/tree/BinaryTreeNode';
 import breadthFirstSearch from '../breadthFirstSearch';
 
 describe('breadthFirstSearch', () => {
-  it('should perform DFS operation on tree', () => {
+  it('should perform BFS operation on tree', () => {
     const nodeA = new BinaryTreeNode('A');
     const nodeB = new BinaryTreeNode('B');
     const nodeC = new BinaryTreeNode('C');

From 8a12653ac3c1ef5fe2059c38fbf83aaf96618301 Mon Sep 17 00:00:00 2001
From: Xiaoming Fu <xmingfu86@gmail.com>
Date: Tue, 8 Dec 2020 23:13:05 -0800
Subject: [PATCH 006/264] Fix typo in comment (#540)

Address issue #528
---
 src/data-structures/tree/red-black-tree/RedBlackTree.js | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/data-structures/tree/red-black-tree/RedBlackTree.js b/src/data-structures/tree/red-black-tree/RedBlackTree.js
index 6bb47130c8..6e747afc75 100644
--- a/src/data-structures/tree/red-black-tree/RedBlackTree.js
+++ b/src/data-structures/tree/red-black-tree/RedBlackTree.js
@@ -155,7 +155,7 @@ export default class RedBlackTree extends BinarySearchTree {
       parentNode.parent = null;
     }
 
-    // Swap colors of granParent and parent nodes.
+    // Swap colors of grandParentNode and parentNode.
     this.swapNodeColors(parentNode, grandParentNode);
 
     // Return new root node.

From 87b5b2b5cffb39b54cc0c474d024bd49a8847d74 Mon Sep 17 00:00:00 2001
From: Kirill Kazakov <33637819+Gorgchap@users.noreply.github.com>
Date: Wed, 9 Dec 2020 10:18:36 +0300
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+# Алгоритмы и структуры данных в JavaScript
+
+[![Build Status](https://travis-ci.org/trekhleb/javascript-algorithms.svg?branch=master)](https://travis-ci.org/trekhleb/javascript-algorithms)
+[![codecov](https://codecov.io/gh/trekhleb/javascript-algorithms/branch/master/graph/badge.svg)](https://codecov.io/gh/trekhleb/javascript-algorithms)
+
+В этом репозитории содержатся базовые JavaScript-примеры
+многих популярных алгоритмов и структур данных.
+
+Для каждого алгоритма и структуры данных есть свой файл README
+с соответствующими пояснениями и ссылками на материалы для дальнейшего
+изучения (в том числе и ссылки на видеоролики в Ютубе).
+
+_Читать на других языках:_
+[_English_](https://github.com/trekhleb/javascript-algorithms/),
+[_简体中文_](README.zh-CN.md),
+[_繁體中文_](README.zh-TW.md),
+[_한국어_](README.ko-KR.md),
+[_日本語_](README.ja-JP.md),
+[_Polski_](README.pl-PL.md),
+[_Français_](README.fr-FR.md),
+[_Español_](README.es-ES.md),
+[_Português_](README.pt-BR.md)
+
+*☝ Замечание: этот репозиторий предназначен только для
+учебно-исследовательских целей (**не** для продакшена).*
+
+## Структуры данных
+
+Структура данных — определённый способ систематизации и хранения данных в компьютере таким образом,
+чтобы они могли быть легко доступны и изменяемы. Структура данных — совокупность коллекции значений
+данных, взаимосвязей между ними и функций или операций, которые могут применяться к данным.
+
+`B` - Новичок, `A` - Продвинутый
+
+* `B` [Связный список](src/data-structures/linked-list)
+* `B` [Двунаправленный связный список](src/data-structures/doubly-linked-list)
+* `B` [Очередь](src/data-structures/queue)
+* `B` [Стек](src/data-structures/stack)
+* `B` [Хеш-табица](src/data-structures/hash-table)
+* `B` [Куча](src/data-structures/heap) — максимальная и минимальная версии
+* `B` [Очередь с приоритетом](src/data-structures/priority-queue)
+* `A` [Префиксное дерево](src/data-structures/trie)
+* `A` [Деревья](src/data-structures/tree)
+  * `A` [Двоичное дерево поиска](src/data-structures/tree/binary-search-tree)
+  * `A` [АВЛ-дерево](src/data-structures/tree/avl-tree)
+  * `A` [Красно-чёрное дерево](src/data-structures/tree/red-black-tree)
+  * `A` [Дерево отрезков](src/data-structures/tree/segment-tree) — для минимума, максимума и суммы отрезков
+  * `A` [Дерево Фенвика](src/data-structures/tree/fenwick-tree) (двоичное индексированное дерево)
+* `A` [Граф](src/data-structures/graph) (ориентированный и неориентированный)
+* `A` [Система непересекающихся множеств](src/data-structures/disjoint-set)
+* `A` [Фильтр Блума](src/data-structures/bloom-filter)
+
+## Алгоритмы
+
+Алгоритм — однозначная спецификация по решению целого ряда задач (иными словами,
+это список правил, чётко определяющих ту или иную последовательность операций).
+
+`B` — Новичок, `A` — Продвинутый
+
+### Тематическое разделение алгоритмов
+
+* **Математика**
+  * `B` [Битовые манипуляции](src/algorithms/math/bits) — получение/запись/сброс/обновление битов, умножение/деление на 2, сделать отрицательным и т.п.
+  * `B` [Факториал](src/algorithms/math/factorial) 
+  * `B` [Числа Фибоначчи](src/algorithms/math/fibonacci) — классическое решение, решение в замкнутой форме
+  * `B` [Тест простоты](src/algorithms/math/primality-test) (метод пробного деления)
+  * `B` [Алгоритм Евклида](src/algorithms/math/euclidean-algorithm) — нахождение наибольшего общего делителя (НОД)
+  * `B` [Наименьшее общее кратное](src/algorithms/math/least-common-multiple) (НОК)
+  * `B` [Решето Эратосфена](src/algorithms/math/sieve-of-eratosthenes) — нахождение всех простых чисел до некоторого целого числа n
+  * `B` [Степень двойки](src/algorithms/math/is-power-of-two) — является ли число степенью двойки (простое и побитовое решения)
+  * `B` [Треугольник Паскаля](src/algorithms/math/pascal-triangle)
+  * `B` [Комплексные числа](src/algorithms/math/complex-number) — комплексные числа, базовые операции над ними
+  * `B` [Радианы и градусы](src/algorithms/math/radian) — конвертирование радианов в градусы и наоборот
+  * `B` [Быстрое возведение в степень](src/algorithms/math/fast-powering)
+  * `A` [Разбиение числа](src/algorithms/math/integer-partition)
+  * `A` [Квадратный корень](src/algorithms/math/square-root) — метод Ньютона
+  * `A` [Алгоритм Лю Хуэя](src/algorithms/math/liu-hui) — расчёт числа π с заданной точностью методом вписанных правильных многоугольников
+  * `A` [Дискретное преобразование Фурье](src/algorithms/math/fourier-transform) — разложение временной функции (сигнала) на частотные составляющие 
+* **Множества**
+  * `B` [Декартово произведение](src/algorithms/sets/cartesian-product) — результат перемножения множеств
+  * `B` [Тасование Фишера — Йетса](src/algorithms/sets/fisher-yates) — создание случайных перестановок конечного множества
+  * `A` [Булеан](src/algorithms/sets/power-set) — все подмножества заданного множества (побитовый поиск и поиск с возвратом)
+  * `A` [Перестановки](src/algorithms/sets/permutations) (с повторениями и без повторений)
+  * `A` [Сочетания](src/algorithms/sets/combinations) (с повторениями и без повторений)
+  * `A` [Наибольшая общая подпоследовательность](src/algorithms/sets/longest-common-subsequence)
+  * `A` [Наибольшая увеличивающаяся подпоследовательность](src/algorithms/sets/longest-increasing-subsequence)
+  * `A` [Наименьшая общая суперпоследовательность](src/algorithms/sets/shortest-common-supersequence)
+  * `A` [Задача о рюкзаке](src/algorithms/sets/knapsack-problem) — "0/1" и "неограниченный" рюкзаки
+  * `A` [Максимальный подмассив](src/algorithms/sets/maximum-subarray) — метод полного перебора и алгоритм Кадане
+  * `A` [Комбинации сумм](src/algorithms/sets/combination-sum) — нахождение всех комбинаций, сумма каждой из которых равна заданному числу
+* **Алгоритмы на строках**
+  * `B` [Расстояние Хэмминга](src/algorithms/string/hamming-distance) — число позиций, в которых соответствующие символы различны
+  * `A` [Расстояние Левенштейна](src/algorithms/string/levenshtein-distance) — метрика, измеряющая разность между двумя последовательностями
+  * `A` [Алгоритм Кнута — Морриса — Пратта](src/algorithms/string/knuth-morris-pratt) — поиск подстроки (сопоставление с шаблоном)
+  * `A` [Z-функция](src/algorithms/string/z-algorithm) — поиск подстроки (сопоставление с шаблоном)
+  * `A` [Алгоритм Рабина — Карпа](src/algorithms/string/rabin-karp) — поиск подстроки
+  * `A` [Наибольшая общая подстрока](src/algorithms/string/longest-common-substring)
+  * `A` [Разборщик регулярных выражений](src/algorithms/string/regular-expression-matching)
+* **Алгоритмы поиска**
+  * `B` [Линейный поиск](src/algorithms/search/linear-search)
+  * `B` [Поиск с перескоком](src/algorithms/search/jump-search) (поиск блоков) — поиск в упорядоченном массиве
+  * `B` [Двоичный поиск](src/algorithms/search/binary-search) — поиск в упорядоченном массиве
+  * `B` [Интерполяционный поиск](src/algorithms/search/interpolation-search) — поиск в равномерно распределённом упорядоченном массиве.
+* **Сортировки**
+  * `B` [Сортировка пузырьком](src/algorithms/sorting/bubble-sort)
+  * `B` [Сортировка выбором](src/algorithms/sorting/selection-sort)
+  * `B` [Сортировка вставками](src/algorithms/sorting/insertion-sort)
+  * `B` [Пирамидальная сортировка (сортировка кучей)](src/algorithms/sorting/heap-sort)
+  * `B` [Сортировка слиянием](src/algorithms/sorting/merge-sort)
+  * `B` [Быстрая сортировка](src/algorithms/sorting/quick-sort) — с использованием дополнительной памяти и без её использования
+  * `B` [Сортировка Шелла](src/algorithms/sorting/shell-sort)
+  * `B` [Сортировка подсчётом](src/algorithms/sorting/counting-sort)
+  * `B` [Поразрядная сортировка](src/algorithms/sorting/radix-sort)
+* **Связный список**
+  * `B` [Прямой обход](src/algorithms/linked-list/traversal)
+  * `B` [Обратный обход](src/algorithms/linked-list/reverse-traversal)
+* **Деревья**
+  * `B` [Поиск в глубину](src/algorithms/tree/depth-first-search)
+  * `B` [Поиск в ширину](src/algorithms/tree/breadth-first-search)
+* **Графы**
+  * `B` [Поиск в глубину](src/algorithms/graph/depth-first-search)
+  * `B` [Поиск в ширину](src/algorithms/graph/breadth-first-search)
+  * `B` [Алгоритм Краскала](src/algorithms/graph/kruskal) — нахождение минимального остовного дерева для взвешенного неориентированного графа
+  * `A` [Алгоритм Дейкстры](src/algorithms/graph/dijkstra) — нахождение кратчайших путей от одной из вершин графа до всех остальных
+  * `A` [Алгоритм Беллмана — Форда](src/algorithms/graph/bellman-ford) — нахождение кратчайших путей от одной из вершин графа до всех остальных
+  * `A` [Алгоритм Флойда — Уоршелла](src/algorithms/graph/floyd-warshall) — нахождение кратчайших расстояний между всеми вершинами графа
+  * `A` [Задача нахождения цикла](src/algorithms/graph/detect-cycle) — для ориентированных и неориентированных графов (на основе поиска в глубину и системы непересекающихся множеств)
+  * `A` [Алгоритм Прима](src/algorithms/graph/prim) — нахождение минимального остовного дерева для взвешенного неориентированного графа
+  * `A` [Топологическая сортировка](src/algorithms/graph/topological-sorting) — на основе поиска в глубину
+  * `A` [Шарниры (разделяющие вершины)](src/algorithms/graph/articulation-points) — алгоритм Тарьяна (на основе поиска в глубину)
+  * `A` [Мосты](src/algorithms/graph/bridges) — на основе поиска в глубину
+  * `A` [Эйлеров путь и Эйлеров цикл](src/algorithms/graph/eulerian-path) — алгоритм Флёри (однократное посещение каждой вершины)
+  * `A` [Гамильтонов цикл](src/algorithms/graph/hamiltonian-cycle) — проходит через каждую вершину графа ровно один раз
+  * `A` [Компоненты сильной связности](src/algorithms/graph/strongly-connected-components) — алгоритм Косарайю
+  * `A` [Задача коммивояжёра](src/algorithms/graph/travelling-salesman) — кратчайший маршрут, проходящий через указанные города с последующим возвратом в исходный город
+* **Криптография**
+  * `B` [Полиноминальный хэш](src/algorithms/cryptography/polynomial-hash) — функция кольцевого хэша, основанная на полиноме
+* **Машинное обучение**
+  * `B` [Нано-нейрон](https://github.com/trekhleb/nano-neuron) — 7 простых JavaScript функций, отображающих способности машины к обучению (прямое и обратное распространение)
+* **Прочие алгоритмы**
+  * `B` [Ханойская башня](src/algorithms/uncategorized/hanoi-tower)
+  * `B` [Поворот квадратной матрицы](src/algorithms/uncategorized/square-matrix-rotation) — используется дополнительная память
+  * `B` [Прыжки](src/algorithms/uncategorized/jump-game) — на основе бэктрекинга, динамического программирования (сверху-вниз + снизу-вверх) и жадных алгоритмов 
+  * `B` [Поиск уникальных путей](src/algorithms/uncategorized/unique-paths) — на основе бэктрекинга, динамического программирования и треугольника Паскаля
+  * `B` [Подсчёт дождевой воды](src/algorithms/uncategorized/rain-terraces) — на основе перебора и динамического программирования
+  * `B` [Задача о рекурсивной лестнице](src/algorithms/uncategorized/recursive-staircase) — подсчёт количества путей, по которым можно достичь верха лестницы (4 способа)
+  * `A` [Задача об N ферзях](src/algorithms/uncategorized/n-queens)
+  * `A` [Маршрут коня](src/algorithms/uncategorized/knight-tour)
+
+### Парадигмы программирования
+
+Парадигма программирования — общий метод или подход, лежащий в основе целого класса алгоритмов.
+Понятие "парадигма программирования" является более абстрактным по отношению к понятию "алгоритм",
+которое в свою очередь является более абстрактным по отношению к понятию "компьютерная пограмма".
+
+* **Алгоритмы полного перебора** — поиск лучшего решения исчерпыванием всевозможных вариантов
+  * `B` [Линейный поиск](src/algorithms/search/linear-search)
+  * `B` [Подсчёт дождевой воды](src/algorithms/uncategorized/rain-terraces)
+  * `B` [Задача о рекурсивной лестнице](src/algorithms/uncategorized/recursive-staircase) — подсчёт количества путей, по которым можно достичь верха лестницы
+  * `A` [Максимальный подмассив](src/algorithms/sets/maximum-subarray)
+  * `A` [Задача коммивояжёра](src/algorithms/graph/travelling-salesman) — кратчайший маршрут, проходящий через указанные города с последующим возвратом в исходный город
+  * `A` [Дискретное преобразование Фурье](src/algorithms/math/fourier-transform) — разложение временной функции (сигнала) на частотные составляющие
+* **Жадные алгоритмы** — принятие локально оптимальных решений с учётом допущения об оптимальности конечного решения 
+  * `B` [Прыжки](src/algorithms/uncategorized/jump-game)
+  * `A` [Задача о неограниченном рюкзаке](src/algorithms/sets/knapsack-problem)
+  * `A` [Алгоритм Дейкстры](src/algorithms/graph/dijkstra) — нахождение кратчайших путей от одной из вершин графа до всех остальных
+  * `A` [Алгоритм Прима](src/algorithms/graph/prim) — нахождение минимального остовного дерева для взвешенного неориентированного графа
+  * `A` [Алгоритм Краскала](src/algorithms/graph/kruskal) — нахождение минимального остовного дерева для взвешенного неориентированного графа
+* **Разделяй и властвуй** — рекурсивное разбиение решаемой задачи на более мелкие
+  * `B` [Двоичный поиск](src/algorithms/search/binary-search)
+  * `B` [Ханойская башня](src/algorithms/uncategorized/hanoi-tower)
+  * `B` [Треугольник Паскаля](src/algorithms/math/pascal-triangle)
+  * `B` [Алгоритм Евклида](src/algorithms/math/euclidean-algorithm) — нахождение наибольшего общего делителя (НОД)
+  * `B` [Сортировка слиянием](src/algorithms/sorting/merge-sort)
+  * `B` [Быстрая сортировка](src/algorithms/sorting/quick-sort)
+  * `B` [Поиск в глубину (дерево)](src/algorithms/tree/depth-first-search)
+  * `B` [Поиск в глубину (граф)](src/algorithms/graph/depth-first-search)
+  * `B` [Прыжки](src/algorithms/uncategorized/jump-game)
+  * `B` [Быстрое возведение в степень](src/algorithms/math/fast-powering)
+  * `A` [Перестановки](src/algorithms/sets/permutations) (с повторениями и без повторений)
+  * `A` [Сочетания](src/algorithms/sets/combinations) (с повторениями и без повторений)
+* **Динамическое программирование** — решение общей задачи конструируется на основе ранее найденных решений подзадач
+  * `B` [Числа Фибоначчи](src/algorithms/math/fibonacci)
+  * `B` [Прыжки](src/algorithms/uncategorized/jump-game)
+  * `B` [Поиск уникальных путей](src/algorithms/uncategorized/unique-paths)
+  * `B` [Подсчёт дождевой воды](src/algorithms/uncategorized/rain-terraces)
+  * `B` [Задача о рекурсивной лестнице](src/algorithms/uncategorized/recursive-staircase) — подсчёт количества путей, по которым можно достичь верха лестницы
+  * `A` [Расстояние Левенштейна](src/algorithms/string/levenshtein-distance) — метрика, измеряющая разность между двумя последовательностями
+  * `A` [Наибольшая общая подпоследовательность](src/algorithms/sets/longest-common-subsequence)
+  * `A` [Наибольшая общая подстрока](src/algorithms/string/longest-common-substring)
+  * `A` [Наибольшая увеличивающаяся подпоследовательность](src/algorithms/sets/longest-increasing-subsequence)
+  * `A` [Наименьшая общая суперпоследовательность](src/algorithms/sets/shortest-common-supersequence)
+  * `A` [Рюкзак 0-1](src/algorithms/sets/knapsack-problem)
+  * `A` [Разбиение числа](src/algorithms/math/integer-partition)
+  * `A` [Максимальный подмассив](src/algorithms/sets/maximum-subarray)
+  * `A` [Алгоритм Беллмана — Форда](src/algorithms/graph/bellman-ford) — поиск кратчайшего пути во взвешенном графе
+  * `A` [Алгоритм Флойда — Уоршелла](src/algorithms/graph/floyd-warshall) — нахождение кратчайших путей от одной из вершин графа до всех остальных
+  * `A` [Разборщик регулярных выражений](src/algorithms/string/regular-expression-matching)
+* **Поиск с возвратом (бэктрекинг)** — при поиске решения многократно делается попытка расширить текущее частичное решение. Если расширение
+невозможно, то происходит возврат к предыдущему более короткому частичному решению, и делается попытка его расширить другим возможным способом.
+Обычно используется обход пространства состояний в глубину.
+  * `B` [Прыжки](src/algorithms/uncategorized/jump-game)
+  * `B` [Поиск уникальных путей](src/algorithms/uncategorized/unique-paths)
+  * `B` [Булеан](src/algorithms/sets/power-set) — все подмножества заданного множества
+  * `A` [Гамильтонов цикл](src/algorithms/graph/hamiltonian-cycle) — проходит через каждую вершину графа ровно один раз
+  * `A` [Задача об N ферзях](src/algorithms/uncategorized/n-queens)
+  * `A` [Маршрут коня](src/algorithms/uncategorized/knight-tour)
+  * `A` [Комбинации сумм](src/algorithms/sets/combination-sum) — нахождение всех комбинаций, сумма каждой из которых равна заданному числу
+* **Метод ветвей и границ** — основан на упорядоченном переборе решений и рассмотрении только тех из них, которые являются перспективными
+(по тем или иным признакам) и отбрасывании бесперспективных множеств решений. Обычно используется обход в ширину в совокупности с обходом
+дерева пространства состояний в глубину.
+
+## Команды по использованию репозитория
+
+**Установка всех зависимостей**
+```
+npm install
+```
+
+**Запустить ESLint**
+
+Возможно, эта команда потребуется Вам для проверки качества кода.
+
+```
+npm run lint
+```
+
+**Запустить все тесты**
+```
+npm test
+```
+
+**Запустить определённый тест**
+```
+npm test -- 'LinkedList'
+```
+
+**Playground**
+
+Вы можете поэкспериментировать с алгоритмами и структурами данных в файле `./src/playground/playground.js` 
+(файл `./src/playground/__test__/playground.test.js` предназначен для написания тестов).
+
+Для проверки работоспособности вашего кода используйте команду:
+
+```
+npm test -- 'playground'
+```
+
+## Полезная информация
+
+### Ссылки
+
+[▶ О структурах данных и алгоритмах](https://www.youtube.com/playlist?list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
+
+### Нотация «О» большое
+
+*Нотация «О» большое* используется для классификации алгоритмов в соответствии с ростом времени выполнения и затрачиваемой памяти при увеличении размера входных данных.
+На диаграмме ниже представлены общие порядки роста алгоритмов в соответствии с нотацией «О» большое.
+
+![Big O graphs](./assets/big-o-graph.png)
+
+Источник: [Big O Cheat Sheet](http://bigocheatsheet.com/).
+
+Ниже представлены часто используемые обозначения в нотации «О» большое, а также сравнение их производительностей на различных размерах входных данных.
+
+| Нотация «О» большое | 10 элементов | 100 элементов | 1000 элементов |
+| ------------------- | ------------ | ------------- | -------------- |
+| **O(1)**            | 1            | 1             | 1              |
+| **O(log N)**        | 3            | 6             | 9              |
+| **O(N)**            | 10           | 100           | 1000           |
+| **O(N log N)**      | 30           | 600           | 9000           |
+| **O(N^2)**          | 100          | 10000         | 1000000        |
+| **O(2^N)**          | 1024         | 1.26e+29      | 1.07e+301      |
+| **O(N!)**           | 3628800      | 9.3e+157      | 4.02e+2567     |
+
+### Сложности операций в структурах данных
+
+| Структура данных           | Получение | Поиск     | Вставка   | Удаление  | Комментарии |
+| -------------------------- | :-------: | :-------: | :-------: | :-------: | :---------- |
+| **Массив**                 | 1         | n         | n         | n         |             |
+| **Стек**                   | n         | n         | 1         | 1         |             |
+| **Очередь**                | n         | n         | 1         | 1         |             |
+| **Связный список**         | n         | n         | 1         | n         |             |
+| **Хеш-таблица**            | -         | n         | n         | n         | Для идеальной хеш-функции — O(1) |
+| **Двоичное дерево поиска** | n         | n         | n         | n         | В сбалансированном дереве — O(log(n)) |
+| **B-дерево**               | log(n)    | log(n)    | log(n)    | log(n)    |           |
+| **Красно-чёрное дерево**   | log(n)    | log(n)    | log(n)    | log(n)    |           |
+| **АВЛ-дерево**             | log(n)    | log(n)    | log(n)    | log(n)    |           |
+| **Фильтр Блума**           | -         | 1         | 1         | -         | Возможно получение ложноположительного срабатывания |
+
+### Сложности алгоритмов сортировки
+
+| Наименование               | Лучший случай | Средний случай | Худший случай | Память | Устойчивость | Комментарии |
+| -------------------------- | :-----------: | :------------: | :-----------: | :----: | :----------: | :---------- |
+| **Сортировка пузырьком**   | n             | n<sup>2</sup>  | n<sup>2</sup> | 1      | Да           |             |
+| **Сортировка вставками**   | n             | n<sup>2</sup>  | n<sup>2</sup> | 1      | Да           |             |
+| **Сортировка выбором**     | n<sup>2</sup> | n<sup>2</sup>  | n<sup>2</sup> | 1      | Нет          |             |
+| **Сортировка кучей**       | n&nbsp;log(n) | n&nbsp;log(n)  | n&nbsp;log(n) | 1      | Нет          |             |
+| **Сортировка слиянием**    | n&nbsp;log(n) | n&nbsp;log(n)  | n&nbsp;log(n) | n      | Да           |             |
+| **Быстрая сортировка**     | n&nbsp;log(n) | n&nbsp;log(n)  | n<sup>2</sup> | log(n) | Нет          | Быстрая сортировка обычно выполняется с использованием O(log(n)) дополнительной памяти |
+| **Сортировка Шелла**       | n&nbsp;log(n) | зависит от выбранных шагов | n&nbsp;(log(n))<sup>2</sup>  | 1      | Нет          |           |
+| **Сортировка подсчётом**   | n + r         | n + r          | n + r         | n + r  | Да           | r — наибольшее число в массиве |
+| **Поразрядная сортировка** | n * k         | n * k          | n * k         | n + k  | Да           | k — длина самого длинного ключа |

From e55dc809b6fc0053747d048ef7b3ecb1fd9a4672 Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Wed, 9 Dec 2020 08:37:37 +0100
Subject: [PATCH 008/264] Add README in Russian.

---
 README.es-ES.md |  3 ++-
 README.fr-FR.md |  3 ++-
 README.ja-JP.md |  3 ++-
 README.ko-KR.md |  3 ++-
 README.md       |  5 ++--
 README.pl-PL.md |  3 ++-
 README.pt-BR.md |  3 ++-
 README.ru-RU.md | 68 ++++++++++++++++++++-----------------------------
 README.tr-TR.md |  3 ++-
 README.zh-CN.md |  3 ++-
 README.zh-TW.md |  3 ++-
 11 files changed, 49 insertions(+), 51 deletions(-)

diff --git a/README.es-ES.md b/README.es-ES.md
index 5f190efc76..a65ca9f096 100644
--- a/README.es-ES.md
+++ b/README.es-ES.md
@@ -18,7 +18,8 @@ _Léelo en otros idiomas:_
 [_Polski_](README.pl-PL.md),
 [_Français_](README.fr-FR.md),
 [_Português_](README.pt-BR.md),
-[_Türk_](README.tr-TR.md)
+[_Türk_](README.tr-TR.md),
+[_Русский_](README.ru-RU.md)
 
 *☝ Nótese que este proyecto está pensado con fines de aprendizaje e investigación,
 y **no** para ser usado en producción.*
diff --git a/README.fr-FR.md b/README.fr-FR.md
index f1c79d77a4..6559542132 100644
--- a/README.fr-FR.md
+++ b/README.fr-FR.md
@@ -19,7 +19,8 @@ _Lisez ceci dans d'autres langues:_
 [_Polski_](README.pl-PL.md),
 [_Español_](README.es-ES.md),
 [_Português_](README.pt-BR.md),
-[_Türk_](README.tr-TR.md)
+[_Türk_](README.tr-TR.md),
+[_Русский_](README.ru-RU.md)
 
 ## Data Structures
 
diff --git a/README.ja-JP.md b/README.ja-JP.md
index d80e6bfbc7..f166cd2d78 100644
--- a/README.ja-JP.md
+++ b/README.ja-JP.md
@@ -18,7 +18,8 @@ _Read this in other languages:_
 [_Français_](README.fr-FR.md),
 [_Español_](README.es-ES.md),
 [_Português_](README.pt-BR.md),
-[_Türk_](README.tr-TR.md)
+[_Türk_](README.tr-TR.md),
+[_Русский_](README.ru-RU.md)
 
 ## データ構造
 
diff --git a/README.ko-KR.md b/README.ko-KR.md
index 2dccf75bd6..7759e33bca 100644
--- a/README.ko-KR.md
+++ b/README.ko-KR.md
@@ -17,7 +17,8 @@ _Read this in other languages:_
 [_Français_](README.fr-FR.md),
 [_Español_](README.es-ES.md),
 [_Português_](README.pt-BR.md),
-[_Türk_](README.tr-TR.md)
+[_Türk_](README.tr-TR.md),
+[_Русский_](README.ru-RU.md)
 
 ## 자료 구조
 
diff --git a/README.md b/README.md
index a8d1b9e7f6..f49f578424 100644
--- a/README.md
+++ b/README.md
@@ -19,10 +19,11 @@ _Read this in other languages:_
 [_Français_](README.fr-FR.md),
 [_Español_](README.es-ES.md),
 [_Português_](README.pt-BR.md),
-[_Türk_](README.tr-TR.md)
+[_Türk_](README.tr-TR.md),
+[_Русский_](README.ru-RU.md)
 
 *☝ Note that this project is meant to be used for learning and researching purposes 
-only and it is **not** meant to be used for production.*
+only, and it is **not** meant to be used for production.*
 
 ## Data Structures
 
diff --git a/README.pl-PL.md b/README.pl-PL.md
index f2b76b1dab..8d2faa4b73 100644
--- a/README.pl-PL.md
+++ b/README.pl-PL.md
@@ -19,7 +19,8 @@ _Read this in other languages:_
 [_Français_](README.fr-FR.md),
 [_Español_](README.es-ES.md),
 [_Português_](README.pt-BR.md),
-[_Türk_](README.tr-TR.md)
+[_Türk_](README.tr-TR.md),
+[_Русский_](README.ru-RU.md)
 
 ## Struktury Danych
 
diff --git a/README.pt-BR.md b/README.pt-BR.md
index a1556c7fc2..74f7709075 100644
--- a/README.pt-BR.md
+++ b/README.pt-BR.md
@@ -19,7 +19,8 @@ _Leia isto em outros idiomas:_
 [_Polski_](README.pl-PL.md),
 [_Français_](README.fr-FR.md),
 [_Español_](README.es-ES.md),
-[_Türk_](README.tr-TR.md)
+[_Türk_](README.tr-TR.md),
+[_Русский_](README.ru-RU.md)
 
 ## Estrutura de Dados
 
diff --git a/README.ru-RU.md b/README.ru-RU.md
index 5669731dd9..b52a5b4232 100644
--- a/README.ru-RU.md
+++ b/README.ru-RU.md
@@ -1,14 +1,11 @@
-# Алгоритмы и структуры данных в JavaScript
+# Алгоритмы и структуры данных на JavaScript
 
 [![Build Status](https://travis-ci.org/trekhleb/javascript-algorithms.svg?branch=master)](https://travis-ci.org/trekhleb/javascript-algorithms)
 [![codecov](https://codecov.io/gh/trekhleb/javascript-algorithms/branch/master/graph/badge.svg)](https://codecov.io/gh/trekhleb/javascript-algorithms)
 
-В этом репозитории содержатся базовые JavaScript-примеры
-многих популярных алгоритмов и структур данных.
+В этом репозитории содержатся базовые JavaScript-примеры многих популярных алгоритмов и структур данных.
 
-Для каждого алгоритма и структуры данных есть свой файл README
-с соответствующими пояснениями и ссылками на материалы для дальнейшего
-изучения (в том числе и ссылки на видеоролики в Ютубе).
+Для каждого алгоритма и структуры данных есть свой файл README с соответствующими пояснениями и ссылками на материалы для дальнейшего изучения (в том числе и ссылки на видеоролики в YouTube).
 
 _Читать на других языках:_
 [_English_](https://github.com/trekhleb/javascript-algorithms/),
@@ -21,16 +18,13 @@ _Читать на других языках:_
 [_Español_](README.es-ES.md),
 [_Português_](README.pt-BR.md)
 
-*☝ Замечание: этот репозиторий предназначен только для
-учебно-исследовательских целей (**не** для продакшена).*
+*☝ Замечание: этот репозиторий предназначен для учебно-исследовательских целей (**не** для использования в продакшн-системах).*
 
 ## Структуры данных
 
-Структура данных — определённый способ систематизации и хранения данных в компьютере таким образом,
-чтобы они могли быть легко доступны и изменяемы. Структура данных — совокупность коллекции значений
-данных, взаимосвязей между ними и функций или операций, которые могут применяться к данным.
+Структура данных (англ. data structure) — программная единица, позволяющая хранить и обрабатывать множество однотипных и/или логически связанных данных в вычислительной технике. Для добавления, поиска, изменения и удаления данных структура данных предоставляет некоторый набор функций, составляющих её интерфейс.
 
-`B` - Новичок, `A` - Продвинутый
+`B` - Базовый уровень, `A` - Продвинутый уровень
 
 * `B` [Связный список](src/data-structures/linked-list)
 * `B` [Двунаправленный связный список](src/data-structures/doubly-linked-list)
@@ -52,12 +46,11 @@ _Читать на других языках:_
 
 ## Алгоритмы
 
-Алгоритм — однозначная спецификация по решению целого ряда задач (иными словами,
-это список правил, чётко определяющих ту или иную последовательность операций).
+Алгоритм — конечная совокупность точно заданных правил решения некоторого класса задач или набор инструкций, описывающих порядок действий исполнителя для решения некоторой задачи.
 
-`B` — Новичок, `A` — Продвинутый
+`B` - Базовый уровень, `A` - Продвинутый уровень
 
-### Тематическое разделение алгоритмов
+### Алгоритмы по тематике
 
 * **Математика**
   * `B` [Битовые манипуляции](src/algorithms/math/bits) — получение/запись/сброс/обновление битов, умножение/деление на 2, сделать отрицательным и т.п.
@@ -84,11 +77,11 @@ _Читать на других языках:_
   * `A` [Сочетания](src/algorithms/sets/combinations) (с повторениями и без повторений)
   * `A` [Наибольшая общая подпоследовательность](src/algorithms/sets/longest-common-subsequence)
   * `A` [Наибольшая увеличивающаяся подпоследовательность](src/algorithms/sets/longest-increasing-subsequence)
-  * `A` [Наименьшая общая суперпоследовательность](src/algorithms/sets/shortest-common-supersequence)
+  * `A` [Наименьшая общая супер-последовательность](src/algorithms/sets/shortest-common-supersequence)
   * `A` [Задача о рюкзаке](src/algorithms/sets/knapsack-problem) — "0/1" и "неограниченный" рюкзаки
-  * `A` [Максимальный подмассив](src/algorithms/sets/maximum-subarray) — метод полного перебора и алгоритм Кадане
+  * `A` [Максимальный под-массив](src/algorithms/sets/maximum-subarray) — метод полного перебора и алгоритм Кадане
   * `A` [Комбинации сумм](src/algorithms/sets/combination-sum) — нахождение всех комбинаций, сумма каждой из которых равна заданному числу
-* **Алгоритмы на строках**
+* **Алгоритмы работы со строками**
   * `B` [Расстояние Хэмминга](src/algorithms/string/hamming-distance) — число позиций, в которых соответствующие символы различны
   * `A` [Расстояние Левенштейна](src/algorithms/string/levenshtein-distance) — метрика, измеряющая разность между двумя последовательностями
   * `A` [Алгоритм Кнута — Морриса — Пратта](src/algorithms/string/knuth-morris-pratt) — поиск подстроки (сопоставление с шаблоном)
@@ -101,7 +94,7 @@ _Читать на других языках:_
   * `B` [Поиск с перескоком](src/algorithms/search/jump-search) (поиск блоков) — поиск в упорядоченном массиве
   * `B` [Двоичный поиск](src/algorithms/search/binary-search) — поиск в упорядоченном массиве
   * `B` [Интерполяционный поиск](src/algorithms/search/interpolation-search) — поиск в равномерно распределённом упорядоченном массиве.
-* **Сортировки**
+* **Алгоритмы сортировки**
   * `B` [Сортировка пузырьком](src/algorithms/sorting/bubble-sort)
   * `B` [Сортировка выбором](src/algorithms/sorting/selection-sort)
   * `B` [Сортировка вставками](src/algorithms/sorting/insertion-sort)
@@ -147,11 +140,9 @@ _Читать на других языках:_
   * `A` [Задача об N ферзях](src/algorithms/uncategorized/n-queens)
   * `A` [Маршрут коня](src/algorithms/uncategorized/knight-tour)
 
-### Парадигмы программирования
+### Алгоритмы по парадигме программирования
 
-Парадигма программирования — общий метод или подход, лежащий в основе целого класса алгоритмов.
-Понятие "парадигма программирования" является более абстрактным по отношению к понятию "алгоритм",
-которое в свою очередь является более абстрактным по отношению к понятию "компьютерная пограмма".
+Парадигма программирования — общий метод или подход, лежащий в основе целого класса алгоритмов. Понятие "парадигма программирования" является более абстрактным по отношению к понятию "алгоритм", которое в свою очередь является более абстрактным по отношению к понятию "компьютерная программа".
 
 * **Алгоритмы полного перебора** — поиск лучшего решения исчерпыванием всевозможных вариантов
   * `B` [Линейный поиск](src/algorithms/search/linear-search)
@@ -196,9 +187,7 @@ _Читать на других языках:_
   * `A` [Алгоритм Беллмана — Форда](src/algorithms/graph/bellman-ford) — поиск кратчайшего пути во взвешенном графе
   * `A` [Алгоритм Флойда — Уоршелла](src/algorithms/graph/floyd-warshall) — нахождение кратчайших путей от одной из вершин графа до всех остальных
   * `A` [Разборщик регулярных выражений](src/algorithms/string/regular-expression-matching)
-* **Поиск с возвратом (бэктрекинг)** — при поиске решения многократно делается попытка расширить текущее частичное решение. Если расширение
-невозможно, то происходит возврат к предыдущему более короткому частичному решению, и делается попытка его расширить другим возможным способом.
-Обычно используется обход пространства состояний в глубину.
+* **Поиск с возвратом (бэктрекинг)** — при поиске решения многократно делается попытка расширить текущее частичное решение. Если расширение невозможно, то происходит возврат к предыдущему более короткому частичному решению, и делается попытка его расширить другим возможным способом. Обычно используется обход пространства состояний в глубину.
   * `B` [Прыжки](src/algorithms/uncategorized/jump-game)
   * `B` [Поиск уникальных путей](src/algorithms/uncategorized/unique-paths)
   * `B` [Булеан](src/algorithms/sets/power-set) — все подмножества заданного множества
@@ -206,38 +195,38 @@ _Читать на других языках:_
   * `A` [Задача об N ферзях](src/algorithms/uncategorized/n-queens)
   * `A` [Маршрут коня](src/algorithms/uncategorized/knight-tour)
   * `A` [Комбинации сумм](src/algorithms/sets/combination-sum) — нахождение всех комбинаций, сумма каждой из которых равна заданному числу
-* **Метод ветвей и границ** — основан на упорядоченном переборе решений и рассмотрении только тех из них, которые являются перспективными
-(по тем или иным признакам) и отбрасывании бесперспективных множеств решений. Обычно используется обход в ширину в совокупности с обходом
-дерева пространства состояний в глубину.
+* **Метод ветвей и границ** — основан на упорядоченном переборе решений и рассмотрении только тех из них, которые являются перспективными (по тем или иным признакам) и отбрасывании бесперспективных множеств решений. Обычно используется обход в ширину в совокупности с обходом дерева пространства состояний в глубину.
 
-## Команды по использованию репозитория
+## Как использовать этот репозиторий
 
 **Установка всех зависимостей**
 ```
 npm install
 ```
 
-**Запустить ESLint**
+**Запуск ESLint**
 
-Возможно, эта команда потребуется Вам для проверки качества кода.
+Эта команда может потребоваться вам для проверки качества кода.
 
 ```
 npm run lint
 ```
 
-**Запустить все тесты**
+**Запуск всех тестов**
+
 ```
 npm test
 ```
 
-**Запустить определённый тест**
+**Запуск определённого теста**
+
 ```
 npm test -- 'LinkedList'
 ```
 
-**Playground**
+**Песочница**
 
-Вы можете поэкспериментировать с алгоритмами и структурами данных в файле `./src/playground/playground.js` 
+Вы можете экспериментировать с алгоритмами и структурами данных в файле `./src/playground/playground.js` 
 (файл `./src/playground/__test__/playground.test.js` предназначен для написания тестов).
 
 Для проверки работоспособности вашего кода используйте команду:
@@ -254,8 +243,7 @@ npm test -- 'playground'
 
 ### Нотация «О» большое
 
-*Нотация «О» большое* используется для классификации алгоритмов в соответствии с ростом времени выполнения и затрачиваемой памяти при увеличении размера входных данных.
-На диаграмме ниже представлены общие порядки роста алгоритмов в соответствии с нотацией «О» большое.
+*Нотация «О» большое* используется для классификации алгоритмов в соответствии с ростом времени выполнения и затрачиваемой памяти при увеличении размера входных данных. На диаграмме ниже представлены общие порядки роста алгоритмов в соответствии с нотацией «О» большое.
 
 ![Big O graphs](./assets/big-o-graph.png)
 
@@ -286,7 +274,7 @@ npm test -- 'playground'
 | **B-дерево**               | log(n)    | log(n)    | log(n)    | log(n)    |           |
 | **Красно-чёрное дерево**   | log(n)    | log(n)    | log(n)    | log(n)    |           |
 | **АВЛ-дерево**             | log(n)    | log(n)    | log(n)    | log(n)    |           |
-| **Фильтр Блума**           | -         | 1         | 1         | -         | Возможно получение ложноположительного срабатывания |
+| **Фильтр Блума**           | -         | 1         | 1         | -         | Возможно получение ложно-положительного срабатывания |
 
 ### Сложности алгоритмов сортировки
 
diff --git a/README.tr-TR.md b/README.tr-TR.md
index c0fc6ee18d..0892e5f4a0 100644
--- a/README.tr-TR.md
+++ b/README.tr-TR.md
@@ -17,7 +17,8 @@ _Read this in other languages:_
 [_Polski_](README.pl-PL.md),
 [_Français_](README.fr-FR.md),
 [_Español_](README.es-ES.md),
-[_Português_](README.pt-BR.md)
+[_Português_](README.pt-BR.md),
+[_Русский_](README.ru-RU.md)
 
 *☝ Not, bu proje araştırma ve öğrenme amacı ile yapılmış 
 olup üretim için **yaplılmamıştır**.*
diff --git a/README.zh-CN.md b/README.zh-CN.md
index cd95bc5c7b..e4f37ec506 100644
--- a/README.zh-CN.md
+++ b/README.zh-CN.md
@@ -16,7 +16,8 @@ _Read this in other languages:_
 [_Français_](README.fr-FR.md),
 [_Español_](README.es-ES.md),
 [_Português_](README.pt-BR.md),
-[_Türk_](README.tr-TR.md)
+[_Türk_](README.tr-TR.md),
+[_Русский_](README.ru-RU.md)
 
 *注意：这个项目仅用于学习和研究，**不是**用于生产环境。*
 
diff --git a/README.zh-TW.md b/README.zh-TW.md
index 9d7bcb6314..8e5699cfdc 100644
--- a/README.zh-TW.md
+++ b/README.zh-TW.md
@@ -15,7 +15,8 @@ _Read this in other languages:_
 [_Français_](README.fr-FR.md),
 [_Español_](README.es-ES.md),
 [_Português_](README.pt-BR.md),
-[_Türk_](README.tr-TR.md)
+[_Türk_](README.tr-TR.md),
+[_Русский_](README.ru-RU.md)
 
 ## 資料結構
 

From 1bfbf1e30642f6535d3b61ae848aa604321cb41c Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Wed, 9 Dec 2020 08:40:51 +0100
Subject: [PATCH 009/264] Add README in Russian.

---
 README.es-ES.md | 4 ++--
 README.fr-FR.md | 4 ++--
 README.ja-JP.md | 4 ++--
 README.ko-KR.md | 4 ++--
 README.md       | 4 ++--
 README.pl-PL.md | 4 ++--
 README.pt-BR.md | 4 ++--
 README.ru-RU.md | 3 ++-
 README.zh-CN.md | 4 ++--
 README.zh-TW.md | 4 ++--
 10 files changed, 20 insertions(+), 19 deletions(-)

diff --git a/README.es-ES.md b/README.es-ES.md
index a65ca9f096..8a6706ce49 100644
--- a/README.es-ES.md
+++ b/README.es-ES.md
@@ -18,8 +18,8 @@ _Léelo en otros idiomas:_
 [_Polski_](README.pl-PL.md),
 [_Français_](README.fr-FR.md),
 [_Português_](README.pt-BR.md),
-[_Türk_](README.tr-TR.md),
-[_Русский_](README.ru-RU.md)
+[_Русский_](README.ru-RU.md),
+[_Türk_](README.tr-TR.md)
 
 *☝ Nótese que este proyecto está pensado con fines de aprendizaje e investigación,
 y **no** para ser usado en producción.*
diff --git a/README.fr-FR.md b/README.fr-FR.md
index 6559542132..a83cce4d01 100644
--- a/README.fr-FR.md
+++ b/README.fr-FR.md
@@ -19,8 +19,8 @@ _Lisez ceci dans d'autres langues:_
 [_Polski_](README.pl-PL.md),
 [_Español_](README.es-ES.md),
 [_Português_](README.pt-BR.md),
-[_Türk_](README.tr-TR.md),
-[_Русский_](README.ru-RU.md)
+[_Русский_](README.ru-RU.md),
+[_Türk_](README.tr-TR.md)
 
 ## Data Structures
 
diff --git a/README.ja-JP.md b/README.ja-JP.md
index f166cd2d78..862a0d2bc0 100644
--- a/README.ja-JP.md
+++ b/README.ja-JP.md
@@ -18,8 +18,8 @@ _Read this in other languages:_
 [_Français_](README.fr-FR.md),
 [_Español_](README.es-ES.md),
 [_Português_](README.pt-BR.md),
-[_Türk_](README.tr-TR.md),
-[_Русский_](README.ru-RU.md)
+[_Русский_](README.ru-RU.md),
+[_Türk_](README.tr-TR.md)
 
 ## データ構造
 
diff --git a/README.ko-KR.md b/README.ko-KR.md
index 7759e33bca..c5fa8b1804 100644
--- a/README.ko-KR.md
+++ b/README.ko-KR.md
@@ -17,8 +17,8 @@ _Read this in other languages:_
 [_Français_](README.fr-FR.md),
 [_Español_](README.es-ES.md),
 [_Português_](README.pt-BR.md),
-[_Türk_](README.tr-TR.md),
-[_Русский_](README.ru-RU.md)
+[_Русский_](README.ru-RU.md),
+[_Türk_](README.tr-TR.md)
 
 ## 자료 구조
 
diff --git a/README.md b/README.md
index f49f578424..9d4d39622b 100644
--- a/README.md
+++ b/README.md
@@ -19,8 +19,8 @@ _Read this in other languages:_
 [_Français_](README.fr-FR.md),
 [_Español_](README.es-ES.md),
 [_Português_](README.pt-BR.md),
-[_Türk_](README.tr-TR.md),
-[_Русский_](README.ru-RU.md)
+[_Русский_](README.ru-RU.md),
+[_Türk_](README.tr-TR.md)
 
 *☝ Note that this project is meant to be used for learning and researching purposes 
 only, and it is **not** meant to be used for production.*
diff --git a/README.pl-PL.md b/README.pl-PL.md
index 8d2faa4b73..26ca99c179 100644
--- a/README.pl-PL.md
+++ b/README.pl-PL.md
@@ -19,8 +19,8 @@ _Read this in other languages:_
 [_Français_](README.fr-FR.md),
 [_Español_](README.es-ES.md),
 [_Português_](README.pt-BR.md),
-[_Türk_](README.tr-TR.md),
-[_Русский_](README.ru-RU.md)
+[_Русский_](README.ru-RU.md),
+[_Türk_](README.tr-TR.md)
 
 ## Struktury Danych
 
diff --git a/README.pt-BR.md b/README.pt-BR.md
index 74f7709075..626c5f65b7 100644
--- a/README.pt-BR.md
+++ b/README.pt-BR.md
@@ -19,8 +19,8 @@ _Leia isto em outros idiomas:_
 [_Polski_](README.pl-PL.md),
 [_Français_](README.fr-FR.md),
 [_Español_](README.es-ES.md),
-[_Türk_](README.tr-TR.md),
-[_Русский_](README.ru-RU.md)
+[_Русский_](README.ru-RU.md),
+[_Türk_](README.tr-TR.md)
 
 ## Estrutura de Dados
 
diff --git a/README.ru-RU.md b/README.ru-RU.md
index b52a5b4232..fcfcf83b9f 100644
--- a/README.ru-RU.md
+++ b/README.ru-RU.md
@@ -16,7 +16,8 @@ _Читать на других языках:_
 [_Polski_](README.pl-PL.md),
 [_Français_](README.fr-FR.md),
 [_Español_](README.es-ES.md),
-[_Português_](README.pt-BR.md)
+[_Português_](README.pt-BR.md),
+[_Türk_](README.tr-TR.md)
 
 *☝ Замечание: этот репозиторий предназначен для учебно-исследовательских целей (**не** для использования в продакшн-системах).*
 
diff --git a/README.zh-CN.md b/README.zh-CN.md
index e4f37ec506..f63eab90b4 100644
--- a/README.zh-CN.md
+++ b/README.zh-CN.md
@@ -16,8 +16,8 @@ _Read this in other languages:_
 [_Français_](README.fr-FR.md),
 [_Español_](README.es-ES.md),
 [_Português_](README.pt-BR.md),
-[_Türk_](README.tr-TR.md),
-[_Русский_](README.ru-RU.md)
+[_Русский_](README.ru-RU.md),
+[_Türk_](README.tr-TR.md)
 
 *注意：这个项目仅用于学习和研究，**不是**用于生产环境。*
 
diff --git a/README.zh-TW.md b/README.zh-TW.md
index 8e5699cfdc..50050b2786 100644
--- a/README.zh-TW.md
+++ b/README.zh-TW.md
@@ -15,8 +15,8 @@ _Read this in other languages:_
 [_Français_](README.fr-FR.md),
 [_Español_](README.es-ES.md),
 [_Português_](README.pt-BR.md),
-[_Türk_](README.tr-TR.md),
-[_Русский_](README.ru-RU.md)
+[_Русский_](README.ru-RU.md),
+[_Türk_](README.tr-TR.md)
 
 ## 資料結構
 

From 7608151d9e598c6d7e1d91b092a72c53b8dc83b3 Mon Sep 17 00:00:00 2001
From: Riccardo Amadio <riccardo.amadio1@gmail.com>
Date: Wed, 9 Dec 2020 09:00:53 +0100
Subject: [PATCH 010/264] Italian Implementation (#432)

* translating README to italian, middle phase

* test

* test grafica

* finish

* review

Co-authored-by: Riccardo Amadio <riccardoamadio@MacBook-Pro-di-Riccardo.local>
---
 README.it-IT.md | 294 ++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 294 insertions(+)
 create mode 100644 README.it-IT.md

diff --git a/README.it-IT.md b/README.it-IT.md
new file mode 100644
index 0000000000..8daa4ac62c
--- /dev/null
+++ b/README.it-IT.md
@@ -0,0 +1,294 @@
+# Algoritmi e Strutture Dati in Javascript
+ 
+[![Build Status](https://travis-ci.org/trekhleb/javascript-algorithms.svg?branch=master)](https://travis-ci.org/trekhleb/javascript-algorithms)
+[![codecov](https://codecov.io/gh/trekhleb/javascript-algorithms/branch/master/graph/badge.svg)](https://codecov.io/gh/trekhleb/javascript-algorithms)
+
+Questa repository contiene esempi in Javascript dei più popolari algoritmi e strutture dati .
+
+Ogni algortimo e struttura dati ha il suo README separato e la relative spiegazioni e i link per ulteriori approfondimenti (compresi quelli su YouTube).
+
+_Leggilo in altre lingue:_
+[_简体中文_](README.zh-CN.md),
+[_繁體中文_](README.zh-TW.md),
+[_한국어_](README.ko-KR.md),
+[_日本語_](README.ja-JP.md),
+[_Polski_](README.pl-PL.md),
+[_Français_](README.fr-FR.md),
+[_Español_](README.es-ES.md),
+[_Português_](README.pt-BR.md),
+[_Italian_](README.it-IT.md)
+
+*☝ Si noti che questo progetto è destinato ad essere utilizzato solo per l'apprendimento e la ricerca e non è destinato ad essere utilizzato per il commercio.*
+
+## Strutture Dati
+
+Una struttura dati è un particolare modo di organizzare e memorizzare i dati in un computer che  permeta di accedervi e modificarli in modo efficiente. Più precisamente, una struttura dati è una raccolta di dati, le relazioni tra di essi e le funzioni o operazioni che possono essere applicate ai dati.
+
+`P` - Principiante, `A` - Avanzato
+
+* `P` [Lista Concatenata](src/data-structures/linked-list)
+* `P` [Doppia Lista Concatenata](src/data-structures/doubly-linked-list)
+* `P` [Coda](src/data-structures/queue)
+* `P` [Pila](src/data-structures/stack)
+* `P` [Hash Table](src/data-structures/hash-table)
+* `P` [Heap](src/data-structures/heap) - versione massimo e minimo heap
+* `P` [Coda di priorità](src/data-structures/priority-queue)
+* `A` [Trie](src/data-structures/trie)
+* `A` [Albero](src/data-structures/tree)
+  * `A` [Albero binario di ricerca](src/data-structures/tree/binary-search-tree)
+  * `A` [Albero AVL](src/data-structures/tree/avl-tree)
+  * `A` [RB Albero](src/data-structures/tree/red-black-tree)
+  * `A` [Albero Segmentato](src/data-structures/tree/segment-tree) - con  min/max/sum esempi di query
+  * `A` [Albero di Fenwick](src/data-structures/tree/fenwick-tree) (Albero binario indicizzato)
+* `A` [Grafo](src/data-structures/graph) (direzionale e unidirezionale)
+* `A` [Set Disgiunto](src/data-structures/disjoint-set)
+* `A` [Filtro Bloom](src/data-structures/bloom-filter)
+
+## Algoritmi
+
+Un algoritmo è una specifica univoca per risolvere una classe di problemi. È
+un insieme di regole che definiscono con precisione una sequenza di operazioni.
+
+`P` - Principiante, `A` - Avanzato
+
+### Algoritmi per Topic
+
+* **Matematica**
+  * `P` [Manipolazione dei Bit](src/algorithms/math/bits) - set/get/update/clear bits, moltiplicazione/divisione per due, gestire numeri negativi etc.
+  * `P` [Fattoriale](src/algorithms/math/factorial) 
+  * `P` [Numeri di Fibonacci](src/algorithms/math/fibonacci) - classico e forma chiusa
+  * `P` [Test di Primalità](src/algorithms/math/primality-test) (metodo del divisore)
+  * `P` [Algoritmo di Euclide](src/algorithms/math/euclidean-algorithm) - trova il massimo comune divisore (MCD)
+  * `P` [Minimo Comune Multiplo](src/algorithms/math/least-common-multiple) (MCM)
+  * `P` [Crivello di Eratostene](src/algorithms/math/sieve-of-eratosthenes) - trova i numeri i primi fino al limite indicato
+  * `P` [Potenza di due](src/algorithms/math/is-power-of-two) - controlla se il numero è una potenza di due
+  * `P` [Triangolo di Pascal](src/algorithms/math/pascal-triangle)
+  * `P` [Numeri Complessi](src/algorithms/math/complex-number) - numeri complessi e operazioni 
+  * `P` [Radiante & Gradi](src/algorithms/math/radian) - conversione da radiante a gradi e viceversa
+  * `P` [Potenza di un Numero](src/algorithms/math/fast-powering)
+  * `A` [Partizione di un Intero](src/algorithms/math/integer-partition)
+  * `A` [Radice Quadrata](src/algorithms/math/square-root) - Metodo di Newton
+  * `A` [Algoritmo di Liu Hui π](src/algorithms/math/liu-hui) - calcolare π usando un poligono
+  * `A` [Trasformata Discreta di Fourier ](src/algorithms/math/fourier-transform) -decomporre una funzione di tempo (un segnale) nelle frequenze che lo compongono 
+* **Set**
+  * `P` [Prodotto Cartesiano](src/algorithms/sets/cartesian-product) - moltiplicazione multipla di set
+  * `P` [Fisher–Yates Shuffle](src/algorithms/sets/fisher-yates) - permutazione casuale di un sequenza finita
+  * `A` [Power Set](src/algorithms/sets/power-set) - tutti i sottoinsiemi di un set (soluzioni bitwise e backtracking)
+  * `A` [Permutazioni](src/algorithms/sets/permutations) (con e senza ripetizioni)
+  * `A` [Combinazioni](src/algorithms/sets/combinations) (con e senza ripetizioni)
+  * `A` [Massima Sottosequenza Comune](src/algorithms/sets/longest-common-subsequence) (LCS)
+  * `A` [Massima Sottosequenza Crescente](src/algorithms/sets/longest-increasing-subsequence)
+  * `A` [Minima Sottosequenza Diffusa](src/algorithms/sets/shortest-common-supersequence) (SCS)
+  * `A` [Problema dello Zaino di Knapsack](src/algorithms/sets/knapsack-problem) - "0/1" e "Senza Restrizioni"
+  * `A` [Massimo SubArray](src/algorithms/sets/maximum-subarray) - "Brute Force" e "Programmazione Dinamica" versione Kadane
+  * `A` [Somma di Combinazioni](src/algorithms/sets/combination-sum) - ricerca di tutte le combinazioni di una somma
+* **String**
+  * `P` [Distanza di Hamming](src/algorithms/string/hamming-distance) - numero di posizioni in cui i caratteri sono diversi
+  * `A` [Distanza di Levenshtein](src/algorithms/string/levenshtein-distance) - numero minimo di modifiche per rendere uguali due stringhe
+  * `A` [Algoritmo di Knuth-Morris-Pratt](src/algorithms/string/knuth-morris-pratt) (KMP) - ricerca nella sottostringa (pattern matching)
+  * `A` [Algoritmo Z](src/algorithms/string/z-algorithm) - ricerca nella sottostringa (pattern matching)
+  * `A` [Algoritmo di Rabin Karp ](src/algorithms/string/rabin-karp) - ricerca nella sottostringa
+  * `A` [Sottostringa Comune più lunga](src/algorithms/string/longest-common-substring)
+  * `A` [Espressioni Regolari](src/algorithms/string/regular-expression-matching)
+* **Searches**
+  * `P` [Ricerca Sequenziale](src/algorithms/search/linear-search)
+  * `P` [Ricerca a Salti](src/algorithms/search/jump-search) (o Ricerca a Blocchi) - per la ricerca in array ordinati
+  * `P` [Ricerca Binari](src/algorithms/search/binary-search) - per la ricerca in array ordinati
+  * `P` [Ricerca Interpolata](src/algorithms/search/interpolation-search) - per la ricerca in un array ordinato uniformemente distibuito
+* **Sorting**
+  * `P` [Bubble Sort](src/algorithms/sorting/bubble-sort)
+  * `P` [Selection Sort](src/algorithms/sorting/selection-sort)
+  * `P` [Insertion Sort](src/algorithms/sorting/insertion-sort)
+  * `P` [Heap Sort](src/algorithms/sorting/heap-sort)
+  * `P` [Merge Sort](src/algorithms/sorting/merge-sort)
+  * `P` [Quicksort](src/algorithms/sorting/quick-sort) - con e senza allocazione di ulteriore memoria
+  * `P` [Shellsort](src/algorithms/sorting/shell-sort)
+  * `P` [Counting Sort](src/algorithms/sorting/counting-sort)
+  * `P` [Radix Sort](src/algorithms/sorting/radix-sort)
+* **Lista Concatenatas**
+  * `P` [Attraversamento Lista Concatenata](src/algorithms/linked-list/traversal)
+  * `P` [Attraversamento Lista Concatenata nel senso Contrario](src/algorithms/linked-list/reverse-traversal)
+* **Alberi**
+  * `P` [Ricerca in Profondità su Alberi](src/algorithms/tree/depth-first-search) (DFS)
+  * `P` [Ricerca in Ampiezza su Alberi](src/algorithms/tree/breadth-first-search) (BFS)
+* **Grafi**
+  * `P` [Ricerca in Profondità su Grafi](src/algorithms/graph/depth-first-search) (DFS)
+  * `P` [Breadth-First Search su Grafi](src/algorithms/graph/breadth-first-search) (BFS)
+  * `P` [Algoritmo di Kruskal](src/algorithms/graph/kruskal) - ricerca dell'Albero con Minima Distanza (MST) per grafi pesati unidirezionali
+  * `A` [Algoritmo di Dijkstra](src/algorithms/graph/dijkstra) - ricerca dei percorsi più breve per raggiungere tutti i vertici del grafo da un singolo vertice 
+  * `A` [Algoritmo di Bellman-Ford](src/algorithms/graph/bellman-ford) - ricerca dei percorsi più breve per raggiungere tutti i vertici del grafo da un singolo vertice 
+  * `A` [Algoritmo di Floyd-Warshall](src/algorithms/graph/floyd-warshall) -  ricerca dei percorsi più brevi tra tutte le coppie di vertici
+  * `A` [Rivelamento dei Cicli](src/algorithms/graph/detect-cycle) - per grafici diretti e non diretti (basate su partizioni DFS e Disjoint Set)
+  * `A` [Algoritmo di Prim](src/algorithms/graph/prim) - ricerca dell'Albero Ricoprente Minimo (MST) per grafi unidirezionali pesati
+  * `A` [Ordinamento Topologico](src/algorithms/graph/topological-sorting) - metodo DFS
+  * `A` [Punti di Articolazione](src/algorithms/graph/articulation-points) - Algoritmo di Tarjan (basato su DFS)
+  * `A` [Bridges](src/algorithms/graph/bridges) - basato su DFS
+  * `A` [Cammino Euleriano e Circuito Euleriano](src/algorithms/graph/eulerian-path) - Algoritmo di Fleury - Visita ogni margine esattamente una volta
+  * `A` [Ciclo di Hamiltonian](src/algorithms/graph/hamiltonian-cycle) - Visita ad ogni vertice solo una volta
+  * `A` [Componenti Fortemente Connessa](src/algorithms/graph/strongly-connected-components) - algoritmo di Kosaraju
+  * `A` [Problema del Commesso Viaggiatore](src/algorithms/graph/travelling-salesman) - il percorso più breve che visita ogni città e ritorna alla città iniziale
+* **Crittografia**
+  * `P` [Hash Polinomiale](src/algorithms/cryptography/polynomial-hash) - Una funzione hash di rolling basata sul polinomio 
+* **Senza categoria**
+  * `P` [Torre di Hanoi](src/algorithms/uncategorized/hanoi-tower)
+  * `P` [Rotazione Matrice Quadrata](src/algorithms/uncategorized/square-matrix-rotation) - algoritmo in memoria
+  * `P` [Jump Game](src/algorithms/uncategorized/jump-game) - backtracking, programmazione dinamica (top-down + bottom-up) ed esempre di greeedy
+  * `P` [Percorsi Unici](src/algorithms/uncategorized/unique-paths) - backtracking, programmazione dinamica and l'esempio del Triangolo di Pascal  
+  * `P` [Rain Terraces](src/algorithms/uncategorized/rain-terraces) - problema dell'acqua piovana in trappola(versione con programmazione dinamica e brute force)
+  * `P` [Recursive Staircase](src/algorithms/uncategorized/recursive-staircase) - contare il numero di percorsi per arrivare in vetta(4 soluzioni)
+  * `A` [Rompicapo delle Otto Regine](src/algorithms/uncategorized/n-queens)
+  * `A` [Percorso del Cavallo](src/algorithms/uncategorized/knight-tour)
+
+### Modelli di Algoritmi
+
+ Un modello di algoritmo è un generico metodo o approcio che sta alla base della progettazione di una classe di algoritmi.
+ Si tratta di un'astrazione ancora più alta di un algoritmo, proprio come un algoritmo è un'astrazione di un programma del computer.
+
+* **Brute Force** - controlla tutte le possibilità e seleziona la migliore
+  * `P` [Ricerca Lineare](src/algorithms/search/linear-search)
+  * `P` [Rain Terraces](src/algorithms/uncategorized/rain-terraces) - problema dell'acqua piovana in trappola
+  * `P` [Recursive Staircase](src/algorithms/uncategorized/recursive-staircase) - contare il numero di percorsi per arrivare in vetta
+  * `A` [Massimo SubArray](src/algorithms/sets/maximum-subarray)
+  * `A` [Problema del commesso viaggiatore](src/algorithms/graph/travelling-salesman) - il percorso più breve che visita ogni città e ritorna alla città iniziale
+  * `A` [Trasformata Discreta di Fourier](src/algorithms/math/fourier-transform) - scomporre la funzione (segnale) del tempo in frequenze che la compongono 
+* **Greedy** - scegliere l'opzione migliore al momento d'eleborazione dell'algoritmo, senza alcuna considerazione per il futuro
+  * `P` [Jump Game](src/algorithms/uncategorized/jump-game)
+  * `A` [Problema dello Zaino di Knapsack](src/algorithms/sets/knapsack-problem)
+  * `A` [Algoritmo di Dijkstra](src/algorithms/graph/dijkstra) - ricerca del percorso più breve tra tutti i vertici del grafo
+  * `A` [Algoritmo di Prim](src/algorithms/graph/prim) - ricerca del Minimo Albero Ricoprente per grafi pesati e unidirezionali 
+  * `A` [Kruskal’s Algorithm](src/algorithms/graph/kruskal) - finding Minimum Spanning Tree (MST) for weighted undirected graph
+* **Divide e Conquista** - divide il problema in piccole parti e risolve ogni parte 
+  * `P` [Ricerca Binaria](src/algorithms/search/binary-search)
+  * `P` [Torre di Hanoi](src/algorithms/uncategorized/hanoi-tower)
+  * `P` [Triangolo di Pascal](src/algorithms/math/pascal-triangle)
+  * `P` [Algoritmo di Euclide](src/algorithms/math/euclidean-algorithm) - calculate the Greatest Common Divisor (GCD)
+  * `P` [Merge Sort](src/algorithms/sorting/merge-sort)
+  * `P` [Quicksort](src/algorithms/sorting/quick-sort)
+  * `P` [Albero per Ricerca in Profondità](src/algorithms/tree/depth-first-search) (DFS)
+  * `P` [Grafo per Ricerca in Profondità](src/algorithms/graph/depth-first-search) (DFS)
+  * `P` [Jump Game](src/algorithms/uncategorized/jump-game)
+  * `P` [Algoritmo di Elevamento a Potenza](src/algorithms/math/fast-powering)
+  * `A` [Permutazioni](src/algorithms/sets/permutations) (con o senza ripetizioni)
+  * `A` [Combinazioni](src/algorithms/sets/combinations) (con o senza ripetizioni)
+* **Programmazione Dinamica** - creare una soluzione utilizzando le sub-solution trovate in precedenza
+  * `P` [Numero di Fibonacci](src/algorithms/math/fibonacci)
+  * `P` [Jump Game](src/algorithms/uncategorized/jump-game)
+  * `P` [Percorsi Unici](src/algorithms/uncategorized/unique-paths)
+  * `P` [Rain Terraces](src/algorithms/uncategorized/rain-terraces) - problema dell'acqua piovana in trappola
+  * `P` [Recursive Staircase](src/algorithms/uncategorized/recursive-staircase) - contare il numero di percorsi per arrivare in vetta
+  * `A` [Distanza di Levenshtein](src/algorithms/string/levenshtein-distance) - minima variazione tra due sequenze
+  * `A` [La Più Lunga Frequente SottoSequenza](src/algorithms/sets/longest-common-subsequence) (LCS)
+  * `A` [La Più Lunga Frequente SubString](src/algorithms/string/longest-common-substring)
+  * `A` [La Più Lunga SottoSequenza Crescente](src/algorithms/sets/longest-increasing-subsequence)
+  * `A` [La Più Corta e Frequente SuperSequenza](src/algorithms/sets/shortest-common-supersequence)
+  * `A` [Problema dello zaino](src/algorithms/sets/knapsack-problem)
+  * `A` [Partizione di un Intero](src/algorithms/math/integer-partition)
+  * `A` [Massimo SubArray](src/algorithms/sets/maximum-subarray)
+  * `A` [Algoritmo di Bellman-Ford](src/algorithms/graph/bellman-ford) - ricerca del percorso più breve per tutti i vertici del grafo
+  * `A` [Algoritmo di Floyd-Warshall](src/algorithms/graph/floyd-warshall) - ricerca del percorso più breve tra tutte le coppie di vertici 
+  * `A` [Espressioni Regolari](src/algorithms/string/regular-expression-matching)
+* **Backtracking** -  come la brute force, provate a generare tutte le soluzioni possibili, ma ogni volta che generate la prossima soluzione testate se soddisfa tutte le condizioni e solo allora continuare a generare soluzioni successive. Altrimenti, fate marcia indietro, e andate su un percorso diverso per trovare una soluzione. Normalmente si utilizza l'algoritmo DFS.
+  * `P` [Jump Game](src/algorithms/uncategorized/jump-game)
+  * `P` [Percorsi Unici](src/algorithms/uncategorized/unique-paths)
+  * `P` [Power Set](src/algorithms/sets/power-set) - tutti i subset di un set
+  * `A` [Ciclo di Hamiltonian](src/algorithms/graph/hamiltonian-cycle) - visita di tutti i vertici solamente una volta
+  * `A` [Problema di N-Queens](src/algorithms/uncategorized/n-queens)
+  * `A` [Knight's Tour](src/algorithms/uncategorized/knight-tour)
+  * `A` [Combinazioni di una Somma](src/algorithms/sets/combination-sum) - trovare tutte le combinazioni che compongono una somma
+* **Branch & Bound** - ricordatevi che la soluzione meno costosa trovata ad ogni step durante il backtracking e
+il costo di usare la soluzione meno costosa trovata fino al limite inferiore al costo minimo della soluzione al problema,
+al fine di scartare soluzioni parziali con costi maggiori della soluzione meno costosa trovata .
+Di solito si usa BFS trasversale in combinazione con DFS trasversale .
+
+## Come usare questa repository
+
+**Installare tutte le dipendenze**
+```
+npm install
+```
+
+**Eseguire ESLint**
+
+Potresti usarlo per controllare la qualità del codice.
+
+```
+npm run lint
+```
+
+**Eseguire tutti i test**
+```
+npm test
+```
+
+**Eseguire un test tramite il nome**
+```
+npm test -- 'LinkedList'
+```
+
+**Playground**
+
+Se vuoi puoi giocare le strutture dati e gli algoritmi nel file ./src/playground/playground.js` e 
+scrivere test nel file `./src/playground/__test__/playground.test.js`.
+
+Poi puoi semplicemente eseguire il seguente comando per testare quello che hai scritto : 
+
+```
+npm test -- 'playground'
+```
+
+## Informazioni Utili
+
+### Bibliografia
+
+[▶ Data Structures and Algorithms on YouTube](https://www.youtube.com/playlist?list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
+
+### Notazione Big O 
+
+* La notazione Big O* è usata per classificare algoritmi in base al tempo di esecuzione o ai 
+requisiti di spazio che crescono in base alla crescita dell'input .
+Nella grafico qua sotto puoi trovare gli ordini di crescita più comuni degli algoritmi usando la notazione Big O.
+
+![Grafi Big O ](./assets/big-o-graph.png)
+
+Riferimento: [Big O Cheat Sheet](http://bigocheatsheet.com/).
+
+Nella tabella qua sotto ci sono riportate la lista delle notazioni Big O più usate e delle loro prestazioni comparate tra differenti grandezze d'input .
+
+| Notazione Big O | Computazione con 10 elementi | Computazione con 100 elementi | Computazione con 1000 elementi  |
+| --------------- | ---------------------------- | ----------------------------- | ------------------------------- |
+| **O(1)**        | 1                            | 1                             | 1                               |
+| **O(log N)**    | 3                            | 6                             | 9                               |
+| **O(N)**        | 10                           | 100                           | 1000                            |
+| **O(N log N)**  | 30                           | 600                           | 9000                            |
+| **O(N^2)**      | 100                          | 10000                         | 1000000                         |
+| **O(2^N)**      | 1024                         | 1.26e+29                      | 1.07e+301                       |
+| **O(N!)**       | 3628800                      | 9.3e+157                      | 4.02e+2567                      |
+
+### Complessità delle Operazion sulle Strutture Dati
+
+| Struttura Dati          | Accesso   | Ricerca   | Inserimento | Rimozione | Commenti  |
+| ----------------------- | :-------: | :-------: | :--------:  | :-------: | :-------- |
+| **Array**               | 1         | n         | n           | n         |           |
+| **Pila**                | n         | n         | 1           | 1         |           |
+| **Coda**                | n         | n         | 1           | 1         |           |
+| **Lista Concatenata**   | n         | n         | 1           | n         |           |
+| **Tabella Hash**        | -         | n         | n           | n         | Nel caso di una funzione di hashing perfetta il costo sarebbe O(1)|
+| **Binary Search Tree**  | n         | n         | n           | n         | Nel caso di albero bilanciato il costo sarebbe O(log(n)) |
+| **B-Tree**              | log(n)    | log(n)    | log(n)      | log(n)    |           |
+| **Red-Black Tree**      | log(n)    | log(n)    | log(n)      | log(n)    |           |
+| **Albero AVL**          | log(n)    | log(n)    | log(n)      | log(n)    |           |
+| **Bloom Filter**        | -         | 1         | 1           | -         | Falsi positivi sono possibili durante la ricerca |
+
+### Complessità degli Algoritmi di Ordinamento di Array
+
+| Nome                  | Milgiore        | Media               | Perggiore           | Memoria   | Stabile   | Commenti  |
+| --------------------- | :-------------: | :-----------------: | :-----------------: | :-------: | :-------: | :-------- |
+| **Bubble sort**       | n               | n<sup>2</sup>       | n<sup>2</sup>       | 1         | Yes       |           |
+| **Insertion sort**    | n               | n<sup>2</sup>       | n<sup>2</sup>       | 1         | Yes       |           |
+| **Selection sort**    | n<sup>2</sup>   | n<sup>2</sup>       | n<sup>2</sup>       | 1         | No        |           |
+| **Heap sort**         | n&nbsp;log(n)   | n&nbsp;log(n)       | n&nbsp;log(n)       | 1         | No        |           |
+| **Merge sort**        | n&nbsp;log(n)   | n&nbsp;log(n)       | n&nbsp;log(n)       | n         | Yes       |           |
+| **Quick sort**        | n&nbsp;log(n)   | n&nbsp;log(n)       | n<sup>2</sup>       | log(n)    | No        | Quicksort viene eseguito in memoria solitamente con una pila di O(log(n)) |
+| **Shell sort**        | n&nbsp;log(n)   | dipende dagli spazi vuoti nella sequenza  | n&nbsp;(log(n))<sup>2</sup>  | 1         | No         |           |
+| **Counting sort**     | n + r           | n + r               | n + r               | n + r     | Yes       | r - numero più grande nell'array |
+| **Radix sort**        | n * k           | n * k               | n * k               | n + k     | Yes       | k - lunghezza della chiave più grande |

From ea8234b49b426c1ea990d1ece0520059072c67e9 Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Wed, 9 Dec 2020 09:20:24 +0100
Subject: [PATCH 011/264] Add README in Italian.

---
 README.es-ES.md | 3 ++-
 README.fr-FR.md | 3 ++-
 README.it-IT.md | 3 ++-
 README.ja-JP.md | 3 ++-
 README.ko-KR.md | 3 ++-
 README.md       | 3 ++-
 README.pl-PL.md | 3 ++-
 README.pt-BR.md | 3 ++-
 README.ru-RU.md | 3 ++-
 README.tr-TR.md | 3 ++-
 README.zh-CN.md | 3 ++-
 README.zh-TW.md | 3 ++-
 12 files changed, 24 insertions(+), 12 deletions(-)

diff --git a/README.es-ES.md b/README.es-ES.md
index 8a6706ce49..e501de63ca 100644
--- a/README.es-ES.md
+++ b/README.es-ES.md
@@ -19,7 +19,8 @@ _Léelo en otros idiomas:_
 [_Français_](README.fr-FR.md),
 [_Português_](README.pt-BR.md),
 [_Русский_](README.ru-RU.md),
-[_Türk_](README.tr-TR.md)
+[_Türk_](README.tr-TR.md),
+[_Italiana_](README.it-IT.md)
 
 *☝ Nótese que este proyecto está pensado con fines de aprendizaje e investigación,
 y **no** para ser usado en producción.*
diff --git a/README.fr-FR.md b/README.fr-FR.md
index a83cce4d01..70b244a301 100644
--- a/README.fr-FR.md
+++ b/README.fr-FR.md
@@ -20,7 +20,8 @@ _Lisez ceci dans d'autres langues:_
 [_Español_](README.es-ES.md),
 [_Português_](README.pt-BR.md),
 [_Русский_](README.ru-RU.md),
-[_Türk_](README.tr-TR.md)
+[_Türk_](README.tr-TR.md),
+[_Italiana_](README.it-IT.md)
 
 ## Data Structures
 
diff --git a/README.it-IT.md b/README.it-IT.md
index 8daa4ac62c..d340ece707 100644
--- a/README.it-IT.md
+++ b/README.it-IT.md
@@ -16,7 +16,8 @@ _Leggilo in altre lingue:_
 [_Français_](README.fr-FR.md),
 [_Español_](README.es-ES.md),
 [_Português_](README.pt-BR.md),
-[_Italian_](README.it-IT.md)
+[_Русский_](README.ru-RU.md),
+[_Türk_](README.tr-TR.md)
 
 *☝ Si noti che questo progetto è destinato ad essere utilizzato solo per l'apprendimento e la ricerca e non è destinato ad essere utilizzato per il commercio.*
 
diff --git a/README.ja-JP.md b/README.ja-JP.md
index 862a0d2bc0..687ea124aa 100644
--- a/README.ja-JP.md
+++ b/README.ja-JP.md
@@ -19,7 +19,8 @@ _Read this in other languages:_
 [_Español_](README.es-ES.md),
 [_Português_](README.pt-BR.md),
 [_Русский_](README.ru-RU.md),
-[_Türk_](README.tr-TR.md)
+[_Türk_](README.tr-TR.md),
+[_Italiana_](README.it-IT.md)
 
 ## データ構造
 
diff --git a/README.ko-KR.md b/README.ko-KR.md
index c5fa8b1804..4dcd3fd34b 100644
--- a/README.ko-KR.md
+++ b/README.ko-KR.md
@@ -18,7 +18,8 @@ _Read this in other languages:_
 [_Español_](README.es-ES.md),
 [_Português_](README.pt-BR.md),
 [_Русский_](README.ru-RU.md),
-[_Türk_](README.tr-TR.md)
+[_Türk_](README.tr-TR.md),
+[_Italiana_](README.it-IT.md)
 
 ## 자료 구조
 
diff --git a/README.md b/README.md
index 9d4d39622b..98d5c43c5e 100644
--- a/README.md
+++ b/README.md
@@ -20,7 +20,8 @@ _Read this in other languages:_
 [_Español_](README.es-ES.md),
 [_Português_](README.pt-BR.md),
 [_Русский_](README.ru-RU.md),
-[_Türk_](README.tr-TR.md)
+[_Türk_](README.tr-TR.md),
+[_Italiana_](README.it-IT.md)
 
 *☝ Note that this project is meant to be used for learning and researching purposes 
 only, and it is **not** meant to be used for production.*
diff --git a/README.pl-PL.md b/README.pl-PL.md
index 26ca99c179..6745307031 100644
--- a/README.pl-PL.md
+++ b/README.pl-PL.md
@@ -20,7 +20,8 @@ _Read this in other languages:_
 [_Español_](README.es-ES.md),
 [_Português_](README.pt-BR.md),
 [_Русский_](README.ru-RU.md),
-[_Türk_](README.tr-TR.md)
+[_Türk_](README.tr-TR.md),
+[_Italiana_](README.it-IT.md)
 
 ## Struktury Danych
 
diff --git a/README.pt-BR.md b/README.pt-BR.md
index 626c5f65b7..f02691c179 100644
--- a/README.pt-BR.md
+++ b/README.pt-BR.md
@@ -20,7 +20,8 @@ _Leia isto em outros idiomas:_
 [_Français_](README.fr-FR.md),
 [_Español_](README.es-ES.md),
 [_Русский_](README.ru-RU.md),
-[_Türk_](README.tr-TR.md)
+[_Türk_](README.tr-TR.md),
+[_Italiana_](README.it-IT.md)
 
 ## Estrutura de Dados
 
diff --git a/README.ru-RU.md b/README.ru-RU.md
index fcfcf83b9f..6317926cef 100644
--- a/README.ru-RU.md
+++ b/README.ru-RU.md
@@ -17,7 +17,8 @@ _Читать на других языках:_
 [_Français_](README.fr-FR.md),
 [_Español_](README.es-ES.md),
 [_Português_](README.pt-BR.md),
-[_Türk_](README.tr-TR.md)
+[_Türk_](README.tr-TR.md),
+[_Italiana_](README.it-IT.md)
 
 *☝ Замечание: этот репозиторий предназначен для учебно-исследовательских целей (**не** для использования в продакшн-системах).*
 
diff --git a/README.tr-TR.md b/README.tr-TR.md
index 0892e5f4a0..260553780e 100644
--- a/README.tr-TR.md
+++ b/README.tr-TR.md
@@ -18,7 +18,8 @@ _Read this in other languages:_
 [_Français_](README.fr-FR.md),
 [_Español_](README.es-ES.md),
 [_Português_](README.pt-BR.md),
-[_Русский_](README.ru-RU.md)
+[_Русский_](README.ru-RU.md),
+[_Italiana_](README.it-IT.md)
 
 *☝ Not, bu proje araştırma ve öğrenme amacı ile yapılmış 
 olup üretim için **yaplılmamıştır**.*
diff --git a/README.zh-CN.md b/README.zh-CN.md
index f63eab90b4..8e8c66172e 100644
--- a/README.zh-CN.md
+++ b/README.zh-CN.md
@@ -17,7 +17,8 @@ _Read this in other languages:_
 [_Español_](README.es-ES.md),
 [_Português_](README.pt-BR.md),
 [_Русский_](README.ru-RU.md),
-[_Türk_](README.tr-TR.md)
+[_Türk_](README.tr-TR.md),
+[_Italiana_](README.it-IT.md)
 
 *注意：这个项目仅用于学习和研究，**不是**用于生产环境。*
 
diff --git a/README.zh-TW.md b/README.zh-TW.md
index 50050b2786..1eba73c941 100644
--- a/README.zh-TW.md
+++ b/README.zh-TW.md
@@ -16,7 +16,8 @@ _Read this in other languages:_
 [_Español_](README.es-ES.md),
 [_Português_](README.pt-BR.md),
 [_Русский_](README.ru-RU.md),
-[_Türk_](README.tr-TR.md)
+[_Türk_](README.tr-TR.md),
+[_Italiana_](README.it-IT.md)
 
 ## 資料結構
 

From bbe0462b1cdeb323ae5964a69189ec218d261198 Mon Sep 17 00:00:00 2001
From: deepthan <deepthan@163.com>
Date: Fri, 11 Dec 2020 00:41:22 +0800
Subject: [PATCH 012/264] fix:  fix playground part  translate error (#587)

Co-authored-by: linkun.he <helinkun@ithinkdt.com>
---
 README.zh-CN.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.zh-CN.md b/README.zh-CN.md
index 8e8c66172e..45a8c8c64f 100644
--- a/README.zh-CN.md
+++ b/README.zh-CN.md
@@ -228,7 +228,7 @@ npm test -- 'LinkedList'
 
 你可以在 `./src/playground/playground.js` 文件中操作数据结构与算法，并在 `./src/playground/__test__/playground.test.js` 中编写测试。
 
-然后，只需运行以下命令来测试你的 Playground 是否按无误:
+然后，只需运行以下命令来测试你的 Playground 是否无误:
 
 ```
 npm test -- 'playground'

From 498ab10b1b8eb71a4f6c80a62f84cc9c289a40c8 Mon Sep 17 00:00:00 2001
From: vladimirschneider <42021006+vladimirschneider@users.noreply.github.com>
Date: Thu, 10 Dec 2020 23:50:47 +0700
Subject: [PATCH 013/264] Repeated Math operation (#584)

Co-authored-by: Oleksii Trekhleb <trehleb@gmail.com>
---
 src/algorithms/uncategorized/rain-terraces/bfRainTerraces.js | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/algorithms/uncategorized/rain-terraces/bfRainTerraces.js b/src/algorithms/uncategorized/rain-terraces/bfRainTerraces.js
index f136e6d4c6..0d3443a4aa 100644
--- a/src/algorithms/uncategorized/rain-terraces/bfRainTerraces.js
+++ b/src/algorithms/uncategorized/rain-terraces/bfRainTerraces.js
@@ -25,7 +25,7 @@ export default function bfRainTerraces(terraces) {
     if (terraceBoundaryLevel > terraces[terraceIndex]) {
       // Terrace will be able to store the water if the lowest of two left and right highest
       // terraces are still higher than the current one.
-      waterAmount += Math.min(leftHighestLevel, rightHighestLevel) - terraces[terraceIndex];
+      waterAmount += terraceBoundaryLevel - terraces[terraceIndex];
     }
   }
 

From 827906c1401a2842575f4d602875b0b4f563507f Mon Sep 17 00:00:00 2001
From: Anmol Gomra <50433033+pineapple45@users.noreply.github.com>
Date: Thu, 10 Dec 2020 22:24:11 +0530
Subject: [PATCH 014/264] added prime-factors algo in src/algorithms/math
 (#532)

---
 README.md                                     |  1 +
 src/algorithms/math/prime-factors/README.md   | 34 ++++++++++++++
 .../__test__/primefactors.test.js             | 40 +++++++++++++++++
 .../math/prime-factors/primefactors.js        | 44 +++++++++++++++++++
 4 files changed, 119 insertions(+)
 create mode 100644 src/algorithms/math/prime-factors/README.md
 create mode 100644 src/algorithms/math/prime-factors/__test__/primefactors.test.js
 create mode 100644 src/algorithms/math/prime-factors/primefactors.js

diff --git a/README.md b/README.md
index 98d5c43c5e..3008a6abda 100644
--- a/README.md
+++ b/README.md
@@ -66,6 +66,7 @@ a set of rules that precisely define a sequence of operations.
   * `B` [Bit Manipulation](src/algorithms/math/bits) - set/get/update/clear bits, multiplication/division by two, make negative etc.
   * `B` [Factorial](src/algorithms/math/factorial) 
   * `B` [Fibonacci Number](src/algorithms/math/fibonacci) - classic and closed-form versions
+  * `B` [Prime Factors](src/algorithms/math/prime-factors) - finding distinct prime-factor count using both accurate & Hardy-Ramanujan's Algorithm   
   * `B` [Primality Test](src/algorithms/math/primality-test) (trial division method)
   * `B` [Euclidean Algorithm](src/algorithms/math/euclidean-algorithm) - calculate the Greatest Common Divisor (GCD)
   * `B` [Least Common Multiple](src/algorithms/math/least-common-multiple) (LCM)
diff --git a/src/algorithms/math/prime-factors/README.md b/src/algorithms/math/prime-factors/README.md
new file mode 100644
index 0000000000..6b855d37d7
--- /dev/null
+++ b/src/algorithms/math/prime-factors/README.md
@@ -0,0 +1,34 @@
+# Prime Factors
+
+Prime factors are basically those prime numbers which multiply together to give the orignal number. For ex: 39 will have prime factors as 3 and 13 which are also prime numbers. Another example is 15 whose prime factors are 3 and 5.
+
+#### Method for finding the prime factors and their count accurately
+
+The approach is to basically keep on dividing the  natural number 'n' by indexes from i = 2 to i = n by prime indexes only. This is ensured by an 'if' check. Then value of 'n' keeps on overriding by (n/i).
+The time complexity till now is O(n) in worst case since the loop run from index i = 2 to i = n even when no index 'i' is left to be divided by 'n' other than n itself. This time complexity can be reduced  to O(sqrt(n)) from O(n). This optimisation is acheivable when loop is ran from i = 2 to i = sqrt(n). Now, we go only till O(sqrt(n)) because when 'i' becomes greater than sqrt(n), we now have the confirmation there is no index 'i' left which can divide 'n' completely other than n itself.
+
+##### Optimised Time Complexity: O(sqrt(n))
+
+
+#### Hardy-Ramanujan formula for approximate calculation of prime-factor count
+
+In 1917, a theorem was formulated by G.H Hardy and Srinivasa Ramanujan which approximately tells the total count of distinct prime factors of most 'n' natural numbers.
+The fomula is given by ln(ln(n)).
+
+#### Code Explaiation
+
+There are on 4 functions used:
+
+- getPrimeFactors : returns array containing all distinct prime factors for given input n.
+
+- getPrimeFactorsCount: returns accurate total count of distinct prime factors of given input n.
+
+- hardyRamanujanApprox:  returns approximate total count of distinct prime factors of given input n using Hardy-Ramanujan formula.
+
+- errorPercent : returns %age of error in approximation using formula to that of accurate result. The formula used is:   **[Modulus(accurate_val - approximate_val) / accurate_val ] * 100**. This shows deviation from accurate result.
+ 
+
+## References
+
+- [Youtube](https://www.youtube.com/watch?v=6PDtgHhpCHo)
+- [Wikipedia](https://en.wikipedia.org/wiki/Hardy%E2%80%93Ramanujan_theorem)
\ No newline at end of file
diff --git a/src/algorithms/math/prime-factors/__test__/primefactors.test.js b/src/algorithms/math/prime-factors/__test__/primefactors.test.js
new file mode 100644
index 0000000000..7a1ba96377
--- /dev/null
+++ b/src/algorithms/math/prime-factors/__test__/primefactors.test.js
@@ -0,0 +1,40 @@
+import primefactors from '../primefactors';
+
+describe('prime-factors', () => {
+      it('should give prime factors', () => {
+        expect(primefactors.getPrimeFactors(510510)).toEqual([2, 3, 5, 7, 11, 13, 17]);
+        expect(primefactors.getPrimeFactors(343434)).toEqual([2, 3, 7, 13, 17, 37]);
+        expect(primefactors.getPrimeFactors(456745)).toEqual([5, 167, 547]);
+        expect(primefactors.getPrimeFactors(8735463)).toEqual([3, 11, 88237]);
+        expect(primefactors.getPrimeFactors(873452453)).toEqual([149, 1637, 3581]);
+        expect(primefactors.getPrimeFactors(52734)).toEqual([2, 3, 11, 17, 47]);
+    });
+
+    it('should give prime factors count accurately', () => {
+        expect(primefactors.getPrimeFactorsCount(primefactors.getPrimeFactors(510510))).toEqual(7);
+        expect(primefactors.getPrimeFactorsCount(primefactors.getPrimeFactors(343434))).toEqual(6);
+        expect(primefactors.getPrimeFactorsCount(primefactors.getPrimeFactors(456745))).toEqual(3);
+        expect(primefactors.getPrimeFactorsCount(primefactors.getPrimeFactors(8735463))).toEqual(3);
+        expect(primefactors.getPrimeFactorsCount(primefactors.getPrimeFactors(873452453))).toEqual(3);
+        expect(primefactors.getPrimeFactorsCount(primefactors.getPrimeFactors(52734))).toEqual(5);
+    });
+
+    it('should give prime factors count approximately using Hardy-Ramanujan-Approx', () => {
+        expect(primefactors.hardyRamanujanApprox(510510)).toBeCloseTo(2.5759018900,5);
+        expect(primefactors.hardyRamanujanApprox(343434)).toBeCloseTo(2.54527635538,5);
+        expect(primefactors.hardyRamanujanApprox(456745)).toBeCloseTo(2.5673987036,5);
+        expect(primefactors.hardyRamanujanApprox(8735463)).toBeCloseTo(2.771519494900,5);
+        expect(primefactors.hardyRamanujanApprox(873452453)).toBeCloseTo(3.0247066455016,5);
+        expect(primefactors.hardyRamanujanApprox(52734)).toBeCloseTo(2.386284094835,5);
+    });
+
+    it('should give error percentage of deviation of Hardy-Ramanujan-Approx prime-factors count from accurate prime-factors count', () => {
+        expect(primefactors.errorPercent(primefactors.getPrimeFactorsCount(primefactors.getPrimeFactors(510510)),primefactors.hardyRamanujanApprox(510510))).toBeCloseTo(63.20140157059997,5);
+        expect(primefactors.errorPercent(primefactors.getPrimeFactorsCount(primefactors.getPrimeFactors(343434)),primefactors.hardyRamanujanApprox(343434))).toBeCloseTo(57.5787274,5);
+        expect(primefactors.errorPercent(primefactors.getPrimeFactorsCount(primefactors.getPrimeFactors(456745)),primefactors.hardyRamanujanApprox(456745))).toBeCloseTo(14.420043212851,5);
+        expect(primefactors.errorPercent(primefactors.getPrimeFactorsCount(primefactors.getPrimeFactors(8735463)),primefactors.hardyRamanujanApprox(8735463))).toBeCloseTo(7.61601683663378,5);
+        expect(primefactors.errorPercent(primefactors.getPrimeFactorsCount(primefactors.getPrimeFactors(873452453)),primefactors.hardyRamanujanApprox(873452453))).toBeCloseTo(0.8235548500,5);
+        expect(primefactors.errorPercent(primefactors.getPrimeFactorsCount(primefactors.getPrimeFactors(52734)),primefactors.hardyRamanujanApprox(52734))).toBeCloseTo(52.27431810328,5);
+    });
+});
+
diff --git a/src/algorithms/math/prime-factors/primefactors.js b/src/algorithms/math/prime-factors/primefactors.js
new file mode 100644
index 0000000000..d951a37153
--- /dev/null
+++ b/src/algorithms/math/prime-factors/primefactors.js
@@ -0,0 +1,44 @@
+export default {
+
+  getPrimeFactors : (n) => {
+    let factorsArray = []; // an array where all the prime factors will be stored
+
+    //over here optimisation is made by running loop till sqrt(n) instead of n
+    for (let i = 2 ; i <= Math.sqrt(n); i++){
+      if(n % i === 0){  // if check to ensure i completely divides n
+        let count = 0;  // This count keeps track of number of times i divides n
+        while(n % i === 0){
+          n = n/i;       // override the value of n
+          count++;        // count value updated
+        }
+        factorsArray.push(i); // array gets populated
+      }
+    }
+    if(n !== 1){ // finally we cannot push 1 to array since it cannot be a prime-factor
+        factorsArray.push(n);
+    }
+  
+    return factorsArray;
+  },
+
+  //returns accurate prime-factors count
+  getPrimeFactorsCount : (factorsArray) => {
+    return factorsArray.length;
+  },
+  
+  
+  //returns Hardy-Ramanujan Approximation of prime-factors count 
+  hardyRamanujanApprox : (n) => {
+    return Math.log(Math.log(n));
+  },
+  
+  //returns %age of error in approximation using formula to that of accurate result. 
+  errorPercent : (exactFactorCount,approximateFactorCount) => {
+  let diff = exactFactorCount-approximateFactorCount > 0 ? exactFactorCount-approximateFactorCount: -(exactFactorCount-approximateFactorCount);
+  return (diff/exactFactorCount * 100);
+  }
+  
+
+}
+
+

From 30ef6a30e11b674510669f0c663d255cb96634ae Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Fri, 11 Dec 2020 08:37:06 +0100
Subject: [PATCH 015/264] Add prime factors calculation.

---
 README.md                                     |  2 +-
 src/algorithms/math/prime-factors/README.md   | 34 ++++----
 .../__test__/primeFactors.test.js             | 87 +++++++++++++++++++
 .../__test__/primefactors.test.js             | 40 ---------
 .../math/prime-factors/primeFactors.js        | 42 +++++++++
 .../math/prime-factors/primefactors.js        | 44 ----------
 6 files changed, 147 insertions(+), 102 deletions(-)
 create mode 100644 src/algorithms/math/prime-factors/__test__/primeFactors.test.js
 delete mode 100644 src/algorithms/math/prime-factors/__test__/primefactors.test.js
 create mode 100644 src/algorithms/math/prime-factors/primeFactors.js
 delete mode 100644 src/algorithms/math/prime-factors/primefactors.js

diff --git a/README.md b/README.md
index 3008a6abda..3886d0bba2 100644
--- a/README.md
+++ b/README.md
@@ -66,7 +66,7 @@ a set of rules that precisely define a sequence of operations.
   * `B` [Bit Manipulation](src/algorithms/math/bits) - set/get/update/clear bits, multiplication/division by two, make negative etc.
   * `B` [Factorial](src/algorithms/math/factorial) 
   * `B` [Fibonacci Number](src/algorithms/math/fibonacci) - classic and closed-form versions
-  * `B` [Prime Factors](src/algorithms/math/prime-factors) - finding distinct prime-factor count using both accurate & Hardy-Ramanujan's Algorithm   
+  * `B` [Prime Factors](src/algorithms/math/prime-factors) - finding prime factors and counting them using Hardy-Ramanujan's theorem  
   * `B` [Primality Test](src/algorithms/math/primality-test) (trial division method)
   * `B` [Euclidean Algorithm](src/algorithms/math/euclidean-algorithm) - calculate the Greatest Common Divisor (GCD)
   * `B` [Least Common Multiple](src/algorithms/math/least-common-multiple) (LCM)
diff --git a/src/algorithms/math/prime-factors/README.md b/src/algorithms/math/prime-factors/README.md
index 6b855d37d7..a0f1d1535d 100644
--- a/src/algorithms/math/prime-factors/README.md
+++ b/src/algorithms/math/prime-factors/README.md
@@ -1,34 +1,34 @@
 # Prime Factors
 
-Prime factors are basically those prime numbers which multiply together to give the orignal number. For ex: 39 will have prime factors as 3 and 13 which are also prime numbers. Another example is 15 whose prime factors are 3 and 5.
+**Prime number** is a whole number greater than `1` that **cannot** be made by multiplying other whole numbers. The first few prime numbers are: `2`, `3`, `5`, `7`, `11`, `13`, `17`, `19` and so on.
 
-#### Method for finding the prime factors and their count accurately
+If we **can** make it by multiplying other whole numbers it is a **Composite Number**.
 
-The approach is to basically keep on dividing the  natural number 'n' by indexes from i = 2 to i = n by prime indexes only. This is ensured by an 'if' check. Then value of 'n' keeps on overriding by (n/i).
-The time complexity till now is O(n) in worst case since the loop run from index i = 2 to i = n even when no index 'i' is left to be divided by 'n' other than n itself. This time complexity can be reduced  to O(sqrt(n)) from O(n). This optimisation is acheivable when loop is ran from i = 2 to i = sqrt(n). Now, we go only till O(sqrt(n)) because when 'i' becomes greater than sqrt(n), we now have the confirmation there is no index 'i' left which can divide 'n' completely other than n itself.
+![Composite numbers](https://www.mathsisfun.com/numbers/images/prime-composite.svg)
 
-##### Optimised Time Complexity: O(sqrt(n))
+_Image source: [Math is Fun](https://www.mathsisfun.com/prime-factorization.html)_
 
+**Prime factors** are those [prime numbers](https://en.wikipedia.org/wiki/Prime_number) which multiply together to give the original number. For example `39` will have prime factors of `3` and `13` which are also prime numbers. Another example is `15` whose prime factors are `3` and `5`.
 
-#### Hardy-Ramanujan formula for approximate calculation of prime-factor count
+![Factors](https://www.mathsisfun.com/numbers/images/factor-2x3.svg)
 
-In 1917, a theorem was formulated by G.H Hardy and Srinivasa Ramanujan which approximately tells the total count of distinct prime factors of most 'n' natural numbers.
-The fomula is given by ln(ln(n)).
+_Image source: [Math is Fun](https://www.mathsisfun.com/prime-factorization.html)_
 
-#### Code Explaiation
+## Finding the prime factors and their count accurately
 
-There are on 4 functions used:
+The approach is to keep on dividing the natural number `n` by indexes from `i = 2` to `i = n` (by prime indexes only). The value of `n` is being overridden by `(n / i)` on each iteration.
 
-- getPrimeFactors : returns array containing all distinct prime factors for given input n.
+The time complexity till now is `O(n)` in the worst case scenario since the loop runs from index `i = 2` to `i = n`. This time complexity can be reduced from `O(n)` to `O(sqrt(n))`. The optimisation is achievable when loop runs from `i = 2` to `i = sqrt(n)`. Now, we go only till `O(sqrt(n))` because when `i` becomes greater than `sqrt(n)`, we have the confirmation that there is no index `i` left which can divide `n` completely other than `n` itself.
 
-- getPrimeFactorsCount: returns accurate total count of distinct prime factors of given input n.
+## Hardy-Ramanujan formula for approximate calculation of prime-factor count
 
-- hardyRamanujanApprox:  returns approximate total count of distinct prime factors of given input n using Hardy-Ramanujan formula.
+In 1917, a theorem was formulated by G.H Hardy and Srinivasa Ramanujan which states that the normal order of the number `ω(n)` of distinct prime factors of a number `n` is `log(log(n))`.
 
-- errorPercent : returns %age of error in approximation using formula to that of accurate result. The formula used is:   **[Modulus(accurate_val - approximate_val) / accurate_val ] * 100**. This shows deviation from accurate result.
- 
+Roughly speaking, this means that most numbers have about this number of distinct prime factors.
 
 ## References
 
-- [Youtube](https://www.youtube.com/watch?v=6PDtgHhpCHo)
-- [Wikipedia](https://en.wikipedia.org/wiki/Hardy%E2%80%93Ramanujan_theorem)
\ No newline at end of file
+- [Prime numbers on Math is Fun](https://www.mathsisfun.com/prime-factorization.html)
+- [Prime numbers on Wikipedia](https://en.wikipedia.org/wiki/Prime_number)
+- [Hardy–Ramanujan theorem on Wikipedia](https://en.wikipedia.org/wiki/Hardy%E2%80%93Ramanujan_theorem)
+- [Prime factorization of a number on Youtube](https://www.youtube.com/watch?v=6PDtgHhpCHo&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8&index=82)
diff --git a/src/algorithms/math/prime-factors/__test__/primeFactors.test.js b/src/algorithms/math/prime-factors/__test__/primeFactors.test.js
new file mode 100644
index 0000000000..92c94d1f6f
--- /dev/null
+++ b/src/algorithms/math/prime-factors/__test__/primeFactors.test.js
@@ -0,0 +1,87 @@
+import {
+  primeFactors,
+  hardyRamanujan,
+} from '../primeFactors';
+
+/**
+ * Calculates the error between exact and approximate prime factor counts.
+ * @param {number} exactCount
+ * @param {number} approximateCount
+ * @returns {number} - approximation error (percentage).
+ */
+function approximationError(exactCount, approximateCount) {
+  return (Math.abs((exactCount - approximateCount) / exactCount) * 100);
+}
+
+describe('primeFactors', () => {
+  it('should find prime factors', () => {
+    expect(primeFactors(1)).toEqual([]);
+    expect(primeFactors(2)).toEqual([2]);
+    expect(primeFactors(3)).toEqual([3]);
+    expect(primeFactors(4)).toEqual([2, 2]);
+    expect(primeFactors(14)).toEqual([2, 7]);
+    expect(primeFactors(40)).toEqual([2, 2, 2, 5]);
+    expect(primeFactors(54)).toEqual([2, 3, 3, 3]);
+    expect(primeFactors(100)).toEqual([2, 2, 5, 5]);
+    expect(primeFactors(156)).toEqual([2, 2, 3, 13]);
+    expect(primeFactors(273)).toEqual([3, 7, 13]);
+    expect(primeFactors(300)).toEqual([2, 2, 3, 5, 5]);
+    expect(primeFactors(980)).toEqual([2, 2, 5, 7, 7]);
+    expect(primeFactors(1000)).toEqual([2, 2, 2, 5, 5, 5]);
+    expect(primeFactors(52734)).toEqual([2, 3, 11, 17, 47]);
+    expect(primeFactors(343434)).toEqual([2, 3, 7, 13, 17, 37]);
+    expect(primeFactors(456745)).toEqual([5, 167, 547]);
+    expect(primeFactors(510510)).toEqual([2, 3, 5, 7, 11, 13, 17]);
+    expect(primeFactors(8735463)).toEqual([3, 3, 11, 88237]);
+    expect(primeFactors(873452453)).toEqual([149, 1637, 3581]);
+  });
+
+  it('should give approximate prime factors count using Hardy-Ramanujan theorem', () => {
+    expect(hardyRamanujan(2)).toBeCloseTo(-0.366, 2);
+    expect(hardyRamanujan(4)).toBeCloseTo(0.326, 2);
+    expect(hardyRamanujan(40)).toBeCloseTo(1.305, 2);
+    expect(hardyRamanujan(156)).toBeCloseTo(1.6193, 2);
+    expect(hardyRamanujan(980)).toBeCloseTo(1.929, 2);
+    expect(hardyRamanujan(52734)).toBeCloseTo(2.386, 2);
+    expect(hardyRamanujan(343434)).toBeCloseTo(2.545, 2);
+    expect(hardyRamanujan(456745)).toBeCloseTo(2.567, 2);
+    expect(hardyRamanujan(510510)).toBeCloseTo(2.575, 2);
+    expect(hardyRamanujan(8735463)).toBeCloseTo(2.771, 2);
+    expect(hardyRamanujan(873452453)).toBeCloseTo(3.024, 2);
+  });
+
+  it('should give correct deviation between exact and approx counts', () => {
+    expect(approximationError(primeFactors(2).length, hardyRamanujan(2)))
+      .toBeCloseTo(136.651, 2);
+
+    expect(approximationError(primeFactors(4).length, hardyRamanujan(2)))
+      .toBeCloseTo(118.325, 2);
+
+    expect(approximationError(primeFactors(40).length, hardyRamanujan(2)))
+      .toBeCloseTo(109.162, 2);
+
+    expect(approximationError(primeFactors(156).length, hardyRamanujan(2)))
+      .toBeCloseTo(109.162, 2);
+
+    expect(approximationError(primeFactors(980).length, hardyRamanujan(2)))
+      .toBeCloseTo(107.330, 2);
+
+    expect(approximationError(primeFactors(52734).length, hardyRamanujan(52734)))
+      .toBeCloseTo(52.274, 2);
+
+    expect(approximationError(primeFactors(343434).length, hardyRamanujan(343434)))
+      .toBeCloseTo(57.578, 2);
+
+    expect(approximationError(primeFactors(456745).length, hardyRamanujan(456745)))
+      .toBeCloseTo(14.420, 2);
+
+    expect(approximationError(primeFactors(510510).length, hardyRamanujan(510510)))
+      .toBeCloseTo(63.201, 2);
+
+    expect(approximationError(primeFactors(8735463).length, hardyRamanujan(8735463)))
+      .toBeCloseTo(30.712, 2);
+
+    expect(approximationError(primeFactors(873452453).length, hardyRamanujan(873452453)))
+      .toBeCloseTo(0.823, 2);
+  });
+});
diff --git a/src/algorithms/math/prime-factors/__test__/primefactors.test.js b/src/algorithms/math/prime-factors/__test__/primefactors.test.js
deleted file mode 100644
index 7a1ba96377..0000000000
--- a/src/algorithms/math/prime-factors/__test__/primefactors.test.js
+++ /dev/null
@@ -1,40 +0,0 @@
-import primefactors from '../primefactors';
-
-describe('prime-factors', () => {
-      it('should give prime factors', () => {
-        expect(primefactors.getPrimeFactors(510510)).toEqual([2, 3, 5, 7, 11, 13, 17]);
-        expect(primefactors.getPrimeFactors(343434)).toEqual([2, 3, 7, 13, 17, 37]);
-        expect(primefactors.getPrimeFactors(456745)).toEqual([5, 167, 547]);
-        expect(primefactors.getPrimeFactors(8735463)).toEqual([3, 11, 88237]);
-        expect(primefactors.getPrimeFactors(873452453)).toEqual([149, 1637, 3581]);
-        expect(primefactors.getPrimeFactors(52734)).toEqual([2, 3, 11, 17, 47]);
-    });
-
-    it('should give prime factors count accurately', () => {
-        expect(primefactors.getPrimeFactorsCount(primefactors.getPrimeFactors(510510))).toEqual(7);
-        expect(primefactors.getPrimeFactorsCount(primefactors.getPrimeFactors(343434))).toEqual(6);
-        expect(primefactors.getPrimeFactorsCount(primefactors.getPrimeFactors(456745))).toEqual(3);
-        expect(primefactors.getPrimeFactorsCount(primefactors.getPrimeFactors(8735463))).toEqual(3);
-        expect(primefactors.getPrimeFactorsCount(primefactors.getPrimeFactors(873452453))).toEqual(3);
-        expect(primefactors.getPrimeFactorsCount(primefactors.getPrimeFactors(52734))).toEqual(5);
-    });
-
-    it('should give prime factors count approximately using Hardy-Ramanujan-Approx', () => {
-        expect(primefactors.hardyRamanujanApprox(510510)).toBeCloseTo(2.5759018900,5);
-        expect(primefactors.hardyRamanujanApprox(343434)).toBeCloseTo(2.54527635538,5);
-        expect(primefactors.hardyRamanujanApprox(456745)).toBeCloseTo(2.5673987036,5);
-        expect(primefactors.hardyRamanujanApprox(8735463)).toBeCloseTo(2.771519494900,5);
-        expect(primefactors.hardyRamanujanApprox(873452453)).toBeCloseTo(3.0247066455016,5);
-        expect(primefactors.hardyRamanujanApprox(52734)).toBeCloseTo(2.386284094835,5);
-    });
-
-    it('should give error percentage of deviation of Hardy-Ramanujan-Approx prime-factors count from accurate prime-factors count', () => {
-        expect(primefactors.errorPercent(primefactors.getPrimeFactorsCount(primefactors.getPrimeFactors(510510)),primefactors.hardyRamanujanApprox(510510))).toBeCloseTo(63.20140157059997,5);
-        expect(primefactors.errorPercent(primefactors.getPrimeFactorsCount(primefactors.getPrimeFactors(343434)),primefactors.hardyRamanujanApprox(343434))).toBeCloseTo(57.5787274,5);
-        expect(primefactors.errorPercent(primefactors.getPrimeFactorsCount(primefactors.getPrimeFactors(456745)),primefactors.hardyRamanujanApprox(456745))).toBeCloseTo(14.420043212851,5);
-        expect(primefactors.errorPercent(primefactors.getPrimeFactorsCount(primefactors.getPrimeFactors(8735463)),primefactors.hardyRamanujanApprox(8735463))).toBeCloseTo(7.61601683663378,5);
-        expect(primefactors.errorPercent(primefactors.getPrimeFactorsCount(primefactors.getPrimeFactors(873452453)),primefactors.hardyRamanujanApprox(873452453))).toBeCloseTo(0.8235548500,5);
-        expect(primefactors.errorPercent(primefactors.getPrimeFactorsCount(primefactors.getPrimeFactors(52734)),primefactors.hardyRamanujanApprox(52734))).toBeCloseTo(52.27431810328,5);
-    });
-});
-
diff --git a/src/algorithms/math/prime-factors/primeFactors.js b/src/algorithms/math/prime-factors/primeFactors.js
new file mode 100644
index 0000000000..691436c49e
--- /dev/null
+++ b/src/algorithms/math/prime-factors/primeFactors.js
@@ -0,0 +1,42 @@
+/**
+ * Finds prime factors of a number.
+ *
+ * @param {number} n - the number that is going to be split into prime factors.
+ * @returns {number[]} - array of prime factors.
+ */
+export function primeFactors(n) {
+  // Clone n to avoid function arguments override.
+  let nn = n;
+
+  // Array that stores the all the prime factors.
+  const factors = [];
+
+  // Running the loop till sqrt(n) instead of n to optimise time complexity from O(n) to O(sqrt(n)).
+  for (let factor = 2; factor <= Math.sqrt(nn); factor += 1) {
+    // Check that factor divides n without a reminder.
+    while (nn % factor === 0) {
+      // Overriding the value of n.
+      nn /= factor;
+      // Saving the factor.
+      factors.push(factor);
+    }
+  }
+
+  // The ultimate reminder should be a last prime factor,
+  // unless it is not 1 (since 1 is not a prime number).
+  if (nn !== 1) {
+    factors.push(nn);
+  }
+
+  return factors;
+}
+
+/**
+ * Hardy-Ramanujan approximation of prime factors count.
+ *
+ * @param {number} n
+ * @returns {number} - approximate number of prime factors.
+ */
+export function hardyRamanujan(n) {
+  return Math.log(Math.log(n));
+}
diff --git a/src/algorithms/math/prime-factors/primefactors.js b/src/algorithms/math/prime-factors/primefactors.js
deleted file mode 100644
index d951a37153..0000000000
--- a/src/algorithms/math/prime-factors/primefactors.js
+++ /dev/null
@@ -1,44 +0,0 @@
-export default {
-
-  getPrimeFactors : (n) => {
-    let factorsArray = []; // an array where all the prime factors will be stored
-
-    //over here optimisation is made by running loop till sqrt(n) instead of n
-    for (let i = 2 ; i <= Math.sqrt(n); i++){
-      if(n % i === 0){  // if check to ensure i completely divides n
-        let count = 0;  // This count keeps track of number of times i divides n
-        while(n % i === 0){
-          n = n/i;       // override the value of n
-          count++;        // count value updated
-        }
-        factorsArray.push(i); // array gets populated
-      }
-    }
-    if(n !== 1){ // finally we cannot push 1 to array since it cannot be a prime-factor
-        factorsArray.push(n);
-    }
-  
-    return factorsArray;
-  },
-
-  //returns accurate prime-factors count
-  getPrimeFactorsCount : (factorsArray) => {
-    return factorsArray.length;
-  },
-  
-  
-  //returns Hardy-Ramanujan Approximation of prime-factors count 
-  hardyRamanujanApprox : (n) => {
-    return Math.log(Math.log(n));
-  },
-  
-  //returns %age of error in approximation using formula to that of accurate result. 
-  errorPercent : (exactFactorCount,approximateFactorCount) => {
-  let diff = exactFactorCount-approximateFactorCount > 0 ? exactFactorCount-approximateFactorCount: -(exactFactorCount-approximateFactorCount);
-  return (diff/exactFactorCount * 100);
-  }
-  
-
-}
-
-

From 97dd96aa7535cb5893ec37e1ec5f4bef91136139 Mon Sep 17 00:00:00 2001
From: Hanseung Yoo <trustyoo86@gmail.com>
Date: Fri, 11 Dec 2020 16:45:54 +0900
Subject: [PATCH 016/264] Add doubly-linked-list doc in Korean (#449)

---
 .../doubly-linked-list/README.ko-KR.md        | 107 ++++++++++++++++++
 .../doubly-linked-list/README.md              |   1 +
 2 files changed, 108 insertions(+)
 create mode 100644 src/data-structures/doubly-linked-list/README.ko-KR.md

diff --git a/src/data-structures/doubly-linked-list/README.ko-KR.md b/src/data-structures/doubly-linked-list/README.ko-KR.md
new file mode 100644
index 0000000000..192b189817
--- /dev/null
+++ b/src/data-structures/doubly-linked-list/README.ko-KR.md
@@ -0,0 +1,107 @@
+# Doubly Linked List
+
+_Read this in other languages:_
+[_Русский_](README.ru-RU.md),
+[_简体中文_](README.zh-CN.md),
+[_日本語_](README.ja-JP.md),
+[_Português_](README.pt-BR.md)
+
+컴퓨터공학에서 **이중 연결 리스트**는 순차적으로 링크된 노드라는 레코드 세트로 구성된 링크된 데이터 구조입니다.
+각 노드에는 링크라고 하는 두 개의 필드가 있으며, 노드 순서에서 이전 노드와 다음 노드에 대한 참조를 가집니다.
+시작 및 종료 노드의 이전 및 다음 링크는 각각 리스트의 순회를 용이하게 하기 위해서 일종의 종결자 (일반적으로 센티넬노드 또는 null)를 나타냅니다.
+센티넬 노드가 하나만 있으면, 목록이 센티넬 노드를 통해서 원형으로 연결됩니다.
+동일한 데이터 항목으로 구성되어 있지만, 반대 순서로 두 개의 단일 연결 리스트로 개념화 할 수 있습니다.
+
+![이중 연결 리스트](https://upload.wikimedia.org/wikipedia/commons/5/5e/Doubly-linked-list.svg)
+
+두 개의 노드 링크를 사용하면 어느 방향으로든 리스트를 순회할 수 있습니다.
+이중 연결 리스트에서 노드를 추가하거나 제거하려면, 단일 연결 리스트에서 동일한 작업보다 더 많은 링크를 변경해야 하지만, 첫 번째 노드 이외의 노드인 경우 작업을 추적할 필요가 없으므로 작업이 더 단순해져 잠재적으로 더 효율적입니다.
+리스트 순회 중 이전 노드 또는 링크를 수정할 수 있도록 이전 노드를 찾기 위해 리스트를 순회할 필요가 없습니다.
+
+## 기본 동작을 위한 Pseudocode
+
+### 삽입
+
+```text
+Add(value)
+  Pre: value는 리스트에 추가하고자 하는 값
+  Post: value는 목록의 끝에 배치됨
+  n ← node(value)
+  if head = ø
+    head ← n
+    tail ← n
+  else
+    n.previous ← tail
+    tail.next ← n
+    tail ← n
+  end if
+end Add
+```
+    
+### 삭제
+
+```text
+Remove(head, value)
+  Pre: head는 리스트의 앞단에 위치
+       value는 리스트에서 제거하고자 하는 값
+  Post: value가 리스트에서 제거되면 true; 아니라면 false;
+  if head = ø
+    return false
+  end if
+  if value = head.value
+    if head = tail
+      head ← ø
+      tail ← ø
+    else
+      head ← head.next
+      head.previous ← ø
+    end if
+    return true
+  end if
+  n ← head.next
+  while n = ø and value !== n.value
+    n ← n.next
+  end while
+  if n = tail
+    tail ← tail.previous
+    tail.next ← ø
+    return true
+  else if n = ø
+    n.previous.next ← n.next
+    n.next.previous ← n.previous
+    return true
+  end if
+  return false
+end Remove
+```
+    
+### 역순회
+
+```text
+ReverseTraversal(tail)
+  Pre: tail은 리스트에서 순회하고자 하는 노드
+  Post: 리스트가 역순으로 순회됨
+  n ← tail
+  while n = ø
+    yield n.value
+    n ← n.previous
+  end while
+end Reverse Traversal
+```
+    
+## 복잡도
+
+## 시간 복잡도
+
+| Access    | Search    | Insertion | Deletion  |
+| :-------: | :-------: | :-------: | :-------: |
+| O(n)      | O(n)      | O(1)      | O(n)      |
+
+### 공간 복잡도
+
+O(n)
+
+## 참고
+
+- [Wikipedia](https://en.wikipedia.org/wiki/Doubly_linked_list)
+- [YouTube](https://www.youtube.com/watch?v=JdQeNxWCguQ&t=7s&index=72&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
diff --git a/src/data-structures/doubly-linked-list/README.md b/src/data-structures/doubly-linked-list/README.md
index ad7f27741c..ec603a8f91 100644
--- a/src/data-structures/doubly-linked-list/README.md
+++ b/src/data-structures/doubly-linked-list/README.md
@@ -5,6 +5,7 @@ _Read this in other languages:_
 [_简体中文_](README.zh-CN.md),
 [_日本語_](README.ja-JP.md),
 [_Português_](README.pt-BR.md)
+[_한국어_](README.ko-KR.md)
 
 In computer science, a **doubly linked list** is a linked data structure that 
 consists of a set of sequentially linked records called nodes. Each node contains 

From 6e95b0cee743952b3963bdadd1e3ae2c533ecc84 Mon Sep 17 00:00:00 2001
From: Donghoon Song <32301380+donghoon-song@users.noreply.github.com>
Date: Fri, 11 Dec 2020 16:48:57 +0900
Subject: [PATCH 017/264] Update README.ko-KR.md (#466)

---
 .../linked-list/README.ko-KR.md               | 149 ++++++++++++++++++
 1 file changed, 149 insertions(+)
 create mode 100644 src/data-structures/linked-list/README.ko-KR.md

diff --git a/src/data-structures/linked-list/README.ko-KR.md b/src/data-structures/linked-list/README.ko-KR.md
new file mode 100644
index 0000000000..dc03327501
--- /dev/null
+++ b/src/data-structures/linked-list/README.ko-KR.md
@@ -0,0 +1,149 @@
+# 링크드 리스트
+
+_Read this in other languages:_
+[_简体中文_](README.zh-CN.md),
+[_Русский_](README.ru-RU.md),
+[_日本語_](README.ja-JP.md),
+[_Português_](README.pt-BR.md)
+
+컴퓨터과학에서, **링크드 리스트**는 데이터 요소의 선형 집합이며, 이 집합에서 논리적 저장 순서는 메모리의 물리적 저장 순서와 일치하지 않습니다. 그 대신, 각각의 원소들은 자기 자신 다음의 원소를 가리킵니다. **링크드 리스트**는 순서를 표현하는 노드들의 집합으로 이루어져 있습니다. 간단하게, 각각의 노드들은 데이터와 다음 순서의 노드를 가리키는 레퍼런스로 이루어져 있습니다. (링크라고 부릅니다.) 이 자료구조는 순회하는 동안 순서에 상관없이 효율적인 삽입이나 삭제가 가능합니다. 더 복잡한 변형은 추가적인 링크를 더해, 임의의 원소 참조로부터 효율적인 삽입과 삭제를 가능하게 합니다. 링크드 리스트의 단점은 접근 시간이 선형이라는 것이고, 병렬처리도 하지 못합니다. 임의 접근처럼 빠른 접근은 불가능합니다. 링크드 리스트에 비해 배열이 더 나은 캐시 지역성을 가지고 있습니다.
+
+![링크드 리스트](https://upload.wikimedia.org/wikipedia/commons/6/6d/Singly-linked-list.svg)
+
+## 기본 연산에 대한 수도코드
+
+### 삽입
+
+```text
+Add(value)
+  Pre: 리스트에 추가할 값
+  Post: 리스트의 맨 마지막에 있는 값
+  n ← node(value)
+  if head = ø
+    head ← n
+    tail ← n
+  else
+    tail.next ← n
+    tail ← n
+  end if
+end Add
+```
+
+```text
+Prepend(value)
+ Pre: 리스트에 추가할 값
+ Post: 리스트의 맨 앞에 있는 값
+ n ← node(value)
+ n.next ← head
+ head ← n
+ if tail = ø
+   tail ← n
+ end
+end Prepend
+```
+
+### 탐색
+
+```text
+Contains(head, value)
+  Pre: head는 리스트에서 맨 앞 노드
+       value는 찾고자 하는 값
+  Post: 항목이 링크드 리스트에 있으면 true;
+        없으면 false
+  n ← head
+  while n != ø and n.value != value
+    n ← n.next
+  end while
+  if n = ø
+    return false
+  end if
+  return true
+end Contains
+```
+    
+### 삭제
+
+```text
+Remove(head, value)
+  Pre: head는 리스트에서 맨 앞 노드
+       value는 삭제하고자 하는 값
+  Post: 항목이 링크드 리스트에서 삭제되면 true;
+        없으면 false
+  if head = ø
+    return false
+  end if
+  n ← head
+  if n.value = value
+    if head = tail
+      head ← ø
+      tail ← ø
+    else
+      head ← head.next
+    end if
+    return true
+  end if
+  while n.next != ø and n.next.value != value
+    n ← n.next
+  end while
+  if n.next != ø
+    if n.next = tail
+      tail ← n
+    end if
+    n.next ← n.next.next
+    return true
+  end if
+  return false
+end Remove
+```
+
+### 순회
+
+```text
+Traverse(head)
+  Pre: head는 리스트에서 맨 앞 노드
+  Post: 순회된 항목들
+  n ← head
+  while n != ø
+    yield n.value
+    n ← n.next
+  end while
+end Traverse
+```
+
+### 역순회
+
+```text
+ReverseTraversal(head, tail)
+  Pre: 같은 리스트에 들어 있는 맨 앞, 맨 뒤 노드
+  Post: 역순회된 항목들
+  if tail != ø
+    curr ← tail
+    while curr != head
+      prev ← head
+      while prev.next != curr
+        prev ← prev.next
+      end while
+      yield curr.value
+      curr ← prev
+    end while
+   yield curr.value
+  end if
+end ReverseTraversal
+```
+
+## 복잡도
+
+### 시간 복잡도
+
+|  접근   |  탐색   |  삽입   |  삭제   |
+| :---: | :---: | :---: | :---: |
+| O(n)  | O(n)  | O(1)  | O(1)  |
+
+### 공간 복잡도
+
+O(n)
+
+## 참조
+
+- [Wikipedia](https://en.wikipedia.org/wiki/Linked_list)
+- [YouTube](https://www.youtube.com/watch?v=njTh_OwMljA&index=2&t=1s&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)

From c3d22956b76a8407eec230f5a4f2078d26fed25d Mon Sep 17 00:00:00 2001
From: Eugene Sinitsyn <djorka91@mail.ru>
Date: Fri, 11 Dec 2020 10:51:13 +0300
Subject: [PATCH 018/264] Fix typo (#459)

---
 src/data-structures/trie/README.ru-RU.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/data-structures/trie/README.ru-RU.md b/src/data-structures/trie/README.ru-RU.md
index 61b7da92d0..f447f8eb0e 100644
--- a/src/data-structures/trie/README.ru-RU.md
+++ b/src/data-structures/trie/README.ru-RU.md
@@ -2,7 +2,7 @@
 
 **Префиксное дерево** (также бор, луч, нагруженное или суффиксное дерево) в информатике - упорядоченная древовидная
 структура данных, которая используется для хранения динамических множеств или ассоциативных массивов, где
-ключём обычно выступают строки. Дерево называется префиксным, потому что поиск осуществляется по префиксам.
+ключом обычно выступают строки. Дерево называется префиксным, потому что поиск осуществляется по префиксам.
 
 В отличие от бинарного дерева, узлы не содержат ключи, соответствующие узлу. Представляет собой корневое дерево, каждое
 ребро которого помечено каким-то символом так, что для любого узла все рёбра, соединяющие этот узел с его сыновьями,

From 46daaf51c5feb3e4fae17988fcd40fe9f55c084d Mon Sep 17 00:00:00 2001
From: JD Medina <jdmedina@gmail.com>
Date: Thu, 10 Dec 2020 23:54:37 -0800
Subject: [PATCH 019/264] Modify HashTable (#447)

Add a getValues() method to the HashTable data structure
---
 src/data-structures/hash-table/HashTable.js          | 12 ++++++++++++
 .../hash-table/__test__/HashTable.test.js            | 10 ++++++++++
 2 files changed, 22 insertions(+)

diff --git a/src/data-structures/hash-table/HashTable.js b/src/data-structures/hash-table/HashTable.js
index 5e19e7b704..6ac83a5273 100644
--- a/src/data-structures/hash-table/HashTable.js
+++ b/src/data-structures/hash-table/HashTable.js
@@ -105,4 +105,16 @@ export default class HashTable {
   getKeys() {
     return Object.keys(this.keys);
   }
+
+  /**
+   * Gets the list of all the stored values in the hash table in the order of
+   * the keys map.
+   *
+   * @return {*[]}
+   */
+  getValues() {
+    const keys = this.getKeys();
+
+    return keys.map(key => this.buckets[this.hash(key)].head.value.value);
+  }
 }
diff --git a/src/data-structures/hash-table/__test__/HashTable.test.js b/src/data-structures/hash-table/__test__/HashTable.test.js
index 27d590cf13..cc8d45d5a7 100644
--- a/src/data-structures/hash-table/__test__/HashTable.test.js
+++ b/src/data-structures/hash-table/__test__/HashTable.test.js
@@ -86,4 +86,14 @@ describe('HashTable', () => {
     expect(hashTable.has('b')).toBe(true);
     expect(hashTable.has('x')).toBe(false);
   });
+
+  it('should get all the values', () => {
+    const hashTable = new HashTable(3);
+
+    hashTable.set('a', 'alpha');
+    hashTable.set('b', 'beta');
+    hashTable.set('c', 'gamma');
+
+    expect(hashTable.getValues()).toEqual(['alpha', 'beta', 'gamma']);
+  });
 });

From 1b0e27ab86dbae97b99620db3ecacffafd17d98a Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Fri, 11 Dec 2020 09:14:48 +0100
Subject: [PATCH 020/264] Add getValues() method to HashTable and update
 LinkedList READMEs.

---
 .../doubly-linked-list/README.md              |  2 +-
 src/data-structures/hash-table/HashTable.js   | 11 +++++-----
 .../hash-table/__test__/HashTable.test.js     | 20 ++++++++++++++++++-
 src/data-structures/linked-list/README.md     |  3 ++-
 4 files changed, 28 insertions(+), 8 deletions(-)

diff --git a/src/data-structures/doubly-linked-list/README.md b/src/data-structures/doubly-linked-list/README.md
index ec603a8f91..c64b51262d 100644
--- a/src/data-structures/doubly-linked-list/README.md
+++ b/src/data-structures/doubly-linked-list/README.md
@@ -12,7 +12,7 @@ consists of a set of sequentially linked records called nodes. Each node contain
 two fields, called links, that are references to the previous and to the next 
 node in the sequence of nodes. The beginning and ending nodes' previous and next 
 links, respectively, point to some kind of terminator, typically a sentinel 
-node or null, to facilitate traversal of the list. If there is only one 
+node or null, to facilitate the traversal of the list. If there is only one 
 sentinel node, then the list is circularly linked via the sentinel node. It can 
 be conceptualized as two singly linked lists formed from the same data items, 
 but in opposite sequential orders.
diff --git a/src/data-structures/hash-table/HashTable.js b/src/data-structures/hash-table/HashTable.js
index 6ac83a5273..b8b523ea85 100644
--- a/src/data-structures/hash-table/HashTable.js
+++ b/src/data-structures/hash-table/HashTable.js
@@ -107,14 +107,15 @@ export default class HashTable {
   }
 
   /**
-   * Gets the list of all the stored values in the hash table in the order of
-   * the keys map.
+   * Gets the list of all the stored values in the hash table.
    *
    * @return {*[]}
    */
   getValues() {
-    const keys = this.getKeys();
-
-    return keys.map(key => this.buckets[this.hash(key)].head.value.value);
+    return this.buckets.reduce((values, bucket) => {
+      const bucketValues = bucket.toArray()
+        .map((linkedListNode) => linkedListNode.value.value);
+      return values.concat(bucketValues);
+    }, []);
   }
 }
diff --git a/src/data-structures/hash-table/__test__/HashTable.test.js b/src/data-structures/hash-table/__test__/HashTable.test.js
index cc8d45d5a7..86bbf3adbd 100644
--- a/src/data-structures/hash-table/__test__/HashTable.test.js
+++ b/src/data-structures/hash-table/__test__/HashTable.test.js
@@ -94,6 +94,24 @@ describe('HashTable', () => {
     hashTable.set('b', 'beta');
     hashTable.set('c', 'gamma');
 
-    expect(hashTable.getValues()).toEqual(['alpha', 'beta', 'gamma']);
+    expect(hashTable.getValues()).toEqual(['gamma', 'alpha', 'beta']);
+  });
+
+  it('should get all the values from empty hash table', () => {
+    const hashTable = new HashTable();
+    expect(hashTable.getValues()).toEqual([]);
+  });
+
+  it('should get all the values in case of hash collision', () => {
+    const hashTable = new HashTable(3);
+
+    // Keys `ab` and `ba` in current implementation should result in one hash (one bucket).
+    // We need to make sure that several items from one bucket will be serialized.
+    hashTable.set('ab', 'one');
+    hashTable.set('ba', 'two');
+
+    hashTable.set('ac', 'three');
+
+    expect(hashTable.getValues()).toEqual(['one', 'two', 'three']);
   });
 });
diff --git a/src/data-structures/linked-list/README.md b/src/data-structures/linked-list/README.md
index 3fd10e24db..2b8a7507b6 100644
--- a/src/data-structures/linked-list/README.md
+++ b/src/data-structures/linked-list/README.md
@@ -4,7 +4,8 @@ _Read this in other languages:_
 [_简体中文_](README.zh-CN.md),
 [_Русский_](README.ru-RU.md),
 [_日本語_](README.ja-JP.md),
-[_Português_](README.pt-BR.md)
+[_Português_](README.pt-BR.md),
+[_한국어_](README.ko-KR.md)
 
 In computer science, a **linked list** is a linear collection 
 of data elements, in which linear order is not given by 

From 40942425151f5fce18c46065bfbfeaa527dcc52f Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Tue, 15 Dec 2020 07:54:58 +0100
Subject: [PATCH 021/264] Add GitHub workflow.

---
 .github/workflows/node.js.yml | 37 +++++++++++++++++++++++++++++++++++
 1 file changed, 37 insertions(+)
 create mode 100644 .github/workflows/node.js.yml

diff --git a/.github/workflows/node.js.yml b/.github/workflows/node.js.yml
new file mode 100644
index 0000000000..f452cecaf9
--- /dev/null
+++ b/.github/workflows/node.js.yml
@@ -0,0 +1,37 @@
+name: CI
+
+on:
+  push:
+    branches: [ source ]
+  pull_request:
+    branches: [ source ]
+
+jobs:
+  build:
+
+    runs-on: ubuntu-latest
+
+    strategy:
+      matrix:
+        node-version: [14.x]
+
+    steps:
+    - name: Checkout repository
+      uses: actions/checkout@v2
+
+    - name: Setup Node.js ${{ matrix.node-version }}
+      uses: actions/setup-node@v1
+      with:
+        node-version: ${{ matrix.node-version }}
+
+    - name: Install dependencies
+      run: npm i
+
+    - name: Run linting
+      run: npm run lint
+
+    - name: Run tests
+      run: npm run coverage
+
+    - name: Upload coverage to Codecov
+      uses: codecov/codecov-action@v1

From ead275d08f470a381a6880fa0f3197c5966898b9 Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Tue, 15 Dec 2020 07:56:29 +0100
Subject: [PATCH 022/264] Delete Travis yml.

---
 .travis.yml | 13 -------------
 1 file changed, 13 deletions(-)
 delete mode 100644 .travis.yml

diff --git a/.travis.yml b/.travis.yml
deleted file mode 100644
index fee3c3cabd..0000000000
--- a/.travis.yml
+++ /dev/null
@@ -1,13 +0,0 @@
-os:
-  - osx
-language: node_js
-node_js:
-  - 14
-install:
-  - npm install -g codecov
-  - npm install
-script:
-  - npm run ci
-  - codecov
-notifications:
-  email: false

From 39a5fa57581235f7673b92e667ad8a337ce88516 Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Tue, 15 Dec 2020 07:57:35 +0100
Subject: [PATCH 023/264] Update the main branch for GitHub actions.

---
 .github/workflows/node.js.yml | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/.github/workflows/node.js.yml b/.github/workflows/node.js.yml
index f452cecaf9..1499ea368e 100644
--- a/.github/workflows/node.js.yml
+++ b/.github/workflows/node.js.yml
@@ -2,9 +2,9 @@ name: CI
 
 on:
   push:
-    branches: [ source ]
+    branches: [ master ]
   pull_request:
-    branches: [ source ]
+    branches: [ master ]
 
 jobs:
   build:

From d470fa13baa73475a58cecac76cd6a96818fbe46 Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Tue, 15 Dec 2020 08:04:46 +0100
Subject: [PATCH 024/264] Update the Build badge to show the info from GitHub
 actions.

---
 README.es-ES.md | 2 +-
 README.fr-FR.md | 2 +-
 README.it-IT.md | 4 ++--
 README.ja-JP.md | 2 +-
 README.ko-KR.md | 2 +-
 README.md       | 2 +-
 README.pl-PL.md | 2 +-
 README.pt-BR.md | 2 +-
 README.ru-RU.md | 2 +-
 README.tr-TR.md | 2 +-
 README.zh-CN.md | 2 +-
 README.zh-TW.md | 2 +-
 12 files changed, 13 insertions(+), 13 deletions(-)

diff --git a/README.es-ES.md b/README.es-ES.md
index e501de63ca..346c19718d 100644
--- a/README.es-ES.md
+++ b/README.es-ES.md
@@ -1,6 +1,6 @@
 # Algoritmos y Estructuras de Datos en JavaScript
 
-[![Build Status](https://travis-ci.org/trekhleb/javascript-algorithms.svg?branch=master)](https://travis-ci.org/trekhleb/javascript-algorithms)
+[![CI](https://github.com/trekhleb/javascript-algorithms/workflows/CI/badge.svg)](https://github.com/trekhleb/javascript-algorithms/actions)
 [![codecov](https://codecov.io/gh/trekhleb/javascript-algorithms/branch/master/graph/badge.svg)](https://codecov.io/gh/trekhleb/javascript-algorithms)
 
 Este repositorio contiene ejemplos basados en JavaScript de muchos
diff --git a/README.fr-FR.md b/README.fr-FR.md
index 70b244a301..440a854cd3 100644
--- a/README.fr-FR.md
+++ b/README.fr-FR.md
@@ -1,6 +1,6 @@
 # Algorithmes et Structures de Données en JavaScript
 
-[![Build Status](https://travis-ci.org/trekhleb/javascript-algorithms.svg?branch=master)](https://travis-ci.org/trekhleb/javascript-algorithms)
+[![CI](https://github.com/trekhleb/javascript-algorithms/workflows/CI/badge.svg)](https://github.com/trekhleb/javascript-algorithms/actions)
 [![codecov](https://codecov.io/gh/trekhleb/javascript-algorithms/branch/master/graph/badge.svg)](https://codecov.io/gh/trekhleb/javascript-algorithms)
 
 Ce dépôt contient des exemples d'implémentation en JavaScript de plusieurs
diff --git a/README.it-IT.md b/README.it-IT.md
index d340ece707..2f7c7cc66c 100644
--- a/README.it-IT.md
+++ b/README.it-IT.md
@@ -1,6 +1,6 @@
 # Algoritmi e Strutture Dati in Javascript
- 
-[![Build Status](https://travis-ci.org/trekhleb/javascript-algorithms.svg?branch=master)](https://travis-ci.org/trekhleb/javascript-algorithms)
+
+[![CI](https://github.com/trekhleb/javascript-algorithms/workflows/CI/badge.svg)](https://github.com/trekhleb/javascript-algorithms/actions)
 [![codecov](https://codecov.io/gh/trekhleb/javascript-algorithms/branch/master/graph/badge.svg)](https://codecov.io/gh/trekhleb/javascript-algorithms)
 
 Questa repository contiene esempi in Javascript dei più popolari algoritmi e strutture dati .
diff --git a/README.ja-JP.md b/README.ja-JP.md
index 687ea124aa..1c145a604e 100644
--- a/README.ja-JP.md
+++ b/README.ja-JP.md
@@ -1,6 +1,6 @@
 # JavaScriptアルゴリズムとデータ構造
 
-[![Build Status](https://travis-ci.org/trekhleb/javascript-algorithms.svg?branch=master)](https://travis-ci.org/trekhleb/javascript-algorithms)
+[![CI](https://github.com/trekhleb/javascript-algorithms/workflows/CI/badge.svg)](https://github.com/trekhleb/javascript-algorithms/actions)
 [![codecov](https://codecov.io/gh/trekhleb/javascript-algorithms/branch/master/graph/badge.svg)](https://codecov.io/gh/trekhleb/javascript-algorithms)
 
 このリポジトリには、JavaScriptベースの一般的なアルゴリズムとデータ構造に関する多数のサンプルが含まれています。
diff --git a/README.ko-KR.md b/README.ko-KR.md
index 4dcd3fd34b..b5be09f69e 100644
--- a/README.ko-KR.md
+++ b/README.ko-KR.md
@@ -1,6 +1,6 @@
 # JavaScript 알고리즘 및 자료 구조
 
-[![Build Status](https://travis-ci.org/trekhleb/javascript-algorithms.svg?branch=master)](https://travis-ci.org/trekhleb/javascript-algorithms)
+[![CI](https://github.com/trekhleb/javascript-algorithms/workflows/CI/badge.svg)](https://github.com/trekhleb/javascript-algorithms/actions)
 [![codecov](https://codecov.io/gh/trekhleb/javascript-algorithms/branch/master/graph/badge.svg)](https://codecov.io/gh/trekhleb/javascript-algorithms)
 
 이 저장소에는 많이 알려진 알고리즘 및 자료 구조의 Javascript 기반 예제를 담고 있습니다.
diff --git a/README.md b/README.md
index 3886d0bba2..9994971043 100644
--- a/README.md
+++ b/README.md
@@ -1,6 +1,6 @@
 # JavaScript Algorithms and Data Structures
 
-[![Build Status](https://travis-ci.org/trekhleb/javascript-algorithms.svg?branch=master)](https://travis-ci.org/trekhleb/javascript-algorithms)
+[![CI](https://github.com/trekhleb/javascript-algorithms/workflows/CI/badge.svg)](https://github.com/trekhleb/javascript-algorithms/actions)
 [![codecov](https://codecov.io/gh/trekhleb/javascript-algorithms/branch/master/graph/badge.svg)](https://codecov.io/gh/trekhleb/javascript-algorithms)
 
 This repository contains JavaScript based examples of many
diff --git a/README.pl-PL.md b/README.pl-PL.md
index 6745307031..bdac149533 100644
--- a/README.pl-PL.md
+++ b/README.pl-PL.md
@@ -1,6 +1,6 @@
 # JavaScript Algorytmy i Struktury Danych
 
-[![Build Status](https://travis-ci.org/trekhleb/javascript-algorithms.svg?branch=master)](https://travis-ci.org/trekhleb/javascript-algorithms)
+[![CI](https://github.com/trekhleb/javascript-algorithms/workflows/CI/badge.svg)](https://github.com/trekhleb/javascript-algorithms/actions)
 [![codecov](https://codecov.io/gh/trekhleb/javascript-algorithms/branch/master/graph/badge.svg)](https://codecov.io/gh/trekhleb/javascript-algorithms)
 
 To repozytorium zawiera wiele przykładów JavaScript opartych na 
diff --git a/README.pt-BR.md b/README.pt-BR.md
index f02691c179..a9fc0d34ce 100644
--- a/README.pt-BR.md
+++ b/README.pt-BR.md
@@ -1,6 +1,6 @@
 # Estrutura de Dados e Algoritmos em JavaScript
 
-[![Build Status](https://travis-ci.org/trekhleb/javascript-algorithms.svg?branch=master)](https://travis-ci.org/trekhleb/javascript-algorithms)
+[![CI](https://github.com/trekhleb/javascript-algorithms/workflows/CI/badge.svg)](https://github.com/trekhleb/javascript-algorithms/actions)
 [![codecov](https://codecov.io/gh/trekhleb/javascript-algorithms/branch/master/graph/badge.svg)](https://codecov.io/gh/trekhleb/javascript-algorithms)
 
 Este repositório contém exemplos baseados em JavaScript de muitos
diff --git a/README.ru-RU.md b/README.ru-RU.md
index 6317926cef..9365bca163 100644
--- a/README.ru-RU.md
+++ b/README.ru-RU.md
@@ -1,6 +1,6 @@
 # Алгоритмы и структуры данных на JavaScript
 
-[![Build Status](https://travis-ci.org/trekhleb/javascript-algorithms.svg?branch=master)](https://travis-ci.org/trekhleb/javascript-algorithms)
+[![CI](https://github.com/trekhleb/javascript-algorithms/workflows/CI/badge.svg)](https://github.com/trekhleb/javascript-algorithms/actions)
 [![codecov](https://codecov.io/gh/trekhleb/javascript-algorithms/branch/master/graph/badge.svg)](https://codecov.io/gh/trekhleb/javascript-algorithms)
 
 В этом репозитории содержатся базовые JavaScript-примеры многих популярных алгоритмов и структур данных.
diff --git a/README.tr-TR.md b/README.tr-TR.md
index 260553780e..62db14d1d0 100644
--- a/README.tr-TR.md
+++ b/README.tr-TR.md
@@ -1,6 +1,6 @@
 # JavaScript Algoritmalar ve Veri Yapıları
 
-[![Build Status](https://travis-ci.org/trekhleb/javascript-algorithms.svg?branch=master)](https://travis-ci.org/trekhleb/javascript-algorithms)
+[![CI](https://github.com/trekhleb/javascript-algorithms/workflows/CI/badge.svg)](https://github.com/trekhleb/javascript-algorithms/actions)
 [![codecov](https://codecov.io/gh/trekhleb/javascript-algorithms/branch/master/graph/badge.svg)](https://codecov.io/gh/trekhleb/javascript-algorithms)
 
 Bu repository JavaScript'e ait popüler
diff --git a/README.zh-CN.md b/README.zh-CN.md
index 45a8c8c64f..064c0dbe11 100644
--- a/README.zh-CN.md
+++ b/README.zh-CN.md
@@ -1,6 +1,6 @@
 # JavaScript 算法与数据结构
 
-[![build status](https://travis-ci.org/trekhleb/javascript-algorithms.svg?branch=master)](https://travis-ci.org/trekhleb/javascript-algorithms)
+[![CI](https://github.com/trekhleb/javascript-algorithms/workflows/CI/badge.svg)](https://github.com/trekhleb/javascript-algorithms/actions)
 [![codecov](https://codecov.io/gh/trekhleb/javascript-algorithms/branch/master/graph/badge.svg)](https://codecov.io/gh/trekhleb/javascript-algorithms)
 
 本仓库包含了多种基于 JavaScript 的算法与数据结构。
diff --git a/README.zh-TW.md b/README.zh-TW.md
index 1eba73c941..bb98d2a140 100644
--- a/README.zh-TW.md
+++ b/README.zh-TW.md
@@ -1,6 +1,6 @@
 # JavaScript 演算法與資料結構
 
-[![build status](https://travis-ci.org/trekhleb/javascript-algorithms.svg?branch=master)](https://travis-ci.org/trekhleb/javascript-algorithms)
+[![CI](https://github.com/trekhleb/javascript-algorithms/workflows/CI/badge.svg)](https://github.com/trekhleb/javascript-algorithms/actions)
 [![codecov](https://codecov.io/gh/trekhleb/javascript-algorithms/branch/master/graph/badge.svg)](https://codecov.io/gh/trekhleb/javascript-algorithms)
 
 這個知識庫包含許多 JavaScript 的資料結構與演算法的基礎範例。

From 94afab0dd95820bc1b150de2fa08120a51573fcd Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Tue, 15 Dec 2020 10:15:37 +0100
Subject: [PATCH 025/264] Add test coverage thresholds.

---
 jest.config.js | 10 ++++++++++
 1 file changed, 10 insertions(+)

diff --git a/jest.config.js b/jest.config.js
index 06e765266f..3fec225237 100644
--- a/jest.config.js
+++ b/jest.config.js
@@ -25,4 +25,14 @@ module.exports = {
   // It is reflected in properties such as location.href.
   // @see: https://github.com/facebook/jest/issues/6769
   testURL: 'http://localhost/',
+
+  // @see: https://jestjs.io/docs/en/configuration#coveragethreshold-object
+  coverageThreshold: {
+    global: {
+      statements: 100,
+      branches: 95,
+      functions: 100,
+      lines: 100,
+    },
+  },
 };

From ae225741fa64a9b5869f37610e626658e2d80108 Mon Sep 17 00:00:00 2001
From: bhaltair <qin.ming101@gmail.com>
Date: Wed, 16 Dec 2020 01:44:44 +0800
Subject: [PATCH 026/264] Update README.zh-CN.md (#439)

---
 src/data-structures/doubly-linked-list/README.zh-CN.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/data-structures/doubly-linked-list/README.zh-CN.md b/src/data-structures/doubly-linked-list/README.zh-CN.md
index dfe9e593a8..03dd53c11d 100644
--- a/src/data-structures/doubly-linked-list/README.zh-CN.md
+++ b/src/data-structures/doubly-linked-list/README.zh-CN.md
@@ -51,7 +51,7 @@ Remove(head, value)
     return true
   end if
   n ← head.next
-  while n = ø and value = n.value
+  while n = ø and value !== n.value
     n ← n.next
   end while
   if n = tail

From 82cf0e6d582c89ed7823025199dd227f9930cb54 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Jos=C3=A9=20Vin=C3=ADcius=20Lacerda=20de=20Arruda?=
 <viniciuslacerda02@hotmail.com>
Date: Tue, 15 Dec 2020 14:52:43 -0300
Subject: [PATCH 027/264] Creating a explanation of Bubblesort in portuguese
 (#423)

Co-authored-by: Oleksii Trekhleb <trehleb@gmail.com>
---
 .../sorting/bubble-sort/README-ptbr.md           | 16 ++++++++++++++++
 1 file changed, 16 insertions(+)
 create mode 100644 src/algorithms/sorting/bubble-sort/README-ptbr.md

diff --git a/src/algorithms/sorting/bubble-sort/README-ptbr.md b/src/algorithms/sorting/bubble-sort/README-ptbr.md
new file mode 100644
index 0000000000..b378d7f5bb
--- /dev/null
+++ b/src/algorithms/sorting/bubble-sort/README-ptbr.md
@@ -0,0 +1,16 @@
+# Bubble Sort
+
+O bubble sort, ou ordenação por flutuação (literalmente "por bolha"), é um algoritmo de ordenação dos mais simples. A ideia é percorrer o vetor diversas vezes, e a cada passagem fazer flutuar para o topo o maior elemento da sequência. Essa movimentação lembra a forma como as bolhas em um tanque de água procuram seu próprio nível, e disso vem o nome do algoritmo. 
+
+![Algorithm Visualization](https://pt.wikipedia.org/wiki/Ficheiro:Bubble_sort_animation.gif)
+
+## Complexity
+
+| Name                  | Best            | Average             | Worst               | Memory    | Stable    | Comments  |
+| --------------------- | :-------------: | :-----------------: | :-----------------: | :-------: | :-------: | :-------- |
+| **Bubble sort**       | n               | n<sup>2</sup>       | n<sup>2</sup>       | 1         | Yes       |           |
+
+## References
+
+- [Wikipedia](https://pt.wikipedia.org/wiki/Bubble_sort)
+

From 802557f1ac83fa299613a9e5332096547712bf6a Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Tue, 15 Dec 2020 18:56:09 +0100
Subject: [PATCH 028/264] Update translation for Bubble Sort.

---
 src/algorithms/sorting/bubble-sort/README.md                   | 3 +++
 .../sorting/bubble-sort/{README-ptbr.md => README.pt-BR.md}    | 3 ++-
 2 files changed, 5 insertions(+), 1 deletion(-)
 rename src/algorithms/sorting/bubble-sort/{README-ptbr.md => README.pt-BR.md} (79%)

diff --git a/src/algorithms/sorting/bubble-sort/README.md b/src/algorithms/sorting/bubble-sort/README.md
index ca784fade6..596d4006af 100644
--- a/src/algorithms/sorting/bubble-sort/README.md
+++ b/src/algorithms/sorting/bubble-sort/README.md
@@ -1,5 +1,8 @@
 # Bubble Sort
 
+_Read this in other languages:_
+[_Português_](README.pt-BR.md)
+
 Bubble sort, sometimes referred to as sinking sort, is a 
 simple sorting algorithm that repeatedly steps through 
 the list to be sorted, compares each pair of adjacent 
diff --git a/src/algorithms/sorting/bubble-sort/README-ptbr.md b/src/algorithms/sorting/bubble-sort/README.pt-BR.md
similarity index 79%
rename from src/algorithms/sorting/bubble-sort/README-ptbr.md
rename to src/algorithms/sorting/bubble-sort/README.pt-BR.md
index b378d7f5bb..39a3029500 100644
--- a/src/algorithms/sorting/bubble-sort/README-ptbr.md
+++ b/src/algorithms/sorting/bubble-sort/README.pt-BR.md
@@ -2,7 +2,7 @@
 
 O bubble sort, ou ordenação por flutuação (literalmente "por bolha"), é um algoritmo de ordenação dos mais simples. A ideia é percorrer o vetor diversas vezes, e a cada passagem fazer flutuar para o topo o maior elemento da sequência. Essa movimentação lembra a forma como as bolhas em um tanque de água procuram seu próprio nível, e disso vem o nome do algoritmo. 
 
-![Algorithm Visualization](https://pt.wikipedia.org/wiki/Ficheiro:Bubble_sort_animation.gif)
+![Algorithm Visualization](https://upload.wikimedia.org/wikipedia/commons/c/c8/Bubble-sort-example-300px.gif)
 
 ## Complexity
 
@@ -13,4 +13,5 @@ O bubble sort, ou ordenação por flutuação (literalmente "por bolha"), é um
 ## References
 
 - [Wikipedia](https://pt.wikipedia.org/wiki/Bubble_sort)
+- [YouTube](https://www.youtube.com/watch?v=6Gv8vg0kcHc&index=27&t=0s&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
 

From 871d20d8685df552d6f5c57b23f420b62404ef5a Mon Sep 17 00:00:00 2001
From: Avi Agrawal <39293511+avi09@users.noreply.github.com>
Date: Wed, 16 Dec 2020 00:44:56 -0500
Subject: [PATCH 029/264] Adding K Nearest Neighbor to ML folder in algorithms
 with README and tests    (#592)

* Updated KNN and README

* Update README.md

* new

* new

* updated tests

* updated knn coverage
---
 README.md                                  | 13 ++---
 src/algorithms/ML/KNN/README.md            | 23 +++++++++
 src/algorithms/ML/KNN/__test__/knn.test.js | 42 +++++++++++++++
 src/algorithms/ML/KNN/knn.js               | 60 ++++++++++++++++++++++
 4 files changed, 132 insertions(+), 6 deletions(-)
 create mode 100644 src/algorithms/ML/KNN/README.md
 create mode 100644 src/algorithms/ML/KNN/__test__/knn.test.js
 create mode 100644 src/algorithms/ML/KNN/knn.js

diff --git a/README.md b/README.md
index 9994971043..2ee72e2268 100644
--- a/README.md
+++ b/README.md
@@ -23,7 +23,7 @@ _Read this in other languages:_
 [_Türk_](README.tr-TR.md),
 [_Italiana_](README.it-IT.md)
 
-*☝ Note that this project is meant to be used for learning and researching purposes 
+*☝ Note that this project is meant to be used for learning and researching purposes
 only, and it is **not** meant to be used for production.*
 
 ## Data Structures
@@ -64,7 +64,7 @@ a set of rules that precisely define a sequence of operations.
 
 * **Math**
   * `B` [Bit Manipulation](src/algorithms/math/bits) - set/get/update/clear bits, multiplication/division by two, make negative etc.
-  * `B` [Factorial](src/algorithms/math/factorial) 
+  * `B` [Factorial](src/algorithms/math/factorial)
   * `B` [Fibonacci Number](src/algorithms/math/fibonacci) - classic and closed-form versions
   * `B` [Prime Factors](src/algorithms/math/prime-factors) - finding prime factors and counting them using Hardy-Ramanujan's theorem  
   * `B` [Primality Test](src/algorithms/math/primality-test) (trial division method)
@@ -80,7 +80,7 @@ a set of rules that precisely define a sequence of operations.
   * `A` [Integer Partition](src/algorithms/math/integer-partition)
   * `A` [Square Root](src/algorithms/math/square-root) - Newton's method
   * `A` [Liu Hui π Algorithm](src/algorithms/math/liu-hui) - approximate π calculations based on N-gons
-  * `A` [Discrete Fourier Transform](src/algorithms/math/fourier-transform) - decompose a function of time (a signal) into the frequencies that make it up 
+  * `A` [Discrete Fourier Transform](src/algorithms/math/fourier-transform) - decompose a function of time (a signal) into the frequencies that make it up
 * **Sets**
   * `B` [Cartesian Product](src/algorithms/sets/cartesian-product) - product of multiple sets
   * `B` [Fisher–Yates Shuffle](src/algorithms/sets/fisher-yates) - random permutation of a finite sequence
@@ -142,12 +142,13 @@ a set of rules that precisely define a sequence of operations.
   * `B` [Polynomial Hash](src/algorithms/cryptography/polynomial-hash) - rolling hash function based on polynomial
   * `B` [Caesar Cipher](src/algorithms/cryptography/caesar-cipher) - simple substitution cipher
 * **Machine Learning**
-  * `B` [NanoNeuron](https://github.com/trekhleb/nano-neuron) - 7 simple JS functions that illustrate how machines can actually learn (forward/backward propagation)
+  * `B` [NanoNeuron](https://github.com/trekhleb/nano-neuron) - 7 simple JS functions that illustrate how machines can actually learn (forward/backward propagation)  
+  * `B` [KNN](src/algorithms/ML/KNN) - K Nearest Neighbors
 * **Uncategorized**
   * `B` [Tower of Hanoi](src/algorithms/uncategorized/hanoi-tower)
   * `B` [Square Matrix Rotation](src/algorithms/uncategorized/square-matrix-rotation) - in-place algorithm
-  * `B` [Jump Game](src/algorithms/uncategorized/jump-game) - backtracking, dynamic programming (top-down + bottom-up) and greedy examples 
-  * `B` [Unique Paths](src/algorithms/uncategorized/unique-paths) - backtracking, dynamic programming and Pascal's Triangle based examples 
+  * `B` [Jump Game](src/algorithms/uncategorized/jump-game) - backtracking, dynamic programming (top-down + bottom-up) and greedy examples
+  * `B` [Unique Paths](src/algorithms/uncategorized/unique-paths) - backtracking, dynamic programming and Pascal's Triangle based examples
   * `B` [Rain Terraces](src/algorithms/uncategorized/rain-terraces) - trapping rain water problem (dynamic programming and brute force versions)
   * `B` [Recursive Staircase](src/algorithms/uncategorized/recursive-staircase) - count the number of ways to reach to the top (4 solutions)
   * `A` [N-Queens Problem](src/algorithms/uncategorized/n-queens)
diff --git a/src/algorithms/ML/KNN/README.md b/src/algorithms/ML/KNN/README.md
new file mode 100644
index 0000000000..d9db66ef46
--- /dev/null
+++ b/src/algorithms/ML/KNN/README.md
@@ -0,0 +1,23 @@
+# KNN Algorithm  
+
+KNN stands for K Nearest Neighbors. KNN is a supervised Machine Learning algorithm. It's a classification algorithm, determining the class of a sample vector using a sample data.  
+
+The idea is to calculate the similarity between two data points on the basis of a distance metric. Euclidean distance is used mostly for this task. The algorithm is as follows -  
+
+1. Check for errors like invalid data/labels.
+2. Calculate the euclidean distance of all the data points in training data with the classification point
+3. Sort the distances of points along with their classes in ascending order
+4. Take the initial "K" classes and find the mode to get the most similar class
+5. Report the most similar class  
+
+Here is a visualization for better understanding -  
+
+![KNN Visualization](https://media.geeksforgeeks.org/wp-content/uploads/graph2-2.png)  
+
+Here, as we can see, the classification of unknown points will be judged by their proximity to other points.
+
+It is important to note that "K" is preferred to have odd values in order to break ties. Usually "K" is taken as 3 or 5.  
+
+## References
+
+- [GeeksforGeeks](https://media.geeksforgeeks.org/wp-content/uploads/graph2-2.png)
diff --git a/src/algorithms/ML/KNN/__test__/knn.test.js b/src/algorithms/ML/KNN/__test__/knn.test.js
new file mode 100644
index 0000000000..6884598505
--- /dev/null
+++ b/src/algorithms/ML/KNN/__test__/knn.test.js
@@ -0,0 +1,42 @@
+import KNN from '../knn';
+
+describe('KNN', () => {
+  test('should throw an error on invalid data', () => {
+    expect(() => {
+      KNN();
+    }).toThrowError();
+  });
+  test('should throw an error on invalid labels', () => {
+    const nolabels = () => {
+      KNN([[1, 1]]);
+    };
+    expect(nolabels).toThrowError();
+  });
+  it('should throw an error on not giving classification vector', () => {
+    const noclassification = () => {
+      KNN([[1, 1]], [1]);
+    };
+    expect(noclassification).toThrowError();
+  });
+  it('should throw an error on not giving classification vector', () => {
+    const inconsistent = () => {
+      KNN([[1, 1]], [1], [1]);
+    };
+    expect(inconsistent).toThrowError();
+  });
+  it('should find the nearest neighbour', () => {
+    let dataX = [[1, 1], [2, 2]];
+    let dataY = [1, 2];
+    expect(KNN(dataX, dataY, [1, 1])).toBe(1);
+
+    dataX = [[1, 1], [6, 2], [3, 3], [4, 5], [9, 2], [2, 4], [8, 7]];
+    dataY = [1, 2, 1, 2, 1, 2, 1];
+    expect(KNN(dataX, dataY, [1.25, 1.25]))
+      .toBe(1);
+
+    dataX = [[1, 1], [6, 2], [3, 3], [4, 5], [9, 2], [2, 4], [8, 7]];
+    dataY = [1, 2, 1, 2, 1, 2, 1];
+    expect(KNN(dataX, dataY, [1.25, 1.25], 5))
+      .toBe(2);
+  });
+});
diff --git a/src/algorithms/ML/KNN/knn.js b/src/algorithms/ML/KNN/knn.js
new file mode 100644
index 0000000000..866b6a22e9
--- /dev/null
+++ b/src/algorithms/ML/KNN/knn.js
@@ -0,0 +1,60 @@
+/**
+ * @param {object} dataY
+ * @param {object} dataX
+ * @param {object} toClassify
+ * @param {number} k
+ * @return {number}
+ */
+export default function KNN(dataX, dataY, toClassify, K) {
+  let k = -1;
+
+  if (K === undefined) {
+    k = 3;
+  } else {
+    k = K;
+  }
+
+  // creating function to calculate the euclidean distance between 2 vectors
+  function euclideanDistance(x1, x2) {
+    // checking errors
+    if (x1.length !== x2.length) {
+      throw new Error('inconsistency between data and classification vector.');
+    }
+    // calculate the euclidean distance between 2 vectors and return
+    let totalSSE = 0;
+    for (let j = 0; j < x1.length; j += 1) {
+      totalSSE += (x1[j] - x2[j]) ** 2;
+    }
+    return Number(Math.sqrt(totalSSE).toFixed(2));
+  }
+
+  // starting algorithm
+
+  // calculate distance from toClassify to each point for all dimensions in dataX
+  // store distance and point's class_index into distance_class_list
+  let distanceList = [];
+  for (let i = 0; i < dataX.length; i += 1) {
+    const tmStore = [];
+    tmStore.push(euclideanDistance(dataX[i], toClassify));
+    tmStore.push(dataY[i]);
+    distanceList[i] = tmStore;
+  }
+
+  // sort distanceList
+  // take initial k values, count with class index
+  distanceList = distanceList.sort().slice(0, k);
+
+  // count the number of instances of each class in top k members
+  // with that maintain record of highest count class simultanously
+  const modeK = {};
+  const maxm = [-1, -1];
+  for (let i = 0; i < Math.min(k, distanceList.length); i += 1) {
+    if (distanceList[i][1] in modeK) modeK[distanceList[i][1]] += 1;
+    else modeK[distanceList[i][1]] = 1;
+    if (modeK[distanceList[i][1]] > maxm[0]) {
+      [maxm[0], maxm[1]] = [modeK[distanceList[i][1]], distanceList[i][1]];
+    }
+  }
+  // return the class with highest count from maxm
+  return maxm[1];
+}

From b13291df62dd67f4e150064b636bfa3c1795cdda Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Wed, 16 Dec 2020 06:49:10 +0100
Subject: [PATCH 030/264] Trim trailing whitespaces.

---
 .editorconfig                                 |  2 +
 README.es-ES.md                               |  8 ++--
 README.it-IT.md                               | 30 ++++++-------
 README.ja-JP.md                               |  4 +-
 README.ko-KR.md                               | 10 ++---
 README.md                                     |  4 +-
 README.pl-PL.md                               | 44 +++++++++----------
 README.pt-BR.md                               |  6 +--
 README.ru-RU.md                               | 10 ++---
 README.tr-TR.md                               | 22 +++++-----
 src/algorithms/sorting/bubble-sort/README.md  | 10 ++---
 .../sorting/bubble-sort/README.pt-BR.md       |  2 +-
 12 files changed, 77 insertions(+), 75 deletions(-)

diff --git a/.editorconfig b/.editorconfig
index 78c6ddee23..11c2bd2445 100644
--- a/.editorconfig
+++ b/.editorconfig
@@ -1,3 +1,4 @@
+# @see: https://editorconfig.org/
 root = true
 
 [*]
@@ -6,3 +7,4 @@ insert_final_newline = true
 charset = utf-8
 indent_style = space
 indent_size = 2
+trim_trailing_whitespace = true
diff --git a/README.es-ES.md b/README.es-ES.md
index 346c19718d..81a3189259 100644
--- a/README.es-ES.md
+++ b/README.es-ES.md
@@ -6,7 +6,7 @@
 Este repositorio contiene ejemplos basados en JavaScript de muchos
 algoritmos y estructuras de datos populares.
 
-Cada algoritmo y estructura de datos tiene su propio LÉAME con explicaciones relacionadas y 
+Cada algoritmo y estructura de datos tiene su propio LÉAME con explicaciones relacionadas y
 enlaces para lecturas adicionales (incluyendo algunas a vídeos de YouTube).
 
 _Léelo en otros idiomas:_
@@ -54,7 +54,7 @@ los datos.
 
 ## Algoritmos
 
-Un algoritmo es una especificación inequívoca de cómo resolver una clase de problemas. Es un conjunto de reglas que 
+Un algoritmo es una especificación inequívoca de cómo resolver una clase de problemas. Es un conjunto de reglas que
 definen con precisión una secuencia de operaciones.
 
 `P` - Principiante, `A` - Avanzado
@@ -231,7 +231,7 @@ npm test -- 'LinkedList'
 
 **Campo de juegos**
 
-Puede jugar con estructuras de datos y algoritmos en el archivo `./src/playground/playground.js` y escribir 
+Puede jugar con estructuras de datos y algoritmos en el archivo `./src/playground/playground.js` y escribir
 pruebas para ello en `./src/playground/__test__/playground.test.js`.
 
 A continuación, simplemente ejecute el siguiente comando para comprobar si el código funciona como se espera:
@@ -254,7 +254,7 @@ Orden de crecimiento de los algoritmos especificados en la notación O grande.
 
 Fuente: [Big O Cheat Sheet](http://bigocheatsheet.com/).
 
-A continuación se muestra la lista de algunas de las notaciones de Big O más utilizadas y sus comparaciones de rendimiento 
+A continuación se muestra la lista de algunas de las notaciones de Big O más utilizadas y sus comparaciones de rendimiento
 frente a diferentes tamaños de los datos de entrada.
 
 | Notación O grande | Cálculos para 10 elementos | Cálculos para 100 elementos | Cálculos para 1000 elementos |
diff --git a/README.it-IT.md b/README.it-IT.md
index 2f7c7cc66c..57c054df1e 100644
--- a/README.it-IT.md
+++ b/README.it-IT.md
@@ -56,7 +56,7 @@ un insieme di regole che definiscono con precisione una sequenza di operazioni.
 
 * **Matematica**
   * `P` [Manipolazione dei Bit](src/algorithms/math/bits) - set/get/update/clear bits, moltiplicazione/divisione per due, gestire numeri negativi etc.
-  * `P` [Fattoriale](src/algorithms/math/factorial) 
+  * `P` [Fattoriale](src/algorithms/math/factorial)
   * `P` [Numeri di Fibonacci](src/algorithms/math/fibonacci) - classico e forma chiusa
   * `P` [Test di Primalità](src/algorithms/math/primality-test) (metodo del divisore)
   * `P` [Algoritmo di Euclide](src/algorithms/math/euclidean-algorithm) - trova il massimo comune divisore (MCD)
@@ -64,13 +64,13 @@ un insieme di regole che definiscono con precisione una sequenza di operazioni.
   * `P` [Crivello di Eratostene](src/algorithms/math/sieve-of-eratosthenes) - trova i numeri i primi fino al limite indicato
   * `P` [Potenza di due](src/algorithms/math/is-power-of-two) - controlla se il numero è una potenza di due
   * `P` [Triangolo di Pascal](src/algorithms/math/pascal-triangle)
-  * `P` [Numeri Complessi](src/algorithms/math/complex-number) - numeri complessi e operazioni 
+  * `P` [Numeri Complessi](src/algorithms/math/complex-number) - numeri complessi e operazioni
   * `P` [Radiante & Gradi](src/algorithms/math/radian) - conversione da radiante a gradi e viceversa
   * `P` [Potenza di un Numero](src/algorithms/math/fast-powering)
   * `A` [Partizione di un Intero](src/algorithms/math/integer-partition)
   * `A` [Radice Quadrata](src/algorithms/math/square-root) - Metodo di Newton
   * `A` [Algoritmo di Liu Hui π](src/algorithms/math/liu-hui) - calcolare π usando un poligono
-  * `A` [Trasformata Discreta di Fourier ](src/algorithms/math/fourier-transform) -decomporre una funzione di tempo (un segnale) nelle frequenze che lo compongono 
+  * `A` [Trasformata Discreta di Fourier ](src/algorithms/math/fourier-transform) -decomporre una funzione di tempo (un segnale) nelle frequenze che lo compongono
 * **Set**
   * `P` [Prodotto Cartesiano](src/algorithms/sets/cartesian-product) - moltiplicazione multipla di set
   * `P` [Fisher–Yates Shuffle](src/algorithms/sets/fisher-yates) - permutazione casuale di un sequenza finita
@@ -116,8 +116,8 @@ un insieme di regole che definiscono con precisione una sequenza di operazioni.
   * `P` [Ricerca in Profondità su Grafi](src/algorithms/graph/depth-first-search) (DFS)
   * `P` [Breadth-First Search su Grafi](src/algorithms/graph/breadth-first-search) (BFS)
   * `P` [Algoritmo di Kruskal](src/algorithms/graph/kruskal) - ricerca dell'Albero con Minima Distanza (MST) per grafi pesati unidirezionali
-  * `A` [Algoritmo di Dijkstra](src/algorithms/graph/dijkstra) - ricerca dei percorsi più breve per raggiungere tutti i vertici del grafo da un singolo vertice 
-  * `A` [Algoritmo di Bellman-Ford](src/algorithms/graph/bellman-ford) - ricerca dei percorsi più breve per raggiungere tutti i vertici del grafo da un singolo vertice 
+  * `A` [Algoritmo di Dijkstra](src/algorithms/graph/dijkstra) - ricerca dei percorsi più breve per raggiungere tutti i vertici del grafo da un singolo vertice
+  * `A` [Algoritmo di Bellman-Ford](src/algorithms/graph/bellman-ford) - ricerca dei percorsi più breve per raggiungere tutti i vertici del grafo da un singolo vertice
   * `A` [Algoritmo di Floyd-Warshall](src/algorithms/graph/floyd-warshall) -  ricerca dei percorsi più brevi tra tutte le coppie di vertici
   * `A` [Rivelamento dei Cicli](src/algorithms/graph/detect-cycle) - per grafici diretti e non diretti (basate su partizioni DFS e Disjoint Set)
   * `A` [Algoritmo di Prim](src/algorithms/graph/prim) - ricerca dell'Albero Ricoprente Minimo (MST) per grafi unidirezionali pesati
@@ -129,12 +129,12 @@ un insieme di regole che definiscono con precisione una sequenza di operazioni.
   * `A` [Componenti Fortemente Connessa](src/algorithms/graph/strongly-connected-components) - algoritmo di Kosaraju
   * `A` [Problema del Commesso Viaggiatore](src/algorithms/graph/travelling-salesman) - il percorso più breve che visita ogni città e ritorna alla città iniziale
 * **Crittografia**
-  * `P` [Hash Polinomiale](src/algorithms/cryptography/polynomial-hash) - Una funzione hash di rolling basata sul polinomio 
+  * `P` [Hash Polinomiale](src/algorithms/cryptography/polynomial-hash) - Una funzione hash di rolling basata sul polinomio
 * **Senza categoria**
   * `P` [Torre di Hanoi](src/algorithms/uncategorized/hanoi-tower)
   * `P` [Rotazione Matrice Quadrata](src/algorithms/uncategorized/square-matrix-rotation) - algoritmo in memoria
   * `P` [Jump Game](src/algorithms/uncategorized/jump-game) - backtracking, programmazione dinamica (top-down + bottom-up) ed esempre di greeedy
-  * `P` [Percorsi Unici](src/algorithms/uncategorized/unique-paths) - backtracking, programmazione dinamica and l'esempio del Triangolo di Pascal  
+  * `P` [Percorsi Unici](src/algorithms/uncategorized/unique-paths) - backtracking, programmazione dinamica and l'esempio del Triangolo di Pascal
   * `P` [Rain Terraces](src/algorithms/uncategorized/rain-terraces) - problema dell'acqua piovana in trappola(versione con programmazione dinamica e brute force)
   * `P` [Recursive Staircase](src/algorithms/uncategorized/recursive-staircase) - contare il numero di percorsi per arrivare in vetta(4 soluzioni)
   * `A` [Rompicapo delle Otto Regine](src/algorithms/uncategorized/n-queens)
@@ -151,14 +151,14 @@ un insieme di regole che definiscono con precisione una sequenza di operazioni.
   * `P` [Recursive Staircase](src/algorithms/uncategorized/recursive-staircase) - contare il numero di percorsi per arrivare in vetta
   * `A` [Massimo SubArray](src/algorithms/sets/maximum-subarray)
   * `A` [Problema del commesso viaggiatore](src/algorithms/graph/travelling-salesman) - il percorso più breve che visita ogni città e ritorna alla città iniziale
-  * `A` [Trasformata Discreta di Fourier](src/algorithms/math/fourier-transform) - scomporre la funzione (segnale) del tempo in frequenze che la compongono 
+  * `A` [Trasformata Discreta di Fourier](src/algorithms/math/fourier-transform) - scomporre la funzione (segnale) del tempo in frequenze che la compongono
 * **Greedy** - scegliere l'opzione migliore al momento d'eleborazione dell'algoritmo, senza alcuna considerazione per il futuro
   * `P` [Jump Game](src/algorithms/uncategorized/jump-game)
   * `A` [Problema dello Zaino di Knapsack](src/algorithms/sets/knapsack-problem)
   * `A` [Algoritmo di Dijkstra](src/algorithms/graph/dijkstra) - ricerca del percorso più breve tra tutti i vertici del grafo
-  * `A` [Algoritmo di Prim](src/algorithms/graph/prim) - ricerca del Minimo Albero Ricoprente per grafi pesati e unidirezionali 
+  * `A` [Algoritmo di Prim](src/algorithms/graph/prim) - ricerca del Minimo Albero Ricoprente per grafi pesati e unidirezionali
   * `A` [Kruskal’s Algorithm](src/algorithms/graph/kruskal) - finding Minimum Spanning Tree (MST) for weighted undirected graph
-* **Divide e Conquista** - divide il problema in piccole parti e risolve ogni parte 
+* **Divide e Conquista** - divide il problema in piccole parti e risolve ogni parte
   * `P` [Ricerca Binaria](src/algorithms/search/binary-search)
   * `P` [Torre di Hanoi](src/algorithms/uncategorized/hanoi-tower)
   * `P` [Triangolo di Pascal](src/algorithms/math/pascal-triangle)
@@ -186,7 +186,7 @@ un insieme di regole che definiscono con precisione una sequenza di operazioni.
   * `A` [Partizione di un Intero](src/algorithms/math/integer-partition)
   * `A` [Massimo SubArray](src/algorithms/sets/maximum-subarray)
   * `A` [Algoritmo di Bellman-Ford](src/algorithms/graph/bellman-ford) - ricerca del percorso più breve per tutti i vertici del grafo
-  * `A` [Algoritmo di Floyd-Warshall](src/algorithms/graph/floyd-warshall) - ricerca del percorso più breve tra tutte le coppie di vertici 
+  * `A` [Algoritmo di Floyd-Warshall](src/algorithms/graph/floyd-warshall) - ricerca del percorso più breve tra tutte le coppie di vertici
   * `A` [Espressioni Regolari](src/algorithms/string/regular-expression-matching)
 * **Backtracking** -  come la brute force, provate a generare tutte le soluzioni possibili, ma ogni volta che generate la prossima soluzione testate se soddisfa tutte le condizioni e solo allora continuare a generare soluzioni successive. Altrimenti, fate marcia indietro, e andate su un percorso diverso per trovare una soluzione. Normalmente si utilizza l'algoritmo DFS.
   * `P` [Jump Game](src/algorithms/uncategorized/jump-game)
@@ -228,10 +228,10 @@ npm test -- 'LinkedList'
 
 **Playground**
 
-Se vuoi puoi giocare le strutture dati e gli algoritmi nel file ./src/playground/playground.js` e 
+Se vuoi puoi giocare le strutture dati e gli algoritmi nel file ./src/playground/playground.js` e
 scrivere test nel file `./src/playground/__test__/playground.test.js`.
 
-Poi puoi semplicemente eseguire il seguente comando per testare quello che hai scritto : 
+Poi puoi semplicemente eseguire il seguente comando per testare quello che hai scritto :
 
 ```
 npm test -- 'playground'
@@ -243,9 +243,9 @@ npm test -- 'playground'
 
 [▶ Data Structures and Algorithms on YouTube](https://www.youtube.com/playlist?list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
 
-### Notazione Big O 
+### Notazione Big O
 
-* La notazione Big O* è usata per classificare algoritmi in base al tempo di esecuzione o ai 
+* La notazione Big O* è usata per classificare algoritmi in base al tempo di esecuzione o ai
 requisiti di spazio che crescono in base alla crescita dell'input .
 Nella grafico qua sotto puoi trovare gli ordini di crescita più comuni degli algoritmi usando la notazione Big O.
 
diff --git a/README.ja-JP.md b/README.ja-JP.md
index 1c145a604e..7ec49e4eeb 100644
--- a/README.ja-JP.md
+++ b/README.ja-JP.md
@@ -60,7 +60,7 @@ _Read this in other languages:_
 
 * **数学**
   * `B` [ビット操作](src/algorithms/math/bits) - set/get/update/clear bits, 2つの乗算/除算, 否定的にする. 等
-  * `B` [因果関係](src/algorithms/math/factorial) 
+  * `B` [因果関係](src/algorithms/math/factorial)
   * `B` [フィボナッチ数](src/algorithms/math/fibonacci) - クラシックとクローズドフォームのバージョン
   * `B` [素数性テスト](src/algorithms/math/primality-test) (trial division 方法)
   * `B` [ユークリッドアルゴリズム](src/algorithms/math/euclidean-algorithm) - 最大公約数を計算する (GCD)
@@ -118,7 +118,7 @@ _Read this in other languages:_
 * **グラフ**
   * `B` [深度優先検索](src/algorithms/graph/depth-first-search) (DFS)
   * `B` [幅優先検索](src/algorithms/graph/breadth-first-search) (BFS)
-  * `B` [Kruskalのアルゴリズム](src/algorithms/graph/kruskal) - 重み付き無向グラフの最小スパニングツリー（MST）の発見 
+  * `B` [Kruskalのアルゴリズム](src/algorithms/graph/kruskal) - 重み付き無向グラフの最小スパニングツリー（MST）の発見
   * `A` [Dijkstraアルゴリズム](src/algorithms/graph/dijkstra) - 単一の頂点からすべてのグラフ頂点への最短経路を見つける
   * `A` [Bellman-Fordアルゴリズム](src/algorithms/graph/bellman-ford) - 単一の頂点からすべてのグラフ頂点への最短経路を見つける
   * `A` [Floyd-Warshallアルゴリズム](src/algorithms/graph/floyd-warshall) - すべての頂点ペア間の最短経路を見つける
diff --git a/README.ko-KR.md b/README.ko-KR.md
index b5be09f69e..8a31e81101 100644
--- a/README.ko-KR.md
+++ b/README.ko-KR.md
@@ -25,7 +25,7 @@ _Read this in other languages:_
 
 자료 구조는 데이터를 특정 방식으로 구성하고 저장함으로써 더 효율적으로
 접근하고 수정할 수 있게 해줍니다. 간단히 말해, 자료 구조는 데이터 값들,
-데이터 간의 관계, 그리고 데이터를 다룰 수 있는 함수와 작업의 모임입니다. 
+데이터 간의 관계, 그리고 데이터를 다룰 수 있는 함수와 작업의 모임입니다.
 
 
 `B` - 입문자, `A` - 숙련자
@@ -50,8 +50,8 @@ _Read this in other languages:_
 
 ## 알고리즘
 
-알고리즘은 어떤 종류의 문제를 풀 수 있는 정확한 방법이며, 
-일련의 작업을 정확하게 정의해 놓은 규칙들입니다. 
+알고리즘은 어떤 종류의 문제를 풀 수 있는 정확한 방법이며,
+일련의 작업을 정확하게 정의해 놓은 규칙들입니다.
 
 `B` - 입문자, `A` - 숙련자
 
@@ -59,7 +59,7 @@ _Read this in other languages:_
 
 * **Math**
   * `B` [Bit Manipulation](src/algorithms/math/bits) - set/get/update/clear bits, 2의 곱 / 나누기, 음수로 만들기 etc.
-  * `B` [팩토리얼](src/algorithms/math/factorial) 
+  * `B` [팩토리얼](src/algorithms/math/factorial)
   * `B` [피보나치 수](src/algorithms/math/fibonacci)
   * `B` [소수 판별](src/algorithms/math/primality-test) (trial division 방식)
   * `B` [유클리드 호제법](src/algorithms/math/euclidean-algorithm) - 최대공약수 (GCD)
@@ -126,7 +126,7 @@ _Read this in other languages:_
 * **Uncategorized**
   * `B` [하노이 탑](src/algorithms/uncategorized/hanoi-tower)
   * `B` [정방 행렬 회전](src/algorithms/uncategorized/square-matrix-rotation) - 제자리(in-place) 알고리즘
-  * `B` [점프 게임](src/algorithms/uncategorized/jump-game) - 백트래킹, 동적계획법 (top-down + bottom-up), 탐욕 알고리즘 예제 
+  * `B` [점프 게임](src/algorithms/uncategorized/jump-game) - 백트래킹, 동적계획법 (top-down + bottom-up), 탐욕 알고리즘 예제
   * `B` [Unique 경로](src/algorithms/uncategorized/unique-paths) - 백트래킹, 동적계획법, 파스칼 삼각형에 기반한 예제
   * `B` [빗물 담기 문제](src/algorithms/uncategorized/rain-terraces) - trapping rain water problem (동적계획법, 브루트포스 버전)
   * `A` [N-Queens 문제](src/algorithms/uncategorized/n-queens)
diff --git a/README.md b/README.md
index 2ee72e2268..e108671a22 100644
--- a/README.md
+++ b/README.md
@@ -66,7 +66,7 @@ a set of rules that precisely define a sequence of operations.
   * `B` [Bit Manipulation](src/algorithms/math/bits) - set/get/update/clear bits, multiplication/division by two, make negative etc.
   * `B` [Factorial](src/algorithms/math/factorial)
   * `B` [Fibonacci Number](src/algorithms/math/fibonacci) - classic and closed-form versions
-  * `B` [Prime Factors](src/algorithms/math/prime-factors) - finding prime factors and counting them using Hardy-Ramanujan's theorem  
+  * `B` [Prime Factors](src/algorithms/math/prime-factors) - finding prime factors and counting them using Hardy-Ramanujan's theorem
   * `B` [Primality Test](src/algorithms/math/primality-test) (trial division method)
   * `B` [Euclidean Algorithm](src/algorithms/math/euclidean-algorithm) - calculate the Greatest Common Divisor (GCD)
   * `B` [Least Common Multiple](src/algorithms/math/least-common-multiple) (LCM)
@@ -142,7 +142,7 @@ a set of rules that precisely define a sequence of operations.
   * `B` [Polynomial Hash](src/algorithms/cryptography/polynomial-hash) - rolling hash function based on polynomial
   * `B` [Caesar Cipher](src/algorithms/cryptography/caesar-cipher) - simple substitution cipher
 * **Machine Learning**
-  * `B` [NanoNeuron](https://github.com/trekhleb/nano-neuron) - 7 simple JS functions that illustrate how machines can actually learn (forward/backward propagation)  
+  * `B` [NanoNeuron](https://github.com/trekhleb/nano-neuron) - 7 simple JS functions that illustrate how machines can actually learn (forward/backward propagation)
   * `B` [KNN](src/algorithms/ML/KNN) - K Nearest Neighbors
 * **Uncategorized**
   * `B` [Tower of Hanoi](src/algorithms/uncategorized/hanoi-tower)
diff --git a/README.pl-PL.md b/README.pl-PL.md
index bdac149533..98fe798913 100644
--- a/README.pl-PL.md
+++ b/README.pl-PL.md
@@ -3,11 +3,11 @@
 [![CI](https://github.com/trekhleb/javascript-algorithms/workflows/CI/badge.svg)](https://github.com/trekhleb/javascript-algorithms/actions)
 [![codecov](https://codecov.io/gh/trekhleb/javascript-algorithms/branch/master/graph/badge.svg)](https://codecov.io/gh/trekhleb/javascript-algorithms)
 
-To repozytorium zawiera wiele przykładów JavaScript opartych na 
+To repozytorium zawiera wiele przykładów JavaScript opartych na
 znanych algorytmach i strukturach danych.
 
 Każdy algorytm i struktura danych zawiera osobny plik README
-wraz z powiązanymi wyjaśnieniami i odnośnikami do dalszego czytania 
+wraz z powiązanymi wyjaśnieniami i odnośnikami do dalszego czytania
 (włącznie z tymi do YouTube videos).
 
 _Read this in other languages:_
@@ -25,10 +25,10 @@ _Read this in other languages:_
 
 ## Struktury Danych
 
-Struktura danych to sposób uporządkowania i przechowywania informacji w 
+Struktura danych to sposób uporządkowania i przechowywania informacji w
 komputerze żeby mogłaby być sprawnie dostępna i efektywnie zmodyfikowana.
-Dokładniej, struktura danych jest zbiorem wartości danych, relacjami 
-pomiędzy nimi, zadaniami lub działaniami, które mogą dotyczyć danych. 
+Dokładniej, struktura danych jest zbiorem wartości danych, relacjami
+pomiędzy nimi, zadaniami lub działaniami, które mogą dotyczyć danych.
 
 `B` - Początkujący, `A` - Zaawansowany
 
@@ -52,8 +52,8 @@ pomiędzy nimi, zadaniami lub działaniami, które mogą dotyczyć danych.
 
 ## Algorytmy
 
-Algorytm jest to skończony ciąg jasno zdefiniowanych czynności, koniecznych 
-do wykonania pewnego rodzaju zadań. Sposób postępowania prowadzący do 
+Algorytm jest to skończony ciąg jasno zdefiniowanych czynności, koniecznych
+do wykonania pewnego rodzaju zadań. Sposób postępowania prowadzący do
 rozwiązania problemu.
 
 `B` - Początkujący, `A` - Zaawansowany
@@ -62,7 +62,7 @@ rozwiązania problemu.
 
 * **Matematyka**
   * `B` [Manipulacja Bitami](src/algorithms/math/bits) - ustaw / uzyskaj / aktualizuj / usuwaj bity, mnożenie / dzielenie przez dwa, tworzenie negatywów itp.
-  * `B` [Silna](src/algorithms/math/factorial) 
+  * `B` [Silna](src/algorithms/math/factorial)
   * `B` [Ciąg Fibonacciego](src/algorithms/math/fibonacci)
   * `B` [Test Pierwszorzędności](src/algorithms/math/primality-test) (metoda podziału na próby)
   * `B` [Algorytm Euclideana](src/algorithms/math/euclidean-algorithm) - obliczyć Największy Wspólny Dzielnik (GCD)
@@ -81,9 +81,9 @@ rozwiązania problemu.
   * `A` [Najdłuższa Wspólna Podsekwencja](src/algorithms/sets/longest-common-subsequence) (LCS)
   * `A` [Najdłuższa Wzrostająca Podsekwencja](src/algorithms/sets/longest-increasing-subsequence)
   * `A` [Najkrótsza Wspólna Supersekwencja](src/algorithms/sets/shortest-common-supersequence) (SCS)
-  * `A` [Problem Knapsacka](src/algorithms/sets/knapsack-problem) - "0/1" i "Rozwiązany" 
+  * `A` [Problem Knapsacka](src/algorithms/sets/knapsack-problem) - "0/1" i "Rozwiązany"
   * `A` [Maksymalna Podtablica](src/algorithms/sets/maximum-subarray) - "Metoda Siłowa" i "Dynamiczne Programowanie" (Kadane-a) wersje
-  * `A` [Suma Kombinacji](src/algorithms/sets/combination-sum) - 
+  * `A` [Suma Kombinacji](src/algorithms/sets/combination-sum) -
 znajdź wszystkie kombinacje, które tworzą określoną sumę
 * **Łańcuchy**
   * `B` [Odległość Hamminga](src/algorithms/string/hamming-distance) - liczba pozycji, w których symbole są różne
@@ -120,26 +120,26 @@ znajdź wszystkie kombinacje, które tworzą określoną sumę
   * `A` [Algorytm Floyd-Warshalla](src/algorithms/graph/floyd-warshall) - znajdź najkrótsze ścieżki między wszystkimi parami wierzchołków
   * `A` [Detect Cycle](src/algorithms/graph/detect-cycle) - zarówno dla wykresów skierowanych, jak i nieukierunkowanych(wersje oparte na DFS i Rozłączny Zestaw)
   * `A` [Algorytm Prima](src/algorithms/graph/prim) - znalezienie Minimalnego Drzewa Opinającego (MST) dla ważonego nieukierunkowanego wykresu
-  * `A` [Sortowanie Topologiczne](src/algorithms/graph/topological-sorting) - metoda DFS 
+  * `A` [Sortowanie Topologiczne](src/algorithms/graph/topological-sorting) - metoda DFS
   * `A` [Punkty Artykulacji](src/algorithms/graph/articulation-points) - Algorytm Tarjana (oparty o DFS)
-  * `A` [Mosty](src/algorithms/graph/bridges) - Oparty na algorytmie DFS 
+  * `A` [Mosty](src/algorithms/graph/bridges) - Oparty na algorytmie DFS
   * `A` [Ścieżka Euleriana i Obwód Euleriana](src/algorithms/graph/eulerian-path) - Algorytm Fleurya - Odwiedź każdą krawędź dokładnie raz
   * `A` [Cykl Hamiltoniana](src/algorithms/graph/hamiltonian-cycle) - Odwiedź każdy wierzchołek dokładnie raz
-  * `A` [Silnie Połączone Komponenty](src/algorithms/graph/strongly-connected-components) - Algorytm Kosaraja 
+  * `A` [Silnie Połączone Komponenty](src/algorithms/graph/strongly-connected-components) - Algorytm Kosaraja
   * `A` [Travelling Salesman Problem](src/algorithms/graph/travelling-salesman) - najkrótsza ścieżka która odwiedza każde miasto i wraca miasta początkującego
 * **Niezkategorizowane**
   * `B` [Wieża Hanoi](src/algorithms/uncategorized/hanoi-tower)
   * `B` [Kwadratowa Matryca Obrotu](src/algorithms/uncategorized/square-matrix-rotation) - algorytm w miejscu
-  * `B` [Jump Game](src/algorithms/uncategorized/jump-game) - cofanie, dynamiczne programowanie (od góry do dołu + od dołu do góry) i przykłady chciwego  
+  * `B` [Jump Game](src/algorithms/uncategorized/jump-game) - cofanie, dynamiczne programowanie (od góry do dołu + od dołu do góry) i przykłady chciwego
   * `B` [Unikatowe Ścieżki](src/algorithms/uncategorized/unique-paths) - cofanie, dynamiczne programowanie i przykłady oparte na Trójkącie Pascala
   * `A` [Problem N-Queens](src/algorithms/uncategorized/n-queens)
   * `A` [Knight's Tour](src/algorithms/uncategorized/knight-tour)
 
 ### Algorytmy według paradygmatu
 
-Paradygmat algorytmiczny jest ogólną metodą lub podejściem, które jest 
-podstawą projektowania klasy algorytmów. Jest abstrakcją wyższą niż 
-pojęcie algorytmu, podobnie jak algorytm jest abstrakcją wyższą niż 
+Paradygmat algorytmiczny jest ogólną metodą lub podejściem, które jest
+podstawą projektowania klasy algorytmów. Jest abstrakcją wyższą niż
+pojęcie algorytmu, podobnie jak algorytm jest abstrakcją wyższą niż
 program komputerowy.
 
 * **Metoda Siłowa** - Sprawdza wszystkie możliwosci i wybiera  najlepsze rozwiązanie.
@@ -149,7 +149,7 @@ program komputerowy.
 * **Chciwy** - wybierz najlepszą opcję w obecnym czasie, bez względu na przyszłość
   * `B` [Jump Game](src/algorithms/uncategorized/jump-game)
   * `A` [Niezwiązany Problem Knapsacka ](src/algorithms/sets/knapsack-problem)
-  * `A` [Algorytm Dijkstry](src/algorithms/graph/dijkstra) - 
+  * `A` [Algorytm Dijkstry](src/algorithms/graph/dijkstra) -
 znalezienie najkrótszej ścieżki do wszystkich wierzchołków grafu
   * `A` [Algorytm Prima](src/algorithms/graph/prim) - znalezienie Minimalnego Drzewa Opinającego (MST) dla ważonego nieukierunkowanego wykresu
   * `A` [Algorytm Kruskala](src/algorithms/graph/kruskal) - znalezienie Minimalnego Drzewa Opinającego (MST) dla ważonego nieukierunkowanego wykresu
@@ -178,7 +178,7 @@ znalezienie najkrótszej ścieżki do wszystkich wierzchołków grafu
   * `A` [Partycja Całkowita](src/algorithms/math/integer-partition)
   * `A` [Maksymalne Podtablice](src/algorithms/sets/maximum-subarray)
   * `A` [Algorytm Bellman-Forda](src/algorithms/graph/bellman-ford) - znalezienie najkrótszej ścieżki wszystkich wierzchołków wykresu
-  * `A` [Algorytm Floyd-Warshalla](src/algorithms/graph/floyd-warshall) - 
+  * `A` [Algorytm Floyd-Warshalla](src/algorithms/graph/floyd-warshall) -
 znajdź najkrótsze ścieżki między wszystkimi parami wierzchołków
   * `A` [Dopasowanie Wyrażeń Regularnych](src/algorithms/string/regular-expression-matching)
 * **Algorytm z nawrotami** - podobny do metody siłowej, próbuje wygenerować wszystkie możliwe rozwiązania, jednak za każdym razem generujesz następne rozwiązanie które testujesz
@@ -192,7 +192,7 @@ jeżeli zaspokaja wszystkie warunki, tylko wtedy generuje kolejne rozwiązania.
 * **Metoda Podziału i Ograniczeń** - Pamięta o niskonakładowym rozwiązaniu znalezionym na każdym etapie szukania nawrotu,
 używa kosztu niskonakładowego kosztu, które dotychczas zostało znalezione jako niska granica najmniejszego kosztu
 do rozwiązanie problemu, aby odrzucić cząstkowe rozwiązania o kosztach większych niż niskonakładowe
-rozwiązanie znalezione do tej pory. 
+rozwiązanie znalezione do tej pory.
 Zazwyczan trajektoria BFS, w połączeniu z trajektorią Przeszukiwania W Głąb (DFS) drzewa przestrzeni stanów jest użyte.
 
 ## Jak używać repozytorium
@@ -225,7 +225,7 @@ npm test -- 'LinkedList'
 Możesz pociwiczyć ze strukturą danych i algorytmami w `./src/playground/playground.js` zakartotekuj i napisz
 testy do tego w `./src/playground/__test__/playground.test.js`.
 
-Następnie uruchom następującą komendę w celu przetestowania czy twoje kod działa według oczekiwań: 
+Następnie uruchom następującą komendę w celu przetestowania czy twoje kod działa według oczekiwań:
 
 ```
 npm test -- 'playground'
@@ -239,7 +239,7 @@ npm test -- 'playground'
 
 ### Big O Notacja
 
-Kolejność wzrastania algorytmów według Big O notacji. 
+Kolejność wzrastania algorytmów według Big O notacji.
 
 ![Big O grafy](./assets/big-o-graph.png)
 
diff --git a/README.pt-BR.md b/README.pt-BR.md
index a9fc0d34ce..e95477ed15 100644
--- a/README.pt-BR.md
+++ b/README.pt-BR.md
@@ -4,7 +4,7 @@
 [![codecov](https://codecov.io/gh/trekhleb/javascript-algorithms/branch/master/graph/badge.svg)](https://codecov.io/gh/trekhleb/javascript-algorithms)
 
 Este repositório contém exemplos baseados em JavaScript de muitos
-algoritmos e estruturas de dados populares. 
+algoritmos e estruturas de dados populares.
 
 Cada algoritmo e estrutura de dado possui seu próprio README
 com explicações relacionadas e links para leitura adicional (incluindo
@@ -61,7 +61,7 @@ um conjunto de regras que define precisamente uma sequência de operações.
 
 * **Matemática**
   * `B` [Manipulação Bit](src/algorithms/math/bits) - set/get/update/clear bits, multiplicação / divisão por dois, tornar negativo etc.
-  * `B` [Fatorial](src/algorithms/math/factorial) 
+  * `B` [Fatorial](src/algorithms/math/factorial)
   * `B` [Número de Fibonacci](src/algorithms/math/fibonacci)
   * `B` [Teste de Primalidade](src/algorithms/math/primality-test) (método de divisão experimental)
   * `B` [Algoritmo Euclidiano](src/algorithms/math/euclidean-algorithm) - calcular o maior divisor comum (GCD)
@@ -119,7 +119,7 @@ um conjunto de regras que define precisamente uma sequência de operações.
   * `A` [Floyd-Warshall Algorithm](src/algorithms/graph/floyd-warshall) - encontrar caminhos mais curtos entre todos os pares de vértices
   * `A` [Detect Cycle](src/algorithms/graph/detect-cycle) - para gráficos direcionados e não direcionados (versões baseadas em DFS e Conjunto Disjuntivo)
   * `A` [Prim’s Algorithm](src/algorithms/graph/prim) - encontrando Árvore Mínima de Abrangência (MST) para grafo não direcionado ponderado
-  * `A` [Topological Sorting](src/algorithms/graph/topological-sorting) - Métodos DFS 
+  * `A` [Topological Sorting](src/algorithms/graph/topological-sorting) - Métodos DFS
   * `A` [Articulation Points](src/algorithms/graph/articulation-points) -O algoritmo de Tarjan (baseado em DFS)
   * `A` [Bridges](src/algorithms/graph/bridges) - Algoritmo baseado em DFS
   * `A` [Eulerian Path and Eulerian Circuit](src/algorithms/graph/eulerian-path) - Algoritmo de Fleury - Visite todas as bordas exatamente uma vez
diff --git a/README.ru-RU.md b/README.ru-RU.md
index 9365bca163..e1bdb49454 100644
--- a/README.ru-RU.md
+++ b/README.ru-RU.md
@@ -56,7 +56,7 @@ _Читать на других языках:_
 
 * **Математика**
   * `B` [Битовые манипуляции](src/algorithms/math/bits) — получение/запись/сброс/обновление битов, умножение/деление на 2, сделать отрицательным и т.п.
-  * `B` [Факториал](src/algorithms/math/factorial) 
+  * `B` [Факториал](src/algorithms/math/factorial)
   * `B` [Числа Фибоначчи](src/algorithms/math/fibonacci) — классическое решение, решение в замкнутой форме
   * `B` [Тест простоты](src/algorithms/math/primality-test) (метод пробного деления)
   * `B` [Алгоритм Евклида](src/algorithms/math/euclidean-algorithm) — нахождение наибольшего общего делителя (НОД)
@@ -70,7 +70,7 @@ _Читать на других языках:_
   * `A` [Разбиение числа](src/algorithms/math/integer-partition)
   * `A` [Квадратный корень](src/algorithms/math/square-root) — метод Ньютона
   * `A` [Алгоритм Лю Хуэя](src/algorithms/math/liu-hui) — расчёт числа π с заданной точностью методом вписанных правильных многоугольников
-  * `A` [Дискретное преобразование Фурье](src/algorithms/math/fourier-transform) — разложение временной функции (сигнала) на частотные составляющие 
+  * `A` [Дискретное преобразование Фурье](src/algorithms/math/fourier-transform) — разложение временной функции (сигнала) на частотные составляющие
 * **Множества**
   * `B` [Декартово произведение](src/algorithms/sets/cartesian-product) — результат перемножения множеств
   * `B` [Тасование Фишера — Йетса](src/algorithms/sets/fisher-yates) — создание случайных перестановок конечного множества
@@ -135,7 +135,7 @@ _Читать на других языках:_
 * **Прочие алгоритмы**
   * `B` [Ханойская башня](src/algorithms/uncategorized/hanoi-tower)
   * `B` [Поворот квадратной матрицы](src/algorithms/uncategorized/square-matrix-rotation) — используется дополнительная память
-  * `B` [Прыжки](src/algorithms/uncategorized/jump-game) — на основе бэктрекинга, динамического программирования (сверху-вниз + снизу-вверх) и жадных алгоритмов 
+  * `B` [Прыжки](src/algorithms/uncategorized/jump-game) — на основе бэктрекинга, динамического программирования (сверху-вниз + снизу-вверх) и жадных алгоритмов
   * `B` [Поиск уникальных путей](src/algorithms/uncategorized/unique-paths) — на основе бэктрекинга, динамического программирования и треугольника Паскаля
   * `B` [Подсчёт дождевой воды](src/algorithms/uncategorized/rain-terraces) — на основе перебора и динамического программирования
   * `B` [Задача о рекурсивной лестнице](src/algorithms/uncategorized/recursive-staircase) — подсчёт количества путей, по которым можно достичь верха лестницы (4 способа)
@@ -153,7 +153,7 @@ _Читать на других языках:_
   * `A` [Максимальный подмассив](src/algorithms/sets/maximum-subarray)
   * `A` [Задача коммивояжёра](src/algorithms/graph/travelling-salesman) — кратчайший маршрут, проходящий через указанные города с последующим возвратом в исходный город
   * `A` [Дискретное преобразование Фурье](src/algorithms/math/fourier-transform) — разложение временной функции (сигнала) на частотные составляющие
-* **Жадные алгоритмы** — принятие локально оптимальных решений с учётом допущения об оптимальности конечного решения 
+* **Жадные алгоритмы** — принятие локально оптимальных решений с учётом допущения об оптимальности конечного решения
   * `B` [Прыжки](src/algorithms/uncategorized/jump-game)
   * `A` [Задача о неограниченном рюкзаке](src/algorithms/sets/knapsack-problem)
   * `A` [Алгоритм Дейкстры](src/algorithms/graph/dijkstra) — нахождение кратчайших путей от одной из вершин графа до всех остальных
@@ -228,7 +228,7 @@ npm test -- 'LinkedList'
 
 **Песочница**
 
-Вы можете экспериментировать с алгоритмами и структурами данных в файле `./src/playground/playground.js` 
+Вы можете экспериментировать с алгоритмами и структурами данных в файле `./src/playground/playground.js`
 (файл `./src/playground/__test__/playground.test.js` предназначен для написания тестов).
 
 Для проверки работоспособности вашего кода используйте команду:
diff --git a/README.tr-TR.md b/README.tr-TR.md
index 62db14d1d0..7d2cc7919f 100644
--- a/README.tr-TR.md
+++ b/README.tr-TR.md
@@ -6,8 +6,8 @@
 Bu repository JavaScript'e ait popüler
 algoritma ve veri yapılarını içermektedir.
 
-Her bir algoritma ve veri yapısı kendine 
-ait açıklama ve videoya sahip README dosyası içerir. 
+Her bir algoritma ve veri yapısı kendine
+ait açıklama ve videoya sahip README dosyası içerir.
 
 _Read this in other languages:_
 [_简体中文_](README.zh-CN.md),
@@ -21,7 +21,7 @@ _Read this in other languages:_
 [_Русский_](README.ru-RU.md),
 [_Italiana_](README.it-IT.md)
 
-*☝ Not, bu proje araştırma ve öğrenme amacı ile yapılmış 
+*☝ Not, bu proje araştırma ve öğrenme amacı ile yapılmış
 olup üretim için **yaplılmamıştır**.*
 
 ## Veri Yapıları
@@ -63,7 +63,7 @@ bir işlem dizisini kesin olarak tanımlayan bir dizi kural.
 
 * **Matematik**
   * `B` [Bit Manipülasyonu](src/algorithms/math/bits) - set/get/update/clear bits, multiplication/division by two, make negative etc.
-  * `B` [Faktöriyel](src/algorithms/math/factorial) 
+  * `B` [Faktöriyel](src/algorithms/math/factorial)
   * `B` [Fibonacci Sayısı](src/algorithms/math/fibonacci) - klasik ve kapalı-form versiyonları
   * `B` [Asallık Testi](src/algorithms/math/primality-test) (trial division method)
   * `B` [Öklid Algoritması](src/algorithms/math/euclidean-algorithm) - En büyük ortak bölen hesaplama (EBOB)
@@ -143,8 +143,8 @@ bir işlem dizisini kesin olarak tanımlayan bir dizi kural.
 * **Kategoriye Ayrılmayanlar**
   * `B` [Tower of Hanoi](src/algorithms/uncategorized/hanoi-tower)
   * `B` [Square Matrix Rotation](src/algorithms/uncategorized/square-matrix-rotation) - in-place algorithm
-  * `B` [Jump Game](src/algorithms/uncategorized/jump-game) - backtracking, dynamic programming (top-down + bottom-up) and greedy examples 
-  * `B` [Unique Paths](src/algorithms/uncategorized/unique-paths) - backtracking, dynamic programming and Pascal's Triangle based examples 
+  * `B` [Jump Game](src/algorithms/uncategorized/jump-game) - backtracking, dynamic programming (top-down + bottom-up) and greedy examples
+  * `B` [Unique Paths](src/algorithms/uncategorized/unique-paths) - backtracking, dynamic programming and Pascal's Triangle based examples
   * `B` [Rain Terraces](src/algorithms/uncategorized/rain-terraces) - trapping rain water problem (dynamic programming and brute force versions)
   * `B` [Recursive Staircase](src/algorithms/uncategorized/recursive-staircase) - tepeye ulaşmanın yollarını sayma (4 çözüm)
   * `A` [N-Queens Problem](src/algorithms/uncategorized/n-queens)
@@ -152,8 +152,8 @@ bir işlem dizisini kesin olarak tanımlayan bir dizi kural.
 
 ### Algoritmik Paradigma
 
-Algoritmik paradigma, bir sınıfın tasarımının altında yatan genel bir yöntem veya yaklaşımdır. 
-Algoritma dizayn tekniği olarak düşünülebilir. Her bir altproblemi (subproblem) asıl problemle 
+Algoritmik paradigma, bir sınıfın tasarımının altında yatan genel bir yöntem veya yaklaşımdır.
+Algoritma dizayn tekniği olarak düşünülebilir. Her bir altproblemi (subproblem) asıl problemle
 benzerlik gösteren problemlere uygulanabilir.
 
 * **Brute Force** - mümkün olan tüm çözümleri tara ve en iyisini seç
@@ -198,7 +198,7 @@ benzerlik gösteren problemlere uygulanabilir.
   * `A` [Maximum Subarray](src/algorithms/sets/maximum-subarray)
   * `A` [Bellman-Ford Algorithm](src/algorithms/graph/bellman-ford) - tüm grafik köşelerine giden en kısa yolu bulmak
   * `A` [Floyd-Warshall Algorithm](src/algorithms/graph/floyd-warshall) - tüm köşe çiftleri arasındaki en kısa yolları bulun
-  * `A` [Regular Expression Matching](src/algorithms/string/regular-expression-matching) 
+  * `A` [Regular Expression Matching](src/algorithms/string/regular-expression-matching)
 * **Backtracking** - brute forceye benzer, mümkün tüm sonuçları tara, ancak bir sonraki çözümü her ürettiğinizde test edersiniz
 tüm koşulları karşılıyorsa ve ancak o zaman sonraki çözümleri üretmeye devam edin. Aksi takdirde, geri dönün ve farklı bir çözüm arayın(?).
 Normally the DFS traversal of state-space is being used.
@@ -242,7 +242,7 @@ npm test -- 'LinkedList'
 
 **Deneme Alanı**
 
-data-structures ve algorithms içerisinde `./src/playground/playground.js` 
+data-structures ve algorithms içerisinde `./src/playground/playground.js`
 yazarak `./src/playground/__test__/playground.test.js` için test edebilirsin.
 
 
@@ -310,4 +310,4 @@ Altta Big O notations ve farklı input boyutlarına karşın yapılmış perform
 
 ## Projeyi Destekleme
 
-Bu projeyi buradan destekleyebilirsiniz ❤️️ [GitHub](https://github.com/sponsors/trekhleb) veya ❤️️ [Patreon](https://www.patreon.com/trekhleb).          
+Bu projeyi buradan destekleyebilirsiniz ❤️️ [GitHub](https://github.com/sponsors/trekhleb) veya ❤️️ [Patreon](https://www.patreon.com/trekhleb).
diff --git a/src/algorithms/sorting/bubble-sort/README.md b/src/algorithms/sorting/bubble-sort/README.md
index 596d4006af..66347d86c7 100644
--- a/src/algorithms/sorting/bubble-sort/README.md
+++ b/src/algorithms/sorting/bubble-sort/README.md
@@ -3,12 +3,12 @@
 _Read this in other languages:_
 [_Português_](README.pt-BR.md)
 
-Bubble sort, sometimes referred to as sinking sort, is a 
-simple sorting algorithm that repeatedly steps through 
-the list to be sorted, compares each pair of adjacent 
-items and swaps them if they are in the wrong order 
+Bubble sort, sometimes referred to as sinking sort, is a
+simple sorting algorithm that repeatedly steps through
+the list to be sorted, compares each pair of adjacent
+items and swaps them if they are in the wrong order
 (ascending or descending arrangement). The pass through
-the list is repeated until no swaps are needed, which 
+the list is repeated until no swaps are needed, which
 indicates that the list is sorted.
 
 ![Algorithm Visualization](https://upload.wikimedia.org/wikipedia/commons/c/c8/Bubble-sort-example-300px.gif)
diff --git a/src/algorithms/sorting/bubble-sort/README.pt-BR.md b/src/algorithms/sorting/bubble-sort/README.pt-BR.md
index 39a3029500..c7862bb957 100644
--- a/src/algorithms/sorting/bubble-sort/README.pt-BR.md
+++ b/src/algorithms/sorting/bubble-sort/README.pt-BR.md
@@ -1,6 +1,6 @@
 # Bubble Sort
 
-O bubble sort, ou ordenação por flutuação (literalmente "por bolha"), é um algoritmo de ordenação dos mais simples. A ideia é percorrer o vetor diversas vezes, e a cada passagem fazer flutuar para o topo o maior elemento da sequência. Essa movimentação lembra a forma como as bolhas em um tanque de água procuram seu próprio nível, e disso vem o nome do algoritmo. 
+O bubble sort, ou ordenação por flutuação (literalmente "por bolha"), é um algoritmo de ordenação dos mais simples. A ideia é percorrer o vetor diversas vezes, e a cada passagem fazer flutuar para o topo o maior elemento da sequência. Essa movimentação lembra a forma como as bolhas em um tanque de água procuram seu próprio nível, e disso vem o nome do algoritmo.
 
 ![Algorithm Visualization](https://upload.wikimedia.org/wikipedia/commons/c/c8/Bubble-sort-example-300px.gif)
 

From 4623bb906f6ba6dee85e304cdac660dd08b79175 Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Wed, 16 Dec 2020 08:07:08 +0100
Subject: [PATCH 031/264] Add k-nearest neighbors algorithm.

---
 README.md                                  |  2 +-
 src/algorithms/ML/KNN/README.md            | 23 -------
 src/algorithms/ML/KNN/__test__/knn.test.js | 42 ------------
 src/algorithms/ML/KNN/knn.js               | 60 -----------------
 src/algorithms/ml/knn/README.md            | 41 ++++++++++++
 src/algorithms/ml/knn/__test__/knn.test.js | 71 ++++++++++++++++++++
 src/algorithms/ml/knn/kNN.js               | 77 ++++++++++++++++++++++
 7 files changed, 190 insertions(+), 126 deletions(-)
 delete mode 100644 src/algorithms/ML/KNN/README.md
 delete mode 100644 src/algorithms/ML/KNN/__test__/knn.test.js
 delete mode 100644 src/algorithms/ML/KNN/knn.js
 create mode 100644 src/algorithms/ml/knn/README.md
 create mode 100644 src/algorithms/ml/knn/__test__/knn.test.js
 create mode 100644 src/algorithms/ml/knn/kNN.js

diff --git a/README.md b/README.md
index e108671a22..58fdab3eaa 100644
--- a/README.md
+++ b/README.md
@@ -143,7 +143,7 @@ a set of rules that precisely define a sequence of operations.
   * `B` [Caesar Cipher](src/algorithms/cryptography/caesar-cipher) - simple substitution cipher
 * **Machine Learning**
   * `B` [NanoNeuron](https://github.com/trekhleb/nano-neuron) - 7 simple JS functions that illustrate how machines can actually learn (forward/backward propagation)
-  * `B` [KNN](src/algorithms/ML/KNN) - K Nearest Neighbors
+  * `B` [k-NN](src/algorithms/ml/knn) - k-nearest neighbors classification algorithm
 * **Uncategorized**
   * `B` [Tower of Hanoi](src/algorithms/uncategorized/hanoi-tower)
   * `B` [Square Matrix Rotation](src/algorithms/uncategorized/square-matrix-rotation) - in-place algorithm
diff --git a/src/algorithms/ML/KNN/README.md b/src/algorithms/ML/KNN/README.md
deleted file mode 100644
index d9db66ef46..0000000000
--- a/src/algorithms/ML/KNN/README.md
+++ /dev/null
@@ -1,23 +0,0 @@
-# KNN Algorithm  
-
-KNN stands for K Nearest Neighbors. KNN is a supervised Machine Learning algorithm. It's a classification algorithm, determining the class of a sample vector using a sample data.  
-
-The idea is to calculate the similarity between two data points on the basis of a distance metric. Euclidean distance is used mostly for this task. The algorithm is as follows -  
-
-1. Check for errors like invalid data/labels.
-2. Calculate the euclidean distance of all the data points in training data with the classification point
-3. Sort the distances of points along with their classes in ascending order
-4. Take the initial "K" classes and find the mode to get the most similar class
-5. Report the most similar class  
-
-Here is a visualization for better understanding -  
-
-![KNN Visualization](https://media.geeksforgeeks.org/wp-content/uploads/graph2-2.png)  
-
-Here, as we can see, the classification of unknown points will be judged by their proximity to other points.
-
-It is important to note that "K" is preferred to have odd values in order to break ties. Usually "K" is taken as 3 or 5.  
-
-## References
-
-- [GeeksforGeeks](https://media.geeksforgeeks.org/wp-content/uploads/graph2-2.png)
diff --git a/src/algorithms/ML/KNN/__test__/knn.test.js b/src/algorithms/ML/KNN/__test__/knn.test.js
deleted file mode 100644
index 6884598505..0000000000
--- a/src/algorithms/ML/KNN/__test__/knn.test.js
+++ /dev/null
@@ -1,42 +0,0 @@
-import KNN from '../knn';
-
-describe('KNN', () => {
-  test('should throw an error on invalid data', () => {
-    expect(() => {
-      KNN();
-    }).toThrowError();
-  });
-  test('should throw an error on invalid labels', () => {
-    const nolabels = () => {
-      KNN([[1, 1]]);
-    };
-    expect(nolabels).toThrowError();
-  });
-  it('should throw an error on not giving classification vector', () => {
-    const noclassification = () => {
-      KNN([[1, 1]], [1]);
-    };
-    expect(noclassification).toThrowError();
-  });
-  it('should throw an error on not giving classification vector', () => {
-    const inconsistent = () => {
-      KNN([[1, 1]], [1], [1]);
-    };
-    expect(inconsistent).toThrowError();
-  });
-  it('should find the nearest neighbour', () => {
-    let dataX = [[1, 1], [2, 2]];
-    let dataY = [1, 2];
-    expect(KNN(dataX, dataY, [1, 1])).toBe(1);
-
-    dataX = [[1, 1], [6, 2], [3, 3], [4, 5], [9, 2], [2, 4], [8, 7]];
-    dataY = [1, 2, 1, 2, 1, 2, 1];
-    expect(KNN(dataX, dataY, [1.25, 1.25]))
-      .toBe(1);
-
-    dataX = [[1, 1], [6, 2], [3, 3], [4, 5], [9, 2], [2, 4], [8, 7]];
-    dataY = [1, 2, 1, 2, 1, 2, 1];
-    expect(KNN(dataX, dataY, [1.25, 1.25], 5))
-      .toBe(2);
-  });
-});
diff --git a/src/algorithms/ML/KNN/knn.js b/src/algorithms/ML/KNN/knn.js
deleted file mode 100644
index 866b6a22e9..0000000000
--- a/src/algorithms/ML/KNN/knn.js
+++ /dev/null
@@ -1,60 +0,0 @@
-/**
- * @param {object} dataY
- * @param {object} dataX
- * @param {object} toClassify
- * @param {number} k
- * @return {number}
- */
-export default function KNN(dataX, dataY, toClassify, K) {
-  let k = -1;
-
-  if (K === undefined) {
-    k = 3;
-  } else {
-    k = K;
-  }
-
-  // creating function to calculate the euclidean distance between 2 vectors
-  function euclideanDistance(x1, x2) {
-    // checking errors
-    if (x1.length !== x2.length) {
-      throw new Error('inconsistency between data and classification vector.');
-    }
-    // calculate the euclidean distance between 2 vectors and return
-    let totalSSE = 0;
-    for (let j = 0; j < x1.length; j += 1) {
-      totalSSE += (x1[j] - x2[j]) ** 2;
-    }
-    return Number(Math.sqrt(totalSSE).toFixed(2));
-  }
-
-  // starting algorithm
-
-  // calculate distance from toClassify to each point for all dimensions in dataX
-  // store distance and point's class_index into distance_class_list
-  let distanceList = [];
-  for (let i = 0; i < dataX.length; i += 1) {
-    const tmStore = [];
-    tmStore.push(euclideanDistance(dataX[i], toClassify));
-    tmStore.push(dataY[i]);
-    distanceList[i] = tmStore;
-  }
-
-  // sort distanceList
-  // take initial k values, count with class index
-  distanceList = distanceList.sort().slice(0, k);
-
-  // count the number of instances of each class in top k members
-  // with that maintain record of highest count class simultanously
-  const modeK = {};
-  const maxm = [-1, -1];
-  for (let i = 0; i < Math.min(k, distanceList.length); i += 1) {
-    if (distanceList[i][1] in modeK) modeK[distanceList[i][1]] += 1;
-    else modeK[distanceList[i][1]] = 1;
-    if (modeK[distanceList[i][1]] > maxm[0]) {
-      [maxm[0], maxm[1]] = [modeK[distanceList[i][1]], distanceList[i][1]];
-    }
-  }
-  // return the class with highest count from maxm
-  return maxm[1];
-}
diff --git a/src/algorithms/ml/knn/README.md b/src/algorithms/ml/knn/README.md
new file mode 100644
index 0000000000..0d61c14fb7
--- /dev/null
+++ b/src/algorithms/ml/knn/README.md
@@ -0,0 +1,41 @@
+# k-Nearest Neighbors Algorithm
+
+The **k-nearest neighbors algorithm (k-NN)** is a supervised Machine Learning algorithm. It's a classification algorithm, determining the class of a sample vector using a sample data.
+
+In k-NN classification, the output is a class membership. An object is classified by a plurality vote of its neighbors, with the object being assigned to the class most common among its `k` nearest neighbors (`k` is a positive integer, typically small). If `k = 1`, then the object is simply assigned to the class of that single nearest neighbor.
+
+The idea is to calculate the similarity between two data points on the basis of a distance metric. [Euclidean distance](https://en.wikipedia.org/wiki/Euclidean_distance) is used mostly for this task.
+
+![Euclidean distance between two points](https://upload.wikimedia.org/wikipedia/commons/5/55/Euclidean_distance_2d.svg)
+
+_Image source: [Wikipedia](https://en.wikipedia.org/wiki/Euclidean_distance)_
+
+The algorithm is as follows:
+
+1. Check for errors like invalid data/labels.
+2. Calculate the euclidean distance of all the data points in training data with the classification point
+3. Sort the distances of points along with their classes in ascending order
+4. Take the initial `K` classes and find the mode to get the most similar class
+5. Report the most similar class
+
+Here is a visualization of k-NN classification for better understanding:
+
+![KNN Visualization 1](https://upload.wikimedia.org/wikipedia/commons/e/e7/KnnClassification.svg)
+
+_Image source: [Wikipedia](https://en.wikipedia.org/wiki/K-nearest_neighbors_algorithm)_
+
+The test sample (green dot) should be classified either to blue squares or to red triangles. If `k = 3` (solid line circle) it is assigned to the red triangles because there are `2` triangles and only `1` square inside the inner circle. If `k = 5` (dashed line circle) it is assigned to the blue squares (`3` squares vs. `2` triangles inside the outer circle).
+
+Another k-NN classification example:
+
+![KNN Visualization 2](https://media.geeksforgeeks.org/wp-content/uploads/graph2-2.png)
+
+_Image source: [GeeksForGeeks](https://media.geeksforgeeks.org/wp-content/uploads/graph2-2.png)_
+
+Here, as we can see, the classification of unknown points will be judged by their proximity to other points.
+
+It is important to note that `K` is preferred to have odd values in order to break ties. Usually `K` is taken as `3` or `5`.
+
+## References
+
+- [k-nearest neighbors algorithm on Wikipedia](https://en.wikipedia.org/wiki/K-nearest_neighbors_algorithm)
diff --git a/src/algorithms/ml/knn/__test__/knn.test.js b/src/algorithms/ml/knn/__test__/knn.test.js
new file mode 100644
index 0000000000..ccd69cd706
--- /dev/null
+++ b/src/algorithms/ml/knn/__test__/knn.test.js
@@ -0,0 +1,71 @@
+import kNN from '../kNN';
+
+describe('kNN', () => {
+  it('should throw an error on invalid data', () => {
+    expect(() => {
+      kNN();
+    }).toThrowError('Either dataSet or labels or toClassify were not set');
+  });
+
+  it('should throw an error on invalid labels', () => {
+    const noLabels = () => {
+      kNN([[1, 1]]);
+    };
+    expect(noLabels).toThrowError('Either dataSet or labels or toClassify were not set');
+  });
+
+  it('should throw an error on not giving classification vector', () => {
+    const noClassification = () => {
+      kNN([[1, 1]], [1]);
+    };
+    expect(noClassification).toThrowError('Either dataSet or labels or toClassify were not set');
+  });
+
+  it('should throw an error on not giving classification vector', () => {
+    const inconsistent = () => {
+      kNN([[1, 1]], [1], [1]);
+    };
+    expect(inconsistent).toThrowError('Inconsistent vector lengths');
+  });
+
+  it('should find the nearest neighbour', () => {
+    let dataSet;
+    let labels;
+    let toClassify;
+    let expectedClass;
+
+    dataSet = [[1, 1], [2, 2]];
+    labels = [1, 2];
+    toClassify = [1, 1];
+    expectedClass = 1;
+    expect(kNN(dataSet, labels, toClassify)).toBe(expectedClass);
+
+    dataSet = [[1, 1], [6, 2], [3, 3], [4, 5], [9, 2], [2, 4], [8, 7]];
+    labels = [1, 2, 1, 2, 1, 2, 1];
+    toClassify = [1.25, 1.25];
+    expectedClass = 1;
+    expect(kNN(dataSet, labels, toClassify)).toBe(expectedClass);
+
+    dataSet = [[1, 1], [6, 2], [3, 3], [4, 5], [9, 2], [2, 4], [8, 7]];
+    labels = [1, 2, 1, 2, 1, 2, 1];
+    toClassify = [1.25, 1.25];
+    expectedClass = 2;
+    expect(kNN(dataSet, labels, toClassify, 5)).toBe(expectedClass);
+  });
+
+  it('should find the nearest neighbour with equal distances', () => {
+    const dataSet = [[0, 0], [1, 1], [0, 2]];
+    const labels = [1, 3, 3];
+    const toClassify = [0, 1];
+    const expectedClass = 3;
+    expect(kNN(dataSet, labels, toClassify)).toBe(expectedClass);
+  });
+
+  it('should find the nearest neighbour in 3D space', () => {
+    const dataSet = [[0, 0, 0], [0, 1, 1], [0, 0, 2]];
+    const labels = [1, 3, 3];
+    const toClassify = [0, 0, 1];
+    const expectedClass = 3;
+    expect(kNN(dataSet, labels, toClassify)).toBe(expectedClass);
+  });
+});
diff --git a/src/algorithms/ml/knn/kNN.js b/src/algorithms/ml/knn/kNN.js
new file mode 100644
index 0000000000..24709af6f2
--- /dev/null
+++ b/src/algorithms/ml/knn/kNN.js
@@ -0,0 +1,77 @@
+/**
+ * Calculates calculate the euclidean distance between 2 vectors.
+ *
+ * @param {number[]} x1
+ * @param {number[]} x2
+ * @returns {number}
+ */
+function euclideanDistance(x1, x2) {
+  // Checking for errors.
+  if (x1.length !== x2.length) {
+    throw new Error('Inconsistent vector lengths');
+  }
+  // Calculate the euclidean distance between 2 vectors and return.
+  let squaresTotal = 0;
+  for (let i = 0; i < x1.length; i += 1) {
+    squaresTotal += (x1[i] - x2[i]) ** 2;
+  }
+  return Number(Math.sqrt(squaresTotal).toFixed(2));
+}
+
+/**
+ * Classifies the point in space based on k-nearest neighbors algorithm.
+ *
+ * @param {number[][]} dataSet - array of data points, i.e. [[0, 1], [3, 4], [5, 7]]
+ * @param {number[]} labels - array of classes (labels), i.e. [1, 1, 2]
+ * @param {number[]} toClassify - the point in space that needs to be classified, i.e. [5, 4]
+ * @param {number} k - number of nearest neighbors which will be taken into account (preferably odd)
+ * @return {number} - the class of the point
+ */
+export default function kNN(
+  dataSet,
+  labels,
+  toClassify,
+  k = 3,
+) {
+  if (!dataSet || !labels || !toClassify) {
+    throw new Error('Either dataSet or labels or toClassify were not set');
+  }
+
+  // Calculate distance from toClassify to each point for all dimensions in dataSet.
+  // Store distance and point's label into distances list.
+  const distances = [];
+  for (let i = 0; i < dataSet.length; i += 1) {
+    distances.push({
+      dist: euclideanDistance(dataSet[i], toClassify),
+      label: labels[i],
+    });
+  }
+
+  // Sort distances list (from closer point to further ones).
+  // Take initial k values, count with class index
+  const kNearest = distances.sort((a, b) => {
+    if (a.dist === b.dist) {
+      return 0;
+    }
+    return a.dist < b.dist ? -1 : 1;
+  }).slice(0, k);
+
+  // Count the number of instances of each class in top k members.
+  const labelsCounter = {};
+  let topClass = 0;
+  let topClassCount = 0;
+  for (let i = 0; i < kNearest.length; i += 1) {
+    if (kNearest[i].label in labelsCounter) {
+      labelsCounter[kNearest[i].label] += 1;
+    } else {
+      labelsCounter[kNearest[i].label] = 1;
+    }
+    if (labelsCounter[kNearest[i].label] > topClassCount) {
+      topClassCount = labelsCounter[kNearest[i].label];
+      topClass = kNearest[i].label;
+    }
+  }
+
+  // Return the class with highest count.
+  return topClass;
+}

From e105460cd6c868c2a38f7a4c8416c34b4eb6ea83 Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Wed, 16 Dec 2020 17:56:57 +0100
Subject: [PATCH 032/264] Update CI badge to point to the master branch status.

---
 README.es-ES.md | 2 +-
 README.fr-FR.md | 2 +-
 README.it-IT.md | 2 +-
 README.ja-JP.md | 2 +-
 README.ko-KR.md | 2 +-
 README.md       | 2 +-
 README.pl-PL.md | 2 +-
 README.pt-BR.md | 2 +-
 README.ru-RU.md | 2 +-
 README.tr-TR.md | 2 +-
 README.zh-CN.md | 2 +-
 README.zh-TW.md | 2 +-
 12 files changed, 12 insertions(+), 12 deletions(-)

diff --git a/README.es-ES.md b/README.es-ES.md
index 81a3189259..b6337a1c3d 100644
--- a/README.es-ES.md
+++ b/README.es-ES.md
@@ -1,6 +1,6 @@
 # Algoritmos y Estructuras de Datos en JavaScript
 
-[![CI](https://github.com/trekhleb/javascript-algorithms/workflows/CI/badge.svg)](https://github.com/trekhleb/javascript-algorithms/actions)
+[![CI](https://github.com/trekhleb/javascript-algorithms/workflows/CI/badge.svg)](https://github.com/trekhleb/javascript-algorithms/actions?query=workflow%3ACI+branch%3Amaster)
 [![codecov](https://codecov.io/gh/trekhleb/javascript-algorithms/branch/master/graph/badge.svg)](https://codecov.io/gh/trekhleb/javascript-algorithms)
 
 Este repositorio contiene ejemplos basados en JavaScript de muchos
diff --git a/README.fr-FR.md b/README.fr-FR.md
index 440a854cd3..7b3705544b 100644
--- a/README.fr-FR.md
+++ b/README.fr-FR.md
@@ -1,6 +1,6 @@
 # Algorithmes et Structures de Données en JavaScript
 
-[![CI](https://github.com/trekhleb/javascript-algorithms/workflows/CI/badge.svg)](https://github.com/trekhleb/javascript-algorithms/actions)
+[![CI](https://github.com/trekhleb/javascript-algorithms/workflows/CI/badge.svg)](https://github.com/trekhleb/javascript-algorithms/actions?query=workflow%3ACI+branch%3Amaster)
 [![codecov](https://codecov.io/gh/trekhleb/javascript-algorithms/branch/master/graph/badge.svg)](https://codecov.io/gh/trekhleb/javascript-algorithms)
 
 Ce dépôt contient des exemples d'implémentation en JavaScript de plusieurs
diff --git a/README.it-IT.md b/README.it-IT.md
index 57c054df1e..9598324058 100644
--- a/README.it-IT.md
+++ b/README.it-IT.md
@@ -1,6 +1,6 @@
 # Algoritmi e Strutture Dati in Javascript
 
-[![CI](https://github.com/trekhleb/javascript-algorithms/workflows/CI/badge.svg)](https://github.com/trekhleb/javascript-algorithms/actions)
+[![CI](https://github.com/trekhleb/javascript-algorithms/workflows/CI/badge.svg)](https://github.com/trekhleb/javascript-algorithms/actions?query=workflow%3ACI+branch%3Amaster)
 [![codecov](https://codecov.io/gh/trekhleb/javascript-algorithms/branch/master/graph/badge.svg)](https://codecov.io/gh/trekhleb/javascript-algorithms)
 
 Questa repository contiene esempi in Javascript dei più popolari algoritmi e strutture dati .
diff --git a/README.ja-JP.md b/README.ja-JP.md
index 7ec49e4eeb..93321556c4 100644
--- a/README.ja-JP.md
+++ b/README.ja-JP.md
@@ -1,6 +1,6 @@
 # JavaScriptアルゴリズムとデータ構造
 
-[![CI](https://github.com/trekhleb/javascript-algorithms/workflows/CI/badge.svg)](https://github.com/trekhleb/javascript-algorithms/actions)
+[![CI](https://github.com/trekhleb/javascript-algorithms/workflows/CI/badge.svg)](https://github.com/trekhleb/javascript-algorithms/actions?query=workflow%3ACI+branch%3Amaster)
 [![codecov](https://codecov.io/gh/trekhleb/javascript-algorithms/branch/master/graph/badge.svg)](https://codecov.io/gh/trekhleb/javascript-algorithms)
 
 このリポジトリには、JavaScriptベースの一般的なアルゴリズムとデータ構造に関する多数のサンプルが含まれています。
diff --git a/README.ko-KR.md b/README.ko-KR.md
index 8a31e81101..0fa189d106 100644
--- a/README.ko-KR.md
+++ b/README.ko-KR.md
@@ -1,6 +1,6 @@
 # JavaScript 알고리즘 및 자료 구조
 
-[![CI](https://github.com/trekhleb/javascript-algorithms/workflows/CI/badge.svg)](https://github.com/trekhleb/javascript-algorithms/actions)
+[![CI](https://github.com/trekhleb/javascript-algorithms/workflows/CI/badge.svg)](https://github.com/trekhleb/javascript-algorithms/actions?query=workflow%3ACI+branch%3Amaster)
 [![codecov](https://codecov.io/gh/trekhleb/javascript-algorithms/branch/master/graph/badge.svg)](https://codecov.io/gh/trekhleb/javascript-algorithms)
 
 이 저장소에는 많이 알려진 알고리즘 및 자료 구조의 Javascript 기반 예제를 담고 있습니다.
diff --git a/README.md b/README.md
index 58fdab3eaa..e805a7a3cc 100644
--- a/README.md
+++ b/README.md
@@ -1,6 +1,6 @@
 # JavaScript Algorithms and Data Structures
 
-[![CI](https://github.com/trekhleb/javascript-algorithms/workflows/CI/badge.svg)](https://github.com/trekhleb/javascript-algorithms/actions)
+[![CI](https://github.com/trekhleb/javascript-algorithms/workflows/CI/badge.svg)](https://github.com/trekhleb/javascript-algorithms/actions?query=workflow%3ACI+branch%3Amaster)
 [![codecov](https://codecov.io/gh/trekhleb/javascript-algorithms/branch/master/graph/badge.svg)](https://codecov.io/gh/trekhleb/javascript-algorithms)
 
 This repository contains JavaScript based examples of many
diff --git a/README.pl-PL.md b/README.pl-PL.md
index 98fe798913..d1ad0ec224 100644
--- a/README.pl-PL.md
+++ b/README.pl-PL.md
@@ -1,6 +1,6 @@
 # JavaScript Algorytmy i Struktury Danych
 
-[![CI](https://github.com/trekhleb/javascript-algorithms/workflows/CI/badge.svg)](https://github.com/trekhleb/javascript-algorithms/actions)
+[![CI](https://github.com/trekhleb/javascript-algorithms/workflows/CI/badge.svg)](https://github.com/trekhleb/javascript-algorithms/actions?query=workflow%3ACI+branch%3Amaster)
 [![codecov](https://codecov.io/gh/trekhleb/javascript-algorithms/branch/master/graph/badge.svg)](https://codecov.io/gh/trekhleb/javascript-algorithms)
 
 To repozytorium zawiera wiele przykładów JavaScript opartych na
diff --git a/README.pt-BR.md b/README.pt-BR.md
index e95477ed15..66894582e1 100644
--- a/README.pt-BR.md
+++ b/README.pt-BR.md
@@ -1,6 +1,6 @@
 # Estrutura de Dados e Algoritmos em JavaScript
 
-[![CI](https://github.com/trekhleb/javascript-algorithms/workflows/CI/badge.svg)](https://github.com/trekhleb/javascript-algorithms/actions)
+[![CI](https://github.com/trekhleb/javascript-algorithms/workflows/CI/badge.svg)](https://github.com/trekhleb/javascript-algorithms/actions?query=workflow%3ACI+branch%3Amaster)
 [![codecov](https://codecov.io/gh/trekhleb/javascript-algorithms/branch/master/graph/badge.svg)](https://codecov.io/gh/trekhleb/javascript-algorithms)
 
 Este repositório contém exemplos baseados em JavaScript de muitos
diff --git a/README.ru-RU.md b/README.ru-RU.md
index e1bdb49454..e85446d31f 100644
--- a/README.ru-RU.md
+++ b/README.ru-RU.md
@@ -1,6 +1,6 @@
 # Алгоритмы и структуры данных на JavaScript
 
-[![CI](https://github.com/trekhleb/javascript-algorithms/workflows/CI/badge.svg)](https://github.com/trekhleb/javascript-algorithms/actions)
+[![CI](https://github.com/trekhleb/javascript-algorithms/workflows/CI/badge.svg)](https://github.com/trekhleb/javascript-algorithms/actions?query=workflow%3ACI+branch%3Amaster)
 [![codecov](https://codecov.io/gh/trekhleb/javascript-algorithms/branch/master/graph/badge.svg)](https://codecov.io/gh/trekhleb/javascript-algorithms)
 
 В этом репозитории содержатся базовые JavaScript-примеры многих популярных алгоритмов и структур данных.
diff --git a/README.tr-TR.md b/README.tr-TR.md
index 7d2cc7919f..c65061e454 100644
--- a/README.tr-TR.md
+++ b/README.tr-TR.md
@@ -1,6 +1,6 @@
 # JavaScript Algoritmalar ve Veri Yapıları
 
-[![CI](https://github.com/trekhleb/javascript-algorithms/workflows/CI/badge.svg)](https://github.com/trekhleb/javascript-algorithms/actions)
+[![CI](https://github.com/trekhleb/javascript-algorithms/workflows/CI/badge.svg)](https://github.com/trekhleb/javascript-algorithms/actions?query=workflow%3ACI+branch%3Amaster)
 [![codecov](https://codecov.io/gh/trekhleb/javascript-algorithms/branch/master/graph/badge.svg)](https://codecov.io/gh/trekhleb/javascript-algorithms)
 
 Bu repository JavaScript'e ait popüler
diff --git a/README.zh-CN.md b/README.zh-CN.md
index 064c0dbe11..05f580817f 100644
--- a/README.zh-CN.md
+++ b/README.zh-CN.md
@@ -1,6 +1,6 @@
 # JavaScript 算法与数据结构
 
-[![CI](https://github.com/trekhleb/javascript-algorithms/workflows/CI/badge.svg)](https://github.com/trekhleb/javascript-algorithms/actions)
+[![CI](https://github.com/trekhleb/javascript-algorithms/workflows/CI/badge.svg)](https://github.com/trekhleb/javascript-algorithms/actions?query=workflow%3ACI+branch%3Amaster)
 [![codecov](https://codecov.io/gh/trekhleb/javascript-algorithms/branch/master/graph/badge.svg)](https://codecov.io/gh/trekhleb/javascript-algorithms)
 
 本仓库包含了多种基于 JavaScript 的算法与数据结构。
diff --git a/README.zh-TW.md b/README.zh-TW.md
index bb98d2a140..1a091720bb 100644
--- a/README.zh-TW.md
+++ b/README.zh-TW.md
@@ -1,6 +1,6 @@
 # JavaScript 演算法與資料結構
 
-[![CI](https://github.com/trekhleb/javascript-algorithms/workflows/CI/badge.svg)](https://github.com/trekhleb/javascript-algorithms/actions)
+[![CI](https://github.com/trekhleb/javascript-algorithms/workflows/CI/badge.svg)](https://github.com/trekhleb/javascript-algorithms/actions?query=workflow%3ACI+branch%3Amaster)
 [![codecov](https://codecov.io/gh/trekhleb/javascript-algorithms/branch/master/graph/badge.svg)](https://codecov.io/gh/trekhleb/javascript-algorithms)
 
 這個知識庫包含許多 JavaScript 的資料結構與演算法的基礎範例。

From 9929ab7fc14fae9e5d685f689583939895ab68a8 Mon Sep 17 00:00:00 2001
From: Sherlyn <31661914+rollingcomma@users.noreply.github.com>
Date: Wed, 16 Dec 2020 22:26:21 -0800
Subject: [PATCH 033/264] add hillCipher at cryptography section (#424)

* add hillCipher.js and its test case first commit

* add README.md

* update style

Co-authored-by: Oleksii Trekhleb <trehleb@gmail.com>
---
 .../cryptography/hillCipher/README.md         | 27 ++++++++
 .../hillCipher/_test_/hillCipher.test.js      | 25 +++++++
 .../cryptography/hillCipher/hillCipher.js     | 68 +++++++++++++++++++
 3 files changed, 120 insertions(+)
 create mode 100644 src/algorithms/cryptography/hillCipher/README.md
 create mode 100644 src/algorithms/cryptography/hillCipher/_test_/hillCipher.test.js
 create mode 100644 src/algorithms/cryptography/hillCipher/hillCipher.js

diff --git a/src/algorithms/cryptography/hillCipher/README.md b/src/algorithms/cryptography/hillCipher/README.md
new file mode 100644
index 0000000000..99e73fa1fd
--- /dev/null
+++ b/src/algorithms/cryptography/hillCipher/README.md
@@ -0,0 +1,27 @@
+# Hill Cipher
+
+* The Hill cipher is a polygraphic substitution cipher based on linear algebra.
+Each letter is represented by a number modulo 26. 
+
+* Encryption: to encrypt a message, each block of n letters (considered as an n-component vector) is multiplied by an invertible n × n matrix, against modulus 26. 
+Consider the message 'ACT', and the key below (or GYB/NQK/URP in letters):
+  | 6   24   1 |
+  | 13  16   10|
+  | 20  17   15|
+The message is the vector:
+  |  0  |
+  |  2  |
+  |  19 |
+Thus the enciphered vector is given by  
+  | 6   24   1 |  |  0  |   |  67  |    |  15 |
+  | 13  16   10|  |  2  | = |  222 | ≡  |  14 | (mod 26)
+  | 20  17   15|  |  19 |   |  319 |    |  7  |
+which corresponds to a ciphertext of 'POH'.
+
+* Decryption: to decrypt the message, each block is multiplied by the inverse of the matrix used for encryption.
+
+
+## Reference
+- [Wikipedia] https://en.wikipedia.org/wiki/Hill_cipher
+- [GeeksforGeeks]https://www.geeksforgeeks.org/hill-cipher/
+
diff --git a/src/algorithms/cryptography/hillCipher/_test_/hillCipher.test.js b/src/algorithms/cryptography/hillCipher/_test_/hillCipher.test.js
new file mode 100644
index 0000000000..7c50f91361
--- /dev/null
+++ b/src/algorithms/cryptography/hillCipher/_test_/hillCipher.test.js
@@ -0,0 +1,25 @@
+import hillCipherEncrypt from '../hillCipher';
+
+describe('hillCipher', () => {
+  it('should throw an error when the length of the keyString does not equal to the power of length of the message ', () => {
+    const invalidLenghOfkeyString = () => {
+      hillCipherEncrypt('hello', 'helloworld');
+    };
+
+    expect(invalidLenghOfkeyString).toThrowError();
+  });
+  it('should throw an error when message or keyString contains none letter character', () => {
+    const invalidCharacterInMessage = () => {
+      hillCipherEncrypt('hell3', 'helloworld');
+    };
+    const invalidCharacterInKeyString = () => {
+      hillCipherEncrypt('hello', 'hel12world');
+    };
+    expect(invalidCharacterInMessage).toThrowError();
+    expect(invalidCharacterInKeyString).toThrowError();
+  });
+  it('should encrypt passed message using Hill Cipher', () => {
+    expect(hillCipherEncrypt('ACT', 'GYBNQKURP')).toBe('POH');
+    expect(hillCipherEncrypt('GFG', 'HILLMAGIC')).toBe('SWK');
+  });
+});
diff --git a/src/algorithms/cryptography/hillCipher/hillCipher.js b/src/algorithms/cryptography/hillCipher/hillCipher.js
new file mode 100644
index 0000000000..ac497a41a0
--- /dev/null
+++ b/src/algorithms/cryptography/hillCipher/hillCipher.js
@@ -0,0 +1,68 @@
+
+/**
+ * generate key matrix from given keyString
+ *
+ * @param {integer} length
+ * @param {string} keyString
+ * @return {Array[][]} keyMatrix
+ */
+const generateKeyMatrix = (length, keyString) => {
+  const keyMatrix = [];
+  let keyStringIndex = 0;
+  for (let i = 0; i < length; i += 1) {
+    const keyMatrixRow = [];
+    for (let j = 0; j < length; j += 1) {
+      keyMatrixRow.push((keyString.codePointAt(keyStringIndex)) % 65);
+      keyStringIndex += 1;
+    }
+    keyMatrix.push(keyMatrixRow);
+  }
+  return keyMatrix;
+};
+
+/**
+ * generate message vector from given message
+ *
+ * @param {*} message
+ * @return {Array} messageVector
+ */
+const generateMessageVector = (message) => {
+  const messageVector = [];
+  for (let i = 0; i < message.length; i += 1) {
+    messageVector.push(message.codePointAt(i) % 65);
+  }
+  return messageVector;
+};
+
+/**
+ * validate data and encrypt message from given message and keyString
+ *
+ * @param {string} message plaintext
+ * @param {string} keyString
+ * @return {string} cipherString
+ *
+ */
+
+export default function hillCipherEncrypt(message, keyString) {
+  const length = keyString.length ** (0.5);
+  // keyString.length must equal to square of message.length
+  if (!Number.isInteger(length) && length !== message.length) {
+    throw new Error('invalid key string length');
+  }
+  // keyString and messange can only contain letters
+  if (!(/^[a-zA-Z]+$/.test(message)) || !(/^[A-Za-z]+$/.test(keyString))) {
+    throw new Error('messange and key string can only contain letters');
+  }
+
+  const keyMatrix = generateKeyMatrix(length, keyString);
+  const messageVector = generateMessageVector(message);
+  let ciperString = '';
+  for (let row = 0; row < length; row += 1) {
+    let item = 0;
+    for (let column = 0; column < length; column += 1) {
+      item += keyMatrix[row][column] * messageVector[column];
+    }
+    ciperString += String.fromCharCode((item % 26) + 65);
+  }
+  return ciperString;
+}

From d899ae1484262999273d7a86c440a2f7e10da850 Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Thu, 17 Dec 2020 08:07:26 +0100
Subject: [PATCH 034/264] Add more details and example to Hill cipher README.

---
 .../cryptography/hill-cipher/README.md        | 96 +++++++++++++++++++
 .../_test_/hillCipher.test.js                 |  0
 .../{hillCipher => hill-cipher}/hillCipher.js |  0
 .../cryptography/hillCipher/README.md         | 27 ------
 4 files changed, 96 insertions(+), 27 deletions(-)
 create mode 100644 src/algorithms/cryptography/hill-cipher/README.md
 rename src/algorithms/cryptography/{hillCipher => hill-cipher}/_test_/hillCipher.test.js (100%)
 rename src/algorithms/cryptography/{hillCipher => hill-cipher}/hillCipher.js (100%)
 delete mode 100644 src/algorithms/cryptography/hillCipher/README.md

diff --git a/src/algorithms/cryptography/hill-cipher/README.md b/src/algorithms/cryptography/hill-cipher/README.md
new file mode 100644
index 0000000000..bf496e2be9
--- /dev/null
+++ b/src/algorithms/cryptography/hill-cipher/README.md
@@ -0,0 +1,96 @@
+# Hill Cipher
+
+The **Hill cipher** is a [polygraphic substitution](https://en.wikipedia.org/wiki/Polygraphic_substitution) cipher based on linear algebra.
+
+Each letter is represented by a number [modulo](https://en.wikipedia.org/wiki/Modular_arithmetic) `26`. Though this is not an essential feature of the cipher, this simple scheme is often used:
+
+| **Letter** | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z |
+| ------ | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
+| **Number** | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 |
+
+## Encryption
+
+To encrypt a message, each block of `n` letters (considered as an `n`-component vector) is multiplied by an invertible `n × n` matrix, against modulus `26`.
+
+The matrix used for encryption is the _cipher key_, and it should be chosen randomly from the set of invertible `n × n` matrices (modulo `26`). The cipher can, of course, be adapted to an alphabet with any number of letters; all arithmetic just needs to be done modulo the number of letters instead of modulo `26`.
+
+Consider the message `ACT`, and the key below (or `GYB/NQK/URP` in letters):
+
+```
+| 6   24   1  |
+| 13  16   10 |
+| 20  17   15 |
+```
+
+Since `A` is`0`, `C` is `2` and `T` is `19`, the message is the vector:
+
+```
+|  0  |
+|  2  |
+|  19 |
+```
+
+Thus, the enciphered vector is given by:
+
+```
+| 6   24   1  |  |  0  |   |  67  |   |  15 |
+| 13  16   10 |  |  2  | = |  222 | ≡ |  14 | (mod 26)
+| 20  17   15 |  |  19 |   |  319 |   |  7  |
+```
+
+which corresponds to a ciphertext of `POH`.
+
+Now, suppose that our message is instead `CAT` (notice how we're using the same letters as in `ACT` here), or:
+
+```
+|  2  |
+|  0  |
+|  19 |
+```
+
+This time, the enciphered vector is given by:
+
+```
+| 6   24   1  |  |  2  |   |  31  |   |  5  |
+| 13  16   10 |  |  0  | = |  216 | ≡ |  8  | (mod 26)
+| 20  17   15 |  |  19 |   |  325 |   |  13 |
+```
+
+which corresponds to a ciphertext of `FIN`. Every letter has changed.
+
+## Decryption
+
+To decrypt the message, each block is multiplied by the inverse of the matrix used for encryption. We turn the ciphertext back into a vector, then simply multiply by the inverse matrix of the key matrix (`IFK/VIV/VMI` in letters). (See [matrix inversion](https://en.wikipedia.org/wiki/Matrix_inversion) for methods to calculate the inverse matrix.) We find that, modulo 26, the inverse of the matrix used in the previous example is:
+
+```
+                -1
+| 6   24   1  |                | 8   5    10 |
+| 13  16   10 |    (mod 26) ≡  | 21  8    21 |
+| 20  17   15 |                | 21  12   8  |
+```
+
+Taking the previous example ciphertext of `POH`, we get:
+
+```
+| 8   5    10 |  |  15 |   |  260 |   |  0  |
+| 21  8    21 |  |  14 | = |  574 | ≡ |  2  | (mod 26)
+| 21  12   8  |  |  7  |   |  539 |   |  19 |
+```
+
+which gets us back to `ACT`, as expected.
+
+## Defining the encrypting matrix
+
+Two complications exist in picking the encrypting matrix:
+
+1. Not all matrices have an inverse. The matrix will have an inverse if and only if its [determinant](https://en.wikipedia.org/wiki/Determinant) is not zero.
+2. The determinant of the encrypting matrix must not have any common factors with the modular base.
+
+Thus, if we work modulo `26` as above, the determinant must be nonzero, and must not be divisible by `2` or `13`. If the determinant is `0`, or has common factors with the modular base, then the matrix cannot be used in the Hill cipher, and another matrix must be chosen (otherwise it will not be possible to decrypt). Fortunately, matrices which satisfy the conditions to be used in the Hill cipher are fairly common.
+
+## References
+
+- [Hill cipher on Wikipedia](https://en.wikipedia.org/wiki/Hill_cipher)
+- [Matrix inversion on MathIsFun](https://www.mathsisfun.com/algebra/matrix-inverse.html)
+- [GeeksForGeeks](https://www.geeksforgeeks.org/hill-cipher/)
+
diff --git a/src/algorithms/cryptography/hillCipher/_test_/hillCipher.test.js b/src/algorithms/cryptography/hill-cipher/_test_/hillCipher.test.js
similarity index 100%
rename from src/algorithms/cryptography/hillCipher/_test_/hillCipher.test.js
rename to src/algorithms/cryptography/hill-cipher/_test_/hillCipher.test.js
diff --git a/src/algorithms/cryptography/hillCipher/hillCipher.js b/src/algorithms/cryptography/hill-cipher/hillCipher.js
similarity index 100%
rename from src/algorithms/cryptography/hillCipher/hillCipher.js
rename to src/algorithms/cryptography/hill-cipher/hillCipher.js
diff --git a/src/algorithms/cryptography/hillCipher/README.md b/src/algorithms/cryptography/hillCipher/README.md
deleted file mode 100644
index 99e73fa1fd..0000000000
--- a/src/algorithms/cryptography/hillCipher/README.md
+++ /dev/null
@@ -1,27 +0,0 @@
-# Hill Cipher
-
-* The Hill cipher is a polygraphic substitution cipher based on linear algebra.
-Each letter is represented by a number modulo 26. 
-
-* Encryption: to encrypt a message, each block of n letters (considered as an n-component vector) is multiplied by an invertible n × n matrix, against modulus 26. 
-Consider the message 'ACT', and the key below (or GYB/NQK/URP in letters):
-  | 6   24   1 |
-  | 13  16   10|
-  | 20  17   15|
-The message is the vector:
-  |  0  |
-  |  2  |
-  |  19 |
-Thus the enciphered vector is given by  
-  | 6   24   1 |  |  0  |   |  67  |    |  15 |
-  | 13  16   10|  |  2  | = |  222 | ≡  |  14 | (mod 26)
-  | 20  17   15|  |  19 |   |  319 |    |  7  |
-which corresponds to a ciphertext of 'POH'.
-
-* Decryption: to decrypt the message, each block is multiplied by the inverse of the matrix used for encryption.
-
-
-## Reference
-- [Wikipedia] https://en.wikipedia.org/wiki/Hill_cipher
-- [GeeksforGeeks]https://www.geeksforgeeks.org/hill-cipher/
-

From 52fbc8a80f67c420b2c50bad71351bc5732e4a04 Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Thu, 17 Dec 2020 08:58:26 +0100
Subject: [PATCH 035/264] Add Hill Cipher.

---
 README.md                                     |  1 +
 .../hill-cipher/_test_/hillCipher.test.js     | 39 +++++++---
 .../cryptography/hill-cipher/hillCipher.js    | 72 +++++++++++--------
 3 files changed, 75 insertions(+), 37 deletions(-)

diff --git a/README.md b/README.md
index e805a7a3cc..b470aeeffd 100644
--- a/README.md
+++ b/README.md
@@ -141,6 +141,7 @@ a set of rules that precisely define a sequence of operations.
 * **Cryptography**
   * `B` [Polynomial Hash](src/algorithms/cryptography/polynomial-hash) - rolling hash function based on polynomial
   * `B` [Caesar Cipher](src/algorithms/cryptography/caesar-cipher) - simple substitution cipher
+  * `B` [Hill Cipher](src/algorithms/cryptography/hill-cipher) - polygraphic substitution cipher
 * **Machine Learning**
   * `B` [NanoNeuron](https://github.com/trekhleb/nano-neuron) - 7 simple JS functions that illustrate how machines can actually learn (forward/backward propagation)
   * `B` [k-NN](src/algorithms/ml/knn) - k-nearest neighbors classification algorithm
diff --git a/src/algorithms/cryptography/hill-cipher/_test_/hillCipher.test.js b/src/algorithms/cryptography/hill-cipher/_test_/hillCipher.test.js
index 7c50f91361..f540ae9ff1 100644
--- a/src/algorithms/cryptography/hill-cipher/_test_/hillCipher.test.js
+++ b/src/algorithms/cryptography/hill-cipher/_test_/hillCipher.test.js
@@ -1,13 +1,10 @@
-import hillCipherEncrypt from '../hillCipher';
+import { hillCipherEncrypt, hillCipherDecrypt } from '../hillCipher';
 
 describe('hillCipher', () => {
-  it('should throw an error when the length of the keyString does not equal to the power of length of the message ', () => {
-    const invalidLenghOfkeyString = () => {
-      hillCipherEncrypt('hello', 'helloworld');
-    };
-
-    expect(invalidLenghOfkeyString).toThrowError();
+  it('should throw an exception when trying to decipher', () => {
+    expect(hillCipherDecrypt).toThrowError('This method is not implemented yet');
   });
+
   it('should throw an error when message or keyString contains none letter character', () => {
     const invalidCharacterInMessage = () => {
       hillCipherEncrypt('hell3', 'helloworld');
@@ -15,11 +12,35 @@ describe('hillCipher', () => {
     const invalidCharacterInKeyString = () => {
       hillCipherEncrypt('hello', 'hel12world');
     };
-    expect(invalidCharacterInMessage).toThrowError();
-    expect(invalidCharacterInKeyString).toThrowError();
+    expect(invalidCharacterInMessage).toThrowError(
+      'The message and key string can only contain letters',
+    );
+    expect(invalidCharacterInKeyString).toThrowError(
+      'The message and key string can only contain letters',
+    );
+  });
+
+  it('should throw an error when the length of the keyString has a square root which is not integer', () => {
+    const invalidLengthOfKeyString = () => {
+      hillCipherEncrypt('ab', 'ab');
+    };
+    expect(invalidLengthOfKeyString).toThrowError(
+      'Invalid key string length. The square root of the key string must be an integer',
+    );
   });
+
+  it('should throw an error when the length of the keyString does not equal to the power of length of the message', () => {
+    const invalidLengthOfKeyString = () => {
+      hillCipherEncrypt('ab', 'aaabbbccc');
+    };
+    expect(invalidLengthOfKeyString).toThrowError(
+      'Invalid key string length. The key length must be a square of message length',
+    );
+  });
+
   it('should encrypt passed message using Hill Cipher', () => {
     expect(hillCipherEncrypt('ACT', 'GYBNQKURP')).toBe('POH');
+    expect(hillCipherEncrypt('CAT', 'GYBNQKURP')).toBe('FIN');
     expect(hillCipherEncrypt('GFG', 'HILLMAGIC')).toBe('SWK');
   });
 });
diff --git a/src/algorithms/cryptography/hill-cipher/hillCipher.js b/src/algorithms/cryptography/hill-cipher/hillCipher.js
index ac497a41a0..f776db6224 100644
--- a/src/algorithms/cryptography/hill-cipher/hillCipher.js
+++ b/src/algorithms/cryptography/hill-cipher/hillCipher.js
@@ -1,18 +1,28 @@
+// The code of an 'A' character (equals to 65).
+const alphabetCodeShift = 'A'.codePointAt(0);
+const englishAlphabetSize = 26;
 
 /**
- * generate key matrix from given keyString
+ * Generates key matrix from given keyString.
  *
- * @param {integer} length
- * @param {string} keyString
- * @return {Array[][]} keyMatrix
+ * @param {string} keyString - a string to build a key matrix (must be of matrixSize^2 length).
+ * @return {number[][]} keyMatrix
  */
-const generateKeyMatrix = (length, keyString) => {
+const generateKeyMatrix = (keyString) => {
+  const matrixSize = Math.sqrt(keyString.length);
+  if (!Number.isInteger(matrixSize)) {
+    throw new Error(
+      'Invalid key string length. The square root of the key string must be an integer',
+    );
+  }
   const keyMatrix = [];
   let keyStringIndex = 0;
-  for (let i = 0; i < length; i += 1) {
+  for (let i = 0; i < matrixSize; i += 1) {
     const keyMatrixRow = [];
-    for (let j = 0; j < length; j += 1) {
-      keyMatrixRow.push((keyString.codePointAt(keyStringIndex)) % 65);
+    for (let j = 0; j < matrixSize; j += 1) {
+      // A → 0, B → 1, ..., a → 32, b → 33, ...
+      const charCodeShifted = (keyString.codePointAt(keyStringIndex)) % alphabetCodeShift;
+      keyMatrixRow.push(charCodeShifted);
       keyStringIndex += 1;
     }
     keyMatrix.push(keyMatrixRow);
@@ -21,48 +31,54 @@ const generateKeyMatrix = (length, keyString) => {
 };
 
 /**
- * generate message vector from given message
+ * Generates a message vector from a given message.
  *
- * @param {*} message
- * @return {Array} messageVector
+ * @param {string} message - the message to encrypt.
+ * @return {number[]} messageVector
  */
 const generateMessageVector = (message) => {
   const messageVector = [];
   for (let i = 0; i < message.length; i += 1) {
-    messageVector.push(message.codePointAt(i) % 65);
+    messageVector.push(message.codePointAt(i) % alphabetCodeShift);
   }
   return messageVector;
 };
 
 /**
- * validate data and encrypt message from given message and keyString
+ * Encrypts the given message using Hill Cipher.
  *
  * @param {string} message plaintext
  * @param {string} keyString
  * @return {string} cipherString
- *
  */
+export function hillCipherEncrypt(message, keyString) {
+  // The keyString and message can only contain letters.
+  const onlyLettersRegExp = /^[a-zA-Z]+$/;
+  if (!onlyLettersRegExp.test(message) || !onlyLettersRegExp.test(keyString)) {
+    throw new Error('The message and key string can only contain letters');
+  }
+
+  const keyMatrix = generateKeyMatrix(keyString);
 
-export default function hillCipherEncrypt(message, keyString) {
-  const length = keyString.length ** (0.5);
   // keyString.length must equal to square of message.length
-  if (!Number.isInteger(length) && length !== message.length) {
-    throw new Error('invalid key string length');
-  }
-  // keyString and messange can only contain letters
-  if (!(/^[a-zA-Z]+$/.test(message)) || !(/^[A-Za-z]+$/.test(keyString))) {
-    throw new Error('messange and key string can only contain letters');
+  if (keyMatrix.length !== message.length) {
+    throw new Error('Invalid key string length. The key length must be a square of message length');
   }
 
-  const keyMatrix = generateKeyMatrix(length, keyString);
   const messageVector = generateMessageVector(message);
-  let ciperString = '';
-  for (let row = 0; row < length; row += 1) {
+  let cipherString = '';
+  for (let row = 0; row < keyMatrix.length; row += 1) {
     let item = 0;
-    for (let column = 0; column < length; column += 1) {
+    for (let column = 0; column < keyMatrix.length; column += 1) {
       item += keyMatrix[row][column] * messageVector[column];
     }
-    ciperString += String.fromCharCode((item % 26) + 65);
+    cipherString += String.fromCharCode((item % englishAlphabetSize) + alphabetCodeShift);
   }
-  return ciperString;
+
+  return cipherString;
 }
+
+// @TODO: Implement this method.
+export const hillCipherDecrypt = () => {
+  throw new Error('This method is not implemented yet');
+};

From 38b2b977cd8804e52c1f85ebe7f8a28d407f9b8c Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Thu, 17 Dec 2020 09:27:32 +0100
Subject: [PATCH 036/264] Add Hill Cipher.

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index b470aeeffd..784dcd7ca6 100644
--- a/README.md
+++ b/README.md
@@ -141,7 +141,7 @@ a set of rules that precisely define a sequence of operations.
 * **Cryptography**
   * `B` [Polynomial Hash](src/algorithms/cryptography/polynomial-hash) - rolling hash function based on polynomial
   * `B` [Caesar Cipher](src/algorithms/cryptography/caesar-cipher) - simple substitution cipher
-  * `B` [Hill Cipher](src/algorithms/cryptography/hill-cipher) - polygraphic substitution cipher
+  * `B` [Hill Cipher](src/algorithms/cryptography/hill-cipher) - substitution cipher based on linear algebra
 * **Machine Learning**
   * `B` [NanoNeuron](https://github.com/trekhleb/nano-neuron) - 7 simple JS functions that illustrate how machines can actually learn (forward/backward propagation)
   * `B` [k-NN](src/algorithms/ml/knn) - k-nearest neighbors classification algorithm

From 07c21083d61ff7784b15158430056fa843cdb635 Mon Sep 17 00:00:00 2001
From: Oleg Maslov <maslovbox@gmail.com>
Date: Thu, 17 Dec 2020 11:36:00 +0300
Subject: [PATCH 037/264] Add missing LinkedList tests (#151)

Co-authored-by: Oleksii Trekhleb <trehleb@gmail.com>
---
 .../linked-list/__test__/LinkedList.test.js   | 23 +++++++++++++++++++
 1 file changed, 23 insertions(+)

diff --git a/src/data-structures/linked-list/__test__/LinkedList.test.js b/src/data-structures/linked-list/__test__/LinkedList.test.js
index f80187a730..bce06f727e 100644
--- a/src/data-structures/linked-list/__test__/LinkedList.test.js
+++ b/src/data-structures/linked-list/__test__/LinkedList.test.js
@@ -218,6 +218,29 @@ describe('LinkedList', () => {
     expect(linkedList.find({ value: 2, customValue: 'test5' })).toBeNull();
   });
 
+  it('should find preferring callback over compare function', () => {
+    const greaterThan = (value, compareTo) => (value > compareTo ? 0 : 1);
+
+    const linkedList = new LinkedList(greaterThan);
+    linkedList.fromArray([1, 2, 3, 4, 5]);
+
+    let node = linkedList.find({ value: 3 });
+    expect(node.value).toBe(4);
+
+    node = linkedList.find({ callback: value => value < 3 });
+    expect(node.value).toBe(1);
+  });
+
+  it('should convert to array', () => {
+    const linkedList = new LinkedList();
+
+    linkedList.append(1);
+    linkedList.append(2);
+    linkedList.append(3);
+
+    expect(linkedList.toArray().join(',')).toBe('1,2,3');
+  });
+  
   it('should reverse linked list', () => {
     const linkedList = new LinkedList();
 

From 431560a4e50040e9927e60bece01f0276e2d1683 Mon Sep 17 00:00:00 2001
From: Askhat Arslanov <caelestes@yandex.ru>
Date: Thu, 17 Dec 2020 11:40:05 +0300
Subject: [PATCH 038/264] Translate Linked List Traversal to Russian (#283)

Co-authored-by: Askhat <caelestes961@gmail.com>
---
 .../linked-list/traversal/README.md           |  5 ++++-
 .../linked-list/traversal/README.ru-RU.md     | 19 +++++++++++++++++++
 2 files changed, 23 insertions(+), 1 deletion(-)
 create mode 100644 src/algorithms/linked-list/traversal/README.ru-RU.md

diff --git a/src/algorithms/linked-list/traversal/README.md b/src/algorithms/linked-list/traversal/README.md
index 25609518f8..2416323dd8 100644
--- a/src/algorithms/linked-list/traversal/README.md
+++ b/src/algorithms/linked-list/traversal/README.md
@@ -1,8 +1,11 @@
 # Linked List Traversal
 
+_Read this in other languages:_
+[_Русский_](README.ru-RU.md)
+
 The task is to traverse the given linked list in straight order.
 
-For example for the following linked list: 
+For example for the following linked list:
 
 ![](https://upload.wikimedia.org/wikipedia/commons/6/6d/Singly-linked-list.svg)
 
diff --git a/src/algorithms/linked-list/traversal/README.ru-RU.md b/src/algorithms/linked-list/traversal/README.ru-RU.md
new file mode 100644
index 0000000000..e4587bf6af
--- /dev/null
+++ b/src/algorithms/linked-list/traversal/README.ru-RU.md
@@ -0,0 +1,19 @@
+# Обход связного списка
+
+Задача состоит в том, чтобы обойти связный список в прямом порядке.
+
+Например, для следующего связного списка:
+
+![](https://upload.wikimedia.org/wikipedia/commons/6/6d/Singly-linked-list.svg)
+
+Порядок обхода будет такой:
+
+```text
+12 → 99 → 37
+```
+
+Временная сложность - `O(n)`, потому что мы посещаем каждый узел только один раз.
+
+## Ссылки
+
+- [Wikipedia](https://ru.wikipedia.org/wiki/%D0%A1%D0%B2%D1%8F%D0%B7%D0%BD%D1%8B%D0%B9_%D1%81%D0%BF%D0%B8%D1%81%D0%BE%D0%BA)

From 536f75a52fde251d98bd52bdc764e79694acdfb3 Mon Sep 17 00:00:00 2001
From: lvzhenbang <lvzhenbang@outlook.com>
Date: Thu, 17 Dec 2020 16:48:19 +0800
Subject: [PATCH 039/264] update desc (#371)

* update desc

* text error
---
 src/data-structures/queue/README.zh-CN.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/data-structures/queue/README.zh-CN.md b/src/data-structures/queue/README.zh-CN.md
index df8d38c75d..d61a2c7dac 100644
--- a/src/data-structures/queue/README.zh-CN.md
+++ b/src/data-structures/queue/README.zh-CN.md
@@ -2,7 +2,7 @@
 
 在计算机科学中, 一个 **队列(queue)** 是一种特殊类型的抽象数据类型或集合。集合中的实体按顺序保存。
 
-队列基本操作有两种: 向队列的后端位置添加实体，称为入队，并从队列的前端位置移除实体，称为出队。
+队列基本操作有两种：入队和出队。从队列的后端位置添加实体，称为入队；从队列的前端位置移除实体，称为出队。
 
 
 队列中元素先进先出 FIFO (first in, first out)的示意

From d87502b5fd155b116ce0bc17b18e6b43ed3f27aa Mon Sep 17 00:00:00 2001
From: Alexander Belov <ipritoflex@yandex.ru>
Date: Thu, 17 Dec 2020 11:48:43 +0300
Subject: [PATCH 040/264] Update README.md (#385)

Co-authored-by: Oleksii Trekhleb <trehleb@gmail.com>

From de1cc0b0479b5e7dd2e28d2487eea6d3d207e5e4 Mon Sep 17 00:00:00 2001
From: Luan Caldas <luanpignat@gmail.com>
Date: Thu, 17 Dec 2020 05:49:11 -0300
Subject: [PATCH 041/264] Translate pt-BR (#386)

Co-authored-by: Oleksii Trekhleb <trehleb@gmail.com>
---
 README.pt-BR.md | 12 ++++++------
 1 file changed, 6 insertions(+), 6 deletions(-)

diff --git a/README.pt-BR.md b/README.pt-BR.md
index 66894582e1..17899af1d9 100644
--- a/README.pt-BR.md
+++ b/README.pt-BR.md
@@ -35,7 +35,7 @@ os dados.
 * `B` [Lista Encadeada (Linked List)](src/data-structures/linked-list/README.pt-BR.md)
 * `B` [Lista Duplamente Ligada (Doubly Linked List)](src/data-structures/doubly-linked-list/README.pt-BR.md)
 * `B` [Fila (Queue)](src/data-structures/queue/README.pt-BR.md)
-* `B` [Stack](src/data-structures/stack/README.pt-BR.md)
+* `B` [Pilha (Stack)](src/data-structures/stack/README.pt-BR.md)
 * `B` [Tabela de Hash (Hash Table)](src/data-structures/hash-table/README.pt-BR.md)
 * `B` [Heap](src/data-structures/heap/README.pt-BR.md)
 * `B` [Fila de Prioridade (Priority Queue)](src/data-structures/priority-queue/README.pt-BR.md)
@@ -46,7 +46,7 @@ os dados.
   * `A` [Árvore Vermelha-Preta (Red-Black Tree)](src/data-structures/tree/red-black-tree/README.pt-BR.md)
   * `A` [Árvore de Segmento (Segment Tree)](src/data-structures/tree/segment-tree/README.pt-BR.md) - com exemplos de consultas min / max / sum range
   * `A` [Árvore Fenwick (Fenwick Tree)](src/data-structures/tree/fenwick-tree/README.pt-BR.md) (Árvore indexada binária)
-* `A` [Gráfico (Graph)](src/data-structures/graph/README.pt-BR.md) (ambos dirigidos e não direcionados)
+* `A` [Grafo (Graph)](src/data-structures/graph/README.pt-BR.md) (ambos dirigidos e não direcionados)
 * `A` [Conjunto Disjuntor (Disjoint Set)](src/data-structures/disjoint-set/README.pt-BR.md)
 * `A` [Filtro Bloom (Bloom Filter)](src/data-structures/bloom-filter/README.pt-BR.md)
 
@@ -110,7 +110,7 @@ um conjunto de regras que define precisamente uma sequência de operações.
 * **Arvóres**
   * `B` [Depth-First Search](src/algorithms/tree/depth-first-search) (DFS)
   * `B` [Breadth-First Search](src/algorithms/tree/breadth-first-search) (BFS)
-* **Gráficos**
+* **Grafos**
   * `B` [Depth-First Search](src/algorithms/graph/depth-first-search) (DFS)
   * `B` [Breadth-First Search](src/algorithms/graph/breadth-first-search) (BFS)
   * `B` [Kruskal’s Algorithm](src/algorithms/graph/kruskal) - encontrando Árvore Mínima de Abrangência (MST) para grafo não direcionado ponderado
@@ -154,8 +154,8 @@ algoritmo é uma abstração maior que um programa de computador.
   * `A` [Dijkstra Algorithm](src/algorithms/graph/dijkstra) - finding shortest path to all graph vertices
   * `A` [Prim’s Algorithm](src/algorithms/graph/prim) - encontrando Árvore Mínima de Abrangência (MST) para grafo não direcionado ponderado
   * `A` [Kruskal’s Algorithm](src/algorithms/graph/kruskal) - encontrando Árvore Mínima de Abrangência (MST) para grafo não direcionado ponderado
-* **Divide and Conquer** - dividir o problema em partes menores e depois resolver essas partes
-  * `B` [Binary Search](src/algorithms/search/binary-search)
+* **Dividir p/ Conquistar** - dividir o problema em partes menores e depois resolver essas partes
+  * `B` [Busca binária (Binary Search)](src/algorithms/search/binary-search)
   * `B` [Tower of Hanoi](src/algorithms/uncategorized/hanoi-tower)
   * `B` [Pascal's Triangle](src/algorithms/math/pascal-triangle)
   * `B` [Euclidean Algorithm](src/algorithms/math/euclidean-algorithm) - calculate the Greatest Common Divisor (GCD)
@@ -166,7 +166,7 @@ algoritmo é uma abstração maior que um programa de computador.
   * `B` [Jump Game](src/algorithms/uncategorized/jump-game)
   * `A` [Permutations](src/algorithms/sets/permutations) (com e sem repetições)
   * `A` [Combinations](src/algorithms/sets/combinations) (com e sem repetições)
-* **Dynamic Programming** - criar uma solução usando sub-soluções encontradas anteriormente
+* **Programação Dinâmica** - criar uma solução usando sub-soluções encontradas anteriormente
   * `B` [Fibonacci Number](src/algorithms/math/fibonacci)
   * `B` [Jump Game](src/algorithms/uncategorized/jump-game)
   * `B` [Unique Paths](src/algorithms/uncategorized/unique-paths)

From e220450d7d35bd59b344a9ed640100c370dca79c Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Thu, 17 Dec 2020 09:49:57 +0100
Subject: [PATCH 042/264] Code style fixes.

---
 src/algorithms/linked-list/traversal/README.md              | 2 +-
 src/algorithms/linked-list/traversal/README.ru-RU.md        | 2 +-
 src/data-structures/linked-list/__test__/LinkedList.test.js | 6 ++----
 3 files changed, 4 insertions(+), 6 deletions(-)

diff --git a/src/algorithms/linked-list/traversal/README.md b/src/algorithms/linked-list/traversal/README.md
index 2416323dd8..79e7b43626 100644
--- a/src/algorithms/linked-list/traversal/README.md
+++ b/src/algorithms/linked-list/traversal/README.md
@@ -7,7 +7,7 @@ The task is to traverse the given linked list in straight order.
 
 For example for the following linked list:
 
-![](https://upload.wikimedia.org/wikipedia/commons/6/6d/Singly-linked-list.svg)
+![Singly linked list](https://upload.wikimedia.org/wikipedia/commons/6/6d/Singly-linked-list.svg)
 
 The order of traversal should be:
 
diff --git a/src/algorithms/linked-list/traversal/README.ru-RU.md b/src/algorithms/linked-list/traversal/README.ru-RU.md
index e4587bf6af..fa3cfb2fb1 100644
--- a/src/algorithms/linked-list/traversal/README.ru-RU.md
+++ b/src/algorithms/linked-list/traversal/README.ru-RU.md
@@ -4,7 +4,7 @@
 
 Например, для следующего связного списка:
 
-![](https://upload.wikimedia.org/wikipedia/commons/6/6d/Singly-linked-list.svg)
+![Singly linked list](https://upload.wikimedia.org/wikipedia/commons/6/6d/Singly-linked-list.svg)
 
 Порядок обхода будет такой:
 
diff --git a/src/data-structures/linked-list/__test__/LinkedList.test.js b/src/data-structures/linked-list/__test__/LinkedList.test.js
index bce06f727e..f4eb83e2bd 100644
--- a/src/data-structures/linked-list/__test__/LinkedList.test.js
+++ b/src/data-structures/linked-list/__test__/LinkedList.test.js
@@ -227,20 +227,18 @@ describe('LinkedList', () => {
     let node = linkedList.find({ value: 3 });
     expect(node.value).toBe(4);
 
-    node = linkedList.find({ callback: value => value < 3 });
+    node = linkedList.find({ callback: (value) => value < 3 });
     expect(node.value).toBe(1);
   });
 
   it('should convert to array', () => {
     const linkedList = new LinkedList();
-
     linkedList.append(1);
     linkedList.append(2);
     linkedList.append(3);
-
     expect(linkedList.toArray().join(',')).toBe('1,2,3');
   });
-  
+
   it('should reverse linked list', () => {
     const linkedList = new LinkedList();
 

From 2c81debb477744d5bb28d0290c16ebf4b3d0197c Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Sat, 19 Dec 2020 18:45:14 +0100
Subject: [PATCH 043/264] Add Matrices section with basic Matrix operations
 (multiplication, transposition, etc.)

---
 README.md                                     |   1 +
 .../cryptography/hill-cipher/hillCipher.js    |  45 +-
 src/algorithms/math/matrix/Matrix.js          | 309 ++++++++++++
 src/algorithms/math/matrix/README.md          |  63 +++
 .../math/matrix/__tests__/Matrix.test.js      | 455 ++++++++++++++++++
 5 files changed, 852 insertions(+), 21 deletions(-)
 create mode 100644 src/algorithms/math/matrix/Matrix.js
 create mode 100644 src/algorithms/math/matrix/README.md
 create mode 100644 src/algorithms/math/matrix/__tests__/Matrix.test.js

diff --git a/README.md b/README.md
index 784dcd7ca6..454d70ff61 100644
--- a/README.md
+++ b/README.md
@@ -77,6 +77,7 @@ a set of rules that precisely define a sequence of operations.
   * `B` [Radian & Degree](src/algorithms/math/radian) - radians to degree and backwards conversion
   * `B` [Fast Powering](src/algorithms/math/fast-powering)
   * `B` [Horner's method](src/algorithms/math/horner-method) - polynomial evaluation
+  * `B` [Matrices](src/algorithms/math/matrix) - matrices and basic matrix operations (multiplication, transposition, etc.)
   * `A` [Integer Partition](src/algorithms/math/integer-partition)
   * `A` [Square Root](src/algorithms/math/square-root) - Newton's method
   * `A` [Liu Hui π Algorithm](src/algorithms/math/liu-hui) - approximate π calculations based on N-gons
diff --git a/src/algorithms/cryptography/hill-cipher/hillCipher.js b/src/algorithms/cryptography/hill-cipher/hillCipher.js
index f776db6224..1fe3033860 100644
--- a/src/algorithms/cryptography/hill-cipher/hillCipher.js
+++ b/src/algorithms/cryptography/hill-cipher/hillCipher.js
@@ -1,3 +1,5 @@
+import * as mtrx from '../../math/matrix/Matrix';
+
 // The code of an 'A' character (equals to 65).
 const alphabetCodeShift = 'A'.codePointAt(0);
 const englishAlphabetSize = 26;
@@ -15,33 +17,36 @@ const generateKeyMatrix = (keyString) => {
       'Invalid key string length. The square root of the key string must be an integer',
     );
   }
-  const keyMatrix = [];
   let keyStringIndex = 0;
-  for (let i = 0; i < matrixSize; i += 1) {
-    const keyMatrixRow = [];
-    for (let j = 0; j < matrixSize; j += 1) {
+  return mtrx.generate(
+    [matrixSize, matrixSize],
+    // Callback to get a value of each matrix cell.
+    // The order the matrix is being filled in is from left to right, from top to bottom.
+    () => {
       // A → 0, B → 1, ..., a → 32, b → 33, ...
       const charCodeShifted = (keyString.codePointAt(keyStringIndex)) % alphabetCodeShift;
-      keyMatrixRow.push(charCodeShifted);
       keyStringIndex += 1;
-    }
-    keyMatrix.push(keyMatrixRow);
-  }
-  return keyMatrix;
+      return charCodeShifted;
+    },
+  );
 };
 
 /**
  * Generates a message vector from a given message.
  *
  * @param {string} message - the message to encrypt.
- * @return {number[]} messageVector
+ * @return {number[][]} messageVector
  */
 const generateMessageVector = (message) => {
-  const messageVector = [];
-  for (let i = 0; i < message.length; i += 1) {
-    messageVector.push(message.codePointAt(i) % alphabetCodeShift);
-  }
-  return messageVector;
+  return mtrx.generate(
+    [message.length, 1],
+    // Callback to get a value of each matrix cell.
+    // The order the matrix is being filled in is from left to right, from top to bottom.
+    (cellIndices) => {
+      const rowIndex = cellIndices[0];
+      return message.codePointAt(rowIndex) % alphabetCodeShift;
+    },
+  );
 };
 
 /**
@@ -59,19 +64,17 @@ export function hillCipherEncrypt(message, keyString) {
   }
 
   const keyMatrix = generateKeyMatrix(keyString);
+  const messageVector = generateMessageVector(message);
 
   // keyString.length must equal to square of message.length
   if (keyMatrix.length !== message.length) {
     throw new Error('Invalid key string length. The key length must be a square of message length');
   }
 
-  const messageVector = generateMessageVector(message);
+  const cipherVector = mtrx.dot(keyMatrix, messageVector);
   let cipherString = '';
-  for (let row = 0; row < keyMatrix.length; row += 1) {
-    let item = 0;
-    for (let column = 0; column < keyMatrix.length; column += 1) {
-      item += keyMatrix[row][column] * messageVector[column];
-    }
+  for (let row = 0; row < cipherVector.length; row += 1) {
+    const item = cipherVector[row];
     cipherString += String.fromCharCode((item % englishAlphabetSize) + alphabetCodeShift);
   }
 
diff --git a/src/algorithms/math/matrix/Matrix.js b/src/algorithms/math/matrix/Matrix.js
new file mode 100644
index 0000000000..2470eb3913
--- /dev/null
+++ b/src/algorithms/math/matrix/Matrix.js
@@ -0,0 +1,309 @@
+/**
+ * @typedef {number} Cell
+ * @typedef {Cell[][]|Cell[][][]} Matrix
+ * @typedef {number[]} Shape
+ * @typedef {number[]} CellIndices
+ */
+
+/**
+ * Gets the matrix's shape.
+ *
+ * @param {Matrix} m
+ * @returns {Shape}
+ */
+export const shape = (m) => {
+  const shapes = [];
+  let dimension = m;
+  while (dimension && Array.isArray(dimension)) {
+    shapes.push(dimension.length);
+    dimension = (dimension.length && [...dimension][0]) || null;
+  }
+  return shapes;
+};
+
+/**
+ * Checks if matrix has a correct type.
+ *
+ * @param {Matrix} m
+ * @throws {Error}
+ */
+const validateType = (m) => {
+  if (
+    !m
+    || !Array.isArray(m)
+    || !Array.isArray(m[0])
+  ) {
+    throw new Error('Invalid matrix format');
+  }
+};
+
+/**
+ * Checks if matrix is two dimensional.
+ *
+ * @param {Matrix} m
+ * @throws {Error}
+ */
+const validate2D = (m) => {
+  validateType(m);
+  const aShape = shape(m);
+  if (aShape.length !== 2) {
+    throw new Error('Matrix is not of 2D shape');
+  }
+};
+
+/**
+ * Validates that matrices are of the same shape.
+ *
+ * @param {Matrix} a
+ * @param {Matrix} b
+ * @trows {Error}
+ */
+const validateSameShape = (a, b) => {
+  validateType(a);
+  validateType(b);
+
+  const aShape = shape(a);
+  const bShape = shape(b);
+
+  if (aShape.length !== bShape.length) {
+    throw new Error('Matrices have different dimensions');
+  }
+
+  while (aShape.length && bShape.length) {
+    if (aShape.pop() !== bShape.pop()) {
+      throw new Error('Matrices have different shapes');
+    }
+  }
+};
+
+/**
+ * Generates the matrix of specific shape with specific values.
+ *
+ * @param {Shape} mShape - the shape of the matrix to generate
+ * @param {function({CellIndex}): Cell} fill - cell values of a generated matrix.
+ * @returns {Matrix}
+ */
+export const generate = (mShape, fill) => {
+  /**
+   * Generates the matrix recursively.
+   *
+   * @param {Shape} recShape - the shape of the matrix to generate
+   * @param {CellIndices} recIndices
+   * @returns {Matrix}
+   */
+  const generateRecursively = (recShape, recIndices) => {
+    if (recShape.length === 1) {
+      return Array(recShape[0])
+        .fill(null)
+        .map((cellValue, cellIndex) => fill([...recIndices, cellIndex]));
+    }
+    const m = [];
+    for (let i = 0; i < recShape[0]; i += 1) {
+      m.push(generateRecursively(recShape.slice(1), [...recIndices, i]));
+    }
+    return m;
+  };
+
+  return generateRecursively(mShape, []);
+};
+
+/**
+ * Generates the matrix of zeros of specified shape.
+ *
+ * @param {Shape} mShape - shape of the matrix
+ * @returns {Matrix}
+ */
+export const zeros = (mShape) => {
+  return generate(mShape, () => 0);
+};
+
+/**
+ * @param {Matrix} a
+ * @param {Matrix} b
+ * @return Matrix
+ * @throws {Error}
+ */
+export const dot = (a, b) => {
+  // Validate inputs.
+  validate2D(a);
+  validate2D(b);
+
+  // Check dimensions.
+  const aShape = shape(a);
+  const bShape = shape(b);
+  if (aShape[1] !== bShape[0]) {
+    throw new Error('Matrices have incompatible shape for multiplication');
+  }
+
+  // Perform matrix multiplication.
+  const outputShape = [aShape[0], bShape[1]];
+  const c = zeros(outputShape);
+
+  for (let bCol = 0; bCol < b[0].length; bCol += 1) {
+    for (let aRow = 0; aRow < a.length; aRow += 1) {
+      let cellSum = 0;
+      for (let aCol = 0; aCol < a[aRow].length; aCol += 1) {
+        cellSum += a[aRow][aCol] * b[aCol][bCol];
+      }
+      c[aRow][bCol] = cellSum;
+    }
+  }
+
+  return c;
+};
+
+/**
+ * Transposes the matrix.
+ *
+ * @param {Matrix} m
+ * @returns Matrix
+ * @throws {Error}
+ */
+export const t = (m) => {
+  validate2D(m);
+  const mShape = shape(m);
+  const transposed = zeros([mShape[1], mShape[0]]);
+  for (let row = 0; row < m.length; row += 1) {
+    for (let col = 0; col < m[0].length; col += 1) {
+      transposed[col][row] = m[row][col];
+    }
+  }
+  return transposed;
+};
+
+/**
+ * Traverses the matrix.
+ *
+ * @param {Matrix} m
+ * @param {function(indices: CellIndices, c: Cell)} visit
+ */
+const walk = (m, visit) => {
+  /**
+   * Traverses the matrix recursively.
+   *
+   * @param {Matrix} recM
+   * @param {CellIndices} cellIndices
+   * @return {Matrix}
+   */
+  const recWalk = (recM, cellIndices) => {
+    const recMShape = shape(recM);
+
+    if (recMShape.length === 1) {
+      for (let i = 0; i < recM.length; i += 1) {
+        visit([...cellIndices, i], recM[i]);
+      }
+    }
+    for (let i = 0; i < recM.length; i += 1) {
+      recWalk(recM[i], [...cellIndices, i]);
+    }
+  };
+
+  recWalk(m, []);
+};
+
+/**
+ * Gets the matrix cell value at specific index.
+ *
+ * @param {Matrix} m - Matrix that contains the cell that needs to be updated
+ * @param {CellIndices} cellIndices - Array of cell indices
+ * @return {Cell}
+ */
+const getCellAtIndex = (m, cellIndices) => {
+  // We start from the row at specific index.
+  let cell = m[cellIndices[0]];
+  // Going deeper into the next dimensions but not to the last one to preserve
+  // the pointer to the last dimension array.
+  for (let dimIdx = 1; dimIdx < cellIndices.length - 1; dimIdx += 1) {
+    cell = cell[cellIndices[dimIdx]];
+  }
+  // At this moment the cell variable points to the array at the last needed dimension.
+  return cell[cellIndices[cellIndices.length - 1]];
+};
+
+/**
+ * Update the matrix cell at specific index.
+ *
+ * @param {Matrix} m - Matrix that contains the cell that needs to be updated
+ * @param {CellIndices} cellIndices - Array of cell indices
+ * @param {Cell} cellValue - New cell value
+ */
+const updateCellAtIndex = (m, cellIndices, cellValue) => {
+  // We start from the row at specific index.
+  let cell = m[cellIndices[0]];
+  // Going deeper into the next dimensions but not to the last one to preserve
+  // the pointer to the last dimension array.
+  for (let dimIdx = 1; dimIdx < cellIndices.length - 1; dimIdx += 1) {
+    cell = cell[cellIndices[dimIdx]];
+  }
+  // At this moment the cell variable points to the array at the last needed dimension.
+  cell[cellIndices[cellIndices.length - 1]] = cellValue;
+};
+
+/**
+ * Adds two matrices element-wise.
+ *
+ * @param {Matrix} a
+ * @param {Matrix} b
+ * @return {Matrix}
+ */
+export const add = (a, b) => {
+  validateSameShape(a, b);
+  const result = zeros(shape(a));
+
+  walk(a, (cellIndices, cellValue) => {
+    updateCellAtIndex(result, cellIndices, cellValue);
+  });
+
+  walk(b, (cellIndices, cellValue) => {
+    const currentCellValue = getCellAtIndex(result, cellIndices);
+    updateCellAtIndex(result, cellIndices, currentCellValue + cellValue);
+  });
+
+  return result;
+};
+
+/**
+ * Multiplies two matrices element-wise.
+ *
+ * @param {Matrix} a
+ * @param {Matrix} b
+ * @return {Matrix}
+ */
+export const mul = (a, b) => {
+  validateSameShape(a, b);
+  const result = zeros(shape(a));
+
+  walk(a, (cellIndices, cellValue) => {
+    updateCellAtIndex(result, cellIndices, cellValue);
+  });
+
+  walk(b, (cellIndices, cellValue) => {
+    const currentCellValue = getCellAtIndex(result, cellIndices);
+    updateCellAtIndex(result, cellIndices, currentCellValue * cellValue);
+  });
+
+  return result;
+};
+
+/**
+ * Subtract two matrices element-wise.
+ *
+ * @param {Matrix} a
+ * @param {Matrix} b
+ * @return {Matrix}
+ */
+export const sub = (a, b) => {
+  validateSameShape(a, b);
+  const result = zeros(shape(a));
+
+  walk(a, (cellIndices, cellValue) => {
+    updateCellAtIndex(result, cellIndices, cellValue);
+  });
+
+  walk(b, (cellIndices, cellValue) => {
+    const currentCellValue = getCellAtIndex(result, cellIndices);
+    updateCellAtIndex(result, cellIndices, currentCellValue - cellValue);
+  });
+
+  return result;
+};
diff --git a/src/algorithms/math/matrix/README.md b/src/algorithms/math/matrix/README.md
new file mode 100644
index 0000000000..8e084403b0
--- /dev/null
+++ b/src/algorithms/math/matrix/README.md
@@ -0,0 +1,63 @@
+# Matrices
+
+In mathematics, a **matrix** (plural **matrices**) is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns. For example, the dimension of the matrix below is `2 × 3` (read "two by three"), because there are two rows and three columns:
+
+```
+| 1  9 -13 |
+| 20 5 -6  |
+```
+
+![An `m × n` matrix](https://upload.wikimedia.org/wikipedia/commons/b/bf/Matris.png)
+
+An `m × n` matrix: the `m` rows are horizontal, and the `n` columns are vertical. Each element of a matrix is often denoted by a variable with two subscripts. For example, <i>a<sub>2,1</sub></i> represents the element at the second row and first column of the matrix
+
+## Operations on matrices
+
+### Addition
+
+To add two matrices: add the numbers in the matching positions:
+
+![Matrices addition](https://www.mathsisfun.com/algebra/images/matrix-addition.gif)
+
+The two matrices must be the same size, i.e. the rows must match in size, and the columns must match in size.
+
+### Subtracting
+
+To subtract two matrices: subtract the numbers in the matching positions:
+
+![Matrices subtraction](https://www.mathsisfun.com/algebra/images/matrix-subtraction.gif)
+
+### Multiply by a Constant
+
+We can multiply a matrix by a constant (the value 2 in this case):
+
+![Matrices multiplication be a constant](https://www.mathsisfun.com/algebra/images/matrix-multiply-constant.gif)
+
+### Multiplying by Another Matrix
+
+To multiply a matrix by another matrix we need to do the [dot product](https://www.mathsisfun.com/algebra/vectors-dot-product.html) of rows and columns.
+
+To work out the answer for the **1st row** and **1st column**:
+
+![Matrices multiplication - 1st step](https://www.mathsisfun.com/algebra/images/matrix-multiply-a.svg)
+
+Here it is for the 1st row and 2nd column:
+
+![Matrices multiplication - 2st step](https://www.mathsisfun.com/algebra/images/matrix-multiply-b.svg)
+
+If we'll do the same for the rest of the rows and columns we'll get the following resulting matrix:
+
+![Matrices multiplication - Result](https://www.mathsisfun.com/algebra/images/matrix-multiply-c.svg)
+
+### Transposing
+
+To "transpose" a matrix, swap the rows and columns.
+
+We put a "T" in the top right-hand corner to mean transpose:
+
+![Transposing](https://www.mathsisfun.com/algebra/images/matrix-transpose.gif)
+
+## References
+
+- [Matrices on MathIsFun](https://www.mathsisfun.com/algebra/matrix-introduction.html)
+- [Matrix on Wikipedia](https://en.wikipedia.org/wiki/Matrix_(mathematics))
diff --git a/src/algorithms/math/matrix/__tests__/Matrix.test.js b/src/algorithms/math/matrix/__tests__/Matrix.test.js
new file mode 100644
index 0000000000..37dc892b0a
--- /dev/null
+++ b/src/algorithms/math/matrix/__tests__/Matrix.test.js
@@ -0,0 +1,455 @@
+import * as mtrx from '../Matrix';
+
+describe('Matrix', () => {
+  it('should throw when trying to add matrices of invalid shapes', () => {
+    expect(
+      () => mtrx.dot([0], [1]),
+    ).toThrowError('Invalid matrix format');
+    expect(
+      () => mtrx.dot([[0]], [1]),
+    ).toThrowError('Invalid matrix format');
+    expect(
+      () => mtrx.dot([[[0]]], [[1]]),
+    ).toThrowError('Matrix is not of 2D shape');
+    expect(
+      () => mtrx.dot([[0]], [[1], [2]]),
+    ).toThrowError('Matrices have incompatible shape for multiplication');
+  });
+
+  it('should calculate matrices dimensions', () => {
+    expect(mtrx.shape([])).toEqual([0]);
+
+    expect(mtrx.shape([
+      [],
+    ])).toEqual([1, 0]);
+
+    expect(mtrx.shape([
+      [0],
+    ])).toEqual([1, 1]);
+
+    expect(mtrx.shape([
+      [0, 0],
+    ])).toEqual([1, 2]);
+
+    expect(mtrx.shape([
+      [0, 0],
+      [0, 0],
+    ])).toEqual([2, 2]);
+
+    expect(mtrx.shape([
+      [0, 0, 0],
+      [0, 0, 0],
+    ])).toEqual([2, 3]);
+
+    expect(mtrx.shape([
+      [0, 0],
+      [0, 0],
+      [0, 0],
+    ])).toEqual([3, 2]);
+
+    expect(mtrx.shape([
+      [0, 0, 0],
+      [0, 0, 0],
+      [0, 0, 0],
+    ])).toEqual([3, 3]);
+
+    expect(mtrx.shape([
+      [0],
+      [0],
+      [0],
+    ])).toEqual([3, 1]);
+
+    expect(mtrx.shape([
+      [[0], [0], [0]],
+      [[0], [0], [0]],
+      [[0], [0], [0]],
+    ])).toEqual([3, 3, 1]);
+
+    expect(mtrx.shape([
+      [[0, 0, 0], [0, 0, 0], [0, 0, 0]],
+      [[0, 0, 0], [0, 0, 0], [0, 0, 0]],
+      [[0, 0, 0], [0, 0, 0], [0, 0, 0]],
+    ])).toEqual([3, 3, 3]);
+  });
+
+  it('should generate the matrix of zeros', () => {
+    expect(mtrx.zeros([1, 0])).toEqual([
+      [],
+    ]);
+
+    expect(mtrx.zeros([1, 1])).toEqual([
+      [0],
+    ]);
+
+    expect(mtrx.zeros([1, 3])).toEqual([
+      [0, 0, 0],
+    ]);
+
+    expect(mtrx.zeros([3, 3])).toEqual([
+      [0, 0, 0],
+      [0, 0, 0],
+      [0, 0, 0],
+    ]);
+
+    expect(mtrx.zeros([3, 3, 1])).toEqual([
+      [[0], [0], [0]],
+      [[0], [0], [0]],
+      [[0], [0], [0]],
+    ]);
+  });
+
+  it('should generate the matrix with custom values', () => {
+    expect(mtrx.generate([1, 0], () => 1)).toEqual([
+      [],
+    ]);
+
+    expect(mtrx.generate([1, 1], () => 1)).toEqual([
+      [1],
+    ]);
+
+    expect(mtrx.generate([1, 3], () => 1)).toEqual([
+      [1, 1, 1],
+    ]);
+
+    expect(mtrx.generate([3, 3], () => 1)).toEqual([
+      [1, 1, 1],
+      [1, 1, 1],
+      [1, 1, 1],
+    ]);
+
+    expect(mtrx.generate([3, 3, 1], () => 1)).toEqual([
+      [[1], [1], [1]],
+      [[1], [1], [1]],
+      [[1], [1], [1]],
+    ]);
+  });
+
+  it('should generate a custom matrix based on specific cell indices', () => {
+    const indicesCallback = jest.fn((indices) => {
+      return indices[0] * 10 + indices[1];
+    });
+    const m = mtrx.generate([3, 3], indicesCallback);
+
+    expect(indicesCallback).toHaveBeenCalledTimes(3 * 3);
+    expect(indicesCallback.mock.calls[0][0]).toEqual([0, 0]);
+    expect(indicesCallback.mock.calls[1][0]).toEqual([0, 1]);
+    expect(indicesCallback.mock.calls[2][0]).toEqual([0, 2]);
+    expect(indicesCallback.mock.calls[3][0]).toEqual([1, 0]);
+    expect(indicesCallback.mock.calls[4][0]).toEqual([1, 1]);
+    expect(indicesCallback.mock.calls[5][0]).toEqual([1, 2]);
+    expect(indicesCallback.mock.calls[6][0]).toEqual([2, 0]);
+    expect(indicesCallback.mock.calls[7][0]).toEqual([2, 1]);
+    expect(indicesCallback.mock.calls[8][0]).toEqual([2, 2]);
+    expect(m).toEqual([
+      [0, 1, 2],
+      [10, 11, 12],
+      [20, 21, 22],
+    ]);
+  });
+
+  it('should multiply two matrices', () => {
+    let c;
+    c = mtrx.dot(
+      [
+        [1, 2],
+        [3, 4],
+      ],
+      [
+        [5, 6],
+        [7, 8],
+      ],
+    );
+    expect(mtrx.shape(c)).toEqual([2, 2]);
+    expect(c).toEqual([
+      [19, 22],
+      [43, 50],
+    ]);
+
+    c = mtrx.dot(
+      [
+        [1, 2],
+        [3, 4],
+      ],
+      [
+        [5],
+        [6],
+      ],
+    );
+    expect(mtrx.shape(c)).toEqual([2, 1]);
+    expect(c).toEqual([
+      [17],
+      [39],
+    ]);
+
+    c = mtrx.dot(
+      [
+        [1, 2, 3],
+        [4, 5, 6],
+      ],
+      [
+        [7, 8],
+        [9, 10],
+        [11, 12],
+      ],
+    );
+    expect(mtrx.shape(c)).toEqual([2, 2]);
+    expect(c).toEqual([
+      [58, 64],
+      [139, 154],
+    ]);
+
+    c = mtrx.dot(
+      [
+        [3, 4, 2],
+      ],
+      [
+        [13, 9, 7, 5],
+        [8, 7, 4, 6],
+        [6, 4, 0, 3],
+      ],
+    );
+    expect(mtrx.shape(c)).toEqual([1, 4]);
+    expect(c).toEqual([
+      [83, 63, 37, 45],
+    ]);
+  });
+
+  it('should transpose matrices', () => {
+    expect(mtrx.t([[1, 2, 3]])).toEqual([
+      [1],
+      [2],
+      [3],
+    ]);
+
+    expect(mtrx.t([
+      [1],
+      [2],
+      [3],
+    ])).toEqual([
+      [1, 2, 3],
+    ]);
+
+    expect(mtrx.t([
+      [1, 2, 3],
+      [4, 5, 6],
+    ])).toEqual([
+      [1, 4],
+      [2, 5],
+      [3, 6],
+    ]);
+
+    expect(mtrx.t([
+      [1, 2, 3],
+      [4, 5, 6],
+      [7, 8, 9],
+    ])).toEqual([
+      [1, 4, 7],
+      [2, 5, 8],
+      [3, 6, 9],
+    ]);
+  });
+
+  it('should throw when trying to transpose non 2D matrix', () => {
+    expect(() => {
+      mtrx.t([[[1]]]);
+    }).toThrowError('Matrix is not of 2D shape');
+  });
+
+  it('should add two matrices', () => {
+    expect(mtrx.add([[1]], [[2]])).toEqual([[3]]);
+
+    expect(mtrx.add(
+      [[1, 2, 3]],
+      [[4, 5, 6]],
+    ))
+      .toEqual(
+        [[5, 7, 9]],
+      );
+
+    expect(mtrx.add(
+      [[1], [2], [3]],
+      [[4], [5], [6]],
+    ))
+      .toEqual(
+        [[5], [7], [9]],
+      );
+
+    expect(mtrx.add(
+      [
+        [1, 2, 3],
+        [4, 5, 6],
+        [7, 8, 9],
+      ],
+      [
+        [10, 11, 12],
+        [13, 14, 15],
+        [16, 17, 18],
+      ],
+    ))
+      .toEqual(
+        [
+          [11, 13, 15],
+          [17, 19, 21],
+          [23, 25, 27],
+        ],
+      );
+
+    expect(mtrx.add(
+      [
+        [[1], [2], [3]],
+        [[4], [5], [6]],
+        [[7], [8], [9]],
+      ],
+      [
+        [[10], [11], [12]],
+        [[13], [14], [15]],
+        [[16], [17], [18]],
+      ],
+    ))
+      .toEqual(
+        [
+          [[11], [13], [15]],
+          [[17], [19], [21]],
+          [[23], [25], [27]],
+        ],
+      );
+  });
+
+  it('should throw when trying to add matrices of different shape', () => {
+    expect(() => mtrx.add([[0]], [[[0]]])).toThrowError(
+      'Matrices have different dimensions',
+    );
+
+    expect(() => mtrx.add([[0]], [[0, 0]])).toThrowError(
+      'Matrices have different shapes',
+    );
+  });
+
+  it('should do element wise multiplication two matrices', () => {
+    expect(mtrx.mul([[2]], [[3]])).toEqual([[6]]);
+
+    expect(mtrx.mul(
+      [[1, 2, 3]],
+      [[4, 5, 6]],
+    ))
+      .toEqual(
+        [[4, 10, 18]],
+      );
+
+    expect(mtrx.mul(
+      [[1], [2], [3]],
+      [[4], [5], [6]],
+    ))
+      .toEqual(
+        [[4], [10], [18]],
+      );
+
+    expect(mtrx.mul(
+      [
+        [1, 2],
+        [3, 4],
+      ],
+      [
+        [5, 6],
+        [7, 8],
+      ],
+    ))
+      .toEqual(
+        [
+          [5, 12],
+          [21, 32],
+        ],
+      );
+
+    expect(mtrx.mul(
+      [
+        [[1], [2]],
+        [[3], [4]],
+      ],
+      [
+        [[5], [6]],
+        [[7], [8]],
+      ],
+    ))
+      .toEqual(
+        [
+          [[5], [12]],
+          [[21], [32]],
+        ],
+      );
+  });
+
+  it('should throw when trying to multiply matrices element-wise of different shape', () => {
+    expect(() => mtrx.mul([[0]], [[[0]]])).toThrowError(
+      'Matrices have different dimensions',
+    );
+
+    expect(() => mtrx.mul([[0]], [[0, 0]])).toThrowError(
+      'Matrices have different shapes',
+    );
+  });
+
+  it('should do element wise subtraction two matrices', () => {
+    expect(mtrx.sub([[3]], [[2]])).toEqual([[1]]);
+
+    expect(mtrx.sub(
+      [[10, 12, 14]],
+      [[4, 5, 6]],
+    ))
+      .toEqual(
+        [[6, 7, 8]],
+      );
+
+    expect(mtrx.sub(
+      [[[10], [12], [14]]],
+      [[[4], [5], [6]]],
+    ))
+      .toEqual(
+        [[[6], [7], [8]]],
+      );
+
+    expect(mtrx.sub(
+      [
+        [10, 20],
+        [30, 40],
+      ],
+      [
+        [5, 6],
+        [7, 8],
+      ],
+    ))
+      .toEqual(
+        [
+          [5, 14],
+          [23, 32],
+        ],
+      );
+
+    expect(mtrx.sub(
+      [
+        [[10], [20]],
+        [[30], [40]],
+      ],
+      [
+        [[5], [6]],
+        [[7], [8]],
+      ],
+    ))
+      .toEqual(
+        [
+          [[5], [14]],
+          [[23], [32]],
+        ],
+      );
+  });
+
+  it('should throw when trying to subtract matrices element-wise of different shape', () => {
+    expect(() => mtrx.sub([[0]], [[[0]]])).toThrowError(
+      'Matrices have different dimensions',
+    );
+
+    expect(() => mtrx.sub([[0]], [[0, 0]])).toThrowError(
+      'Matrices have different shapes',
+    );
+  });
+});

From 8d52ae5d03fec152c715ef2a018d5d4b502c1488 Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Sat, 19 Dec 2020 18:48:10 +0100
Subject: [PATCH 044/264] Add Matrices section with basic Matrix operations
 (multiplication, transposition, etc.) (#600)

---
 README.md                                     |   1 +
 .../cryptography/hill-cipher/hillCipher.js    |  45 +-
 src/algorithms/math/matrix/Matrix.js          | 309 ++++++++++++
 src/algorithms/math/matrix/README.md          |  63 +++
 .../math/matrix/__tests__/Matrix.test.js      | 455 ++++++++++++++++++
 5 files changed, 852 insertions(+), 21 deletions(-)
 create mode 100644 src/algorithms/math/matrix/Matrix.js
 create mode 100644 src/algorithms/math/matrix/README.md
 create mode 100644 src/algorithms/math/matrix/__tests__/Matrix.test.js

diff --git a/README.md b/README.md
index 784dcd7ca6..454d70ff61 100644
--- a/README.md
+++ b/README.md
@@ -77,6 +77,7 @@ a set of rules that precisely define a sequence of operations.
   * `B` [Radian & Degree](src/algorithms/math/radian) - radians to degree and backwards conversion
   * `B` [Fast Powering](src/algorithms/math/fast-powering)
   * `B` [Horner's method](src/algorithms/math/horner-method) - polynomial evaluation
+  * `B` [Matrices](src/algorithms/math/matrix) - matrices and basic matrix operations (multiplication, transposition, etc.)
   * `A` [Integer Partition](src/algorithms/math/integer-partition)
   * `A` [Square Root](src/algorithms/math/square-root) - Newton's method
   * `A` [Liu Hui π Algorithm](src/algorithms/math/liu-hui) - approximate π calculations based on N-gons
diff --git a/src/algorithms/cryptography/hill-cipher/hillCipher.js b/src/algorithms/cryptography/hill-cipher/hillCipher.js
index f776db6224..1fe3033860 100644
--- a/src/algorithms/cryptography/hill-cipher/hillCipher.js
+++ b/src/algorithms/cryptography/hill-cipher/hillCipher.js
@@ -1,3 +1,5 @@
+import * as mtrx from '../../math/matrix/Matrix';
+
 // The code of an 'A' character (equals to 65).
 const alphabetCodeShift = 'A'.codePointAt(0);
 const englishAlphabetSize = 26;
@@ -15,33 +17,36 @@ const generateKeyMatrix = (keyString) => {
       'Invalid key string length. The square root of the key string must be an integer',
     );
   }
-  const keyMatrix = [];
   let keyStringIndex = 0;
-  for (let i = 0; i < matrixSize; i += 1) {
-    const keyMatrixRow = [];
-    for (let j = 0; j < matrixSize; j += 1) {
+  return mtrx.generate(
+    [matrixSize, matrixSize],
+    // Callback to get a value of each matrix cell.
+    // The order the matrix is being filled in is from left to right, from top to bottom.
+    () => {
       // A → 0, B → 1, ..., a → 32, b → 33, ...
       const charCodeShifted = (keyString.codePointAt(keyStringIndex)) % alphabetCodeShift;
-      keyMatrixRow.push(charCodeShifted);
       keyStringIndex += 1;
-    }
-    keyMatrix.push(keyMatrixRow);
-  }
-  return keyMatrix;
+      return charCodeShifted;
+    },
+  );
 };
 
 /**
  * Generates a message vector from a given message.
  *
  * @param {string} message - the message to encrypt.
- * @return {number[]} messageVector
+ * @return {number[][]} messageVector
  */
 const generateMessageVector = (message) => {
-  const messageVector = [];
-  for (let i = 0; i < message.length; i += 1) {
-    messageVector.push(message.codePointAt(i) % alphabetCodeShift);
-  }
-  return messageVector;
+  return mtrx.generate(
+    [message.length, 1],
+    // Callback to get a value of each matrix cell.
+    // The order the matrix is being filled in is from left to right, from top to bottom.
+    (cellIndices) => {
+      const rowIndex = cellIndices[0];
+      return message.codePointAt(rowIndex) % alphabetCodeShift;
+    },
+  );
 };
 
 /**
@@ -59,19 +64,17 @@ export function hillCipherEncrypt(message, keyString) {
   }
 
   const keyMatrix = generateKeyMatrix(keyString);
+  const messageVector = generateMessageVector(message);
 
   // keyString.length must equal to square of message.length
   if (keyMatrix.length !== message.length) {
     throw new Error('Invalid key string length. The key length must be a square of message length');
   }
 
-  const messageVector = generateMessageVector(message);
+  const cipherVector = mtrx.dot(keyMatrix, messageVector);
   let cipherString = '';
-  for (let row = 0; row < keyMatrix.length; row += 1) {
-    let item = 0;
-    for (let column = 0; column < keyMatrix.length; column += 1) {
-      item += keyMatrix[row][column] * messageVector[column];
-    }
+  for (let row = 0; row < cipherVector.length; row += 1) {
+    const item = cipherVector[row];
     cipherString += String.fromCharCode((item % englishAlphabetSize) + alphabetCodeShift);
   }
 
diff --git a/src/algorithms/math/matrix/Matrix.js b/src/algorithms/math/matrix/Matrix.js
new file mode 100644
index 0000000000..2470eb3913
--- /dev/null
+++ b/src/algorithms/math/matrix/Matrix.js
@@ -0,0 +1,309 @@
+/**
+ * @typedef {number} Cell
+ * @typedef {Cell[][]|Cell[][][]} Matrix
+ * @typedef {number[]} Shape
+ * @typedef {number[]} CellIndices
+ */
+
+/**
+ * Gets the matrix's shape.
+ *
+ * @param {Matrix} m
+ * @returns {Shape}
+ */
+export const shape = (m) => {
+  const shapes = [];
+  let dimension = m;
+  while (dimension && Array.isArray(dimension)) {
+    shapes.push(dimension.length);
+    dimension = (dimension.length && [...dimension][0]) || null;
+  }
+  return shapes;
+};
+
+/**
+ * Checks if matrix has a correct type.
+ *
+ * @param {Matrix} m
+ * @throws {Error}
+ */
+const validateType = (m) => {
+  if (
+    !m
+    || !Array.isArray(m)
+    || !Array.isArray(m[0])
+  ) {
+    throw new Error('Invalid matrix format');
+  }
+};
+
+/**
+ * Checks if matrix is two dimensional.
+ *
+ * @param {Matrix} m
+ * @throws {Error}
+ */
+const validate2D = (m) => {
+  validateType(m);
+  const aShape = shape(m);
+  if (aShape.length !== 2) {
+    throw new Error('Matrix is not of 2D shape');
+  }
+};
+
+/**
+ * Validates that matrices are of the same shape.
+ *
+ * @param {Matrix} a
+ * @param {Matrix} b
+ * @trows {Error}
+ */
+const validateSameShape = (a, b) => {
+  validateType(a);
+  validateType(b);
+
+  const aShape = shape(a);
+  const bShape = shape(b);
+
+  if (aShape.length !== bShape.length) {
+    throw new Error('Matrices have different dimensions');
+  }
+
+  while (aShape.length && bShape.length) {
+    if (aShape.pop() !== bShape.pop()) {
+      throw new Error('Matrices have different shapes');
+    }
+  }
+};
+
+/**
+ * Generates the matrix of specific shape with specific values.
+ *
+ * @param {Shape} mShape - the shape of the matrix to generate
+ * @param {function({CellIndex}): Cell} fill - cell values of a generated matrix.
+ * @returns {Matrix}
+ */
+export const generate = (mShape, fill) => {
+  /**
+   * Generates the matrix recursively.
+   *
+   * @param {Shape} recShape - the shape of the matrix to generate
+   * @param {CellIndices} recIndices
+   * @returns {Matrix}
+   */
+  const generateRecursively = (recShape, recIndices) => {
+    if (recShape.length === 1) {
+      return Array(recShape[0])
+        .fill(null)
+        .map((cellValue, cellIndex) => fill([...recIndices, cellIndex]));
+    }
+    const m = [];
+    for (let i = 0; i < recShape[0]; i += 1) {
+      m.push(generateRecursively(recShape.slice(1), [...recIndices, i]));
+    }
+    return m;
+  };
+
+  return generateRecursively(mShape, []);
+};
+
+/**
+ * Generates the matrix of zeros of specified shape.
+ *
+ * @param {Shape} mShape - shape of the matrix
+ * @returns {Matrix}
+ */
+export const zeros = (mShape) => {
+  return generate(mShape, () => 0);
+};
+
+/**
+ * @param {Matrix} a
+ * @param {Matrix} b
+ * @return Matrix
+ * @throws {Error}
+ */
+export const dot = (a, b) => {
+  // Validate inputs.
+  validate2D(a);
+  validate2D(b);
+
+  // Check dimensions.
+  const aShape = shape(a);
+  const bShape = shape(b);
+  if (aShape[1] !== bShape[0]) {
+    throw new Error('Matrices have incompatible shape for multiplication');
+  }
+
+  // Perform matrix multiplication.
+  const outputShape = [aShape[0], bShape[1]];
+  const c = zeros(outputShape);
+
+  for (let bCol = 0; bCol < b[0].length; bCol += 1) {
+    for (let aRow = 0; aRow < a.length; aRow += 1) {
+      let cellSum = 0;
+      for (let aCol = 0; aCol < a[aRow].length; aCol += 1) {
+        cellSum += a[aRow][aCol] * b[aCol][bCol];
+      }
+      c[aRow][bCol] = cellSum;
+    }
+  }
+
+  return c;
+};
+
+/**
+ * Transposes the matrix.
+ *
+ * @param {Matrix} m
+ * @returns Matrix
+ * @throws {Error}
+ */
+export const t = (m) => {
+  validate2D(m);
+  const mShape = shape(m);
+  const transposed = zeros([mShape[1], mShape[0]]);
+  for (let row = 0; row < m.length; row += 1) {
+    for (let col = 0; col < m[0].length; col += 1) {
+      transposed[col][row] = m[row][col];
+    }
+  }
+  return transposed;
+};
+
+/**
+ * Traverses the matrix.
+ *
+ * @param {Matrix} m
+ * @param {function(indices: CellIndices, c: Cell)} visit
+ */
+const walk = (m, visit) => {
+  /**
+   * Traverses the matrix recursively.
+   *
+   * @param {Matrix} recM
+   * @param {CellIndices} cellIndices
+   * @return {Matrix}
+   */
+  const recWalk = (recM, cellIndices) => {
+    const recMShape = shape(recM);
+
+    if (recMShape.length === 1) {
+      for (let i = 0; i < recM.length; i += 1) {
+        visit([...cellIndices, i], recM[i]);
+      }
+    }
+    for (let i = 0; i < recM.length; i += 1) {
+      recWalk(recM[i], [...cellIndices, i]);
+    }
+  };
+
+  recWalk(m, []);
+};
+
+/**
+ * Gets the matrix cell value at specific index.
+ *
+ * @param {Matrix} m - Matrix that contains the cell that needs to be updated
+ * @param {CellIndices} cellIndices - Array of cell indices
+ * @return {Cell}
+ */
+const getCellAtIndex = (m, cellIndices) => {
+  // We start from the row at specific index.
+  let cell = m[cellIndices[0]];
+  // Going deeper into the next dimensions but not to the last one to preserve
+  // the pointer to the last dimension array.
+  for (let dimIdx = 1; dimIdx < cellIndices.length - 1; dimIdx += 1) {
+    cell = cell[cellIndices[dimIdx]];
+  }
+  // At this moment the cell variable points to the array at the last needed dimension.
+  return cell[cellIndices[cellIndices.length - 1]];
+};
+
+/**
+ * Update the matrix cell at specific index.
+ *
+ * @param {Matrix} m - Matrix that contains the cell that needs to be updated
+ * @param {CellIndices} cellIndices - Array of cell indices
+ * @param {Cell} cellValue - New cell value
+ */
+const updateCellAtIndex = (m, cellIndices, cellValue) => {
+  // We start from the row at specific index.
+  let cell = m[cellIndices[0]];
+  // Going deeper into the next dimensions but not to the last one to preserve
+  // the pointer to the last dimension array.
+  for (let dimIdx = 1; dimIdx < cellIndices.length - 1; dimIdx += 1) {
+    cell = cell[cellIndices[dimIdx]];
+  }
+  // At this moment the cell variable points to the array at the last needed dimension.
+  cell[cellIndices[cellIndices.length - 1]] = cellValue;
+};
+
+/**
+ * Adds two matrices element-wise.
+ *
+ * @param {Matrix} a
+ * @param {Matrix} b
+ * @return {Matrix}
+ */
+export const add = (a, b) => {
+  validateSameShape(a, b);
+  const result = zeros(shape(a));
+
+  walk(a, (cellIndices, cellValue) => {
+    updateCellAtIndex(result, cellIndices, cellValue);
+  });
+
+  walk(b, (cellIndices, cellValue) => {
+    const currentCellValue = getCellAtIndex(result, cellIndices);
+    updateCellAtIndex(result, cellIndices, currentCellValue + cellValue);
+  });
+
+  return result;
+};
+
+/**
+ * Multiplies two matrices element-wise.
+ *
+ * @param {Matrix} a
+ * @param {Matrix} b
+ * @return {Matrix}
+ */
+export const mul = (a, b) => {
+  validateSameShape(a, b);
+  const result = zeros(shape(a));
+
+  walk(a, (cellIndices, cellValue) => {
+    updateCellAtIndex(result, cellIndices, cellValue);
+  });
+
+  walk(b, (cellIndices, cellValue) => {
+    const currentCellValue = getCellAtIndex(result, cellIndices);
+    updateCellAtIndex(result, cellIndices, currentCellValue * cellValue);
+  });
+
+  return result;
+};
+
+/**
+ * Subtract two matrices element-wise.
+ *
+ * @param {Matrix} a
+ * @param {Matrix} b
+ * @return {Matrix}
+ */
+export const sub = (a, b) => {
+  validateSameShape(a, b);
+  const result = zeros(shape(a));
+
+  walk(a, (cellIndices, cellValue) => {
+    updateCellAtIndex(result, cellIndices, cellValue);
+  });
+
+  walk(b, (cellIndices, cellValue) => {
+    const currentCellValue = getCellAtIndex(result, cellIndices);
+    updateCellAtIndex(result, cellIndices, currentCellValue - cellValue);
+  });
+
+  return result;
+};
diff --git a/src/algorithms/math/matrix/README.md b/src/algorithms/math/matrix/README.md
new file mode 100644
index 0000000000..8e084403b0
--- /dev/null
+++ b/src/algorithms/math/matrix/README.md
@@ -0,0 +1,63 @@
+# Matrices
+
+In mathematics, a **matrix** (plural **matrices**) is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns. For example, the dimension of the matrix below is `2 × 3` (read "two by three"), because there are two rows and three columns:
+
+```
+| 1  9 -13 |
+| 20 5 -6  |
+```
+
+![An `m × n` matrix](https://upload.wikimedia.org/wikipedia/commons/b/bf/Matris.png)
+
+An `m × n` matrix: the `m` rows are horizontal, and the `n` columns are vertical. Each element of a matrix is often denoted by a variable with two subscripts. For example, <i>a<sub>2,1</sub></i> represents the element at the second row and first column of the matrix
+
+## Operations on matrices
+
+### Addition
+
+To add two matrices: add the numbers in the matching positions:
+
+![Matrices addition](https://www.mathsisfun.com/algebra/images/matrix-addition.gif)
+
+The two matrices must be the same size, i.e. the rows must match in size, and the columns must match in size.
+
+### Subtracting
+
+To subtract two matrices: subtract the numbers in the matching positions:
+
+![Matrices subtraction](https://www.mathsisfun.com/algebra/images/matrix-subtraction.gif)
+
+### Multiply by a Constant
+
+We can multiply a matrix by a constant (the value 2 in this case):
+
+![Matrices multiplication be a constant](https://www.mathsisfun.com/algebra/images/matrix-multiply-constant.gif)
+
+### Multiplying by Another Matrix
+
+To multiply a matrix by another matrix we need to do the [dot product](https://www.mathsisfun.com/algebra/vectors-dot-product.html) of rows and columns.
+
+To work out the answer for the **1st row** and **1st column**:
+
+![Matrices multiplication - 1st step](https://www.mathsisfun.com/algebra/images/matrix-multiply-a.svg)
+
+Here it is for the 1st row and 2nd column:
+
+![Matrices multiplication - 2st step](https://www.mathsisfun.com/algebra/images/matrix-multiply-b.svg)
+
+If we'll do the same for the rest of the rows and columns we'll get the following resulting matrix:
+
+![Matrices multiplication - Result](https://www.mathsisfun.com/algebra/images/matrix-multiply-c.svg)
+
+### Transposing
+
+To "transpose" a matrix, swap the rows and columns.
+
+We put a "T" in the top right-hand corner to mean transpose:
+
+![Transposing](https://www.mathsisfun.com/algebra/images/matrix-transpose.gif)
+
+## References
+
+- [Matrices on MathIsFun](https://www.mathsisfun.com/algebra/matrix-introduction.html)
+- [Matrix on Wikipedia](https://en.wikipedia.org/wiki/Matrix_(mathematics))
diff --git a/src/algorithms/math/matrix/__tests__/Matrix.test.js b/src/algorithms/math/matrix/__tests__/Matrix.test.js
new file mode 100644
index 0000000000..37dc892b0a
--- /dev/null
+++ b/src/algorithms/math/matrix/__tests__/Matrix.test.js
@@ -0,0 +1,455 @@
+import * as mtrx from '../Matrix';
+
+describe('Matrix', () => {
+  it('should throw when trying to add matrices of invalid shapes', () => {
+    expect(
+      () => mtrx.dot([0], [1]),
+    ).toThrowError('Invalid matrix format');
+    expect(
+      () => mtrx.dot([[0]], [1]),
+    ).toThrowError('Invalid matrix format');
+    expect(
+      () => mtrx.dot([[[0]]], [[1]]),
+    ).toThrowError('Matrix is not of 2D shape');
+    expect(
+      () => mtrx.dot([[0]], [[1], [2]]),
+    ).toThrowError('Matrices have incompatible shape for multiplication');
+  });
+
+  it('should calculate matrices dimensions', () => {
+    expect(mtrx.shape([])).toEqual([0]);
+
+    expect(mtrx.shape([
+      [],
+    ])).toEqual([1, 0]);
+
+    expect(mtrx.shape([
+      [0],
+    ])).toEqual([1, 1]);
+
+    expect(mtrx.shape([
+      [0, 0],
+    ])).toEqual([1, 2]);
+
+    expect(mtrx.shape([
+      [0, 0],
+      [0, 0],
+    ])).toEqual([2, 2]);
+
+    expect(mtrx.shape([
+      [0, 0, 0],
+      [0, 0, 0],
+    ])).toEqual([2, 3]);
+
+    expect(mtrx.shape([
+      [0, 0],
+      [0, 0],
+      [0, 0],
+    ])).toEqual([3, 2]);
+
+    expect(mtrx.shape([
+      [0, 0, 0],
+      [0, 0, 0],
+      [0, 0, 0],
+    ])).toEqual([3, 3]);
+
+    expect(mtrx.shape([
+      [0],
+      [0],
+      [0],
+    ])).toEqual([3, 1]);
+
+    expect(mtrx.shape([
+      [[0], [0], [0]],
+      [[0], [0], [0]],
+      [[0], [0], [0]],
+    ])).toEqual([3, 3, 1]);
+
+    expect(mtrx.shape([
+      [[0, 0, 0], [0, 0, 0], [0, 0, 0]],
+      [[0, 0, 0], [0, 0, 0], [0, 0, 0]],
+      [[0, 0, 0], [0, 0, 0], [0, 0, 0]],
+    ])).toEqual([3, 3, 3]);
+  });
+
+  it('should generate the matrix of zeros', () => {
+    expect(mtrx.zeros([1, 0])).toEqual([
+      [],
+    ]);
+
+    expect(mtrx.zeros([1, 1])).toEqual([
+      [0],
+    ]);
+
+    expect(mtrx.zeros([1, 3])).toEqual([
+      [0, 0, 0],
+    ]);
+
+    expect(mtrx.zeros([3, 3])).toEqual([
+      [0, 0, 0],
+      [0, 0, 0],
+      [0, 0, 0],
+    ]);
+
+    expect(mtrx.zeros([3, 3, 1])).toEqual([
+      [[0], [0], [0]],
+      [[0], [0], [0]],
+      [[0], [0], [0]],
+    ]);
+  });
+
+  it('should generate the matrix with custom values', () => {
+    expect(mtrx.generate([1, 0], () => 1)).toEqual([
+      [],
+    ]);
+
+    expect(mtrx.generate([1, 1], () => 1)).toEqual([
+      [1],
+    ]);
+
+    expect(mtrx.generate([1, 3], () => 1)).toEqual([
+      [1, 1, 1],
+    ]);
+
+    expect(mtrx.generate([3, 3], () => 1)).toEqual([
+      [1, 1, 1],
+      [1, 1, 1],
+      [1, 1, 1],
+    ]);
+
+    expect(mtrx.generate([3, 3, 1], () => 1)).toEqual([
+      [[1], [1], [1]],
+      [[1], [1], [1]],
+      [[1], [1], [1]],
+    ]);
+  });
+
+  it('should generate a custom matrix based on specific cell indices', () => {
+    const indicesCallback = jest.fn((indices) => {
+      return indices[0] * 10 + indices[1];
+    });
+    const m = mtrx.generate([3, 3], indicesCallback);
+
+    expect(indicesCallback).toHaveBeenCalledTimes(3 * 3);
+    expect(indicesCallback.mock.calls[0][0]).toEqual([0, 0]);
+    expect(indicesCallback.mock.calls[1][0]).toEqual([0, 1]);
+    expect(indicesCallback.mock.calls[2][0]).toEqual([0, 2]);
+    expect(indicesCallback.mock.calls[3][0]).toEqual([1, 0]);
+    expect(indicesCallback.mock.calls[4][0]).toEqual([1, 1]);
+    expect(indicesCallback.mock.calls[5][0]).toEqual([1, 2]);
+    expect(indicesCallback.mock.calls[6][0]).toEqual([2, 0]);
+    expect(indicesCallback.mock.calls[7][0]).toEqual([2, 1]);
+    expect(indicesCallback.mock.calls[8][0]).toEqual([2, 2]);
+    expect(m).toEqual([
+      [0, 1, 2],
+      [10, 11, 12],
+      [20, 21, 22],
+    ]);
+  });
+
+  it('should multiply two matrices', () => {
+    let c;
+    c = mtrx.dot(
+      [
+        [1, 2],
+        [3, 4],
+      ],
+      [
+        [5, 6],
+        [7, 8],
+      ],
+    );
+    expect(mtrx.shape(c)).toEqual([2, 2]);
+    expect(c).toEqual([
+      [19, 22],
+      [43, 50],
+    ]);
+
+    c = mtrx.dot(
+      [
+        [1, 2],
+        [3, 4],
+      ],
+      [
+        [5],
+        [6],
+      ],
+    );
+    expect(mtrx.shape(c)).toEqual([2, 1]);
+    expect(c).toEqual([
+      [17],
+      [39],
+    ]);
+
+    c = mtrx.dot(
+      [
+        [1, 2, 3],
+        [4, 5, 6],
+      ],
+      [
+        [7, 8],
+        [9, 10],
+        [11, 12],
+      ],
+    );
+    expect(mtrx.shape(c)).toEqual([2, 2]);
+    expect(c).toEqual([
+      [58, 64],
+      [139, 154],
+    ]);
+
+    c = mtrx.dot(
+      [
+        [3, 4, 2],
+      ],
+      [
+        [13, 9, 7, 5],
+        [8, 7, 4, 6],
+        [6, 4, 0, 3],
+      ],
+    );
+    expect(mtrx.shape(c)).toEqual([1, 4]);
+    expect(c).toEqual([
+      [83, 63, 37, 45],
+    ]);
+  });
+
+  it('should transpose matrices', () => {
+    expect(mtrx.t([[1, 2, 3]])).toEqual([
+      [1],
+      [2],
+      [3],
+    ]);
+
+    expect(mtrx.t([
+      [1],
+      [2],
+      [3],
+    ])).toEqual([
+      [1, 2, 3],
+    ]);
+
+    expect(mtrx.t([
+      [1, 2, 3],
+      [4, 5, 6],
+    ])).toEqual([
+      [1, 4],
+      [2, 5],
+      [3, 6],
+    ]);
+
+    expect(mtrx.t([
+      [1, 2, 3],
+      [4, 5, 6],
+      [7, 8, 9],
+    ])).toEqual([
+      [1, 4, 7],
+      [2, 5, 8],
+      [3, 6, 9],
+    ]);
+  });
+
+  it('should throw when trying to transpose non 2D matrix', () => {
+    expect(() => {
+      mtrx.t([[[1]]]);
+    }).toThrowError('Matrix is not of 2D shape');
+  });
+
+  it('should add two matrices', () => {
+    expect(mtrx.add([[1]], [[2]])).toEqual([[3]]);
+
+    expect(mtrx.add(
+      [[1, 2, 3]],
+      [[4, 5, 6]],
+    ))
+      .toEqual(
+        [[5, 7, 9]],
+      );
+
+    expect(mtrx.add(
+      [[1], [2], [3]],
+      [[4], [5], [6]],
+    ))
+      .toEqual(
+        [[5], [7], [9]],
+      );
+
+    expect(mtrx.add(
+      [
+        [1, 2, 3],
+        [4, 5, 6],
+        [7, 8, 9],
+      ],
+      [
+        [10, 11, 12],
+        [13, 14, 15],
+        [16, 17, 18],
+      ],
+    ))
+      .toEqual(
+        [
+          [11, 13, 15],
+          [17, 19, 21],
+          [23, 25, 27],
+        ],
+      );
+
+    expect(mtrx.add(
+      [
+        [[1], [2], [3]],
+        [[4], [5], [6]],
+        [[7], [8], [9]],
+      ],
+      [
+        [[10], [11], [12]],
+        [[13], [14], [15]],
+        [[16], [17], [18]],
+      ],
+    ))
+      .toEqual(
+        [
+          [[11], [13], [15]],
+          [[17], [19], [21]],
+          [[23], [25], [27]],
+        ],
+      );
+  });
+
+  it('should throw when trying to add matrices of different shape', () => {
+    expect(() => mtrx.add([[0]], [[[0]]])).toThrowError(
+      'Matrices have different dimensions',
+    );
+
+    expect(() => mtrx.add([[0]], [[0, 0]])).toThrowError(
+      'Matrices have different shapes',
+    );
+  });
+
+  it('should do element wise multiplication two matrices', () => {
+    expect(mtrx.mul([[2]], [[3]])).toEqual([[6]]);
+
+    expect(mtrx.mul(
+      [[1, 2, 3]],
+      [[4, 5, 6]],
+    ))
+      .toEqual(
+        [[4, 10, 18]],
+      );
+
+    expect(mtrx.mul(
+      [[1], [2], [3]],
+      [[4], [5], [6]],
+    ))
+      .toEqual(
+        [[4], [10], [18]],
+      );
+
+    expect(mtrx.mul(
+      [
+        [1, 2],
+        [3, 4],
+      ],
+      [
+        [5, 6],
+        [7, 8],
+      ],
+    ))
+      .toEqual(
+        [
+          [5, 12],
+          [21, 32],
+        ],
+      );
+
+    expect(mtrx.mul(
+      [
+        [[1], [2]],
+        [[3], [4]],
+      ],
+      [
+        [[5], [6]],
+        [[7], [8]],
+      ],
+    ))
+      .toEqual(
+        [
+          [[5], [12]],
+          [[21], [32]],
+        ],
+      );
+  });
+
+  it('should throw when trying to multiply matrices element-wise of different shape', () => {
+    expect(() => mtrx.mul([[0]], [[[0]]])).toThrowError(
+      'Matrices have different dimensions',
+    );
+
+    expect(() => mtrx.mul([[0]], [[0, 0]])).toThrowError(
+      'Matrices have different shapes',
+    );
+  });
+
+  it('should do element wise subtraction two matrices', () => {
+    expect(mtrx.sub([[3]], [[2]])).toEqual([[1]]);
+
+    expect(mtrx.sub(
+      [[10, 12, 14]],
+      [[4, 5, 6]],
+    ))
+      .toEqual(
+        [[6, 7, 8]],
+      );
+
+    expect(mtrx.sub(
+      [[[10], [12], [14]]],
+      [[[4], [5], [6]]],
+    ))
+      .toEqual(
+        [[[6], [7], [8]]],
+      );
+
+    expect(mtrx.sub(
+      [
+        [10, 20],
+        [30, 40],
+      ],
+      [
+        [5, 6],
+        [7, 8],
+      ],
+    ))
+      .toEqual(
+        [
+          [5, 14],
+          [23, 32],
+        ],
+      );
+
+    expect(mtrx.sub(
+      [
+        [[10], [20]],
+        [[30], [40]],
+      ],
+      [
+        [[5], [6]],
+        [[7], [8]],
+      ],
+    ))
+      .toEqual(
+        [
+          [[5], [14]],
+          [[23], [32]],
+        ],
+      );
+  });
+
+  it('should throw when trying to subtract matrices element-wise of different shape', () => {
+    expect(() => mtrx.sub([[0]], [[[0]]])).toThrowError(
+      'Matrices have different dimensions',
+    );
+
+    expect(() => mtrx.sub([[0]], [[0, 0]])).toThrowError(
+      'Matrices have different shapes',
+    );
+  });
+});

From 610f16fe209d78e9d14de245a0d92beb208f0da3 Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Sat, 19 Dec 2020 19:21:32 +0100
Subject: [PATCH 045/264] Add Euclidean Distance algorithm.

---
 README.md                                     |  1 +
 .../math/euclidean-distance/README.md         | 36 +++++++++++++++++++
 .../__tests__/euclideanDistance.test.js       | 23 ++++++++++++
 .../euclidean-distance/euclideanDistance.js   | 28 +++++++++++++++
 src/algorithms/math/matrix/Matrix.js          |  8 ++---
 src/algorithms/ml/knn/__test__/knn.test.js    |  2 +-
 src/algorithms/ml/knn/kNN.js                  | 25 +++----------
 7 files changed, 97 insertions(+), 26 deletions(-)
 create mode 100644 src/algorithms/math/euclidean-distance/README.md
 create mode 100644 src/algorithms/math/euclidean-distance/__tests__/euclideanDistance.test.js
 create mode 100644 src/algorithms/math/euclidean-distance/euclideanDistance.js

diff --git a/README.md b/README.md
index 454d70ff61..8f52db1d38 100644
--- a/README.md
+++ b/README.md
@@ -78,6 +78,7 @@ a set of rules that precisely define a sequence of operations.
   * `B` [Fast Powering](src/algorithms/math/fast-powering)
   * `B` [Horner's method](src/algorithms/math/horner-method) - polynomial evaluation
   * `B` [Matrices](src/algorithms/math/matrix) - matrices and basic matrix operations (multiplication, transposition, etc.)
+  * `B` [Euclidean Distance](src/algorithms/math/euclidean-distance) - distance between two points/vectors/matrices
   * `A` [Integer Partition](src/algorithms/math/integer-partition)
   * `A` [Square Root](src/algorithms/math/square-root) - Newton's method
   * `A` [Liu Hui π Algorithm](src/algorithms/math/liu-hui) - approximate π calculations based on N-gons
diff --git a/src/algorithms/math/euclidean-distance/README.md b/src/algorithms/math/euclidean-distance/README.md
new file mode 100644
index 0000000000..d67c217efe
--- /dev/null
+++ b/src/algorithms/math/euclidean-distance/README.md
@@ -0,0 +1,36 @@
+# Euclidean Distance
+
+In mathematics, the **Euclidean distance** between two points in Euclidean space is the length of a line segment between the two points. It can be calculated from the Cartesian coordinates of the points using the Pythagorean theorem, therefore occasionally being called the Pythagorean distance.
+
+![Euclidean distance between two points](https://upload.wikimedia.org/wikipedia/commons/5/55/Euclidean_distance_2d.svg)
+
+## Distance formulas
+
+### One dimension
+
+The distance between any two points on the real line is the absolute value of the numerical difference of their coordinates
+
+![One dimension formula](https://wikimedia.org/api/rest_v1/media/math/render/svg/7d75418dbec9482dbcb70f9063ad66e9cf7b5db9)
+
+### Two dimensions
+
+![Two dimensions formula](https://wikimedia.org/api/rest_v1/media/math/render/svg/9c0157084fd89f5f3d462efeedc47d3d7aa0b773)
+
+### Higher dimensions
+
+In three dimensions, for points given by their Cartesian coordinates, the distance is
+
+![Three dimensions formula](https://wikimedia.org/api/rest_v1/media/math/render/svg/d1d13a40a7b203b455ae6d4be8b3cce898bda625)
+
+Example: the distance between the two points `(8,2,6)` and `(3,5,7)`:
+
+![3-dimension example](https://www.mathsisfun.com/algebra/images/dist-2-points-3d.svg)
+
+In general, for points given by Cartesian coordinates in `n`-dimensional Euclidean space, the distance is
+
+![n-dimensional formula](https://wikimedia.org/api/rest_v1/media/math/render/svg/a0ef4fe055b2a51b4cca43a05e5d1cd93f758dcc)
+
+## References
+
+- [Euclidean Distance on MathIsFun](https://www.mathsisfun.com/algebra/distance-2-points.html)
+- [Euclidean Distance on Wikipedia](https://en.wikipedia.org/wiki/Euclidean_distance)
diff --git a/src/algorithms/math/euclidean-distance/__tests__/euclideanDistance.test.js b/src/algorithms/math/euclidean-distance/__tests__/euclideanDistance.test.js
new file mode 100644
index 0000000000..78d7d8dc86
--- /dev/null
+++ b/src/algorithms/math/euclidean-distance/__tests__/euclideanDistance.test.js
@@ -0,0 +1,23 @@
+import euclideanDistance from '../euclideanDistance';
+
+describe('euclideanDistance', () => {
+  it('should calculate euclidean distance between vectors', () => {
+    expect(euclideanDistance([[1]], [[2]])).toEqual(1);
+    expect(euclideanDistance([[2]], [[1]])).toEqual(1);
+    expect(euclideanDistance([[5, 8]], [[7, 3]])).toEqual(5.39);
+    expect(euclideanDistance([[5], [8]], [[7], [3]])).toEqual(5.39);
+    expect(euclideanDistance([[8, 2, 6]], [[3, 5, 7]])).toEqual(5.92);
+    expect(euclideanDistance([[8], [2], [6]], [[3], [5], [7]])).toEqual(5.92);
+    expect(euclideanDistance([[[8]], [[2]], [[6]]], [[[3]], [[5]], [[7]]])).toEqual(5.92);
+  });
+
+  it('should throw an error in case if two matrices are of different shapes', () => {
+    expect(() => euclideanDistance([[1]], [[[2]]])).toThrowError(
+      'Matrices have different dimensions',
+    );
+
+    expect(() => euclideanDistance([[1]], [[2, 3]])).toThrowError(
+      'Matrices have different shapes',
+    );
+  });
+});
diff --git a/src/algorithms/math/euclidean-distance/euclideanDistance.js b/src/algorithms/math/euclidean-distance/euclideanDistance.js
new file mode 100644
index 0000000000..afa5c2fece
--- /dev/null
+++ b/src/algorithms/math/euclidean-distance/euclideanDistance.js
@@ -0,0 +1,28 @@
+/**
+ * @typedef {import('../matrix/Matrix.js').Matrix} Matrix
+ */
+
+import * as mtrx from '../matrix/Matrix';
+
+/**
+ * Calculates the euclidean distance between 2 matrices.
+ *
+ * @param {Matrix} a
+ * @param {Matrix} b
+ * @returns {number}
+ * @trows {Error}
+ */
+const euclideanDistance = (a, b) => {
+  mtrx.validateSameShape(a, b);
+
+  let squaresTotal = 0;
+
+  mtrx.walk(a, (indices, aCellValue) => {
+    const bCellValue = mtrx.getCellAtIndex(b, indices);
+    squaresTotal += (aCellValue - bCellValue) ** 2;
+  });
+
+  return Number(Math.sqrt(squaresTotal).toFixed(2));
+};
+
+export default euclideanDistance;
diff --git a/src/algorithms/math/matrix/Matrix.js b/src/algorithms/math/matrix/Matrix.js
index 2470eb3913..2aee126ba2 100644
--- a/src/algorithms/math/matrix/Matrix.js
+++ b/src/algorithms/math/matrix/Matrix.js
@@ -58,7 +58,7 @@ const validate2D = (m) => {
  * @param {Matrix} b
  * @trows {Error}
  */
-const validateSameShape = (a, b) => {
+export const validateSameShape = (a, b) => {
   validateType(a);
   validateType(b);
 
@@ -177,7 +177,7 @@ export const t = (m) => {
  * @param {Matrix} m
  * @param {function(indices: CellIndices, c: Cell)} visit
  */
-const walk = (m, visit) => {
+export const walk = (m, visit) => {
   /**
    * Traverses the matrix recursively.
    *
@@ -208,7 +208,7 @@ const walk = (m, visit) => {
  * @param {CellIndices} cellIndices - Array of cell indices
  * @return {Cell}
  */
-const getCellAtIndex = (m, cellIndices) => {
+export const getCellAtIndex = (m, cellIndices) => {
   // We start from the row at specific index.
   let cell = m[cellIndices[0]];
   // Going deeper into the next dimensions but not to the last one to preserve
@@ -227,7 +227,7 @@ const getCellAtIndex = (m, cellIndices) => {
  * @param {CellIndices} cellIndices - Array of cell indices
  * @param {Cell} cellValue - New cell value
  */
-const updateCellAtIndex = (m, cellIndices, cellValue) => {
+export const updateCellAtIndex = (m, cellIndices, cellValue) => {
   // We start from the row at specific index.
   let cell = m[cellIndices[0]];
   // Going deeper into the next dimensions but not to the last one to preserve
diff --git a/src/algorithms/ml/knn/__test__/knn.test.js b/src/algorithms/ml/knn/__test__/knn.test.js
index ccd69cd706..302bf3b7a9 100644
--- a/src/algorithms/ml/knn/__test__/knn.test.js
+++ b/src/algorithms/ml/knn/__test__/knn.test.js
@@ -25,7 +25,7 @@ describe('kNN', () => {
     const inconsistent = () => {
       kNN([[1, 1]], [1], [1]);
     };
-    expect(inconsistent).toThrowError('Inconsistent vector lengths');
+    expect(inconsistent).toThrowError('Matrices have different shapes');
   });
 
   it('should find the nearest neighbour', () => {
diff --git a/src/algorithms/ml/knn/kNN.js b/src/algorithms/ml/knn/kNN.js
index 24709af6f2..350e7ce176 100644
--- a/src/algorithms/ml/knn/kNN.js
+++ b/src/algorithms/ml/knn/kNN.js
@@ -1,23 +1,3 @@
-/**
- * Calculates calculate the euclidean distance between 2 vectors.
- *
- * @param {number[]} x1
- * @param {number[]} x2
- * @returns {number}
- */
-function euclideanDistance(x1, x2) {
-  // Checking for errors.
-  if (x1.length !== x2.length) {
-    throw new Error('Inconsistent vector lengths');
-  }
-  // Calculate the euclidean distance between 2 vectors and return.
-  let squaresTotal = 0;
-  for (let i = 0; i < x1.length; i += 1) {
-    squaresTotal += (x1[i] - x2[i]) ** 2;
-  }
-  return Number(Math.sqrt(squaresTotal).toFixed(2));
-}
-
 /**
  * Classifies the point in space based on k-nearest neighbors algorithm.
  *
@@ -27,6 +7,9 @@ function euclideanDistance(x1, x2) {
  * @param {number} k - number of nearest neighbors which will be taken into account (preferably odd)
  * @return {number} - the class of the point
  */
+
+import euclideanDistance from '../../math/euclidean-distance/euclideanDistance';
+
 export default function kNN(
   dataSet,
   labels,
@@ -42,7 +25,7 @@ export default function kNN(
   const distances = [];
   for (let i = 0; i < dataSet.length; i += 1) {
     distances.push({
-      dist: euclideanDistance(dataSet[i], toClassify),
+      dist: euclideanDistance([dataSet[i]], [toClassify]),
       label: labels[i],
     });
   }

From adda5c53b37c221573480ec6b949f0f424e4034f Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Sat, 19 Dec 2020 19:26:02 +0100
Subject: [PATCH 046/264] Add Euclidean Distance formula (#602)

* Add Matrices section with basic Matrix operations (multiplication, transposition, etc.)

* Add Euclidean Distance algorithm.
---
 README.md                                     |  1 +
 .../math/euclidean-distance/README.md         | 36 +++++++++++++++++++
 .../__tests__/euclideanDistance.test.js       | 23 ++++++++++++
 .../euclidean-distance/euclideanDistance.js   | 28 +++++++++++++++
 src/algorithms/math/matrix/Matrix.js          |  8 ++---
 src/algorithms/ml/knn/__test__/knn.test.js    |  2 +-
 src/algorithms/ml/knn/kNN.js                  | 25 +++----------
 7 files changed, 97 insertions(+), 26 deletions(-)
 create mode 100644 src/algorithms/math/euclidean-distance/README.md
 create mode 100644 src/algorithms/math/euclidean-distance/__tests__/euclideanDistance.test.js
 create mode 100644 src/algorithms/math/euclidean-distance/euclideanDistance.js

diff --git a/README.md b/README.md
index 454d70ff61..8f52db1d38 100644
--- a/README.md
+++ b/README.md
@@ -78,6 +78,7 @@ a set of rules that precisely define a sequence of operations.
   * `B` [Fast Powering](src/algorithms/math/fast-powering)
   * `B` [Horner's method](src/algorithms/math/horner-method) - polynomial evaluation
   * `B` [Matrices](src/algorithms/math/matrix) - matrices and basic matrix operations (multiplication, transposition, etc.)
+  * `B` [Euclidean Distance](src/algorithms/math/euclidean-distance) - distance between two points/vectors/matrices
   * `A` [Integer Partition](src/algorithms/math/integer-partition)
   * `A` [Square Root](src/algorithms/math/square-root) - Newton's method
   * `A` [Liu Hui π Algorithm](src/algorithms/math/liu-hui) - approximate π calculations based on N-gons
diff --git a/src/algorithms/math/euclidean-distance/README.md b/src/algorithms/math/euclidean-distance/README.md
new file mode 100644
index 0000000000..d67c217efe
--- /dev/null
+++ b/src/algorithms/math/euclidean-distance/README.md
@@ -0,0 +1,36 @@
+# Euclidean Distance
+
+In mathematics, the **Euclidean distance** between two points in Euclidean space is the length of a line segment between the two points. It can be calculated from the Cartesian coordinates of the points using the Pythagorean theorem, therefore occasionally being called the Pythagorean distance.
+
+![Euclidean distance between two points](https://upload.wikimedia.org/wikipedia/commons/5/55/Euclidean_distance_2d.svg)
+
+## Distance formulas
+
+### One dimension
+
+The distance between any two points on the real line is the absolute value of the numerical difference of their coordinates
+
+![One dimension formula](https://wikimedia.org/api/rest_v1/media/math/render/svg/7d75418dbec9482dbcb70f9063ad66e9cf7b5db9)
+
+### Two dimensions
+
+![Two dimensions formula](https://wikimedia.org/api/rest_v1/media/math/render/svg/9c0157084fd89f5f3d462efeedc47d3d7aa0b773)
+
+### Higher dimensions
+
+In three dimensions, for points given by their Cartesian coordinates, the distance is
+
+![Three dimensions formula](https://wikimedia.org/api/rest_v1/media/math/render/svg/d1d13a40a7b203b455ae6d4be8b3cce898bda625)
+
+Example: the distance between the two points `(8,2,6)` and `(3,5,7)`:
+
+![3-dimension example](https://www.mathsisfun.com/algebra/images/dist-2-points-3d.svg)
+
+In general, for points given by Cartesian coordinates in `n`-dimensional Euclidean space, the distance is
+
+![n-dimensional formula](https://wikimedia.org/api/rest_v1/media/math/render/svg/a0ef4fe055b2a51b4cca43a05e5d1cd93f758dcc)
+
+## References
+
+- [Euclidean Distance on MathIsFun](https://www.mathsisfun.com/algebra/distance-2-points.html)
+- [Euclidean Distance on Wikipedia](https://en.wikipedia.org/wiki/Euclidean_distance)
diff --git a/src/algorithms/math/euclidean-distance/__tests__/euclideanDistance.test.js b/src/algorithms/math/euclidean-distance/__tests__/euclideanDistance.test.js
new file mode 100644
index 0000000000..78d7d8dc86
--- /dev/null
+++ b/src/algorithms/math/euclidean-distance/__tests__/euclideanDistance.test.js
@@ -0,0 +1,23 @@
+import euclideanDistance from '../euclideanDistance';
+
+describe('euclideanDistance', () => {
+  it('should calculate euclidean distance between vectors', () => {
+    expect(euclideanDistance([[1]], [[2]])).toEqual(1);
+    expect(euclideanDistance([[2]], [[1]])).toEqual(1);
+    expect(euclideanDistance([[5, 8]], [[7, 3]])).toEqual(5.39);
+    expect(euclideanDistance([[5], [8]], [[7], [3]])).toEqual(5.39);
+    expect(euclideanDistance([[8, 2, 6]], [[3, 5, 7]])).toEqual(5.92);
+    expect(euclideanDistance([[8], [2], [6]], [[3], [5], [7]])).toEqual(5.92);
+    expect(euclideanDistance([[[8]], [[2]], [[6]]], [[[3]], [[5]], [[7]]])).toEqual(5.92);
+  });
+
+  it('should throw an error in case if two matrices are of different shapes', () => {
+    expect(() => euclideanDistance([[1]], [[[2]]])).toThrowError(
+      'Matrices have different dimensions',
+    );
+
+    expect(() => euclideanDistance([[1]], [[2, 3]])).toThrowError(
+      'Matrices have different shapes',
+    );
+  });
+});
diff --git a/src/algorithms/math/euclidean-distance/euclideanDistance.js b/src/algorithms/math/euclidean-distance/euclideanDistance.js
new file mode 100644
index 0000000000..afa5c2fece
--- /dev/null
+++ b/src/algorithms/math/euclidean-distance/euclideanDistance.js
@@ -0,0 +1,28 @@
+/**
+ * @typedef {import('../matrix/Matrix.js').Matrix} Matrix
+ */
+
+import * as mtrx from '../matrix/Matrix';
+
+/**
+ * Calculates the euclidean distance between 2 matrices.
+ *
+ * @param {Matrix} a
+ * @param {Matrix} b
+ * @returns {number}
+ * @trows {Error}
+ */
+const euclideanDistance = (a, b) => {
+  mtrx.validateSameShape(a, b);
+
+  let squaresTotal = 0;
+
+  mtrx.walk(a, (indices, aCellValue) => {
+    const bCellValue = mtrx.getCellAtIndex(b, indices);
+    squaresTotal += (aCellValue - bCellValue) ** 2;
+  });
+
+  return Number(Math.sqrt(squaresTotal).toFixed(2));
+};
+
+export default euclideanDistance;
diff --git a/src/algorithms/math/matrix/Matrix.js b/src/algorithms/math/matrix/Matrix.js
index 2470eb3913..2aee126ba2 100644
--- a/src/algorithms/math/matrix/Matrix.js
+++ b/src/algorithms/math/matrix/Matrix.js
@@ -58,7 +58,7 @@ const validate2D = (m) => {
  * @param {Matrix} b
  * @trows {Error}
  */
-const validateSameShape = (a, b) => {
+export const validateSameShape = (a, b) => {
   validateType(a);
   validateType(b);
 
@@ -177,7 +177,7 @@ export const t = (m) => {
  * @param {Matrix} m
  * @param {function(indices: CellIndices, c: Cell)} visit
  */
-const walk = (m, visit) => {
+export const walk = (m, visit) => {
   /**
    * Traverses the matrix recursively.
    *
@@ -208,7 +208,7 @@ const walk = (m, visit) => {
  * @param {CellIndices} cellIndices - Array of cell indices
  * @return {Cell}
  */
-const getCellAtIndex = (m, cellIndices) => {
+export const getCellAtIndex = (m, cellIndices) => {
   // We start from the row at specific index.
   let cell = m[cellIndices[0]];
   // Going deeper into the next dimensions but not to the last one to preserve
@@ -227,7 +227,7 @@ const getCellAtIndex = (m, cellIndices) => {
  * @param {CellIndices} cellIndices - Array of cell indices
  * @param {Cell} cellValue - New cell value
  */
-const updateCellAtIndex = (m, cellIndices, cellValue) => {
+export const updateCellAtIndex = (m, cellIndices, cellValue) => {
   // We start from the row at specific index.
   let cell = m[cellIndices[0]];
   // Going deeper into the next dimensions but not to the last one to preserve
diff --git a/src/algorithms/ml/knn/__test__/knn.test.js b/src/algorithms/ml/knn/__test__/knn.test.js
index ccd69cd706..302bf3b7a9 100644
--- a/src/algorithms/ml/knn/__test__/knn.test.js
+++ b/src/algorithms/ml/knn/__test__/knn.test.js
@@ -25,7 +25,7 @@ describe('kNN', () => {
     const inconsistent = () => {
       kNN([[1, 1]], [1], [1]);
     };
-    expect(inconsistent).toThrowError('Inconsistent vector lengths');
+    expect(inconsistent).toThrowError('Matrices have different shapes');
   });
 
   it('should find the nearest neighbour', () => {
diff --git a/src/algorithms/ml/knn/kNN.js b/src/algorithms/ml/knn/kNN.js
index 24709af6f2..350e7ce176 100644
--- a/src/algorithms/ml/knn/kNN.js
+++ b/src/algorithms/ml/knn/kNN.js
@@ -1,23 +1,3 @@
-/**
- * Calculates calculate the euclidean distance between 2 vectors.
- *
- * @param {number[]} x1
- * @param {number[]} x2
- * @returns {number}
- */
-function euclideanDistance(x1, x2) {
-  // Checking for errors.
-  if (x1.length !== x2.length) {
-    throw new Error('Inconsistent vector lengths');
-  }
-  // Calculate the euclidean distance between 2 vectors and return.
-  let squaresTotal = 0;
-  for (let i = 0; i < x1.length; i += 1) {
-    squaresTotal += (x1[i] - x2[i]) ** 2;
-  }
-  return Number(Math.sqrt(squaresTotal).toFixed(2));
-}
-
 /**
  * Classifies the point in space based on k-nearest neighbors algorithm.
  *
@@ -27,6 +7,9 @@ function euclideanDistance(x1, x2) {
  * @param {number} k - number of nearest neighbors which will be taken into account (preferably odd)
  * @return {number} - the class of the point
  */
+
+import euclideanDistance from '../../math/euclidean-distance/euclideanDistance';
+
 export default function kNN(
   dataSet,
   labels,
@@ -42,7 +25,7 @@ export default function kNN(
   const distances = [];
   for (let i = 0; i < dataSet.length; i += 1) {
     distances.push({
-      dist: euclideanDistance(dataSet[i], toClassify),
+      dist: euclideanDistance([dataSet[i]], [toClassify]),
       label: labels[i],
     });
   }

From 3e5ddb81431a9967fe1eb28328709ea2c320a48e Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Sat, 19 Dec 2020 19:32:57 +0100
Subject: [PATCH 047/264] Adding the Matrix traversal and generation to the
 Divide and Conquer section.

---
 README.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/README.md b/README.md
index 8f52db1d38..8e26125c1e 100644
--- a/README.md
+++ b/README.md
@@ -185,6 +185,7 @@ algorithm is an abstraction higher than a computer program.
   * `B` [Quicksort](src/algorithms/sorting/quick-sort)
   * `B` [Tree Depth-First Search](src/algorithms/tree/depth-first-search) (DFS)
   * `B` [Graph Depth-First Search](src/algorithms/graph/depth-first-search) (DFS)
+  * `B` [Matrices](src/algorithms/math/matrix) - generating and traversing the matrices of different depths
   * `B` [Jump Game](src/algorithms/uncategorized/jump-game)
   * `B` [Fast Powering](src/algorithms/math/fast-powering)
   * `A` [Permutations](src/algorithms/sets/permutations) (with and without repetitions)

From 636ebe1e268b1aeb226072c3285e5e3f28813e59 Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Sat, 19 Dec 2020 19:33:35 +0100
Subject: [PATCH 048/264] Adding the Matrix traversal and generation to the
 Divide and Conquer section.

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 8e26125c1e..4d88a064db 100644
--- a/README.md
+++ b/README.md
@@ -185,7 +185,7 @@ algorithm is an abstraction higher than a computer program.
   * `B` [Quicksort](src/algorithms/sorting/quick-sort)
   * `B` [Tree Depth-First Search](src/algorithms/tree/depth-first-search) (DFS)
   * `B` [Graph Depth-First Search](src/algorithms/graph/depth-first-search) (DFS)
-  * `B` [Matrices](src/algorithms/math/matrix) - generating and traversing the matrices of different depths
+  * `B` [Matrices](src/algorithms/math/matrix) - generating and traversing the matrices of different shapes
   * `B` [Jump Game](src/algorithms/uncategorized/jump-game)
   * `B` [Fast Powering](src/algorithms/math/fast-powering)
   * `A` [Permutations](src/algorithms/sets/permutations) (with and without repetitions)

From b7cd425ce9a3fc0238321e717c26505335764322 Mon Sep 17 00:00:00 2001
From: Avi Agrawal <39293511+avi09@users.noreply.github.com>
Date: Sat, 19 Dec 2020 13:36:08 -0500
Subject: [PATCH 049/264] Added kmeans clustering (#595)

* added kmeans

* added kmeans

* added kmeans

Co-authored-by: Oleksii Trekhleb <trehleb@gmail.com>
---
 README.md                                     |  1 +
 src/algorithms/ml/kmeans/README.md            | 32 ++++++
 .../ml/kmeans/__test__/kmeans.test.js         | 36 +++++++
 src/algorithms/ml/kmeans/kmeans.js            | 98 +++++++++++++++++++
 4 files changed, 167 insertions(+)
 create mode 100644 src/algorithms/ml/kmeans/README.md
 create mode 100644 src/algorithms/ml/kmeans/__test__/kmeans.test.js
 create mode 100644 src/algorithms/ml/kmeans/kmeans.js

diff --git a/README.md b/README.md
index 4d88a064db..11be805ae5 100644
--- a/README.md
+++ b/README.md
@@ -147,6 +147,7 @@ a set of rules that precisely define a sequence of operations.
 * **Machine Learning**
   * `B` [NanoNeuron](https://github.com/trekhleb/nano-neuron) - 7 simple JS functions that illustrate how machines can actually learn (forward/backward propagation)
   * `B` [k-NN](src/algorithms/ml/knn) - k-nearest neighbors classification algorithm
+  * `B` [k-Means](src/algorithms/ml/kmeans) - k-Means clustering algorithm
 * **Uncategorized**
   * `B` [Tower of Hanoi](src/algorithms/uncategorized/hanoi-tower)
   * `B` [Square Matrix Rotation](src/algorithms/uncategorized/square-matrix-rotation) - in-place algorithm
diff --git a/src/algorithms/ml/kmeans/README.md b/src/algorithms/ml/kmeans/README.md
new file mode 100644
index 0000000000..1c0d53ee8c
--- /dev/null
+++ b/src/algorithms/ml/kmeans/README.md
@@ -0,0 +1,32 @@
+# k-Means Algorithm
+
+The **k-Means algorithm** is an unsupervised Machine Learning algorithm. It's a clustering algorithm, which groups the sample data on the basis of similarity between dimentions of vectors.
+
+In k-Means classification, the output is a set of classess asssigned to each vector. Each cluster location is continously optimized in order to get the accurate locations of each cluster such that they represent each group clearly.
+
+The idea is to calculate the similarity between cluster location and data vectors, and reassign clusters based on it. [Euclidean distance](https://en.wikipedia.org/wiki/Euclidean_distance) is used mostly for this task.
+
+![Euclidean distance between two points](https://upload.wikimedia.org/wikipedia/commons/5/55/Euclidean_distance_2d.svg)
+
+_Image source: [Wikipedia](https://en.wikipedia.org/wiki/Euclidean_distance)_
+
+The algorithm is as follows:
+
+1. Check for errors like invalid/inconsistent data
+2. Initialize the k cluster locations with initial/random k points
+3. Calculate the distance of each data point from each cluster
+4. Assign the cluster label of each data point equal to that of the cluster at it's minimum distance
+5. Calculate the centroid of each cluster based on the data points it contains
+6. Repeat each of the above steps until the centroid locations are varying
+
+Here is a visualization of k-Means clustering for better understanding:
+
+![KNN Visualization 1](https://upload.wikimedia.org/wikipedia/commons/e/ea/K-means_convergence.gif)
+
+_Image source: [Wikipedia](https://en.wikipedia.org/wiki/K-nearest_neighbors_algorithm)_
+
+The centroids are moving continously in order to create better distinction between the different set of data points. As we can see, after a few iterations, the difference in centroids is quite low between iterations. For example between itrations `13` and `14` the difference is quite small because there the optimizer is tuning boundary cases.
+
+## References
+
+- [k-Means neighbors algorithm on Wikipedia](https://en.wikipedia.org/wiki/K-means_clustering)
diff --git a/src/algorithms/ml/kmeans/__test__/kmeans.test.js b/src/algorithms/ml/kmeans/__test__/kmeans.test.js
new file mode 100644
index 0000000000..ed90e9f78e
--- /dev/null
+++ b/src/algorithms/ml/kmeans/__test__/kmeans.test.js
@@ -0,0 +1,36 @@
+import kMeans from '../kmeans';
+
+describe('kMeans', () => {
+  it('should throw an error on invalid data', () => {
+    expect(() => {
+      kMeans();
+    }).toThrowError('Either dataSet or labels or toClassify were not set');
+  });
+
+  it('should throw an error on inconsistent data', () => {
+    expect(() => {
+      kMeans([[1, 2], [1]], 2);
+    }).toThrowError('Inconsistent vector lengths');
+  });
+
+  it('should find the nearest neighbour', () => {
+    const dataSet = [[1, 1], [6, 2], [3, 3], [4, 5], [9, 2], [2, 4], [8, 7]];
+    const k = 2;
+    const expectedCluster = [0, 1, 0, 1, 1, 0, 1];
+    expect(kMeans(dataSet, k)).toEqual(expectedCluster);
+  });
+
+  it('should find the clusters with equal distances', () => {
+    const dataSet = [[0, 0], [1, 1], [2, 2]];
+    const k = 3;
+    const expectedCluster = [0, 1, 2];
+    expect(kMeans(dataSet, k)).toEqual(expectedCluster);
+  });
+
+  it('should find the nearest neighbour in 3D space', () => {
+    const dataSet = [[0, 0, 0], [0, 1, 0], [2, 0, 2]];
+    const k = 2;
+    const expectedCluster = [1, 1, 0];
+    expect(kMeans(dataSet, k)).toEqual(expectedCluster);
+  });
+});
diff --git a/src/algorithms/ml/kmeans/kmeans.js b/src/algorithms/ml/kmeans/kmeans.js
new file mode 100644
index 0000000000..099ddab558
--- /dev/null
+++ b/src/algorithms/ml/kmeans/kmeans.js
@@ -0,0 +1,98 @@
+/**
+ * Calculates calculate the euclidean distance between 2 vectors.
+ *
+ * @param {number[]} x1
+ * @param {number[]} x2
+ * @returns {number}
+ */
+function euclideanDistance(x1, x2) {
+  // Checking for errors.
+  if (x1.length !== x2.length) {
+    throw new Error('Inconsistent vector lengths');
+  }
+  // Calculate the euclidean distance between 2 vectors and return.
+  let squaresTotal = 0;
+  for (let i = 0; i < x1.length; i += 1) {
+    squaresTotal += (x1[i] - x2[i]) ** 2;
+  }
+  return Number(Math.sqrt(squaresTotal).toFixed(2));
+}
+/**
+ * Classifies the point in space based on k-nearest neighbors algorithm.
+ *
+ * @param {number[][]} dataSet - array of dataSet points, i.e. [[0, 1], [3, 4], [5, 7]]
+ * @param {number} k - number of nearest neighbors which will be taken into account (preferably odd)
+ * @return {number[]} - the class of the point
+ */
+export default function kMeans(
+  dataSetm,
+  k = 1,
+) {
+  const dataSet = dataSetm;
+  if (!dataSet) {
+    throw new Error('Either dataSet or labels or toClassify were not set');
+  }
+
+  // starting algorithm
+  // assign k clusters locations equal to the location of initial k points
+  const clusterCenters = [];
+  const nDim = dataSet[0].length;
+  for (let i = 0; i < k; i += 1) {
+    clusterCenters[clusterCenters.length] = Array.from(dataSet[i]);
+  }
+
+  // continue optimization till convergence
+  // centroids should not be moving once optimized
+  // calculate distance of each candidate vector from each cluster center
+  // assign cluster number to each data vector according to minimum distance
+  let flag = true;
+  while (flag) {
+    flag = false;
+    // calculate and store distance of each dataSet point from each cluster
+    for (let i = 0; i < dataSet.length; i += 1) {
+      for (let n = 0; n < k; n += 1) {
+        dataSet[i][nDim + n] = euclideanDistance(clusterCenters[n], dataSet[i].slice(0, nDim));
+      }
+
+      // assign the cluster number to each dataSet point
+      const sliced = dataSet[i].slice(nDim, nDim + k);
+      let minmDistCluster = Math.min(...sliced);
+      for (let j = 0; j < sliced.length; j += 1) {
+        if (minmDistCluster === sliced[j]) {
+          minmDistCluster = j;
+          break;
+        }
+      }
+
+      if (dataSet[i].length !== nDim + k + 1) {
+        flag = true;
+        dataSet[i][nDim + k] = minmDistCluster;
+      } else if (dataSet[i][nDim + k] !== minmDistCluster) {
+        flag = true;
+        dataSet[i][nDim + k] = minmDistCluster;
+      }
+    }
+    // recalculate cluster centriod values via all dimensions of the points under it
+    for (let i = 0; i < k; i += 1) {
+      clusterCenters[i] = Array(nDim).fill(0);
+      let classCount = 0;
+      for (let j = 0; j < dataSet.length; j += 1) {
+        if (dataSet[j][dataSet[j].length - 1] === i) {
+          classCount += 1;
+          for (let n = 0; n < nDim; n += 1) {
+            clusterCenters[i][n] += dataSet[j][n];
+          }
+        }
+      }
+      for (let n = 0; n < nDim; n += 1) {
+        clusterCenters[i][n] = Number((clusterCenters[i][n] / classCount).toFixed(2));
+      }
+    }
+  }
+  // return the clusters assigned
+  const soln = [];
+  for (let i = 0; i < dataSet.length; i += 1) {
+    soln.push(dataSet[i][dataSet[i].length - 1]);
+  }
+  return soln;
+}

From 569fd95bd08c1a0cb3f21cfeaa9f7324d86902ce Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Sat, 19 Dec 2020 21:13:11 +0100
Subject: [PATCH 050/264] Simplify k-Means clustering algorithm.

---
 README.md                                     |  2 +-
 .../ml/{kmeans => k-means}/README.md          | 14 +--
 .../__test__/kMeans.test.js}                  | 24 +++--
 src/algorithms/ml/k-means/kMeans.js           | 85 ++++++++++++++++
 src/algorithms/ml/kmeans/kmeans.js            | 98 -------------------
 5 files changed, 107 insertions(+), 116 deletions(-)
 rename src/algorithms/ml/{kmeans => k-means}/README.md (53%)
 rename src/algorithms/ml/{kmeans/__test__/kmeans.test.js => k-means/__test__/kMeans.test.js} (52%)
 create mode 100644 src/algorithms/ml/k-means/kMeans.js
 delete mode 100644 src/algorithms/ml/kmeans/kmeans.js

diff --git a/README.md b/README.md
index 11be805ae5..ffec78a9e2 100644
--- a/README.md
+++ b/README.md
@@ -147,7 +147,7 @@ a set of rules that precisely define a sequence of operations.
 * **Machine Learning**
   * `B` [NanoNeuron](https://github.com/trekhleb/nano-neuron) - 7 simple JS functions that illustrate how machines can actually learn (forward/backward propagation)
   * `B` [k-NN](src/algorithms/ml/knn) - k-nearest neighbors classification algorithm
-  * `B` [k-Means](src/algorithms/ml/kmeans) - k-Means clustering algorithm
+  * `B` [k-Means](src/algorithms/ml/k-means) - k-Means clustering algorithm
 * **Uncategorized**
   * `B` [Tower of Hanoi](src/algorithms/uncategorized/hanoi-tower)
   * `B` [Square Matrix Rotation](src/algorithms/uncategorized/square-matrix-rotation) - in-place algorithm
diff --git a/src/algorithms/ml/kmeans/README.md b/src/algorithms/ml/k-means/README.md
similarity index 53%
rename from src/algorithms/ml/kmeans/README.md
rename to src/algorithms/ml/k-means/README.md
index 1c0d53ee8c..aebd60e100 100644
--- a/src/algorithms/ml/kmeans/README.md
+++ b/src/algorithms/ml/k-means/README.md
@@ -1,10 +1,10 @@
 # k-Means Algorithm
 
-The **k-Means algorithm** is an unsupervised Machine Learning algorithm. It's a clustering algorithm, which groups the sample data on the basis of similarity between dimentions of vectors.
+The **k-Means algorithm** is an unsupervised Machine Learning algorithm. It's a clustering algorithm, which groups the sample data on the basis of similarity between dimensions of vectors.
 
-In k-Means classification, the output is a set of classess asssigned to each vector. Each cluster location is continously optimized in order to get the accurate locations of each cluster such that they represent each group clearly.
+In k-Means classification, the output is a set of classes assigned to each vector. Each cluster location is continuously optimized in order to get the accurate locations of each cluster such that they represent each group clearly.
 
-The idea is to calculate the similarity between cluster location and data vectors, and reassign clusters based on it. [Euclidean distance](https://en.wikipedia.org/wiki/Euclidean_distance) is used mostly for this task.
+The idea is to calculate the similarity between cluster location and data vectors, and reassign clusters based on it. [Euclidean distance](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/euclidean-distance) is used mostly for this task.
 
 ![Euclidean distance between two points](https://upload.wikimedia.org/wikipedia/commons/5/55/Euclidean_distance_2d.svg)
 
@@ -13,9 +13,9 @@ _Image source: [Wikipedia](https://en.wikipedia.org/wiki/Euclidean_distance)_
 The algorithm is as follows:
 
 1. Check for errors like invalid/inconsistent data
-2. Initialize the k cluster locations with initial/random k points
+2. Initialize the `k` cluster locations with initial/random `k` points
 3. Calculate the distance of each data point from each cluster
-4. Assign the cluster label of each data point equal to that of the cluster at it's minimum distance
+4. Assign the cluster label of each data point equal to that of the cluster at its minimum distance
 5. Calculate the centroid of each cluster based on the data points it contains
 6. Repeat each of the above steps until the centroid locations are varying
 
@@ -23,9 +23,9 @@ Here is a visualization of k-Means clustering for better understanding:
 
 ![KNN Visualization 1](https://upload.wikimedia.org/wikipedia/commons/e/ea/K-means_convergence.gif)
 
-_Image source: [Wikipedia](https://en.wikipedia.org/wiki/K-nearest_neighbors_algorithm)_
+_Image source: [Wikipedia](https://en.wikipedia.org/wiki/K-means_clustering)_
 
-The centroids are moving continously in order to create better distinction between the different set of data points. As we can see, after a few iterations, the difference in centroids is quite low between iterations. For example between itrations `13` and `14` the difference is quite small because there the optimizer is tuning boundary cases.
+The centroids are moving continuously in order to create better distinction between the different set of data points. As we can see, after a few iterations, the difference in centroids is quite low between iterations. For example between iterations `13` and `14` the difference is quite small because there the optimizer is tuning boundary cases.
 
 ## References
 
diff --git a/src/algorithms/ml/kmeans/__test__/kmeans.test.js b/src/algorithms/ml/k-means/__test__/kMeans.test.js
similarity index 52%
rename from src/algorithms/ml/kmeans/__test__/kmeans.test.js
rename to src/algorithms/ml/k-means/__test__/kMeans.test.js
index ed90e9f78e..44a6f538e2 100644
--- a/src/algorithms/ml/kmeans/__test__/kmeans.test.js
+++ b/src/algorithms/ml/k-means/__test__/kMeans.test.js
@@ -1,36 +1,40 @@
-import kMeans from '../kmeans';
+import KMeans from '../kMeans';
 
 describe('kMeans', () => {
   it('should throw an error on invalid data', () => {
     expect(() => {
-      kMeans();
-    }).toThrowError('Either dataSet or labels or toClassify were not set');
+      KMeans();
+    }).toThrowError('The data is empty');
   });
 
   it('should throw an error on inconsistent data', () => {
     expect(() => {
-      kMeans([[1, 2], [1]], 2);
-    }).toThrowError('Inconsistent vector lengths');
+      KMeans([[1, 2], [1]], 2);
+    }).toThrowError('Matrices have different shapes');
   });
 
   it('should find the nearest neighbour', () => {
-    const dataSet = [[1, 1], [6, 2], [3, 3], [4, 5], [9, 2], [2, 4], [8, 7]];
+    const data = [[1, 1], [6, 2], [3, 3], [4, 5], [9, 2], [2, 4], [8, 7]];
     const k = 2;
-    const expectedCluster = [0, 1, 0, 1, 1, 0, 1];
-    expect(kMeans(dataSet, k)).toEqual(expectedCluster);
+    const expectedClusters = [0, 1, 0, 1, 1, 0, 1];
+    expect(KMeans(data, k)).toEqual(expectedClusters);
+
+    expect(KMeans([[0, 0], [0, 1], [10, 10]], 2)).toEqual(
+      [0, 0, 1],
+    );
   });
 
   it('should find the clusters with equal distances', () => {
     const dataSet = [[0, 0], [1, 1], [2, 2]];
     const k = 3;
     const expectedCluster = [0, 1, 2];
-    expect(kMeans(dataSet, k)).toEqual(expectedCluster);
+    expect(KMeans(dataSet, k)).toEqual(expectedCluster);
   });
 
   it('should find the nearest neighbour in 3D space', () => {
     const dataSet = [[0, 0, 0], [0, 1, 0], [2, 0, 2]];
     const k = 2;
     const expectedCluster = [1, 1, 0];
-    expect(kMeans(dataSet, k)).toEqual(expectedCluster);
+    expect(KMeans(dataSet, k)).toEqual(expectedCluster);
   });
 });
diff --git a/src/algorithms/ml/k-means/kMeans.js b/src/algorithms/ml/k-means/kMeans.js
new file mode 100644
index 0000000000..4361eed689
--- /dev/null
+++ b/src/algorithms/ml/k-means/kMeans.js
@@ -0,0 +1,85 @@
+import * as mtrx from '../../math/matrix/Matrix';
+import euclideanDistance from '../../math/euclidean-distance/euclideanDistance';
+
+/**
+ * Classifies the point in space based on k-Means algorithm.
+ *
+ * @param {number[][]} data - array of dataSet points, i.e. [[0, 1], [3, 4], [5, 7]]
+ * @param {number} k - number of clusters
+ * @return {number[]} - the class of the point
+ */
+export default function KMeans(
+  data,
+  k = 1,
+) {
+  if (!data) {
+    throw new Error('The data is empty');
+  }
+
+  // Assign k clusters locations equal to the location of initial k points.
+  const dataDim = data[0].length;
+  const clusterCenters = data.slice(0, k);
+
+  // Continue optimization till convergence.
+  // Centroids should not be moving once optimized.
+  // Calculate distance of each candidate vector from each cluster center.
+  // Assign cluster number to each data vector according to minimum distance.
+
+  // Matrix of distance from each data point to each cluster centroid.
+  const distances = mtrx.zeros([data.length, k]);
+
+  // Vector data points' classes. The value of -1 means that no class has bee assigned yet.
+  const classes = Array(data.length).fill(-1);
+
+  let iterate = true;
+  while (iterate) {
+    iterate = false;
+
+    // Calculate and store the distance of each data point from each cluster.
+    for (let dataIndex = 0; dataIndex < data.length; dataIndex += 1) {
+      for (let clusterIndex = 0; clusterIndex < k; clusterIndex += 1) {
+        distances[dataIndex][clusterIndex] = euclideanDistance(
+          [clusterCenters[clusterIndex]],
+          [data[dataIndex]],
+        );
+      }
+      // Assign the closest cluster number to each dataSet point.
+      const closestClusterIdx = distances[dataIndex].indexOf(
+        Math.min(...distances[dataIndex]),
+      );
+
+      // Check if data point class has been changed and we still need to re-iterate.
+      if (classes[dataIndex] !== closestClusterIdx) {
+        iterate = true;
+      }
+
+      classes[dataIndex] = closestClusterIdx;
+    }
+
+    // Recalculate cluster centroid values via all dimensions of the points under it.
+    for (let clusterIndex = 0; clusterIndex < k; clusterIndex += 1) {
+      // Reset cluster center coordinates since we need to recalculate them.
+      clusterCenters[clusterIndex] = Array(dataDim).fill(0);
+      let clusterSize = 0;
+      for (let dataIndex = 0; dataIndex < data.length; dataIndex += 1) {
+        if (classes[dataIndex] === clusterIndex) {
+          // Register one more data point of current cluster.
+          clusterSize += 1;
+          for (let dimensionIndex = 0; dimensionIndex < dataDim; dimensionIndex += 1) {
+            // Add data point coordinates to the cluster center coordinates.
+            clusterCenters[clusterIndex][dimensionIndex] += data[dataIndex][dimensionIndex];
+          }
+        }
+      }
+      // Calculate the average for each cluster center coordinate.
+      for (let dimensionIndex = 0; dimensionIndex < dataDim; dimensionIndex += 1) {
+        clusterCenters[clusterIndex][dimensionIndex] = parseFloat(Number(
+          clusterCenters[clusterIndex][dimensionIndex] / clusterSize,
+        ).toFixed(2));
+      }
+    }
+  }
+
+  // Return the clusters assigned.
+  return classes;
+}
diff --git a/src/algorithms/ml/kmeans/kmeans.js b/src/algorithms/ml/kmeans/kmeans.js
deleted file mode 100644
index 099ddab558..0000000000
--- a/src/algorithms/ml/kmeans/kmeans.js
+++ /dev/null
@@ -1,98 +0,0 @@
-/**
- * Calculates calculate the euclidean distance between 2 vectors.
- *
- * @param {number[]} x1
- * @param {number[]} x2
- * @returns {number}
- */
-function euclideanDistance(x1, x2) {
-  // Checking for errors.
-  if (x1.length !== x2.length) {
-    throw new Error('Inconsistent vector lengths');
-  }
-  // Calculate the euclidean distance between 2 vectors and return.
-  let squaresTotal = 0;
-  for (let i = 0; i < x1.length; i += 1) {
-    squaresTotal += (x1[i] - x2[i]) ** 2;
-  }
-  return Number(Math.sqrt(squaresTotal).toFixed(2));
-}
-/**
- * Classifies the point in space based on k-nearest neighbors algorithm.
- *
- * @param {number[][]} dataSet - array of dataSet points, i.e. [[0, 1], [3, 4], [5, 7]]
- * @param {number} k - number of nearest neighbors which will be taken into account (preferably odd)
- * @return {number[]} - the class of the point
- */
-export default function kMeans(
-  dataSetm,
-  k = 1,
-) {
-  const dataSet = dataSetm;
-  if (!dataSet) {
-    throw new Error('Either dataSet or labels or toClassify were not set');
-  }
-
-  // starting algorithm
-  // assign k clusters locations equal to the location of initial k points
-  const clusterCenters = [];
-  const nDim = dataSet[0].length;
-  for (let i = 0; i < k; i += 1) {
-    clusterCenters[clusterCenters.length] = Array.from(dataSet[i]);
-  }
-
-  // continue optimization till convergence
-  // centroids should not be moving once optimized
-  // calculate distance of each candidate vector from each cluster center
-  // assign cluster number to each data vector according to minimum distance
-  let flag = true;
-  while (flag) {
-    flag = false;
-    // calculate and store distance of each dataSet point from each cluster
-    for (let i = 0; i < dataSet.length; i += 1) {
-      for (let n = 0; n < k; n += 1) {
-        dataSet[i][nDim + n] = euclideanDistance(clusterCenters[n], dataSet[i].slice(0, nDim));
-      }
-
-      // assign the cluster number to each dataSet point
-      const sliced = dataSet[i].slice(nDim, nDim + k);
-      let minmDistCluster = Math.min(...sliced);
-      for (let j = 0; j < sliced.length; j += 1) {
-        if (minmDistCluster === sliced[j]) {
-          minmDistCluster = j;
-          break;
-        }
-      }
-
-      if (dataSet[i].length !== nDim + k + 1) {
-        flag = true;
-        dataSet[i][nDim + k] = minmDistCluster;
-      } else if (dataSet[i][nDim + k] !== minmDistCluster) {
-        flag = true;
-        dataSet[i][nDim + k] = minmDistCluster;
-      }
-    }
-    // recalculate cluster centriod values via all dimensions of the points under it
-    for (let i = 0; i < k; i += 1) {
-      clusterCenters[i] = Array(nDim).fill(0);
-      let classCount = 0;
-      for (let j = 0; j < dataSet.length; j += 1) {
-        if (dataSet[j][dataSet[j].length - 1] === i) {
-          classCount += 1;
-          for (let n = 0; n < nDim; n += 1) {
-            clusterCenters[i][n] += dataSet[j][n];
-          }
-        }
-      }
-      for (let n = 0; n < nDim; n += 1) {
-        clusterCenters[i][n] = Number((clusterCenters[i][n] / classCount).toFixed(2));
-      }
-    }
-  }
-  // return the clusters assigned
-  const soln = [];
-  for (let i = 0; i < dataSet.length; i += 1) {
-    soln.push(dataSet[i][dataSet[i].length - 1]);
-  }
-  return soln;
-}

From 4bc72734269daa6f8d39f429944b264d94b9f9e3 Mon Sep 17 00:00:00 2001
From: Adjie Djaka Permana <spiritjaeger@gmail.com>
Date: Sun, 20 Dec 2020 18:52:01 +0700
Subject: [PATCH 051/264] feat(lang): add README.id-ID.md translation for
 Bahasa Indonesia (#603)

---
 README.id-ID.md | 303 ++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 303 insertions(+)
 create mode 100644 README.id-ID.md

diff --git a/README.id-ID.md b/README.id-ID.md
new file mode 100644
index 0000000000..784fb76961
--- /dev/null
+++ b/README.id-ID.md
@@ -0,0 +1,303 @@
+# Algoritme dan Struktur Data Javascript
+
+[![Build Status](https://travis-ci.org/trekhleb/javascript-algorithms.svg?branch=master)](https://travis-ci.org/trekhleb/javascript-algorithms)
+[![codecov](https://codecov.io/gh/trekhleb/javascript-algorithms/branch/master/graph/badge.svg)](https://codecov.io/gh/trekhleb/javascript-algorithms)
+
+Repositori ini berisi contoh-contoh algoritme dan struktur data yang populer menggunakan JavaScript.
+
+Setiap algoritme dan struktur data memiliki README-nya tersendiri dengan penjelasan yang berkaitan dan tautan untuk bacaan lebih lanjut (termasuk tautan menuju video YouTube).
+
+_Baca ini dalam bahasa yang lain:_
+[_English_](https://github.com/trekhleb/javascript-algorithms/),
+[_简体中文_](README.zh-CN.md),
+[_繁體中文_](README.zh-TW.md),
+[_한국어_](README.ko-KR.md),
+[_日本語_](README.ja-JP.md),
+[_Polski_](README.pl-PL.md),
+[_Français_](README.fr-FR.md),
+[_Español_](README.es-ES.md),
+[_Português_](README.pt-BR.md),
+[_Русский_](README.ru-RU.md),
+[_Türk_](README.tr-TR.md),
+[_Italiana_](README.it-IT.md)
+
+_☝ Perhatikan bahwa proyek ini hanya dimaksudkan untuk tujuan pembelajaran dan riset, dan **tidak** dimaksudkan untuk digunakan sebagai produksi._
+
+## Struktur Data
+
+Struktur data adalah cara tertentu untuk mengatur dan menyimpan data dalam komputer sehingga dapat diakses dan diubah secara efisien. Lebih tepatnya, struktur data adalah kumpulan dari nilai data, relasi di antara data-data, dan fungsi atau operasi yang dapat diterapkan pada data.
+
+`P` - Pemula, `L` - Lanjutan
+
+- `P` [Senarai Berantai](src/data-structures/linked-list)
+- `P` [Senarai Berantai Ganda](src/data-structures/doubly-linked-list)
+- `P` [Antrean](src/data-structures/queue)
+- `P` [Tumpukan](src/data-structures/stack)
+- `P` [Tabel Hash](src/data-structures/hash-table)
+- `P` [_Heap_](src/data-structures/heap) - versi _heap_ maksimum dan minimum
+- `P` [Antrean Prioritas](src/data-structures/priority-queue)
+- `L` [_Trie_](src/data-structures/trie)
+- `L` [Pohon](src/data-structures/tree)
+  - `L` [Pohon Telusur Biner](src/data-structures/tree/binary-search-tree)
+  - `L` [_AVL Tree_](src/data-structures/tree/avl-tree)
+  - `L` [Pohon Merah Hitam](src/data-structures/tree/red-black-tree)
+  - `L` [_Segment Tree_](src/data-structures/tree/segment-tree) - dengan contoh min/max/sum range query
+  - `L` [Pohon Fenwick](src/data-structures/tree/fenwick-tree) (Binary Indexed Tree)
+- `L` [Graf](src/data-structures/graph) (directed dan undirected)
+- `L` [_Disjoint Set_](src/data-structures/disjoint-set)
+- `L` [_Bloom Filter_](src/data-structures/bloom-filter)
+
+## Algoritme
+
+Algoritme adalah sebuah perincian yang jelas tentang cara untuk memecahkan suatu masalah. Ia adalah sekumpulan aturan yang menjelaskan secara tepat urutan-urutan dari sebuah operasi.
+
+`P` - Pemula, `L` - Lanjutan
+
+### Algoritme Berdasarkanan Topik
+
+- **Matematika**
+  - `P` [Manipulasi Bit](src/algorithms/math/bits) - menetapkan/mendapatkan/memperbarui/mengahpus bit, perkalian/pembagian dengan angka 2, membuat bilangan negatif etc.
+  - `P` [Faktorial](src/algorithms/math/Faktorial)
+  - `P` [Bilangan Fibonacci](src/algorithms/math/fibonacci) - versi klasik dan bentuk tertutup
+  - `P` [Faktor Prima](src/algorithms/math/prime-factors) - menemukan faktor prima dan menghitungnya menggunakan teorema Hardy-Ramanujan
+  - `P` [Pengujian Bilangan Prima](src/algorithms/math/primality-test) (metode _trial division_)
+  - `P` [Algoritme Euclidean](src/algorithms/math/euclidean-algorithm) - menghitung Faktor Persekutuan Terbesar (FPB)
+  - `P` [_Least Common Multiple_](src/algorithms/math/least-common-multiple) (LCM)
+  - `P` [_Sieve of Eratosthenes_](src/algorithms/math/sieve-of-eratosthenes) - menemukan semua bilangan prima hingga batas yang ditentukan
+  - `P` [_Is Power of Two_](src/algorithms/math/is-power-of-two) - mengecek apakah sebuah bilangan adalah hasil dari pangkat dua (algoritme _naive_ dan _bitwise_)
+  - `P` [Segitiga Pascal](src/algorithms/math/pascal-triangle)
+  - `P` [Bilangan Kompleks](src/algorithms/math/complex-number) - bilangan kompleks dengan operasi dasarnya
+  - `P` [Radian & Derajat](src/algorithms/math/radian) - konversi radian ke derajat dan sebaliknya
+  - `P` [_Fast Powering_](src/algorithms/math/fast-powering)
+  - `P` [Metode Horner](src/algorithms/math/horner-method) - evaluasi polinomial
+  - `L` [Partisi Bilangan Bulat](src/algorithms/math/integer-partition)
+  - `L` [Akar Pangkat Dua](src/algorithms/math/square-root) - metode Newton
+  - `L` [Algoritme π Liu Hui](src/algorithms/math/liu-hui) - perkiraan perhitungan π berdasarkan segibanyak
+  - `L` [Transformasi Diskrit Fourier](src/algorithms/math/fourier-transform) - menguraikan fungsi waktu (sinyal) menjadi frekuensi yang menyusunnya
+- **Himpunan**
+  - `P` [Produk Kartesian](src/algorithms/sets/cartesian-product) - hasil dari beberapa himpunan
+  - `P` [Pengocokan Fisher–Yates](src/algorithms/sets/fisher-yates) - permutasi acak dari sebuah urutan terhingga
+  - `L` [Himpunan Kuasa](src/algorithms/sets/power-set) - semua himpunan bagian dari sebuah himpunan
+  - `L` [Permutasi](src/algorithms/sets/permutations) (dengan dan tanpa pengulangan)
+  - `L` [Kombinasi](src/algorithms/sets/combinations) (dengan dan tanpa pengulangan)
+  - `L` [_Longest Common Subsequence_](src/algorithms/sets/longest-common-subsequence) (LCS)
+  - `L` [_Longest Increasing Subsequence_](src/algorithms/sets/longest-increasing-subsequence)
+  - `L` [_Shortest Common Supersequence_](src/algorithms/sets/shortest-common-supersequence) (SCS)
+  - `L` [Permasalahan Knapsack](src/algorithms/sets/knapsack-problem) - "0/1" dan yang tidak "dibatasi"
+  - `L` [Upalarik Maksimum](src/algorithms/sets/maximum-subarray) - "_Brute Force_" dan "Pemrograman Dinamis" versi Kadane
+  - `L` [_Combination Sum_](src/algorithms/sets/combination-sum) - menemukan semua kombinasi yang membentuk jumlah tertentu
+- **String**
+  - `P` [Jarak Hamming](src/algorithms/string/hamming-distance) - jumlah posisi di mana ditemukan simbol-simbol yang berbeda
+  - `L` [Algoritme Jarak Levenshtein](src/algorithms/string/levenshtein-distance) - _edit distance_ minimum antara dua urutan
+  - `L` [Algoritme Knuth–Morris–Pratt](src/algorithms/string/knuth-morris-pratt) (Algoritme KMP) - pencarian substring (pencocokan pola)
+  - `L` [AlgoritmeZ](src/algorithms/string/z-algorithm) - pencarian substring (pencocokan pola)
+  - `L` [Algoritme Rabin Karp](src/algorithms/string/rabin-karp) - pencarian substring
+  - `L` [_Longest Common Substring_](src/algorithms/string/longest-common-substring)
+  - `L` [Pencocokan Ekspresi Reguler](src/algorithms/string/regular-expression-matching)
+- **Pencarian**
+  - `P` [Pencarian Linier](src/algorithms/search/linear-search)
+  - `P` [Pencarian Lompat](src/algorithms/search/jump-search) (atau Block Search) - pencarian di larik tersortir
+  - `P` [Pencarian Biner](src/algorithms/search/binary-search) - pencarian di larik tersortir
+  - `P` [Pencarian Interpolasi](src/algorithms/search/interpolation-search) - pencarian di larik tersortir yang terdistribusi seragam
+- **Penyortiran**
+  - `P` [Sortir Gelembung](src/algorithms/sorting/bubble-sort)
+  - `P` [Sortir Seleksi](src/algorithms/sorting/selection-sort)
+  - `P` [Sortir Sisipan](src/algorithms/sorting/insertion-sort)
+  - `P` [Sortir _Heap_](src/algorithms/sorting/heap-sort)
+  - `P` [Sortir Gabungan](src/algorithms/sorting/merge-sort)
+  - `P` [Sortir Cepat](src/algorithms/sorting/quick-sort) - implementasi _in-place_ dan _non-in-place_
+  - `P` [Sortir Shell](src/algorithms/sorting/shell-sort)
+  - `P` [Sortir Perhitungan](src/algorithms/sorting/counting-sort)
+  - `P` [Sortir Akar](src/algorithms/sorting/radix-sort)
+- **Senarai Berantai**
+  - `P` [Lintas Lurus](src/algorithms/linked-list/traversal)
+  - `P` [Lintas Terbalik](src/algorithms/linked-list/reverse-traversal)
+- **Pohon**
+  - `P` [Pencarian Kedalaman Pertama](src/algorithms/tree/depth-first-search) (DFS)
+  - `P` [Pencarian Luas Pertama](src/algorithms/tree/breadth-first-search) (BFS)
+- **Graf**
+  - `P` [Pencarian Kedalaman Pertama](src/algorithms/graph/depth-first-search) (DFS)
+  - `P` [Pencarian Luas Pertama](src/algorithms/graph/breadth-first-search) (BFS)
+  - `P` [Algoritme Kruskal](src/algorithms/graph/kruskal) - mencari rentang pohon minimum untuk graf tidak berarah berbobot
+  - `L` [Algoritme Dijkstra](src/algorithms/graph/dijkstra) - menemukan jalur terpendek ke semua sudut graf dari sudut tunggal
+  - `L` [Algoritme Bellman-Ford](src/algorithms/graph/bellman-ford) - menemukan jalur terpendek ke semua sudut graf dari sudut tunggal
+  - `L` [Algoritme Floyd-Warshall](src/algorithms/graph/floyd-warshall) - menemukan jalur terpendek antara semua pasangan sudut
+  - `L` [Mendeteksi Siklus](src/algorithms/graph/detect-cycle) - untuk graf berarah dan tidak berarah (berdasarkan versi DFS dan _Disjoint Set_)
+  - `L` [ALgoritme Prim](src/algorithms/graph/prim) - mencari rentang pohon minimum untuk graf tidak berarah berbobot
+  - `L` [Sortir Topologi](src/algorithms/graph/topological-sorting) - metode DFS
+  - `L` [Poin Artikulasi](src/algorithms/graph/articulation-points) - Algoritme Tarjan (berdasarkan DFS)
+  - `L` [Jembatan](src/algorithms/graph/bridges) - Algoritme berdasarkan DFS
+  - `L` [Jalur dan Sirkuit Eulerian](src/algorithms/graph/eulerian-path) - Algoritme Fleury - Mengunjungi setiap tepinya tepat satu kali
+  - `L` [Siklus Hamiltonian](src/algorithms/graph/hamiltonian-cycle) - mengunjungi setiap sudutnya tepat satu kali
+  - `L` [Komponen yang Terkoneksi dengan Kuat](src/algorithms/graph/strongly-connected-components) - Algoritme Kosaraju
+  - `L` [Permasalahan Penjual Keliling](src/algorithms/graph/travelling-salesman) - kemungkinan rute terpendek untuk mengunjungi setiap kota dan kembali lagi ke kota asal
+- **Kriptografi**
+  - `P` [Polinomial Hash](src/algorithms/cryptography/polynomial-hash) - fungsi rolling hash berdasarkan polinomial
+  - `P` [Sandi Caesar](src/algorithms/cryptography/caesar-cipher) - sandi pengganti sederhana
+- **Pembelajaran Mesin**
+  - `P` [NanoNeuron](https://github.com/trekhleb/nano-neuron) - 7 fungsi JS sederhana yang mengilustrasikan bagaimana mesin-mesin dapat benar-benar belajar (perambatan maju/mundur)
+- **Tidak Dikategorikan**
+  - `P` [Menara Hanoi](src/algorithms/uncategorized/hanoi-tower)
+  - `P` [Perputaran Matriks Persegi](src/algorithms/uncategorized/square-matrix-rotation) - algoritme _in-place_
+  - `P` [Permainan Melompat](src/algorithms/uncategorized/jump-game) - runut-balik, pemrograman dinamis (atas ke bawah + bawah ke atas) and contoh-contoh _greedy_
+  - `P` [_Unique Paths_](src/algorithms/uncategorized/unique-paths) - runut-balik, pemrograman dinamis and contoh-contoh beradsarkan Segitiga Pascal
+  - `P` [_Rain Terraces_](src/algorithms/uncategorized/rain-terraces) - permasalahan _trapping rain water_ (versi pemrograman dinamis and _brute force_)
+  - `P` [Tangga Rekursif](src/algorithms/uncategorized/recursive-staircase) - menghitung jumlah cara untuk mencapai ke atas tangga (4 solusi)
+  - `L` [Permainan N-Queen](src/algorithms/uncategorized/n-queens)
+  - `L` [Permainan Knight's Tour](src/algorithms/uncategorized/knight-tour)
+
+### Algoritme Berdasarkan Paradigma
+
+Paradigma algoritmik adalah sebuah metode atau pendekatan umum yang mendasari desain sebuah tingkatan algoritme. Paradigma algoritmik merupakan abstraksi yang lebih tinggi dari gagasan sebuah algoritme, seperti halnya sebuah algoritme merupakan abstraksi yang lebih tinggi dari sebuah program komputer.
+
+- **_Brute Force_** - melihat ke semua kemungkinan dan memilih solusi yang terbaik
+  - `P` [Pencarian Linier](src/algorithms/search/linear-search)
+  - `P` [_Rain Terraces_](src/algorithms/uncategorized/rain-terraces) - permasalahan _trapping rain water_
+  - `P` [Tangga Rekursif](src/algorithms/uncategorized/recursive-staircase) - menghitung jumlah cara untuk mencapai ke atas tangga
+  - `L` [Upalarik Maksimum](src/algorithms/sets/maximum-subarray)
+  - `L` [Permasalahan Penjual Keliling](src/algorithms/graph/travelling-salesman) - kemungkinan rute terpendek untuk mengunjungi setiap kota dan kembali lagi ke kota asal
+  - `L` [Transformasi Diskrit Fourier](src/algorithms/math/fourier-transform) - menguraikan fungsi waktu (sinyal) menjadi frekuensi yang menyusunnya
+- **_Greedy_** - memilih pilihan terbaik pada saat ini tanpa mempertimbangkan masa yang akan datang
+  - `P` [Permainan Melompat](src/algorithms/uncategorized/jump-game)
+  - `L` [Permasalahan Knapsack yang Tidak Dibatasi](src/algorithms/sets/knapsack-problem)
+  - `L` [Algoritme Dijkstra](src/algorithms/graph/dijkstra) - menemukan jalur terpendek ke semua sudut graf dari sudut tunggal
+  - `L` [Algoritme Prim](src/algorithms/graph/prim) - mencari rentang pohon minimum untuk graf tidak berarah berbobot
+  - `L` [Algoritme Kruskal](src/algorithms/graph/kruskal) - mencari rentang pohon minimum untuk graf tidak berarah berbobot
+- **Memecah dan Menaklukkan** - membagi masalah menjadi bagian-bagian yang kecil, lalu memcahkan bagian-bagian tersebut
+  - `P` [Pencarian Biner](src/algorithms/search/binary-search)
+  - `P` [Menara Hanoi](src/algorithms/uncategorized/hanoi-tower)
+  - `P` [Segitiga Pascal](src/algorithms/math/pascal-triangle)
+  - `P` [Algoritme Euclidean](src/algorithms/math/euclidean-algorithm) - menghitung Faktor Persekutuan Terbesar (FPB)
+  - `P` [Sortir Gabungan](src/algorithms/sorting/merge-sort)
+  - `P` [Sortir Cepat](src/algorithms/sorting/quick-sort)
+  - `P` [Pencarian Kedalaman Pertama untuk Pohon](src/algorithms/tree/depth-first-search) (DFS)
+  - `P` [Pencarian Kedalaman Pertama untuk Graf](src/algorithms/graph/depth-first-search) (DFS)
+  - `P` [Permainan Melompat](src/algorithms/uncategorized/jump-game)
+  - `P` [_Fast Powering_](src/algorithms/math/fast-powering)
+  - `L` [Permutasi](src/algorithms/sets/permutations) (dengan dan tanpa pengulangan)
+  - `L` [Kombinasi](src/algorithms/sets/combinations) (dengan dan tanpa pengulangan)
+- **Pemrograman Dinamis** - membangun sebuah solusi menggunakan upasolusi yang ditemukan sebelumnya
+  - `P` [Bilangan Fibonacci](src/algorithms/math/fibonacci)
+  - `P` [Permainan Melompat](src/algorithms/uncategorized/jump-game)
+  - `P` [_Unique Paths_](src/algorithms/uncategorized/unique-paths)
+  - `P` [_Rain Terraces_](src/algorithms/uncategorized/rain-terraces) - permasalahan _trapping rain water_
+  - `P` [Tangga Rekursif](src/algorithms/uncategorized/recursive-staircase) - menghitung jumlah cara untuk mencapai ke atas tangga
+  - `L` [Algoritme Jarak Levenshtein](src/algorithms/string/levenshtein-distance) - _edit distance_ minimum antara dua urutan
+  - `L` [_Longest Common Subsquence_](src/algorithms/sets/longest-common-subsequence) (LCS)
+  - `L` [_Longest Common Substring_](src/algorithms/string/longest-common-substring)
+  - `L` [_Longest Increasing Subsequence_](src/algorithms/sets/longest-increasing-subsequence)
+  - `L` [_Shortest Common Supersequence_](src/algorithms/sets/shortest-common-supersequence)
+  - `L` [Permasalahan Knapsack 0/1](src/algorithms/sets/knapsack-problem)
+  - `L` [Partisi Bilangan Bulat](src/algorithms/math/integer-partition)
+  - `L` [Upalarik Maksimum](src/algorithms/sets/maximum-subarray)
+  - `L` [Algoritme Bellman-Ford](src/algorithms/graph/bellman-ford) - menemukan jalur terpendek ke semua sudut graf dari sudut tunggal
+  - `L` [Algoritme Floyd-Warshall](src/algorithms/graph/floyd-warshall) - menemukan jalur terpendek antara semua pasangan sudut
+  - `L` [Pencocokan Ekspresi Reguler](src/algorithms/string/regular-expression-matching)
+- **Runut-balik** - sama halnya dengan _brute force_, algoritme ini mencoba untuk menghasilkan segala kemungkinan solusi, tetapi setiap kali anda menghasilkan solusi selanjutnya, anda akan menguji apakah solusi tersebut memenuhi semua kondisi dan setelah itu baru akan menghasilkan solusi berikutnya. Apabila tidak, maka akan merunut-balik dan mencari solusi di jalur yang berbeda. Biasanya menggunakan lintas DFS dari ruang keadaan.
+  - `P` [Permainan Melompat](src/algorithms/uncategorized/jump-game)
+  - `P` [_Unique Paths_](src/algorithms/uncategorized/unique-paths)
+  - `P` [Himpunan Kuasa](src/algorithms/sets/power-set) - semua himpunan bagian dari sebuah himpunan
+  - `L` [Siklus Hamiltonian](src/algorithms/graph/hamiltonian-cycle) - mengunjungi setiap sudutnya tepat satu kali
+  - `L` [Permainan N-Queen](src/algorithms/uncategorized/n-queens)
+  - `L` [Permainan Knight's Tour](src/algorithms/uncategorized/knight-tour)
+  - `L` [_Combination Sum_](src/algorithms/sets/combination-sum) - menemukan semua kombinasi yang membentuk jumlah tertentu
+- **_Mencabang dan Membatasi_** - digunakan untuk membuang solusi parsial dengan biaya yang lebih besar dari solusi dengan biaya yang terendah yang ditemukan sejauh ini dengan cara mengingat solusi dengan biaya terendah yang ditemukan pada setiap tahap dari pencarian runut-balik dan menggunakan biaya dari solusi dengan biaya terendah sejauh ini sebagai batas bawah pada biaya dari solusi dengan biaya yang paling sedikit untuk permasalahannya. Biasanya menggunakan lintas BFS yang berkombinasi dengan lintas DFS dari pohon ruang keadaan.
+
+## Cara menggunakan repositori ini
+
+**Meng-_install_ semua dependensi**
+
+```
+npm install
+```
+
+**Menjalankan ESLint**
+
+Anda dapat menjalankannya untuk memeriksa kualitas kode.
+
+```
+npm run lint
+```
+
+**Menjalankan semua tes**
+
+```
+npm test
+```
+
+**Menjalankan tes berdasarkan nama**
+
+```
+npm test -- 'LinkedList'
+```
+
+**_Playground_**
+
+Anda dapat bermain dengan algoritme dan struktur data di _file_ `./src/playground/playground.js` dan menuliskan tesnya di `./src/playground/__test__/playground.test.js`.
+
+Lalu, hanya tinggal menjalankan perintah berikut untuk mengetes apakah kode _playground_ anda bekerja sesuai dengan keinginan:
+
+```
+npm test -- 'playground'
+```
+
+## Informasi Bermanfaat
+
+### Referensi
+
+[▶ Algoritme dan Struktur Data di YouTube](https://www.youtube.com/playlist?list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
+
+### Notasi _Big O_
+
+Notasi _Big O_ digunakan untuk mengklasifikasikan algoritme berdasarkan durasi atau ruang yang dibutuhkan seiring bertambahnya _input_. Pada grafik dibawah, anda dapat menemukan urutan pertumbuhan yang paling umum dari algoritme yang ditentukan dalam notasi _Big O_.
+
+![Big O graphs](./assets/big-o-graph.png)
+
+Sumber: [Big O Cheat Sheet](http://bigocheatsheet.com/).
+
+Di bawah ini adalah daftar dari beberapa notasi _Bog O_ yang sering digunakan dan perbandingan kinerjanya terhadap berbagai ukuran _input data_.
+
+| Notasi _Big O_ | Komputasi untuk 10 elemen | Komputasi untuk 100 elemen | Komputasi untuk 1000 elemen |
+| -------------- | ------------------------- | -------------------------- | --------------------------- |
+| **O(1)**       | 1                         | 1                          | 1                           |
+| **O(log N)**   | 3                         | 6                          | 9                           |
+| **O(N)**       | 10                        | 100                        | 1000                        |
+| **O(N log N)** | 30                        | 600                        | 9000                        |
+| **O(N^2)**     | 100                       | 10000                      | 1000000                     |
+| **O(2^N)**     | 1024                      | 1.26e+29                   | 1.07e+301                   |
+| **O(N!)**      | 3628800                   | 9.3e+157                   | 4.02e+2567                  |
+
+### Kompleksitas Operasi Struktur Data
+
+| Struktur Data                                | Akses  | Pencarian | Penyisipan | Penghapusan | Keterangan                                               |
+| -------------------------------------------- | :----: | :-------: | :--------: | :---------: | :------------------------------------------------------- |
+| **Array (Larik)**                            |   1    |     n     |     n      |      n      |                                                          |
+| **Stack (Tumpukan)**                         |   n    |     n     |     1      |      1      |                                                          |
+| **Queue (Antrean)**                          |   n    |     n     |     1      |      1      |                                                          |
+| **Linked List (Senarai Berantai)**           |   n    |     n     |     1      |      n      |                                                          |
+| **Hash Table**                               |   -    |     n     |     n      |      n      | Apabila fungsi hash sempurna, biayanya akan menjadi O(1) |
+| **Binary Search Tree (Pohon Telusur Biner)** |   n    |     n     |     n      |      n      | Apabila pohon seimbang, biayanya akan menjadi O(log(n))  |
+| **B-Tree**                                   | log(n) |  log(n)   |   log(n)   |   log(n)    |                                                          |
+| **Red-Black Tree (Pohon Merah-Hitam)**       | log(n) |  log(n)   |   log(n)   |   log(n)    |                                                          |
+| **AVL Tree**                                 | log(n) |  log(n)   |   log(n)   |   log(n)    |                                                          |
+| **Bloom Filter**                             |   -    |     1     |     1      |      -      | Positif palsu dimungkinkan saat pencarian                |
+
+### Kompleksitas Algoritme Sortir Larik
+
+| Nama                                   |    Terbaik    |          Rata-rata           |          Terburuk           | Memori | Stabil | Keterangan                                                                        |
+| -------------------------------------- | :-----------: | :--------------------------: | :-------------------------: | :----: | :----: | :-------------------------------------------------------------------------------- |
+| **Bubble sort (Sortir Gelembung)**     |       n       |        n<sup>2</sup>         |        n<sup>2</sup>        |   1    |   Ya   |                                                                                   |
+| **Insertion sort (Sortir Sisipan)**    |       n       |        n<sup>2</sup>         |        n<sup>2</sup>        |   1    |   Ya   |                                                                                   |
+| **Selection sort (Sortir Seleksi)**    | n<sup>2</sup> |        n<sup>2</sup>         |        n<sup>2</sup>        |   1    | Tidak  |                                                                                   |
+| **Heap sort (Sortir _Heap_)**          | n&nbsp;log(n) |        n&nbsp;log(n)         |        n&nbsp;log(n)        |   1    | Tidak  |                                                                                   |
+| **Merge Sort (Sortir Gabungan)**       | n&nbsp;log(n) |        n&nbsp;log(n)         |        n&nbsp;log(n)        |   n    |   Ya   |                                                                                   |
+| **Quick sort (Sortir Cepat)**          | n&nbsp;log(n) |        n&nbsp;log(n)         |        n<sup>2</sup>        | log(n) | Tidak  | Sortir Cepat biasanya dilakukan secara _in-place_ dengan O(log(n)) ruang tumpukan |
+| **Shell sort (Sortir Shell)**          | n&nbsp;log(n) | tergantung pada jarak urutan | n&nbsp;(log(n))<sup>2</sup> |   1    | Tidak  |                                                                                   |
+| **Counting sort (Sortir Perhitungan)** |     n + r     |            n + r             |            n + r            | n + r  |   Ya   | r - angka terbesar dalam larik                                                    |
+| **Radix sort (Sortir Akar)**           |    n \* k     |            n \* k            |           n \* k            | n + k  |   Ya   | k - panjang dari kunci terpanjang                                                 |
+
+## Pendukung Proyek
+
+> Anda dapat mendukung proyek ini via ❤️️ [GitHub](https://github.com/sponsors/trekhleb) atau ❤️️ [Patreon](https://www.patreon.com/trekhleb).
+
+[Orang-orang yang mendukung proyek ini](https://github.com/trekhleb/javascript-algorithms/blob/master/BACKERS.md) `∑ = 1`

From c755110eb19229058ef80f607eaf31b5bb244d79 Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Sun, 20 Dec 2020 13:01:46 +0100
Subject: [PATCH 052/264] Adding Bahasa Indonesia.

---
 README.es-ES.md | 3 ++-
 README.fr-FR.md | 3 ++-
 README.id-ID.md | 2 +-
 README.it-IT.md | 3 ++-
 README.ja-JP.md | 3 ++-
 README.ko-KR.md | 3 ++-
 README.md       | 3 ++-
 README.pl-PL.md | 3 ++-
 README.pt-BR.md | 3 ++-
 README.ru-RU.md | 3 ++-
 README.tr-TR.md | 3 ++-
 README.zh-CN.md | 3 ++-
 README.zh-TW.md | 3 ++-
 13 files changed, 25 insertions(+), 13 deletions(-)

diff --git a/README.es-ES.md b/README.es-ES.md
index b6337a1c3d..ee0e0d6289 100644
--- a/README.es-ES.md
+++ b/README.es-ES.md
@@ -20,7 +20,8 @@ _Léelo en otros idiomas:_
 [_Português_](README.pt-BR.md),
 [_Русский_](README.ru-RU.md),
 [_Türk_](README.tr-TR.md),
-[_Italiana_](README.it-IT.md)
+[_Italiana_](README.it-IT.md),
+[_Bahasa Indonesia_](README.id-ID.md)
 
 *☝ Nótese que este proyecto está pensado con fines de aprendizaje e investigación,
 y **no** para ser usado en producción.*
diff --git a/README.fr-FR.md b/README.fr-FR.md
index 7b3705544b..1e21add710 100644
--- a/README.fr-FR.md
+++ b/README.fr-FR.md
@@ -21,7 +21,8 @@ _Lisez ceci dans d'autres langues:_
 [_Português_](README.pt-BR.md),
 [_Русский_](README.ru-RU.md),
 [_Türk_](README.tr-TR.md),
-[_Italiana_](README.it-IT.md)
+[_Italiana_](README.it-IT.md),
+[_Bahasa Indonesia_](README.id-ID.md)
 
 ## Data Structures
 
diff --git a/README.id-ID.md b/README.id-ID.md
index 784fb76961..5a31ff8b35 100644
--- a/README.id-ID.md
+++ b/README.id-ID.md
@@ -1,6 +1,6 @@
 # Algoritme dan Struktur Data Javascript
 
-[![Build Status](https://travis-ci.org/trekhleb/javascript-algorithms.svg?branch=master)](https://travis-ci.org/trekhleb/javascript-algorithms)
+[![CI](https://github.com/trekhleb/javascript-algorithms/workflows/CI/badge.svg)](https://github.com/trekhleb/javascript-algorithms/actions?query=workflow%3ACI+branch%3Amaster)
 [![codecov](https://codecov.io/gh/trekhleb/javascript-algorithms/branch/master/graph/badge.svg)](https://codecov.io/gh/trekhleb/javascript-algorithms)
 
 Repositori ini berisi contoh-contoh algoritme dan struktur data yang populer menggunakan JavaScript.
diff --git a/README.it-IT.md b/README.it-IT.md
index 9598324058..31a7def923 100644
--- a/README.it-IT.md
+++ b/README.it-IT.md
@@ -17,7 +17,8 @@ _Leggilo in altre lingue:_
 [_Español_](README.es-ES.md),
 [_Português_](README.pt-BR.md),
 [_Русский_](README.ru-RU.md),
-[_Türk_](README.tr-TR.md)
+[_Türk_](README.tr-TR.md),
+[_Bahasa Indonesia_](README.id-ID.md)
 
 *☝ Si noti che questo progetto è destinato ad essere utilizzato solo per l'apprendimento e la ricerca e non è destinato ad essere utilizzato per il commercio.*
 
diff --git a/README.ja-JP.md b/README.ja-JP.md
index 93321556c4..e955c3ae30 100644
--- a/README.ja-JP.md
+++ b/README.ja-JP.md
@@ -20,7 +20,8 @@ _Read this in other languages:_
 [_Português_](README.pt-BR.md),
 [_Русский_](README.ru-RU.md),
 [_Türk_](README.tr-TR.md),
-[_Italiana_](README.it-IT.md)
+[_Italiana_](README.it-IT.md),
+[_Bahasa Indonesia_](README.id-ID.md)
 
 ## データ構造
 
diff --git a/README.ko-KR.md b/README.ko-KR.md
index 0fa189d106..45c59cbe8e 100644
--- a/README.ko-KR.md
+++ b/README.ko-KR.md
@@ -19,7 +19,8 @@ _Read this in other languages:_
 [_Português_](README.pt-BR.md),
 [_Русский_](README.ru-RU.md),
 [_Türk_](README.tr-TR.md),
-[_Italiana_](README.it-IT.md)
+[_Italiana_](README.it-IT.md),
+[_Bahasa Indonesia_](README.id-ID.md)
 
 ## 자료 구조
 
diff --git a/README.md b/README.md
index ffec78a9e2..11293da799 100644
--- a/README.md
+++ b/README.md
@@ -21,7 +21,8 @@ _Read this in other languages:_
 [_Português_](README.pt-BR.md),
 [_Русский_](README.ru-RU.md),
 [_Türk_](README.tr-TR.md),
-[_Italiana_](README.it-IT.md)
+[_Italiana_](README.it-IT.md),
+[_Bahasa Indonesia_](README.id-ID.md)
 
 *☝ Note that this project is meant to be used for learning and researching purposes
 only, and it is **not** meant to be used for production.*
diff --git a/README.pl-PL.md b/README.pl-PL.md
index d1ad0ec224..0ede13db43 100644
--- a/README.pl-PL.md
+++ b/README.pl-PL.md
@@ -21,7 +21,8 @@ _Read this in other languages:_
 [_Português_](README.pt-BR.md),
 [_Русский_](README.ru-RU.md),
 [_Türk_](README.tr-TR.md),
-[_Italiana_](README.it-IT.md)
+[_Italiana_](README.it-IT.md),
+[_Bahasa Indonesia_](README.id-ID.md)
 
 ## Struktury Danych
 
diff --git a/README.pt-BR.md b/README.pt-BR.md
index 17899af1d9..7517bb5086 100644
--- a/README.pt-BR.md
+++ b/README.pt-BR.md
@@ -21,7 +21,8 @@ _Leia isto em outros idiomas:_
 [_Español_](README.es-ES.md),
 [_Русский_](README.ru-RU.md),
 [_Türk_](README.tr-TR.md),
-[_Italiana_](README.it-IT.md)
+[_Italiana_](README.it-IT.md),
+[_Bahasa Indonesia_](README.id-ID.md)
 
 ## Estrutura de Dados
 
diff --git a/README.ru-RU.md b/README.ru-RU.md
index e85446d31f..12c1324d36 100644
--- a/README.ru-RU.md
+++ b/README.ru-RU.md
@@ -18,7 +18,8 @@ _Читать на других языках:_
 [_Español_](README.es-ES.md),
 [_Português_](README.pt-BR.md),
 [_Türk_](README.tr-TR.md),
-[_Italiana_](README.it-IT.md)
+[_Italiana_](README.it-IT.md),
+[_Bahasa Indonesia_](README.id-ID.md)
 
 *☝ Замечание: этот репозиторий предназначен для учебно-исследовательских целей (**не** для использования в продакшн-системах).*
 
diff --git a/README.tr-TR.md b/README.tr-TR.md
index c65061e454..2b453000b9 100644
--- a/README.tr-TR.md
+++ b/README.tr-TR.md
@@ -19,7 +19,8 @@ _Read this in other languages:_
 [_Español_](README.es-ES.md),
 [_Português_](README.pt-BR.md),
 [_Русский_](README.ru-RU.md),
-[_Italiana_](README.it-IT.md)
+[_Italiana_](README.it-IT.md),
+[_Bahasa Indonesia_](README.id-ID.md)
 
 *☝ Not, bu proje araştırma ve öğrenme amacı ile yapılmış
 olup üretim için **yaplılmamıştır**.*
diff --git a/README.zh-CN.md b/README.zh-CN.md
index 05f580817f..c039524447 100644
--- a/README.zh-CN.md
+++ b/README.zh-CN.md
@@ -18,7 +18,8 @@ _Read this in other languages:_
 [_Português_](README.pt-BR.md),
 [_Русский_](README.ru-RU.md),
 [_Türk_](README.tr-TR.md),
-[_Italiana_](README.it-IT.md)
+[_Italiana_](README.it-IT.md),
+[_Bahasa Indonesia_](README.id-ID.md)
 
 *注意：这个项目仅用于学习和研究，**不是**用于生产环境。*
 
diff --git a/README.zh-TW.md b/README.zh-TW.md
index 1a091720bb..69df9717cb 100644
--- a/README.zh-TW.md
+++ b/README.zh-TW.md
@@ -17,7 +17,8 @@ _Read this in other languages:_
 [_Português_](README.pt-BR.md),
 [_Русский_](README.ru-RU.md),
 [_Türk_](README.tr-TR.md),
-[_Italiana_](README.it-IT.md)
+[_Italiana_](README.it-IT.md),
+[_Bahasa Indonesia_](README.id-ID.md)
 
 ## 資料結構
 

From 22abc6f8080e5f97266c18bdb8eff35245a95a67 Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Sun, 20 Dec 2020 13:05:41 +0100
Subject: [PATCH 053/264] Rename the CI workflow file.

---
 .github/workflows/{node.js.yml => ci.yml} | 0
 1 file changed, 0 insertions(+), 0 deletions(-)
 rename .github/workflows/{node.js.yml => ci.yml} (100%)

diff --git a/.github/workflows/node.js.yml b/.github/workflows/ci.yml
similarity index 100%
rename from .github/workflows/node.js.yml
rename to .github/workflows/ci.yml

From 9641940fd78fce6766237118a36647204c67343c Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Jo=C3=A3o=20Pedro=20Raskopf?= <jpraskys@gmail.com>
Date: Sun, 20 Dec 2020 14:40:22 -0300
Subject: [PATCH 054/264] Add rail fence cipher (#516)

* Add rail fence cipher encoder & decoder

* Add functions to encode & decode strings using the rail fence cipher method
* Add unit tests covering empty strings, pair & odd number of characters in the input string, n=3 & n=4
* Add a README.md for the algorithm
* Update root README.md to link to the new algorithm

* Rename the CI workflow file.

Co-authored-by: Oleksii Trekhleb <trehleb@gmail.com>
---
 .github/workflows/{node.js.yml => ci.yml}     |   0
 README.md                                     |   1 +
 .../cryptography/rail-fence-cipher/README.md  |  25 ++++
 .../__test__/railFenceCypher.test.js          |  26 +++++
 .../rail-fence-cipher/decodeRailFence.js      | 108 ++++++++++++++++++
 .../rail-fence-cipher/encodeRailFence.js      |  52 +++++++++
 .../rail-fence-cipher/railFenceCipher.js      |  50 ++++++++
 7 files changed, 262 insertions(+)
 rename .github/workflows/{node.js.yml => ci.yml} (100%)
 create mode 100644 src/algorithms/cryptography/rail-fence-cipher/README.md
 create mode 100644 src/algorithms/cryptography/rail-fence-cipher/__test__/railFenceCypher.test.js
 create mode 100644 src/algorithms/cryptography/rail-fence-cipher/decodeRailFence.js
 create mode 100644 src/algorithms/cryptography/rail-fence-cipher/encodeRailFence.js
 create mode 100644 src/algorithms/cryptography/rail-fence-cipher/railFenceCipher.js

diff --git a/.github/workflows/node.js.yml b/.github/workflows/ci.yml
similarity index 100%
rename from .github/workflows/node.js.yml
rename to .github/workflows/ci.yml
diff --git a/README.md b/README.md
index 11293da799..c6d8713451 100644
--- a/README.md
+++ b/README.md
@@ -143,6 +143,7 @@ a set of rules that precisely define a sequence of operations.
   * `A` [Travelling Salesman Problem](src/algorithms/graph/travelling-salesman) - shortest possible route that visits each city and returns to the origin city
 * **Cryptography**
   * `B` [Polynomial Hash](src/algorithms/cryptography/polynomial-hash) - rolling hash function based on polynomial
+  * `B` [Rail Fence Cypher](src/algorithms/cryptography/rail-fence-cipher) - a transposition cipher algorithm for encoding messages
   * `B` [Caesar Cipher](src/algorithms/cryptography/caesar-cipher) - simple substitution cipher
   * `B` [Hill Cipher](src/algorithms/cryptography/hill-cipher) - substitution cipher based on linear algebra
 * **Machine Learning**
diff --git a/src/algorithms/cryptography/rail-fence-cipher/README.md b/src/algorithms/cryptography/rail-fence-cipher/README.md
new file mode 100644
index 0000000000..e090f557eb
--- /dev/null
+++ b/src/algorithms/cryptography/rail-fence-cipher/README.md
@@ -0,0 +1,25 @@
+# Rail fence Cipher
+
+This is a [transposition cipher](https://en.wikipedia.org/wiki/Transposition_cipher) in which the message is split accross a set of rails on a fence for encoding. The fence is populated with the message's characters, starting at the top left and adding a character on each position, traversing them diagonally to the bottom. Upon reaching the last rail, the direction should then turn diagonal and upwards up to the very first rail in a zig-zag motion. Rinse and repeat until the message is fully disposed across the fence. The encoded message is the result of concatenating the text in each rail, from top to bottom.
+
+From [wikipedia](https://en.wikipedia.org/wiki/Rail_fence_cipher), this is what the message `WE ARE DISCOVERED. FLEE AT ONCE` looks like on a 3-rail fence:
+
+```
+W . . . E . . . C . . . R . . . L . . . T . . . E
+. E . R . D . S . O . E . E . F . E . A . O . C .
+. . A . . . I . . . V . . . D . . . E . . . N . .
+-------------------------------------------------
+             ECRLTEERDSOEEFEAOCAIVDEN            
+```
+
+The message can then be decoded by re-creating the encode fence, with the same traversal pattern, except characters should only be added on one rail at a time. To ilustrate that, a dash can be added on the rails that are not supposed to be poupated yet. This is what the fence would look like after populating the first rail, the dashes represent positions that were visited but not populated.
+
+```
+W . . . E . . . C . . . R . . . L . . . T . . . E
+. - . - . - . - . - . - . - . - . - . - . - . - .
+. . - . . . - . . . - . . . - . . . - . . . - . .
+```
+
+It's time to start populating the next rail once the number of visited fence positions is equal to the number of characters in the message.
+
+[Learn more](https://crypto.interactive-maths.com/rail-fence-cipher.html)
diff --git a/src/algorithms/cryptography/rail-fence-cipher/__test__/railFenceCypher.test.js b/src/algorithms/cryptography/rail-fence-cipher/__test__/railFenceCypher.test.js
new file mode 100644
index 0000000000..285841e2ce
--- /dev/null
+++ b/src/algorithms/cryptography/rail-fence-cipher/__test__/railFenceCypher.test.js
@@ -0,0 +1,26 @@
+import encodeRailFenceCipher from '../encodeRailFence';
+import decodeRailFenceCipher from '../decodeRailFence';
+
+describe('rail fence cipher', () => {
+  it('encodes a string correctly for base=3', () => {
+    expect(encodeRailFenceCipher('', 3)).toBe('');
+    expect(encodeRailFenceCipher('WEAREDISCOVEREDFLEEATONCE', 3)).toBe('WECRLTEERDSOEEFEAOCAIVDEN');
+    expect(encodeRailFenceCipher('Hello, World!', 3)).toBe('Hoo!el,Wrdl l');
+  });
+
+  it('decodes a string correctly for base=3', () => {
+    expect(decodeRailFenceCipher('', 3)).toBe('');
+    expect(decodeRailFenceCipher('WECRLTEERDSOEEFEAOCAIVDEN', 3)).toBe('WEAREDISCOVEREDFLEEATONCE');
+    expect(decodeRailFenceCipher('Hoo!el,Wrdl l', 3)).toBe('Hello, World!');
+  });
+
+  it('encodes a string correctly for base=4', () => {
+    expect(encodeRailFenceCipher('', 4)).toBe('');
+    expect(encodeRailFenceCipher('THEYAREATTACKINGFROMTHENORTH', 4)).toBe('TEKOOHRACIRMNREATANFTETYTGHH');
+  });
+
+  it('decodes a string correctly for base=4', () => {
+    expect(decodeRailFenceCipher('', 4)).toBe('');
+    expect(decodeRailFenceCipher('TEKOOHRACIRMNREATANFTETYTGHH', 4)).toBe('THEYAREATTACKINGFROMTHENORTH');
+  });
+});
diff --git a/src/algorithms/cryptography/rail-fence-cipher/decodeRailFence.js b/src/algorithms/cryptography/rail-fence-cipher/decodeRailFence.js
new file mode 100644
index 0000000000..b1826b4883
--- /dev/null
+++ b/src/algorithms/cryptography/rail-fence-cipher/decodeRailFence.js
@@ -0,0 +1,108 @@
+import {
+  addChar,
+  buildFence,
+  DIRECTIONS,
+  getNextDirection,
+} from './railFenceCipher';
+
+/**
+ * @param {object} params
+ * @param {number} params.railCount
+ * @param {number} params.strLen
+ * @param {Array} params.string
+ * @param {Array} params.fence
+ * @param {number} params.targetRail
+ * @param {number} params.direction
+ * @param {Array} params.coords
+ *
+ * @returns {Array}
+ */
+const fillDecodeFence = ({
+  railCount, strLen, string, fence, targetRail, direction, coords,
+}) => {
+  if (string.length === 0) return fence;
+
+  const [currentRail, currentColumn] = coords;
+  const shouldGoNextRail = currentColumn === strLen - 1;
+  const nextDirection = shouldGoNextRail
+    ? DIRECTIONS.DOWN
+    : getNextDirection({ railCount, currentRail, direction });
+  const nextRail = shouldGoNextRail ? targetRail + 1 : targetRail;
+  const nextCoords = [
+    shouldGoNextRail ? 0 : currentRail + nextDirection,
+    shouldGoNextRail ? 0 : currentColumn + 1,
+  ];
+
+  const shouldAddChar = currentRail === targetRail;
+  const [currentChar, ...remainderString] = string;
+  const nextString = shouldAddChar ? remainderString : string;
+  const nextFence = shouldAddChar ? fence.map(addChar(currentRail, currentChar)) : fence;
+
+  return fillDecodeFence({
+    railCount,
+    strLen,
+    string: nextString,
+    fence: nextFence,
+    targetRail: nextRail,
+    direction: nextDirection,
+    coords: nextCoords,
+  });
+};
+
+/**
+ * @param {object} params
+ * @param {number} params.railCount
+ * @param {number} params.strLen
+ * @param {Array} params.fence
+ * @param {number} params.currentRail
+ * @param {number} params.direction
+ * @param {Array} params.code
+ *
+ * @returns {string}
+ */
+const decodeFence = ({
+  railCount, strLen, fence, currentRail, direction, code,
+}) => {
+  if (code.length === strLen) return code.join('');
+
+  const [currentChar, ...nextRail] = fence[currentRail];
+  const nextDirection = getNextDirection({ railCount, currentRail, direction });
+
+  return decodeFence({
+    railCount,
+    strLen,
+    currentRail: currentRail + nextDirection,
+    direction: nextDirection,
+    code: [...code, currentChar],
+    fence: fence.map((rail, idx) => (idx === currentRail ? nextRail : rail)),
+  });
+};
+
+/**
+ * @param {string} string
+ * @param {number} railCount
+ *
+ * @returns {string}
+ */
+export default function decodeRailFenceCipher(string, railCount) {
+  const strLen = string.length;
+  const emptyFence = buildFence(railCount);
+  const filledFence = fillDecodeFence({
+    railCount,
+    strLen,
+    string: string.split(''),
+    fence: emptyFence,
+    targetRail: 0,
+    direction: DIRECTIONS.DOWN,
+    coords: [0, 0],
+  });
+
+  return decodeFence({
+    railCount,
+    strLen,
+    fence: filledFence,
+    currentRail: 0,
+    direction: DIRECTIONS.DOWN,
+    code: [],
+  });
+}
diff --git a/src/algorithms/cryptography/rail-fence-cipher/encodeRailFence.js b/src/algorithms/cryptography/rail-fence-cipher/encodeRailFence.js
new file mode 100644
index 0000000000..9a58131253
--- /dev/null
+++ b/src/algorithms/cryptography/rail-fence-cipher/encodeRailFence.js
@@ -0,0 +1,52 @@
+import {
+  addChar,
+  buildFence,
+  DIRECTIONS,
+  getNextDirection,
+} from './railFenceCipher';
+
+/**
+ * @param {object} params
+ * @param {number} params.railCount
+ * @param {number} params.currentRail
+ * @param {number} params.direction
+ * @param {Array} params.string
+ *
+ * @returns {Array}
+ */
+const fillEncodeFence = ({
+  railCount, fence, currentRail, direction, string,
+}) => {
+  if (string.length === 0) return fence;
+
+  const [letter, ...nextString] = string;
+  const nextDirection = getNextDirection({ railCount, currentRail, direction });
+
+  return fillEncodeFence({
+    railCount,
+    fence: fence.map(addChar(currentRail, letter)),
+    currentRail: currentRail + nextDirection,
+    direction: nextDirection,
+    string: nextString,
+  });
+};
+
+/**
+ * @param {string} string
+ * @param {number} railCount
+ *
+ * @returns {string}
+ */
+export default function encodeRailFenceCipher(string, railCount) {
+  const fence = buildFence(railCount);
+
+  const filledFence = fillEncodeFence({
+    railCount,
+    fence,
+    currentRail: 0,
+    direction: DIRECTIONS.DOWN,
+    string: string.split(''),
+  });
+
+  return filledFence.flat().join('');
+}
diff --git a/src/algorithms/cryptography/rail-fence-cipher/railFenceCipher.js b/src/algorithms/cryptography/rail-fence-cipher/railFenceCipher.js
new file mode 100644
index 0000000000..e50b477a36
--- /dev/null
+++ b/src/algorithms/cryptography/rail-fence-cipher/railFenceCipher.js
@@ -0,0 +1,50 @@
+/**
+ * @constant DIRECTIONS
+ * @type {object}
+ * @property {number} UP
+ * @property {number} DOWN
+ */
+export const DIRECTIONS = { UP: -1, DOWN: 1 };
+
+/**
+ * @param {number} rows
+ *
+ * @returns {Array}
+ */
+export const buildFence = (rows) => Array(rows)
+  .fill()
+  .map(() => []);
+
+/**
+ * @param {object} params
+ * @param {number} params.railCount
+ * @param {number} params.currentRail
+ * @param {number} params.direction
+ *
+ * @returns {number}
+ */
+export const getNextDirection = ({ railCount, currentRail, direction }) => {
+  switch (currentRail) {
+    case 0: return DIRECTIONS.DOWN;
+    case railCount - 1: return DIRECTIONS.UP;
+    default: return direction;
+  }
+};
+
+/**
+ * Given a rail, adds a char to it
+ * if it matches a targetIndex.
+ * @callback charAdder
+ * @param {number} rail
+ * @param {currentRail} number
+ */
+
+/**
+ * @param {number} targetIndex
+ * @param {string} letter
+ *
+ * @returns {charAdder}
+ */
+export const addChar = (targetIndex, letter) => (rail, currentRail) => {
+  return (currentRail === targetIndex ? [...rail, letter] : rail);
+};

From 2794445f9537d8acee3bba3142335a71f0e0628b Mon Sep 17 00:00:00 2001
From: Sagid M <kofon95@mail.ru>
Date: Sun, 20 Dec 2020 21:57:03 +0300
Subject: [PATCH 055/264] Add the word "set" to avoid misinterpretation in
 description (#286)

* Add word to avoid misinterpretation

* Rename the CI workflow file.

Co-authored-by: Sagid Magomedov <sagid-m@yandex-team.ru>
Co-authored-by: Oleksii Trekhleb <trehleb@gmail.com>
---
 src/algorithms/math/is-power-of-two/README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/algorithms/math/is-power-of-two/README.md b/src/algorithms/math/is-power-of-two/README.md
index 5b66b7c6cf..8253cb8700 100644
--- a/src/algorithms/math/is-power-of-two/README.md
+++ b/src/algorithms/math/is-power-of-two/README.md
@@ -12,7 +12,7 @@ the number can't be a power of two.
 
 **Bitwise solution**
 
-Powers of two in binary form always have just one bit.
+Powers of two in binary form always have just one bit set.
 The only exception is with a signed integer (e.g. an 8-bit
 signed integer with a value of -128 looks like: `10000000`)
 

From cfba1d9954ab5b4a33251c7af3f7f55a256a0de5 Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Sun, 20 Dec 2020 19:57:51 +0100
Subject: [PATCH 056/264] Add Rail Fence Cipher.

---
 README.md                                     |   2 +-
 .../cryptography/rail-fence-cipher/README.md  |  15 +-
 ...Cypher.test.js => railFenceCipher.test.js} |  35 ++-
 .../rail-fence-cipher/decodeRailFence.js      | 108 --------
 .../rail-fence-cipher/encodeRailFence.js      |  52 ----
 .../rail-fence-cipher/railFenceCipher.js      | 244 ++++++++++++++++--
 6 files changed, 254 insertions(+), 202 deletions(-)
 rename src/algorithms/cryptography/rail-fence-cipher/__test__/{railFenceCypher.test.js => railFenceCipher.test.js} (51%)
 delete mode 100644 src/algorithms/cryptography/rail-fence-cipher/decodeRailFence.js
 delete mode 100644 src/algorithms/cryptography/rail-fence-cipher/encodeRailFence.js

diff --git a/README.md b/README.md
index c6d8713451..feb9832d36 100644
--- a/README.md
+++ b/README.md
@@ -143,7 +143,7 @@ a set of rules that precisely define a sequence of operations.
   * `A` [Travelling Salesman Problem](src/algorithms/graph/travelling-salesman) - shortest possible route that visits each city and returns to the origin city
 * **Cryptography**
   * `B` [Polynomial Hash](src/algorithms/cryptography/polynomial-hash) - rolling hash function based on polynomial
-  * `B` [Rail Fence Cypher](src/algorithms/cryptography/rail-fence-cipher) - a transposition cipher algorithm for encoding messages
+  * `B` [Rail Fence Cipher](src/algorithms/cryptography/rail-fence-cipher) - a transposition cipher algorithm for encoding messages
   * `B` [Caesar Cipher](src/algorithms/cryptography/caesar-cipher) - simple substitution cipher
   * `B` [Hill Cipher](src/algorithms/cryptography/hill-cipher) - substitution cipher based on linear algebra
 * **Machine Learning**
diff --git a/src/algorithms/cryptography/rail-fence-cipher/README.md b/src/algorithms/cryptography/rail-fence-cipher/README.md
index e090f557eb..d01395f554 100644
--- a/src/algorithms/cryptography/rail-fence-cipher/README.md
+++ b/src/algorithms/cryptography/rail-fence-cipher/README.md
@@ -1,18 +1,18 @@
-# Rail fence Cipher
+# Rail Fence Cipher
 
-This is a [transposition cipher](https://en.wikipedia.org/wiki/Transposition_cipher) in which the message is split accross a set of rails on a fence for encoding. The fence is populated with the message's characters, starting at the top left and adding a character on each position, traversing them diagonally to the bottom. Upon reaching the last rail, the direction should then turn diagonal and upwards up to the very first rail in a zig-zag motion. Rinse and repeat until the message is fully disposed across the fence. The encoded message is the result of concatenating the text in each rail, from top to bottom.
+The **rail fence cipher** (also called a **zigzag cipher**) is a [transposition cipher](https://en.wikipedia.org/wiki/Transposition_cipher) in which the message is split across a set of rails on a fence for encoding. The fence is populated with the message's characters, starting at the top left and adding a character on each position, traversing them diagonally to the bottom. Upon reaching the last rail, the direction should then turn diagonal and upwards up to the very first rail in a zig-zag motion. Rinse and repeat until the message is fully disposed across the fence. The encoded message is the result of concatenating the text in each rail, from top to bottom.
 
-From [wikipedia](https://en.wikipedia.org/wiki/Rail_fence_cipher), this is what the message `WE ARE DISCOVERED. FLEE AT ONCE` looks like on a 3-rail fence:
+From [wikipedia](https://en.wikipedia.org/wiki/Rail_fence_cipher), this is what the message `WE ARE DISCOVERED. FLEE AT ONCE` looks like on a `3`-rail fence:
 
 ```
 W . . . E . . . C . . . R . . . L . . . T . . . E
 . E . R . D . S . O . E . E . F . E . A . O . C .
 . . A . . . I . . . V . . . D . . . E . . . N . .
 -------------------------------------------------
-             ECRLTEERDSOEEFEAOCAIVDEN            
+             WECRLTEERDSOEEFEAOCAIVDEN
 ```
 
-The message can then be decoded by re-creating the encode fence, with the same traversal pattern, except characters should only be added on one rail at a time. To ilustrate that, a dash can be added on the rails that are not supposed to be poupated yet. This is what the fence would look like after populating the first rail, the dashes represent positions that were visited but not populated.
+The message can then be decoded by re-creating the encoded fence, with the same traversal pattern, except characters should only be added on one rail at a time. To illustrate that, a dash can be added on the rails that are not supposed to be populated yet. This is what the fence would look like after populating the first rail, the dashes represent positions that were visited but not populated.
 
 ```
 W . . . E . . . C . . . R . . . L . . . T . . . E
@@ -22,4 +22,7 @@ W . . . E . . . C . . . R . . . L . . . T . . . E
 
 It's time to start populating the next rail once the number of visited fence positions is equal to the number of characters in the message.
 
-[Learn more](https://crypto.interactive-maths.com/rail-fence-cipher.html)
+## References
+
+- [Rail Fence Cipher on Wikipedia](https://en.wikipedia.org/wiki/Rail_fence_cipher)
+- [Rail Fence Cipher Calculator](https://crypto.interactive-maths.com/rail-fence-cipher.html)
diff --git a/src/algorithms/cryptography/rail-fence-cipher/__test__/railFenceCypher.test.js b/src/algorithms/cryptography/rail-fence-cipher/__test__/railFenceCipher.test.js
similarity index 51%
rename from src/algorithms/cryptography/rail-fence-cipher/__test__/railFenceCypher.test.js
rename to src/algorithms/cryptography/rail-fence-cipher/__test__/railFenceCipher.test.js
index 285841e2ce..db0c49eb6b 100644
--- a/src/algorithms/cryptography/rail-fence-cipher/__test__/railFenceCypher.test.js
+++ b/src/algorithms/cryptography/rail-fence-cipher/__test__/railFenceCipher.test.js
@@ -1,26 +1,43 @@
-import encodeRailFenceCipher from '../encodeRailFence';
-import decodeRailFenceCipher from '../decodeRailFence';
+import { encodeRailFenceCipher, decodeRailFenceCipher } from '../railFenceCipher';
 
-describe('rail fence cipher', () => {
+describe('railFenceCipher', () => {
   it('encodes a string correctly for base=3', () => {
     expect(encodeRailFenceCipher('', 3)).toBe('');
-    expect(encodeRailFenceCipher('WEAREDISCOVEREDFLEEATONCE', 3)).toBe('WECRLTEERDSOEEFEAOCAIVDEN');
-    expect(encodeRailFenceCipher('Hello, World!', 3)).toBe('Hoo!el,Wrdl l');
+    expect(encodeRailFenceCipher('12345', 3)).toBe(
+      '15243',
+    );
+    expect(encodeRailFenceCipher('WEAREDISCOVEREDFLEEATONCE', 3)).toBe(
+      'WECRLTEERDSOEEFEAOCAIVDEN',
+    );
+    expect(encodeRailFenceCipher('Hello, World!', 3)).toBe(
+      'Hoo!el,Wrdl l',
+    );
   });
 
   it('decodes a string correctly for base=3', () => {
     expect(decodeRailFenceCipher('', 3)).toBe('');
-    expect(decodeRailFenceCipher('WECRLTEERDSOEEFEAOCAIVDEN', 3)).toBe('WEAREDISCOVEREDFLEEATONCE');
-    expect(decodeRailFenceCipher('Hoo!el,Wrdl l', 3)).toBe('Hello, World!');
+    expect(decodeRailFenceCipher('WECRLTEERDSOEEFEAOCAIVDEN', 3)).toBe(
+      'WEAREDISCOVEREDFLEEATONCE',
+    );
+    expect(decodeRailFenceCipher('Hoo!el,Wrdl l', 3)).toBe(
+      'Hello, World!',
+    );
+    expect(decodeRailFenceCipher('15243', 3)).toBe(
+      '12345',
+    );
   });
 
   it('encodes a string correctly for base=4', () => {
     expect(encodeRailFenceCipher('', 4)).toBe('');
-    expect(encodeRailFenceCipher('THEYAREATTACKINGFROMTHENORTH', 4)).toBe('TEKOOHRACIRMNREATANFTETYTGHH');
+    expect(encodeRailFenceCipher('THEYAREATTACKINGFROMTHENORTH', 4)).toBe(
+      'TEKOOHRACIRMNREATANFTETYTGHH',
+    );
   });
 
   it('decodes a string correctly for base=4', () => {
     expect(decodeRailFenceCipher('', 4)).toBe('');
-    expect(decodeRailFenceCipher('TEKOOHRACIRMNREATANFTETYTGHH', 4)).toBe('THEYAREATTACKINGFROMTHENORTH');
+    expect(decodeRailFenceCipher('TEKOOHRACIRMNREATANFTETYTGHH', 4)).toBe(
+      'THEYAREATTACKINGFROMTHENORTH',
+    );
   });
 });
diff --git a/src/algorithms/cryptography/rail-fence-cipher/decodeRailFence.js b/src/algorithms/cryptography/rail-fence-cipher/decodeRailFence.js
deleted file mode 100644
index b1826b4883..0000000000
--- a/src/algorithms/cryptography/rail-fence-cipher/decodeRailFence.js
+++ /dev/null
@@ -1,108 +0,0 @@
-import {
-  addChar,
-  buildFence,
-  DIRECTIONS,
-  getNextDirection,
-} from './railFenceCipher';
-
-/**
- * @param {object} params
- * @param {number} params.railCount
- * @param {number} params.strLen
- * @param {Array} params.string
- * @param {Array} params.fence
- * @param {number} params.targetRail
- * @param {number} params.direction
- * @param {Array} params.coords
- *
- * @returns {Array}
- */
-const fillDecodeFence = ({
-  railCount, strLen, string, fence, targetRail, direction, coords,
-}) => {
-  if (string.length === 0) return fence;
-
-  const [currentRail, currentColumn] = coords;
-  const shouldGoNextRail = currentColumn === strLen - 1;
-  const nextDirection = shouldGoNextRail
-    ? DIRECTIONS.DOWN
-    : getNextDirection({ railCount, currentRail, direction });
-  const nextRail = shouldGoNextRail ? targetRail + 1 : targetRail;
-  const nextCoords = [
-    shouldGoNextRail ? 0 : currentRail + nextDirection,
-    shouldGoNextRail ? 0 : currentColumn + 1,
-  ];
-
-  const shouldAddChar = currentRail === targetRail;
-  const [currentChar, ...remainderString] = string;
-  const nextString = shouldAddChar ? remainderString : string;
-  const nextFence = shouldAddChar ? fence.map(addChar(currentRail, currentChar)) : fence;
-
-  return fillDecodeFence({
-    railCount,
-    strLen,
-    string: nextString,
-    fence: nextFence,
-    targetRail: nextRail,
-    direction: nextDirection,
-    coords: nextCoords,
-  });
-};
-
-/**
- * @param {object} params
- * @param {number} params.railCount
- * @param {number} params.strLen
- * @param {Array} params.fence
- * @param {number} params.currentRail
- * @param {number} params.direction
- * @param {Array} params.code
- *
- * @returns {string}
- */
-const decodeFence = ({
-  railCount, strLen, fence, currentRail, direction, code,
-}) => {
-  if (code.length === strLen) return code.join('');
-
-  const [currentChar, ...nextRail] = fence[currentRail];
-  const nextDirection = getNextDirection({ railCount, currentRail, direction });
-
-  return decodeFence({
-    railCount,
-    strLen,
-    currentRail: currentRail + nextDirection,
-    direction: nextDirection,
-    code: [...code, currentChar],
-    fence: fence.map((rail, idx) => (idx === currentRail ? nextRail : rail)),
-  });
-};
-
-/**
- * @param {string} string
- * @param {number} railCount
- *
- * @returns {string}
- */
-export default function decodeRailFenceCipher(string, railCount) {
-  const strLen = string.length;
-  const emptyFence = buildFence(railCount);
-  const filledFence = fillDecodeFence({
-    railCount,
-    strLen,
-    string: string.split(''),
-    fence: emptyFence,
-    targetRail: 0,
-    direction: DIRECTIONS.DOWN,
-    coords: [0, 0],
-  });
-
-  return decodeFence({
-    railCount,
-    strLen,
-    fence: filledFence,
-    currentRail: 0,
-    direction: DIRECTIONS.DOWN,
-    code: [],
-  });
-}
diff --git a/src/algorithms/cryptography/rail-fence-cipher/encodeRailFence.js b/src/algorithms/cryptography/rail-fence-cipher/encodeRailFence.js
deleted file mode 100644
index 9a58131253..0000000000
--- a/src/algorithms/cryptography/rail-fence-cipher/encodeRailFence.js
+++ /dev/null
@@ -1,52 +0,0 @@
-import {
-  addChar,
-  buildFence,
-  DIRECTIONS,
-  getNextDirection,
-} from './railFenceCipher';
-
-/**
- * @param {object} params
- * @param {number} params.railCount
- * @param {number} params.currentRail
- * @param {number} params.direction
- * @param {Array} params.string
- *
- * @returns {Array}
- */
-const fillEncodeFence = ({
-  railCount, fence, currentRail, direction, string,
-}) => {
-  if (string.length === 0) return fence;
-
-  const [letter, ...nextString] = string;
-  const nextDirection = getNextDirection({ railCount, currentRail, direction });
-
-  return fillEncodeFence({
-    railCount,
-    fence: fence.map(addChar(currentRail, letter)),
-    currentRail: currentRail + nextDirection,
-    direction: nextDirection,
-    string: nextString,
-  });
-};
-
-/**
- * @param {string} string
- * @param {number} railCount
- *
- * @returns {string}
- */
-export default function encodeRailFenceCipher(string, railCount) {
-  const fence = buildFence(railCount);
-
-  const filledFence = fillEncodeFence({
-    railCount,
-    fence,
-    currentRail: 0,
-    direction: DIRECTIONS.DOWN,
-    string: string.split(''),
-  });
-
-  return filledFence.flat().join('');
-}
diff --git a/src/algorithms/cryptography/rail-fence-cipher/railFenceCipher.js b/src/algorithms/cryptography/rail-fence-cipher/railFenceCipher.js
index e50b477a36..7b58037e22 100644
--- a/src/algorithms/cryptography/rail-fence-cipher/railFenceCipher.js
+++ b/src/algorithms/cryptography/rail-fence-cipher/railFenceCipher.js
@@ -1,50 +1,242 @@
+/**
+ * @typedef {string[]} Rail
+ * @typedef {Rail[]} Fence
+ * @typedef {number} Direction
+ */
+
 /**
  * @constant DIRECTIONS
  * @type {object}
- * @property {number} UP
- * @property {number} DOWN
+ * @property {Direction} UP
+ * @property {Direction} DOWN
  */
-export const DIRECTIONS = { UP: -1, DOWN: 1 };
+const DIRECTIONS = { UP: -1, DOWN: 1 };
 
 /**
- * @param {number} rows
+ * Builds a fence with a specific number of rows.
  *
- * @returns {Array}
+ * @param {number} rowsNum
+ * @returns {Fence}
  */
-export const buildFence = (rows) => Array(rows)
-  .fill()
+const buildFence = (rowsNum) => Array(rowsNum)
+  .fill(null)
   .map(() => []);
 
 /**
- * @param {object} params
- * @param {number} params.railCount
- * @param {number} params.currentRail
- * @param {number} params.direction
+ * Get next direction to move (based on the current one) while traversing the fence.
  *
- * @returns {number}
+ * @param {object} params
+ * @param {number} params.railCount - Number of rows in the fence
+ * @param {number} params.currentRail - Current row that we're visiting
+ * @param {Direction} params.direction - Current direction
+ * @returns {Direction} - The next direction to take
  */
-export const getNextDirection = ({ railCount, currentRail, direction }) => {
+const getNextDirection = ({ railCount, currentRail, direction }) => {
   switch (currentRail) {
-    case 0: return DIRECTIONS.DOWN;
-    case railCount - 1: return DIRECTIONS.UP;
-    default: return direction;
+    case 0:
+      // Go down if we're on top of the fence.
+      return DIRECTIONS.DOWN;
+    case railCount - 1:
+      // Go up if we're at the bottom of the fence.
+      return DIRECTIONS.UP;
+    default:
+      // Continue with the same direction if we're in the middle of the fence.
+      return direction;
   }
 };
 
 /**
- * Given a rail, adds a char to it
- * if it matches a targetIndex.
- * @callback charAdder
- * @param {number} rail
- * @param {currentRail} number
+ * @param {number} targetRailIndex
+ * @param {string} letter
+ * @returns {Function}
  */
+const addCharToRail = (targetRailIndex, letter) => {
+  /**
+   * Given a rail, adds a char to it if it matches a targetIndex.
+   *
+   * @param {Rail} rail
+   * @param {number} currentRail
+   * @returns {Rail}
+   */
+  function onEachRail(rail, currentRail) {
+    return currentRail === targetRailIndex
+      ? [...rail, letter]
+      : rail;
+  }
+  return onEachRail;
+};
 
 /**
- * @param {number} targetIndex
- * @param {string} letter
+ * Hangs the characters on the fence.
  *
- * @returns {charAdder}
+ * @param {object} params
+ * @param {Fence} params.fence
+ * @param {number} params.currentRail
+ * @param {Direction} params.direction
+ * @param {string[]} params.chars
+ * @returns {Fence}
+ */
+const fillEncodeFence = ({
+  fence,
+  currentRail,
+  direction,
+  chars,
+}) => {
+  if (chars.length === 0) {
+    // All chars have been placed on a fence.
+    return fence;
+  }
+
+  const railCount = fence.length;
+
+  // Getting the next character to place on a fence.
+  const [letter, ...nextChars] = chars;
+  const nextDirection = getNextDirection({
+    railCount,
+    currentRail,
+    direction,
+  });
+
+  return fillEncodeFence({
+    fence: fence.map(addCharToRail(currentRail, letter)),
+    currentRail: currentRail + nextDirection,
+    direction: nextDirection,
+    chars: nextChars,
+  });
+};
+
+/**
+ * @param {object} params
+ * @param {number} params.strLen
+ * @param {string[]} params.chars
+ * @param {Fence} params.fence
+ * @param {number} params.targetRail
+ * @param {Direction} params.direction
+ * @param {number[]} params.coords
+ * @returns {Fence}
  */
-export const addChar = (targetIndex, letter) => (rail, currentRail) => {
-  return (currentRail === targetIndex ? [...rail, letter] : rail);
+const fillDecodeFence = (params) => {
+  const {
+    strLen, chars, fence, targetRail, direction, coords,
+  } = params;
+
+  const railCount = fence.length;
+
+  if (chars.length === 0) {
+    return fence;
+  }
+
+  const [currentRail, currentColumn] = coords;
+  const shouldGoNextRail = currentColumn === strLen - 1;
+  const nextDirection = shouldGoNextRail
+    ? DIRECTIONS.DOWN
+    : getNextDirection(
+      { railCount, currentRail, direction },
+    );
+  const nextRail = shouldGoNextRail ? targetRail + 1 : targetRail;
+  const nextCoords = [
+    shouldGoNextRail ? 0 : currentRail + nextDirection,
+    shouldGoNextRail ? 0 : currentColumn + 1,
+  ];
+
+  const shouldAddChar = currentRail === targetRail;
+  const [currentChar, ...remainderChars] = chars;
+  const nextString = shouldAddChar ? remainderChars : chars;
+  const nextFence = shouldAddChar ? fence.map(addCharToRail(currentRail, currentChar)) : fence;
+
+  return fillDecodeFence({
+    strLen,
+    chars: nextString,
+    fence: nextFence,
+    targetRail: nextRail,
+    direction: nextDirection,
+    coords: nextCoords,
+  });
+};
+
+/**
+ * @param {object} params
+ * @param {number} params.strLen
+ * @param {Fence} params.fence
+ * @param {number} params.currentRail
+ * @param {Direction} params.direction
+ * @param {number[]} params.code
+ * @returns {string}
+ */
+const decodeFence = (params) => {
+  const {
+    strLen,
+    fence,
+    currentRail,
+    direction,
+    code,
+  } = params;
+
+  if (code.length === strLen) {
+    return code.join('');
+  }
+
+  const railCount = fence.length;
+
+  const [currentChar, ...nextRail] = fence[currentRail];
+  const nextDirection = getNextDirection(
+    { railCount, currentRail, direction },
+  );
+
+  return decodeFence({
+    railCount,
+    strLen,
+    currentRail: currentRail + nextDirection,
+    direction: nextDirection,
+    code: [...code, currentChar],
+    fence: fence.map((rail, idx) => (idx === currentRail ? nextRail : rail)),
+  });
+};
+
+/**
+ * Encodes the message using Rail Fence Cipher.
+ *
+ * @param {string} string - The string to be encoded
+ * @param {number} railCount - The number of rails in a fence
+ * @returns {string} - Encoded string
+ */
+export const encodeRailFenceCipher = (string, railCount) => {
+  const fence = buildFence(railCount);
+
+  const filledFence = fillEncodeFence({
+    fence,
+    currentRail: 0,
+    direction: DIRECTIONS.DOWN,
+    chars: string.split(''),
+  });
+
+  return filledFence.flat().join('');
+};
+
+/**
+ * Decodes the message using Rail Fence Cipher.
+ *
+ * @param {string} string - Encoded string
+ * @param {number} railCount - The number of rows in a fence
+ * @returns {string} - Decoded string.
+ */
+export const decodeRailFenceCipher = (string, railCount) => {
+  const strLen = string.length;
+  const emptyFence = buildFence(railCount);
+  const filledFence = fillDecodeFence({
+    strLen,
+    chars: string.split(''),
+    fence: emptyFence,
+    targetRail: 0,
+    direction: DIRECTIONS.DOWN,
+    coords: [0, 0],
+  });
+
+  return decodeFence({
+    strLen,
+    fence: filledFence,
+    currentRail: 0,
+    direction: DIRECTIONS.DOWN,
+    code: [],
+  });
 };

From 521e0a9bbd8f4e2ff5bd29840a3d7305fd07351c Mon Sep 17 00:00:00 2001
From: Andy Chen <25174488+KsRyY@users.noreply.github.com>
Date: Mon, 21 Dec 2020 03:00:44 +0800
Subject: [PATCH 057/264] Remove a extra space (#291)


From fa1f930c99bf869e0074515f981cd018da185412 Mon Sep 17 00:00:00 2001
From: Brandon Villa <bornofos@gmail.com>
Date: Sun, 20 Dec 2020 13:05:18 -0600
Subject: [PATCH 058/264] Add missing step (#345)

---
 src/data-structures/linked-list/README.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/src/data-structures/linked-list/README.md b/src/data-structures/linked-list/README.md
index 2b8a7507b6..f357889de6 100644
--- a/src/data-structures/linked-list/README.md
+++ b/src/data-structures/linked-list/README.md
@@ -102,6 +102,7 @@ Remove(head, value)
   if n.next != ø
     if n.next = tail
       tail ← n
+      tail.next = null
     end if
     n.next ← n.next.next
     return true

From f617569760979d540f795e41f039e93204c91af0 Mon Sep 17 00:00:00 2001
From: Go <monkeywzr@gmail.com>
Date: Mon, 21 Dec 2020 04:06:36 +0900
Subject: [PATCH 059/264] fix typo (#350)

---
 src/algorithms/string/levenshtein-distance/README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/algorithms/string/levenshtein-distance/README.md b/src/algorithms/string/levenshtein-distance/README.md
index 4d4078b854..8876d6791c 100644
--- a/src/algorithms/string/levenshtein-distance/README.md
+++ b/src/algorithms/string/levenshtein-distance/README.md
@@ -50,7 +50,7 @@ to assist natural language translation based on translation memory.
 
 Let’s take a simple example of finding minimum edit distance between 
 strings `ME` and `MY`. Intuitively you already know that minimum edit distance 
-here is `1` operation and this operation. And it is replacing `E` with `Y`. But 
+here is `1` operation, which is replacing `E` with `Y`. But 
 let’s try to formalize it in a form of the algorithm in order to be able to 
 do more complex examples like transforming `Saturday` into `Sunday`.
 

From e07620359090a8f372fe2b4297bb9e806d5d0343 Mon Sep 17 00:00:00 2001
From: Yura Sherman <yurasherman+github@gmail.com>
Date: Sun, 20 Dec 2020 21:09:09 +0200
Subject: [PATCH 060/264] Fix a grammar mistake (#396)

---
 src/data-structures/bloom-filter/README.ru-RU.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/data-structures/bloom-filter/README.ru-RU.md b/src/data-structures/bloom-filter/README.ru-RU.md
index 38830f9efb..b5c19c06c8 100644
--- a/src/data-structures/bloom-filter/README.ru-RU.md
+++ b/src/data-structures/bloom-filter/README.ru-RU.md
@@ -19,7 +19,7 @@
 срабатываний фильтра.
 
 Вот пример Блум фильтра, представляющего набор `{x, y, z}`. Цветные стрелки показывают позиции в битовом массиве,
-которым привязан каждый элемент набора. Элемент `w` не в набора `{x, y, z}`, потому что он привязан к позиции в битовом
+которым привязан каждый элемент набора. Элемент `w` не в наборе `{x, y, z}`, потому что он привязан к позиции в битовом
 массиве, равной `0`. Для этой формы , `m = 18`, а `k = 3`.
 
 Фильтр Блума представляет собой битовый массив из `m` бит. Изначально, когда структура данных хранит пустое множество, все

From 148f9179c941d9586e36930af4d80c9f2f74bbbf Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Javier=20Savi=C3=B1on?=
 <44041766+Mengeroshi@users.noreply.github.com>
Date: Sun, 20 Dec 2020 13:16:35 -0600
Subject: [PATCH 061/264] Linked List Spanish Traslation (#409)

* Linked List Spanish Traslation

* Rename the CI workflow file.

Co-authored-by: Oleksii Trekhleb <trehleb@gmail.com>
---
 .../linked-list/README.es-ES.md               | 164 ++++++++++++++++++
 1 file changed, 164 insertions(+)
 create mode 100644 src/data-structures/linked-list/README.es-ES.md

diff --git a/src/data-structures/linked-list/README.es-ES.md b/src/data-structures/linked-list/README.es-ES.md
new file mode 100644
index 0000000000..978e234ddf
--- /dev/null
+++ b/src/data-structures/linked-list/README.es-ES.md
@@ -0,0 +1,164 @@
+# Lista Enlazada (Linked List)
+
+_Lee esto en otros idiomas:_
+[_简体中文_](README.zh-CN.md),
+[_Русский_](README.ru-RU.md),
+[_日本語_](README.ja-JP.md),
+[_Português_](README.pt-BR.md)
+[_English_](README.md)
+
+En ciencias de la computaciòn una **lista enlazada** es una  coleccion linear 
+de elemntos de datos, en los cuales el orden linear no es dado por
+su posciòn fisica en memoria. En cambio, cada 
+elemento señala al siguiente. Es una estructura de datos 
+que consiste en un grupo de nodos los cuales juntos representan
+una secuencia. Bajo la forma mas simple, cada nodo es 
+compuesto de datos y una referencia (en otras palabras, 
+un lazo) al siguiente nodo en la secuencia. Esta estructura
+permite la insercion o remocion de elementos 
+desde cualquier posicion en la secuencia durante la iteracion. 
+Variantes mas complejas agregan lazos adicionales, permitiendo 
+una eficiente insercion o remocion desde referencias arbitrarias
+del elemento. Una desventaja de las listas lazadas es que el tiempo de
+acceso es linear (y dificil de canalizar) Un acceso
+mas rapido, como un acceso aleatorio, no es factible. Los arreglos
+tienen una mejor locazion comparados con las listas lazadas.
+
+
+![Linked List](https://upload.wikimedia.org/wikipedia/commons/6/6d/Singly-linked-list.svg)
+
+## Pseudocodigo para operacones basicas
+
+### Insertar
+
+```text
+Add(value)
+  Pre: value is the value to add to the list
+  Post: value has been placed at the tail of the list
+  n ← node(value)
+  if head = ø
+    head ← n
+    tail ← n
+  else
+    tail.next ← n
+    tail ← n
+  end if
+end Add
+```
+
+```text
+Prepend(value)
+ Pre: value is the value to add to the list
+ Post: value has been placed at the head of the list
+ n ← node(value)
+ n.next ← head
+ head ← n
+ if tail = ø
+   tail ← n
+ end
+end Prepend
+```
+
+### Buscar
+
+```text
+Contains(head, value)
+  Pre: head is the head node in the list
+       value is the value to search for
+  Post: the item is either in the linked list, true; otherwise false
+  n ← head
+  while n != ø and n.value != value
+    n ← n.next
+  end while
+  if n = ø
+    return false
+  end if
+  return true
+end Contains
+```
+    
+### Borrar
+
+```text
+Remove(head, value)
+  Pre: head is the head node in the list
+       value is the value to remove from the list
+  Post: value is removed from the list, true, otherwise false
+  if head = ø
+    return false
+  end if
+  n ← head
+  if n.value = value
+    if head = tail
+      head ← ø
+      tail ← ø
+    else
+      head ← head.next
+    end if
+    return true
+  end if
+  while n.next != ø and n.next.value != value
+    n ← n.next
+  end while
+  if n.next != ø
+    if n.next = tail
+      tail ← n
+    end if
+    n.next ← n.next.next
+    return true
+  end if
+  return false
+end Remove
+```
+
+### Atrevesar
+
+```text
+Traverse(head)
+  Pre: head is the head node in the list
+  Post: the items in the list have been traversed
+  n ← head
+  while n != ø
+    yield n.value
+    n ← n.next
+  end while
+end Traverse
+```
+
+### Atravesar en Reversa
+
+```text
+ReverseTraversal(head, tail)
+  Pre: head and tail belong to the same list
+  Post: the items in the list have been traversed in reverse order
+  if tail != ø
+    curr ← tail
+    while curr != head
+      prev ← head
+      while prev.next != curr
+        prev ← prev.next
+      end while
+      yield curr.value
+      curr ← prev
+    end while
+   yield curr.value
+  end if
+end ReverseTraversal
+```
+
+## Complexities
+
+### Time Complexity
+
+| Access    | Search    | Insertion | Deletion  |
+| :-------: | :-------: | :-------: | :-------: |
+| O(n)      | O(n)      | O(1)      | O(n)      |
+
+### Space Complexity
+
+O(n)
+
+## References
+
+- [Wikipedia](https://en.wikipedia.org/wiki/Linked_list)
+- [YouTube](https://www.youtube.com/watch?v=njTh_OwMljA&index=2&t=1s&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)

From 4b6c601158b7b0284c9aad3a899fe97285fc7c1a Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Sun, 20 Dec 2020 20:18:12 +0100
Subject: [PATCH 062/264] Add Spanish link for the Linked List README.

---
 src/algorithms/math/is-power-of-two/README.md | 15 ++++----
 src/data-structures/linked-list/README.md     | 35 ++++++++++---------
 2 files changed, 25 insertions(+), 25 deletions(-)

diff --git a/src/algorithms/math/is-power-of-two/README.md b/src/algorithms/math/is-power-of-two/README.md
index 8253cb8700..6ed1e92568 100644
--- a/src/algorithms/math/is-power-of-two/README.md
+++ b/src/algorithms/math/is-power-of-two/README.md
@@ -1,14 +1,13 @@
 # Is a power of two
 
-Given a positive integer, write a function to find if it is 
+Given a positive integer, write a function to find if it is
 a power of two or not.
 
 **Naive solution**
 
 In naive solution we just keep dividing the number by two
-unless the number becomes `1` and every time we do so we
-check that remainder after division is always `0`. Otherwise
-the number can't be a power of two.
+unless the number becomes `1` and every time we do so, we
+check that remainder after division is always `0`. Otherwise, the number can't be a power of two.
 
 **Bitwise solution**
 
@@ -23,8 +22,8 @@ signed integer with a value of -128 looks like: `10000000`)
 8: 1000
 ```
 
-So after checking that the number is greater than zero, 
-we can use a bitwise hack to test that one and only one 
+So after checking that the number is greater than zero,
+we can use a bitwise hack to test that one and only one
 bit is set.
 
 ```
@@ -38,11 +37,11 @@ For example for number `8` that operations will look like:
 - 0001
   ----
   0111
-  
+
   1000
 & 0111
   ----
-  0000    
+  0000
 ```
 
 ## References
diff --git a/src/data-structures/linked-list/README.md b/src/data-structures/linked-list/README.md
index f357889de6..656ad68f58 100644
--- a/src/data-structures/linked-list/README.md
+++ b/src/data-structures/linked-list/README.md
@@ -5,23 +5,24 @@ _Read this in other languages:_
 [_Русский_](README.ru-RU.md),
 [_日本語_](README.ja-JP.md),
 [_Português_](README.pt-BR.md),
-[_한국어_](README.ko-KR.md)
-
-In computer science, a **linked list** is a linear collection 
-of data elements, in which linear order is not given by 
-their physical placement in memory. Instead, each 
-element points to the next. It is a data structure 
-consisting of a group of nodes which together represent 
-a sequence. Under the simplest form, each node is 
-composed of data and a reference (in other words, 
+[_한국어_](README.ko-KR.md),
+[_Español_](README.es-ES.md),
+
+In computer science, a **linked list** is a linear collection
+of data elements, in which linear order is not given by
+their physical placement in memory. Instead, each
+element points to the next. It is a data structure
+consisting of a group of nodes which together represent
+a sequence. Under the simplest form, each node is
+composed of data and a reference (in other words,
 a link) to the next node in the sequence. This structure
-allows for efficient insertion or removal of elements 
-from any position in the sequence during iteration. 
-More complex variants add additional links, allowing 
-efficient insertion or removal from arbitrary element 
-references. A drawback of linked lists is that access 
-time is linear (and difficult to pipeline). Faster 
-access, such as random access, is not feasible. Arrays 
+allows for efficient insertion or removal of elements
+from any position in the sequence during iteration.
+More complex variants add additional links, allowing
+efficient insertion or removal from arbitrary element
+references. A drawback of linked lists is that access
+time is linear (and difficult to pipeline). Faster
+access, such as random access, is not feasible. Arrays
 have better cache locality as compared to linked lists.
 
 ![Linked List](https://upload.wikimedia.org/wikipedia/commons/6/6d/Singly-linked-list.svg)
@@ -75,7 +76,7 @@ Contains(head, value)
   return true
 end Contains
 ```
-    
+
 ### Delete
 
 ```text

From 37871171a5f20cb6ccd3d1409af483852f22423f Mon Sep 17 00:00:00 2001
From: "dependabot[bot]" <49699333+dependabot[bot]@users.noreply.github.com>
Date: Tue, 22 Dec 2020 16:59:06 +0100
Subject: [PATCH 063/264] Bump node-notifier from 8.0.0 to 8.0.1 (#607)

Bumps [node-notifier](https://github.com/mikaelbr/node-notifier) from 8.0.0 to 8.0.1.
- [Release notes](https://github.com/mikaelbr/node-notifier/releases)
- [Changelog](https://github.com/mikaelbr/node-notifier/blob/v8.0.1/CHANGELOG.md)
- [Commits](https://github.com/mikaelbr/node-notifier/compare/v8.0.0...v8.0.1)

Signed-off-by: dependabot[bot] <support@github.com>

Co-authored-by: dependabot[bot] <49699333+dependabot[bot]@users.noreply.github.com>
---
 package-lock.json | 18 ++++++------------
 1 file changed, 6 insertions(+), 12 deletions(-)

diff --git a/package-lock.json b/package-lock.json
index e68c95c1e5..7b212c5f47 100644
--- a/package-lock.json
+++ b/package-lock.json
@@ -4432,8 +4432,7 @@
       "version": "1.3.0",
       "resolved": "https://registry.npmjs.org/growly/-/growly-1.3.0.tgz",
       "integrity": "sha1-8QdIy+dq+WS3yWyTxrzCivEgwIE=",
-      "dev": true,
-      "optional": true
+      "dev": true
     },
     "har-schema": {
       "version": "2.0.0",
@@ -5069,7 +5068,6 @@
       "resolved": "https://registry.npmjs.org/is-wsl/-/is-wsl-2.2.0.tgz",
       "integrity": "sha512-fKzAra0rGJUUBwGBgNkHZuToZcn+TtXHpeCgmkMJMMYx1sQDYaCSyjJBSCa2nH1DGm7s3n1oBnohoVTBaN7Lww==",
       "dev": true,
-      "optional": true,
       "requires": {
         "is-docker": "^2.0.0"
       }
@@ -7140,11 +7138,10 @@
       "dev": true
     },
     "node-notifier": {
-      "version": "8.0.0",
-      "resolved": "https://registry.npmjs.org/node-notifier/-/node-notifier-8.0.0.tgz",
-      "integrity": "sha512-46z7DUmcjoYdaWyXouuFNNfUo6eFa94t23c53c+lG/9Cvauk4a98rAUp9672X5dxGdQmLpPzTxzu8f/OeEPaFA==",
+      "version": "8.0.1",
+      "resolved": "https://registry.npmjs.org/node-notifier/-/node-notifier-8.0.1.tgz",
+      "integrity": "sha512-BvEXF+UmsnAfYfoapKM9nGxnP+Wn7P91YfXmrKnfcYCx6VBeoN5Ez5Ogck6I8Bi5k4RlpqRYaw75pAwzX9OphA==",
       "dev": true,
-      "optional": true,
       "requires": {
         "growly": "^1.3.0",
         "is-wsl": "^2.2.0",
@@ -7159,7 +7156,6 @@
           "resolved": "https://registry.npmjs.org/semver/-/semver-7.3.4.tgz",
           "integrity": "sha512-tCfb2WLjqFAtXn4KEdxIhalnRtoKFN7nAwj0B3ZXCbQloV2tq5eDbcTmT68JJD3nRJq24/XgxtQKFIpQdtvmVw==",
           "dev": true,
-          "optional": true,
           "requires": {
             "lru-cache": "^6.0.0"
           }
@@ -8113,8 +8109,7 @@
       "version": "0.1.1",
       "resolved": "https://registry.npmjs.org/shellwords/-/shellwords-0.1.1.tgz",
       "integrity": "sha512-vFwSUfQvqybiICwZY5+DAWIPLKsWO31Q91JSKl3UYv+K5c2QRPzn0qzec6QPu1Qc9eHYItiP3NdJqNVqetYAww==",
-      "dev": true,
-      "optional": true
+      "dev": true
     },
     "side-channel": {
       "version": "1.0.3",
@@ -8881,8 +8876,7 @@
       "version": "8.3.1",
       "resolved": "https://registry.npmjs.org/uuid/-/uuid-8.3.1.tgz",
       "integrity": "sha512-FOmRr+FmWEIG8uhZv6C2bTgEVXsHk08kE7mPlrBbEe+c3r9pjceVPgupIfNIhc4yx55H69OXANrUaSuu9eInKg==",
-      "dev": true,
-      "optional": true
+      "dev": true
     },
     "v8-compile-cache": {
       "version": "2.2.0",

From bc53ba7362517f8d4b821c26304f570d37708488 Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Tue, 22 Dec 2020 17:04:51 +0100
Subject: [PATCH 064/264] Update dependencies.

---
 package-lock.json | 12 +++++++++---
 1 file changed, 9 insertions(+), 3 deletions(-)

diff --git a/package-lock.json b/package-lock.json
index 7b212c5f47..ce714a9c07 100644
--- a/package-lock.json
+++ b/package-lock.json
@@ -4432,7 +4432,8 @@
       "version": "1.3.0",
       "resolved": "https://registry.npmjs.org/growly/-/growly-1.3.0.tgz",
       "integrity": "sha1-8QdIy+dq+WS3yWyTxrzCivEgwIE=",
-      "dev": true
+      "dev": true,
+      "optional": true
     },
     "har-schema": {
       "version": "2.0.0",
@@ -5068,6 +5069,7 @@
       "resolved": "https://registry.npmjs.org/is-wsl/-/is-wsl-2.2.0.tgz",
       "integrity": "sha512-fKzAra0rGJUUBwGBgNkHZuToZcn+TtXHpeCgmkMJMMYx1sQDYaCSyjJBSCa2nH1DGm7s3n1oBnohoVTBaN7Lww==",
       "dev": true,
+      "optional": true,
       "requires": {
         "is-docker": "^2.0.0"
       }
@@ -7142,6 +7144,7 @@
       "resolved": "https://registry.npmjs.org/node-notifier/-/node-notifier-8.0.1.tgz",
       "integrity": "sha512-BvEXF+UmsnAfYfoapKM9nGxnP+Wn7P91YfXmrKnfcYCx6VBeoN5Ez5Ogck6I8Bi5k4RlpqRYaw75pAwzX9OphA==",
       "dev": true,
+      "optional": true,
       "requires": {
         "growly": "^1.3.0",
         "is-wsl": "^2.2.0",
@@ -7156,6 +7159,7 @@
           "resolved": "https://registry.npmjs.org/semver/-/semver-7.3.4.tgz",
           "integrity": "sha512-tCfb2WLjqFAtXn4KEdxIhalnRtoKFN7nAwj0B3ZXCbQloV2tq5eDbcTmT68JJD3nRJq24/XgxtQKFIpQdtvmVw==",
           "dev": true,
+          "optional": true,
           "requires": {
             "lru-cache": "^6.0.0"
           }
@@ -8109,7 +8113,8 @@
       "version": "0.1.1",
       "resolved": "https://registry.npmjs.org/shellwords/-/shellwords-0.1.1.tgz",
       "integrity": "sha512-vFwSUfQvqybiICwZY5+DAWIPLKsWO31Q91JSKl3UYv+K5c2QRPzn0qzec6QPu1Qc9eHYItiP3NdJqNVqetYAww==",
-      "dev": true
+      "dev": true,
+      "optional": true
     },
     "side-channel": {
       "version": "1.0.3",
@@ -8876,7 +8881,8 @@
       "version": "8.3.1",
       "resolved": "https://registry.npmjs.org/uuid/-/uuid-8.3.1.tgz",
       "integrity": "sha512-FOmRr+FmWEIG8uhZv6C2bTgEVXsHk08kE7mPlrBbEe+c3r9pjceVPgupIfNIhc4yx55H69OXANrUaSuu9eInKg==",
-      "dev": true
+      "dev": true,
+      "optional": true
     },
     "v8-compile-cache": {
       "version": "2.2.0",

From e71dc8dc1690a631d55dd07d15369dc3d87fcb3d Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Tue, 22 Dec 2020 17:08:53 +0100
Subject: [PATCH 065/264] Update dependencies.

---
 package-lock.json | 310 +++++++++++++++++++++++++---------------------
 package.json      |  22 ++--
 2 files changed, 180 insertions(+), 152 deletions(-)

diff --git a/package-lock.json b/package-lock.json
index ce714a9c07..aeeed97b47 100644
--- a/package-lock.json
+++ b/package-lock.json
@@ -5,9 +5,9 @@
   "requires": true,
   "dependencies": {
     "@babel/cli": {
-      "version": "7.12.8",
-      "resolved": "https://registry.npmjs.org/@babel/cli/-/cli-7.12.8.tgz",
-      "integrity": "sha512-/6nQj11oaGhLmZiuRUfxsujiPDc9BBReemiXgIbxc+M5W+MIiFKYwvNDJvBfnGKNsJTKbUfEheKc9cwoPHAVQA==",
+      "version": "7.12.10",
+      "resolved": "https://registry.npmjs.org/@babel/cli/-/cli-7.12.10.tgz",
+      "integrity": "sha512-+y4ZnePpvWs1fc/LhZRTHkTesbXkyBYuOB+5CyodZqrEuETXi3zOVfpAQIdgC3lXbHLTDG9dQosxR9BhvLKDLQ==",
       "dev": true,
       "requires": {
         "@nicolo-ribaudo/chokidar-2": "2.1.8-no-fsevents",
@@ -99,12 +99,31 @@
       }
     },
     "@babel/helper-annotate-as-pure": {
-      "version": "7.10.4",
-      "resolved": "https://registry.npmjs.org/@babel/helper-annotate-as-pure/-/helper-annotate-as-pure-7.10.4.tgz",
-      "integrity": "sha512-XQlqKQP4vXFB7BN8fEEerrmYvHp3fK/rBkRFz9jaJbzK0B1DSfej9Kc7ZzE8Z/OnId1jpJdNAZ3BFQjWG68rcA==",
+      "version": "7.12.10",
+      "resolved": "https://registry.npmjs.org/@babel/helper-annotate-as-pure/-/helper-annotate-as-pure-7.12.10.tgz",
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diff --git a/package.json b/package.json
index b740fa4878..73da04e0cf 100644
--- a/package.json
+++ b/package.json
@@ -34,17 +34,17 @@
   },
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-    "eslint-plugin-react": "^7.21.5",
-    "husky": "^4.3.0",
-    "jest": "^26.6.3"
+    "@babel/cli": "7.12.10",
+    "@babel/preset-env": "7.12.11",
+    "@types/jest": "26.0.19",
+    "eslint": "7.16.0",
+    "eslint-config-airbnb": "18.2.1",
+    "eslint-plugin-import": "2.22.1",
+    "eslint-plugin-jest": "24.1.3",
+    "eslint-plugin-jsx-a11y": "6.4.1",
+    "eslint-plugin-react": "7.21.5",
+    "husky": "4.3.6",
+    "jest": "26.6.3"
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   "dependencies": {}
 }

From 4973392cb9f676a2605a1abe16fb8f5025e1c28e Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Wed, 23 Dec 2020 17:01:13 +0100
Subject: [PATCH 066/264] Add divide and conquer example: best time to buy and
 sell stocks.

---
 README.md                                     |  14 ++-
 .../best-time-to-buy-sell-stocks/README.md    | 107 ++++++++++++++++++
 ...accumulatorBestTimeToBuySellStocks.test.js |  48 ++++++++
 .../dqBestTimeToBuySellStocks.test.js         |  48 ++++++++
 .../peakvalleyBestTimeToBuySellStocks.test.js |  48 ++++++++
 .../accumulatorBestTimeToBuySellStocks.js     |  20 ++++
 .../dqBestTimeToBuySellStocks.js              |  42 +++++++
 .../peakvalleyBestTimeToBuySellStocks.js      |  35 ++++++
 8 files changed, 356 insertions(+), 6 deletions(-)
 create mode 100644 src/algorithms/uncategorized/best-time-to-buy-sell-stocks/README.md
 create mode 100644 src/algorithms/uncategorized/best-time-to-buy-sell-stocks/__tests__/accumulatorBestTimeToBuySellStocks.test.js
 create mode 100644 src/algorithms/uncategorized/best-time-to-buy-sell-stocks/__tests__/dqBestTimeToBuySellStocks.test.js
 create mode 100644 src/algorithms/uncategorized/best-time-to-buy-sell-stocks/__tests__/peakvalleyBestTimeToBuySellStocks.test.js
 create mode 100644 src/algorithms/uncategorized/best-time-to-buy-sell-stocks/accumulatorBestTimeToBuySellStocks.js
 create mode 100644 src/algorithms/uncategorized/best-time-to-buy-sell-stocks/dqBestTimeToBuySellStocks.js
 create mode 100644 src/algorithms/uncategorized/best-time-to-buy-sell-stocks/peakvalleyBestTimeToBuySellStocks.js

diff --git a/README.md b/README.md
index feb9832d36..f7ae004523 100644
--- a/README.md
+++ b/README.md
@@ -129,9 +129,9 @@ a set of rules that precisely define a sequence of operations.
   * `B` [Depth-First Search](src/algorithms/graph/depth-first-search) (DFS)
   * `B` [Breadth-First Search](src/algorithms/graph/breadth-first-search) (BFS)
   * `B` [Kruskal’s Algorithm](src/algorithms/graph/kruskal) - finding Minimum Spanning Tree (MST) for weighted undirected graph
-  * `A` [Dijkstra Algorithm](src/algorithms/graph/dijkstra) - finding shortest paths to all graph vertices from single vertex
-  * `A` [Bellman-Ford Algorithm](src/algorithms/graph/bellman-ford) - finding shortest paths to all graph vertices from single vertex
-  * `A` [Floyd-Warshall Algorithm](src/algorithms/graph/floyd-warshall) - find shortest paths between all pairs of vertices
+  * `A` [Dijkstra Algorithm](src/algorithms/graph/dijkstra) - finding the shortest paths to all graph vertices from single vertex
+  * `A` [Bellman-Ford Algorithm](src/algorithms/graph/bellman-ford) - finding the shortest paths to all graph vertices from single vertex
+  * `A` [Floyd-Warshall Algorithm](src/algorithms/graph/floyd-warshall) - find the shortest paths between all pairs of vertices
   * `A` [Detect Cycle](src/algorithms/graph/detect-cycle) - for both directed and undirected graphs (DFS and Disjoint Set based versions)
   * `A` [Prim’s Algorithm](src/algorithms/graph/prim) - finding Minimum Spanning Tree (MST) for weighted undirected graph
   * `A` [Topological Sorting](src/algorithms/graph/topological-sorting) - DFS method
@@ -157,6 +157,7 @@ a set of rules that precisely define a sequence of operations.
   * `B` [Unique Paths](src/algorithms/uncategorized/unique-paths) - backtracking, dynamic programming and Pascal's Triangle based examples
   * `B` [Rain Terraces](src/algorithms/uncategorized/rain-terraces) - trapping rain water problem (dynamic programming and brute force versions)
   * `B` [Recursive Staircase](src/algorithms/uncategorized/recursive-staircase) - count the number of ways to reach to the top (4 solutions)
+  * `B` [Best Time To Buy Sell Stocks](src/algorithms/uncategorized/best-time-to-buy-sell-stocks) - divide and conquer and one-pass examples
   * `A` [N-Queens Problem](src/algorithms/uncategorized/n-queens)
   * `A` [Knight's Tour](src/algorithms/uncategorized/knight-tour)
 
@@ -176,7 +177,7 @@ algorithm is an abstraction higher than a computer program.
 * **Greedy** - choose the best option at the current time, without any consideration for the future
   * `B` [Jump Game](src/algorithms/uncategorized/jump-game)
   * `A` [Unbound Knapsack Problem](src/algorithms/sets/knapsack-problem)
-  * `A` [Dijkstra Algorithm](src/algorithms/graph/dijkstra) - finding shortest path to all graph vertices
+  * `A` [Dijkstra Algorithm](src/algorithms/graph/dijkstra) - finding the shortest path to all graph vertices
   * `A` [Prim’s Algorithm](src/algorithms/graph/prim) - finding Minimum Spanning Tree (MST) for weighted undirected graph
   * `A` [Kruskal’s Algorithm](src/algorithms/graph/kruskal) - finding Minimum Spanning Tree (MST) for weighted undirected graph
 * **Divide and Conquer** - divide the problem into smaller parts and then solve those parts
@@ -191,6 +192,7 @@ algorithm is an abstraction higher than a computer program.
   * `B` [Matrices](src/algorithms/math/matrix) - generating and traversing the matrices of different shapes
   * `B` [Jump Game](src/algorithms/uncategorized/jump-game)
   * `B` [Fast Powering](src/algorithms/math/fast-powering)
+  * `B` [Best Time To Buy Sell Stocks](src/algorithms/uncategorized/best-time-to-buy-sell-stocks) - divide and conquer and one-pass examples
   * `A` [Permutations](src/algorithms/sets/permutations) (with and without repetitions)
   * `A` [Combinations](src/algorithms/sets/combinations) (with and without repetitions)
 * **Dynamic Programming** - build up a solution using previously found sub-solutions
@@ -207,8 +209,8 @@ algorithm is an abstraction higher than a computer program.
   * `A` [0/1 Knapsack Problem](src/algorithms/sets/knapsack-problem)
   * `A` [Integer Partition](src/algorithms/math/integer-partition)
   * `A` [Maximum Subarray](src/algorithms/sets/maximum-subarray)
-  * `A` [Bellman-Ford Algorithm](src/algorithms/graph/bellman-ford) - finding shortest path to all graph vertices
-  * `A` [Floyd-Warshall Algorithm](src/algorithms/graph/floyd-warshall) - find shortest paths between all pairs of vertices
+  * `A` [Bellman-Ford Algorithm](src/algorithms/graph/bellman-ford) - finding the shortest path to all graph vertices
+  * `A` [Floyd-Warshall Algorithm](src/algorithms/graph/floyd-warshall) - find the shortest paths between all pairs of vertices
   * `A` [Regular Expression Matching](src/algorithms/string/regular-expression-matching)
 * **Backtracking** - similarly to brute force, try to generate all possible solutions, but each time you generate next solution you test
 if it satisfies all conditions, and only then continue generating subsequent solutions. Otherwise, backtrack, and go on a
diff --git a/src/algorithms/uncategorized/best-time-to-buy-sell-stocks/README.md b/src/algorithms/uncategorized/best-time-to-buy-sell-stocks/README.md
new file mode 100644
index 0000000000..982262d94d
--- /dev/null
+++ b/src/algorithms/uncategorized/best-time-to-buy-sell-stocks/README.md
@@ -0,0 +1,107 @@
+# Best Time to Buy and Sell Stock
+
+## Task Description
+
+Say you have an array prices for which the `i`-th element is the price of a given stock on day `i`.
+
+Find the maximum profit. You may complete as many transactions as you like (i.e., buy one and sell one share of the stock multiple times).
+
+> Note: You may not engage in multiple transactions at the same time (i.e., you must sell the stock before you buy again).
+
+**Example #1**
+
+```
+Input: [7, 1, 5, 3, 6, 4]
+Output: 7
+```
+
+_Explanation:_ Buy on day `2` (`price = 1`) and sell on day `3` (`price = 5`), `profit = 5-1 = 4`. Then buy on day `4` (`price = 3`) and sell on day `5` (`price = 6`), `profit = 6-3 = 3`.
+
+**Example #2**
+
+```
+Input: [1, 2, 3, 4, 5]
+Output: 4
+```
+
+_Explanation:_ Buy on day `1` (`price = 1`) and sell on day `5` (`price = 5`), `profit = 5-1 = 4`. Note that you cannot buy on day 1, buy on day 2 and sell them later, as you are engaging multiple transactions at the same time. You must sell before buying again.
+
+**Example #3**
+
+```
+Input: [7, 6, 4, 3, 1]
+Output: 0
+```
+
+_Explanation:_ In this case, no transaction is done, i.e. max `profit = 0`.
+
+## Possible Solutions
+
+### Divide and conquer approach
+
+We may try **all** combinations of buying and selling and find out the most profitable one by applying _divide and conquer approach_.
+
+Let's say we have an array of prices `[7, 6, 4, 3, 1]` and we're on the _1st_ day of trading (at the very beginning of the array). At this point we may say that the overall maximum profit would be the _maximum_ of two following values:
+
+1. _Option 1: Keep the money_ → profit would equal to the profit from buying/selling the rest of the stocks → `keepProfit = profit([6, 4, 3, 1])`.
+2. _Option 2: Buy/sell at current price_ → profit in this case would equal to the profit from buying/selling the rest of the stocks plus (or minus, depending on whether we're selling or buying) the current stock price → `buySellProfit = -7 + profit([6, 4, 3, 1])`.
+
+The overall profit would be equal to → `overalProfit = Max(keepProfit, buySellProfit)`.
+
+As you can see the `profit([6, 4, 3, 1])` task is being solved in the same recursive manner.
+
+> See the full code example in [dqBestTimeToBuySellStocks.js](dqBestTimeToBuySellStocks.js)
+
+#### Time Complexity
+
+As you may see, every recursive call will produce _2_ more recursive branches. The depth of the recursion will be `n` (size of prices array) and thus, the time complexity will equal to `O(2^n)`.
+
+As you may see, this is very inefficient. For example for just `20` prices the number of recursive calls will be somewhere close to `2M`!
+
+#### Additional Space Complexity
+
+If we avoid cloning the prices array between recursive function calls and will use the array pointer then additional space complexity will be proportional to the depth of the recursion: `O(n)`
+
+## Peak Valley Approach
+
+If we plot the prices array (i.e. `[7, 1, 5, 3, 6, 4]`) we may notice that the points of interest are the consecutive valleys and peaks
+
+![Peak Valley Approach](https://leetcode.com/media/original_images/122_maxprofit_1.PNG)
+
+_Image source: [LeetCode](https://leetcode.com/problems/best-time-to-buy-and-sell-stock-ii/solution/)_
+
+So, if we will track the growing price and will sell the stocks immediately _before_ the price goes down we'll get the maximum profit (remember, we bought the stock in the valley at its low price).
+
+> See the full code example in [peakvalleyBestTimeToBuySellStocks.js](peakvalleyBestTimeToBuySellStocks.js)
+
+#### Time Complexity
+
+Since the algorithm requires only one pass through the prices array, the time complexity would equal `O(n)`.
+
+#### Additional Space Complexity
+
+Except of the prices array itself the algorithm consumes the constant amount of memory. Thus, additional space complexity is `O(1)`.
+
+## Accumulator Approach
+
+There is even simpler approach exists. Let's say we have the prices array which looks like this `[1, 7, 2, 3, 6, 7, 6, 7]`:
+
+![Simple One Pass](https://leetcode.com/media/original_images/122_maxprofit_2.PNG)
+
+_Image source: [LeetCode](https://leetcode.com/problems/best-time-to-buy-and-sell-stock-ii/solution/)_
+
+You may notice, that we don't even need to keep tracking of a constantly growing price. Instead, we may simply add the price difference for _all growing segments_ of the chart which eventually sums up to the highest possible profit,
+
+> See the full code example in [accumulatorBestTimeToBuySellStocks.js](accumulatorBestTimeToBuySellStocks.js)
+
+#### Time Complexity
+
+Since the algorithm requires only one pass through the prices array, the time complexity would equal `O(n)`.
+
+#### Additional Space Complexity
+
+Except of the prices array itself the algorithm consumes the constant amount of memory. Thus, additional space complexity is `O(1)`.
+
+## References
+
+- [Best Time to Buy and Sell Stock on LeetCode](https://leetcode.com/problems/best-time-to-buy-and-sell-stock-ii/)
diff --git a/src/algorithms/uncategorized/best-time-to-buy-sell-stocks/__tests__/accumulatorBestTimeToBuySellStocks.test.js b/src/algorithms/uncategorized/best-time-to-buy-sell-stocks/__tests__/accumulatorBestTimeToBuySellStocks.test.js
new file mode 100644
index 0000000000..40c1557770
--- /dev/null
+++ b/src/algorithms/uncategorized/best-time-to-buy-sell-stocks/__tests__/accumulatorBestTimeToBuySellStocks.test.js
@@ -0,0 +1,48 @@
+import accumulatorBestTimeToBuySellStocks from '../accumulatorBestTimeToBuySellStocks';
+
+describe('accumulatorBestTimeToBuySellStocks', () => {
+  it('should find the best time to buy and sell stocks', () => {
+    let visit;
+
+    expect(accumulatorBestTimeToBuySellStocks([1, 5])).toEqual(4);
+
+    visit = jest.fn();
+    expect(accumulatorBestTimeToBuySellStocks([1], visit)).toEqual(0);
+    expect(visit).toHaveBeenCalledTimes(1);
+
+    visit = jest.fn();
+    expect(accumulatorBestTimeToBuySellStocks([1, 5], visit)).toEqual(4);
+    expect(visit).toHaveBeenCalledTimes(2);
+
+    visit = jest.fn();
+    expect(accumulatorBestTimeToBuySellStocks([5, 1], visit)).toEqual(0);
+    expect(visit).toHaveBeenCalledTimes(2);
+
+    visit = jest.fn();
+    expect(accumulatorBestTimeToBuySellStocks([1, 5, 10], visit)).toEqual(9);
+    expect(visit).toHaveBeenCalledTimes(3);
+
+    visit = jest.fn();
+    expect(accumulatorBestTimeToBuySellStocks([10, 1, 5, 20, 15, 21], visit)).toEqual(25);
+    expect(visit).toHaveBeenCalledTimes(6);
+
+    visit = jest.fn();
+    expect(accumulatorBestTimeToBuySellStocks([7, 1, 5, 3, 6, 4], visit)).toEqual(7);
+    expect(visit).toHaveBeenCalledTimes(6);
+
+    visit = jest.fn();
+    expect(accumulatorBestTimeToBuySellStocks([1, 2, 3, 4, 5], visit)).toEqual(4);
+    expect(visit).toHaveBeenCalledTimes(5);
+
+    visit = jest.fn();
+    expect(accumulatorBestTimeToBuySellStocks([7, 6, 4, 3, 1], visit)).toEqual(0);
+    expect(visit).toHaveBeenCalledTimes(5);
+
+    visit = jest.fn();
+    expect(accumulatorBestTimeToBuySellStocks(
+      [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],
+      visit,
+    )).toEqual(19);
+    expect(visit).toHaveBeenCalledTimes(20);
+  });
+});
diff --git a/src/algorithms/uncategorized/best-time-to-buy-sell-stocks/__tests__/dqBestTimeToBuySellStocks.test.js b/src/algorithms/uncategorized/best-time-to-buy-sell-stocks/__tests__/dqBestTimeToBuySellStocks.test.js
new file mode 100644
index 0000000000..f4fe9ad3f5
--- /dev/null
+++ b/src/algorithms/uncategorized/best-time-to-buy-sell-stocks/__tests__/dqBestTimeToBuySellStocks.test.js
@@ -0,0 +1,48 @@
+import dqBestTimeToBuySellStocks from '../dqBestTimeToBuySellStocks';
+
+describe('dqBestTimeToBuySellStocks', () => {
+  it('should find the best time to buy and sell stocks', () => {
+    let visit;
+
+    expect(dqBestTimeToBuySellStocks([1, 5])).toEqual(4);
+
+    visit = jest.fn();
+    expect(dqBestTimeToBuySellStocks([1], visit)).toEqual(0);
+    expect(visit).toHaveBeenCalledTimes(3);
+
+    visit = jest.fn();
+    expect(dqBestTimeToBuySellStocks([1, 5], visit)).toEqual(4);
+    expect(visit).toHaveBeenCalledTimes(7);
+
+    visit = jest.fn();
+    expect(dqBestTimeToBuySellStocks([5, 1], visit)).toEqual(0);
+    expect(visit).toHaveBeenCalledTimes(7);
+
+    visit = jest.fn();
+    expect(dqBestTimeToBuySellStocks([1, 5, 10], visit)).toEqual(9);
+    expect(visit).toHaveBeenCalledTimes(15);
+
+    visit = jest.fn();
+    expect(dqBestTimeToBuySellStocks([10, 1, 5, 20, 15, 21], visit)).toEqual(25);
+    expect(visit).toHaveBeenCalledTimes(127);
+
+    visit = jest.fn();
+    expect(dqBestTimeToBuySellStocks([7, 1, 5, 3, 6, 4], visit)).toEqual(7);
+    expect(visit).toHaveBeenCalledTimes(127);
+
+    visit = jest.fn();
+    expect(dqBestTimeToBuySellStocks([1, 2, 3, 4, 5], visit)).toEqual(4);
+    expect(visit).toHaveBeenCalledTimes(63);
+
+    visit = jest.fn();
+    expect(dqBestTimeToBuySellStocks([7, 6, 4, 3, 1], visit)).toEqual(0);
+    expect(visit).toHaveBeenCalledTimes(63);
+
+    visit = jest.fn();
+    expect(dqBestTimeToBuySellStocks(
+      [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],
+      visit,
+    )).toEqual(19);
+    expect(visit).toHaveBeenCalledTimes(2097151);
+  });
+});
diff --git a/src/algorithms/uncategorized/best-time-to-buy-sell-stocks/__tests__/peakvalleyBestTimeToBuySellStocks.test.js b/src/algorithms/uncategorized/best-time-to-buy-sell-stocks/__tests__/peakvalleyBestTimeToBuySellStocks.test.js
new file mode 100644
index 0000000000..4eeadf673c
--- /dev/null
+++ b/src/algorithms/uncategorized/best-time-to-buy-sell-stocks/__tests__/peakvalleyBestTimeToBuySellStocks.test.js
@@ -0,0 +1,48 @@
+import peakvalleyBestTimeToBuySellStocks from '../peakvalleyBestTimeToBuySellStocks';
+
+describe('peakvalleyBestTimeToBuySellStocks', () => {
+  it('should find the best time to buy and sell stocks', () => {
+    let visit;
+
+    expect(peakvalleyBestTimeToBuySellStocks([1, 5])).toEqual(4);
+
+    visit = jest.fn();
+    expect(peakvalleyBestTimeToBuySellStocks([1], visit)).toEqual(0);
+    expect(visit).toHaveBeenCalledTimes(1);
+
+    visit = jest.fn();
+    expect(peakvalleyBestTimeToBuySellStocks([1, 5], visit)).toEqual(4);
+    expect(visit).toHaveBeenCalledTimes(2);
+
+    visit = jest.fn();
+    expect(peakvalleyBestTimeToBuySellStocks([5, 1], visit)).toEqual(0);
+    expect(visit).toHaveBeenCalledTimes(2);
+
+    visit = jest.fn();
+    expect(peakvalleyBestTimeToBuySellStocks([1, 5, 10], visit)).toEqual(9);
+    expect(visit).toHaveBeenCalledTimes(3);
+
+    visit = jest.fn();
+    expect(peakvalleyBestTimeToBuySellStocks([10, 1, 5, 20, 15, 21], visit)).toEqual(25);
+    expect(visit).toHaveBeenCalledTimes(6);
+
+    visit = jest.fn();
+    expect(peakvalleyBestTimeToBuySellStocks([7, 1, 5, 3, 6, 4], visit)).toEqual(7);
+    expect(visit).toHaveBeenCalledTimes(6);
+
+    visit = jest.fn();
+    expect(peakvalleyBestTimeToBuySellStocks([1, 2, 3, 4, 5], visit)).toEqual(4);
+    expect(visit).toHaveBeenCalledTimes(5);
+
+    visit = jest.fn();
+    expect(peakvalleyBestTimeToBuySellStocks([7, 6, 4, 3, 1], visit)).toEqual(0);
+    expect(visit).toHaveBeenCalledTimes(5);
+
+    visit = jest.fn();
+    expect(peakvalleyBestTimeToBuySellStocks(
+      [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],
+      visit,
+    )).toEqual(19);
+    expect(visit).toHaveBeenCalledTimes(20);
+  });
+});
diff --git a/src/algorithms/uncategorized/best-time-to-buy-sell-stocks/accumulatorBestTimeToBuySellStocks.js b/src/algorithms/uncategorized/best-time-to-buy-sell-stocks/accumulatorBestTimeToBuySellStocks.js
new file mode 100644
index 0000000000..9e244c89e1
--- /dev/null
+++ b/src/algorithms/uncategorized/best-time-to-buy-sell-stocks/accumulatorBestTimeToBuySellStocks.js
@@ -0,0 +1,20 @@
+/**
+ * Finds the maximum profit from selling and buying the stocks.
+ * ACCUMULATOR APPROACH.
+ *
+ * @param {number[]} prices - Array of stock prices, i.e. [7, 6, 4, 3, 1]
+ * @param {function(): void} visit - Visiting callback to calculate the number of iterations.
+ * @return {number} - The maximum profit
+ */
+const accumulatorBestTimeToBuySellStocks = (prices, visit = () => {}) => {
+  visit();
+  let profit = 0;
+  for (let day = 1; day < prices.length; day += 1) {
+    visit();
+    // Add the increase of the price from yesterday till today (if there was any) to the profit.
+    profit += Math.max(prices[day] - prices[day - 1], 0);
+  }
+  return profit;
+};
+
+export default accumulatorBestTimeToBuySellStocks;
diff --git a/src/algorithms/uncategorized/best-time-to-buy-sell-stocks/dqBestTimeToBuySellStocks.js b/src/algorithms/uncategorized/best-time-to-buy-sell-stocks/dqBestTimeToBuySellStocks.js
new file mode 100644
index 0000000000..188ad9fe1e
--- /dev/null
+++ b/src/algorithms/uncategorized/best-time-to-buy-sell-stocks/dqBestTimeToBuySellStocks.js
@@ -0,0 +1,42 @@
+/**
+ * Finds the maximum profit from selling and buying the stocks.
+ * DIVIDE & CONQUER APPROACH.
+ *
+ * @param {number[]} prices - Array of stock prices, i.e. [7, 6, 4, 3, 1]
+ * @param {function(): void} visit - Visiting callback to calculate the number of iterations.
+ * @return {number} - The maximum profit
+ */
+const dqBestTimeToBuySellStocks = (prices, visit = () => {}) => {
+  /**
+   * Recursive implementation of the main function. It is hidden from the users.
+   *
+   * @param {boolean} buy - Whether we're allow to sell or to buy now
+   * @param {number} day - Current day of trading (current index of prices array)
+   * @returns {number} - Max profit from buying/selling
+   */
+  const recursiveBuyerSeller = (buy, day) => {
+    // Registering the recursive call visit to calculate the complexity.
+    visit();
+
+    // Quitting the recursion if this is the last day of trading (prices array ended).
+    if (day === prices.length) {
+      return 0;
+    }
+
+    // If we're buying - we're loosing money (-1), if we're selling we're getting money (+1).
+    const operationSign = buy ? -1 : +1;
+    return Math.max(
+      // Option 1: Don't do anything.
+      recursiveBuyerSeller(buy, day + 1),
+      // Option 2: Sell or Buy at the current price.
+      operationSign * prices[day] + recursiveBuyerSeller(!buy, day + 1),
+    );
+  };
+
+  const buy = true;
+  const day = 0;
+
+  return recursiveBuyerSeller(buy, day);
+};
+
+export default dqBestTimeToBuySellStocks;
diff --git a/src/algorithms/uncategorized/best-time-to-buy-sell-stocks/peakvalleyBestTimeToBuySellStocks.js b/src/algorithms/uncategorized/best-time-to-buy-sell-stocks/peakvalleyBestTimeToBuySellStocks.js
new file mode 100644
index 0000000000..44e8bcbd7d
--- /dev/null
+++ b/src/algorithms/uncategorized/best-time-to-buy-sell-stocks/peakvalleyBestTimeToBuySellStocks.js
@@ -0,0 +1,35 @@
+/**
+ * Finds the maximum profit from selling and buying the stocks.
+ * PEAK VALLEY APPROACH.
+ *
+ * @param {number[]} prices - Array of stock prices, i.e. [7, 6, 4, 3, 1]
+ * @param {function(): void} visit - Visiting callback to calculate the number of iterations.
+ * @return {number} - The maximum profit
+ */
+const peakvalleyBestTimeToBuySellStocks = (prices, visit = () => {}) => {
+  visit();
+  let profit = 0;
+  let low = prices[0];
+  let high = prices[0];
+
+  prices.slice(1).forEach((currentPrice) => {
+    visit();
+    if (currentPrice < high) {
+      // If price went down, we need to sell.
+      profit += high - low;
+      low = currentPrice;
+      high = currentPrice;
+    } else {
+      // If price went up, we don't need to do anything but increase a high record.
+      high = currentPrice;
+    }
+  });
+
+  // In case if price went up during the last day
+  // and we didn't have chance to sell inside the forEach loop.
+  profit += high - low;
+
+  return profit;
+};
+
+export default peakvalleyBestTimeToBuySellStocks;

From 79cf9eb4343ae78151eace6d26705c63f955b9d0 Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Wed, 23 Dec 2020 17:04:02 +0100
Subject: [PATCH 067/264] Add divide and conquer example: best time to buy and
 sell stocks.

---
 .../uncategorized/best-time-to-buy-sell-stocks/README.md    | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/src/algorithms/uncategorized/best-time-to-buy-sell-stocks/README.md b/src/algorithms/uncategorized/best-time-to-buy-sell-stocks/README.md
index 982262d94d..9446993e98 100644
--- a/src/algorithms/uncategorized/best-time-to-buy-sell-stocks/README.md
+++ b/src/algorithms/uncategorized/best-time-to-buy-sell-stocks/README.md
@@ -37,7 +37,7 @@ _Explanation:_ In this case, no transaction is done, i.e. max `profit = 0`.
 
 ## Possible Solutions
 
-### Divide and conquer approach
+### Divide and conquer approach `O(2^n)`
 
 We may try **all** combinations of buying and selling and find out the most profitable one by applying _divide and conquer approach_.
 
@@ -62,7 +62,7 @@ As you may see, this is very inefficient. For example for just `20` prices the n
 
 If we avoid cloning the prices array between recursive function calls and will use the array pointer then additional space complexity will be proportional to the depth of the recursion: `O(n)`
 
-## Peak Valley Approach
+## Peak Valley Approach `O(n)`
 
 If we plot the prices array (i.e. `[7, 1, 5, 3, 6, 4]`) we may notice that the points of interest are the consecutive valleys and peaks
 
@@ -82,7 +82,7 @@ Since the algorithm requires only one pass through the prices array, the time co
 
 Except of the prices array itself the algorithm consumes the constant amount of memory. Thus, additional space complexity is `O(1)`.
 
-## Accumulator Approach
+## Accumulator Approach `O(n)`
 
 There is even simpler approach exists. Let's say we have the prices array which looks like this `[1, 7, 2, 3, 6, 7, 6, 7]`:
 

From 1c1b244d972f2d32f3bc7162886cd93653e469e4 Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Wed, 23 Dec 2020 17:19:53 +0100
Subject: [PATCH 068/264] Add dynamic programming version.

---
 .../dpBestTimeToBuySellStocks.test.js         | 48 +++++++++++++++++++
 .../dpBestTimeToBuySellStocks.js              | 25 ++++++++++
 2 files changed, 73 insertions(+)
 create mode 100644 src/algorithms/uncategorized/best-time-to-buy-sell-stocks/__tests__/dpBestTimeToBuySellStocks.test.js
 create mode 100644 src/algorithms/uncategorized/best-time-to-buy-sell-stocks/dpBestTimeToBuySellStocks.js

diff --git a/src/algorithms/uncategorized/best-time-to-buy-sell-stocks/__tests__/dpBestTimeToBuySellStocks.test.js b/src/algorithms/uncategorized/best-time-to-buy-sell-stocks/__tests__/dpBestTimeToBuySellStocks.test.js
new file mode 100644
index 0000000000..5904ee54f0
--- /dev/null
+++ b/src/algorithms/uncategorized/best-time-to-buy-sell-stocks/__tests__/dpBestTimeToBuySellStocks.test.js
@@ -0,0 +1,48 @@
+import dpBestTimeToBuySellStocks from '../dpBestTimeToBuySellStocks';
+
+describe('dpBestTimeToBuySellStocks', () => {
+  it('should find the best time to buy and sell stocks', () => {
+    let visit;
+
+    expect(dpBestTimeToBuySellStocks([1, 5])).toEqual(4);
+
+    visit = jest.fn();
+    expect(dpBestTimeToBuySellStocks([1], visit)).toEqual(0);
+    expect(visit).toHaveBeenCalledTimes(1);
+
+    visit = jest.fn();
+    expect(dpBestTimeToBuySellStocks([1, 5], visit)).toEqual(4);
+    expect(visit).toHaveBeenCalledTimes(2);
+
+    visit = jest.fn();
+    expect(dpBestTimeToBuySellStocks([5, 1], visit)).toEqual(0);
+    expect(visit).toHaveBeenCalledTimes(2);
+
+    visit = jest.fn();
+    expect(dpBestTimeToBuySellStocks([1, 5, 10], visit)).toEqual(9);
+    expect(visit).toHaveBeenCalledTimes(3);
+
+    visit = jest.fn();
+    expect(dpBestTimeToBuySellStocks([10, 1, 5, 20, 15, 21], visit)).toEqual(25);
+    expect(visit).toHaveBeenCalledTimes(6);
+
+    visit = jest.fn();
+    expect(dpBestTimeToBuySellStocks([7, 1, 5, 3, 6, 4], visit)).toEqual(7);
+    expect(visit).toHaveBeenCalledTimes(6);
+
+    visit = jest.fn();
+    expect(dpBestTimeToBuySellStocks([1, 2, 3, 4, 5], visit)).toEqual(4);
+    expect(visit).toHaveBeenCalledTimes(5);
+
+    visit = jest.fn();
+    expect(dpBestTimeToBuySellStocks([7, 6, 4, 3, 1], visit)).toEqual(0);
+    expect(visit).toHaveBeenCalledTimes(5);
+
+    visit = jest.fn();
+    expect(dpBestTimeToBuySellStocks(
+      [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],
+      visit,
+    )).toEqual(19);
+    expect(visit).toHaveBeenCalledTimes(20);
+  });
+});
diff --git a/src/algorithms/uncategorized/best-time-to-buy-sell-stocks/dpBestTimeToBuySellStocks.js b/src/algorithms/uncategorized/best-time-to-buy-sell-stocks/dpBestTimeToBuySellStocks.js
new file mode 100644
index 0000000000..8bf1645f11
--- /dev/null
+++ b/src/algorithms/uncategorized/best-time-to-buy-sell-stocks/dpBestTimeToBuySellStocks.js
@@ -0,0 +1,25 @@
+/**
+ * Finds the maximum profit from selling and buying the stocks.
+ * DYNAMIC PROGRAMMING APPROACH.
+ *
+ * @param {number[]} prices - Array of stock prices, i.e. [7, 6, 4, 3, 1]
+ * @param {function(): void} visit - Visiting callback to calculate the number of iterations.
+ * @return {number} - The maximum profit
+ */
+const dpBestTimeToBuySellStocks = (prices, visit = () => {}) => {
+  visit();
+  let lastBuy = -prices[0];
+  let lastSold = 0;
+
+  for (let day = 1; day < prices.length; day += 1) {
+    visit();
+    const curBuy = Math.max(lastBuy, lastSold - prices[day]);
+    const curSold = Math.max(lastSold, lastBuy + prices[day]);
+    lastBuy = curBuy;
+    lastSold = curSold;
+  }
+
+  return lastSold;
+};
+
+export default dpBestTimeToBuySellStocks;

From 2bbe12b83befddb6e8c1080d535795c9dee4a639 Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Wed, 23 Dec 2020 17:24:49 +0100
Subject: [PATCH 069/264] Add divide and conquer example: best time to buy and
 sell stocks (#612)

* Add divide and conquer example: best time to buy and sell stocks.

* Add divide and conquer example: best time to buy and sell stocks.

* Add dynamic programming version.
---
 README.md                                     |  14 ++-
 .../best-time-to-buy-sell-stocks/README.md    | 107 ++++++++++++++++++
 ...accumulatorBestTimeToBuySellStocks.test.js |  48 ++++++++
 .../dpBestTimeToBuySellStocks.test.js         |  48 ++++++++
 .../dqBestTimeToBuySellStocks.test.js         |  48 ++++++++
 .../peakvalleyBestTimeToBuySellStocks.test.js |  48 ++++++++
 .../accumulatorBestTimeToBuySellStocks.js     |  20 ++++
 .../dpBestTimeToBuySellStocks.js              |  25 ++++
 .../dqBestTimeToBuySellStocks.js              |  42 +++++++
 .../peakvalleyBestTimeToBuySellStocks.js      |  35 ++++++
 10 files changed, 429 insertions(+), 6 deletions(-)
 create mode 100644 src/algorithms/uncategorized/best-time-to-buy-sell-stocks/README.md
 create mode 100644 src/algorithms/uncategorized/best-time-to-buy-sell-stocks/__tests__/accumulatorBestTimeToBuySellStocks.test.js
 create mode 100644 src/algorithms/uncategorized/best-time-to-buy-sell-stocks/__tests__/dpBestTimeToBuySellStocks.test.js
 create mode 100644 src/algorithms/uncategorized/best-time-to-buy-sell-stocks/__tests__/dqBestTimeToBuySellStocks.test.js
 create mode 100644 src/algorithms/uncategorized/best-time-to-buy-sell-stocks/__tests__/peakvalleyBestTimeToBuySellStocks.test.js
 create mode 100644 src/algorithms/uncategorized/best-time-to-buy-sell-stocks/accumulatorBestTimeToBuySellStocks.js
 create mode 100644 src/algorithms/uncategorized/best-time-to-buy-sell-stocks/dpBestTimeToBuySellStocks.js
 create mode 100644 src/algorithms/uncategorized/best-time-to-buy-sell-stocks/dqBestTimeToBuySellStocks.js
 create mode 100644 src/algorithms/uncategorized/best-time-to-buy-sell-stocks/peakvalleyBestTimeToBuySellStocks.js

diff --git a/README.md b/README.md
index feb9832d36..f7ae004523 100644
--- a/README.md
+++ b/README.md
@@ -129,9 +129,9 @@ a set of rules that precisely define a sequence of operations.
   * `B` [Depth-First Search](src/algorithms/graph/depth-first-search) (DFS)
   * `B` [Breadth-First Search](src/algorithms/graph/breadth-first-search) (BFS)
   * `B` [Kruskal’s Algorithm](src/algorithms/graph/kruskal) - finding Minimum Spanning Tree (MST) for weighted undirected graph
-  * `A` [Dijkstra Algorithm](src/algorithms/graph/dijkstra) - finding shortest paths to all graph vertices from single vertex
-  * `A` [Bellman-Ford Algorithm](src/algorithms/graph/bellman-ford) - finding shortest paths to all graph vertices from single vertex
-  * `A` [Floyd-Warshall Algorithm](src/algorithms/graph/floyd-warshall) - find shortest paths between all pairs of vertices
+  * `A` [Dijkstra Algorithm](src/algorithms/graph/dijkstra) - finding the shortest paths to all graph vertices from single vertex
+  * `A` [Bellman-Ford Algorithm](src/algorithms/graph/bellman-ford) - finding the shortest paths to all graph vertices from single vertex
+  * `A` [Floyd-Warshall Algorithm](src/algorithms/graph/floyd-warshall) - find the shortest paths between all pairs of vertices
   * `A` [Detect Cycle](src/algorithms/graph/detect-cycle) - for both directed and undirected graphs (DFS and Disjoint Set based versions)
   * `A` [Prim’s Algorithm](src/algorithms/graph/prim) - finding Minimum Spanning Tree (MST) for weighted undirected graph
   * `A` [Topological Sorting](src/algorithms/graph/topological-sorting) - DFS method
@@ -157,6 +157,7 @@ a set of rules that precisely define a sequence of operations.
   * `B` [Unique Paths](src/algorithms/uncategorized/unique-paths) - backtracking, dynamic programming and Pascal's Triangle based examples
   * `B` [Rain Terraces](src/algorithms/uncategorized/rain-terraces) - trapping rain water problem (dynamic programming and brute force versions)
   * `B` [Recursive Staircase](src/algorithms/uncategorized/recursive-staircase) - count the number of ways to reach to the top (4 solutions)
+  * `B` [Best Time To Buy Sell Stocks](src/algorithms/uncategorized/best-time-to-buy-sell-stocks) - divide and conquer and one-pass examples
   * `A` [N-Queens Problem](src/algorithms/uncategorized/n-queens)
   * `A` [Knight's Tour](src/algorithms/uncategorized/knight-tour)
 
@@ -176,7 +177,7 @@ algorithm is an abstraction higher than a computer program.
 * **Greedy** - choose the best option at the current time, without any consideration for the future
   * `B` [Jump Game](src/algorithms/uncategorized/jump-game)
   * `A` [Unbound Knapsack Problem](src/algorithms/sets/knapsack-problem)
-  * `A` [Dijkstra Algorithm](src/algorithms/graph/dijkstra) - finding shortest path to all graph vertices
+  * `A` [Dijkstra Algorithm](src/algorithms/graph/dijkstra) - finding the shortest path to all graph vertices
   * `A` [Prim’s Algorithm](src/algorithms/graph/prim) - finding Minimum Spanning Tree (MST) for weighted undirected graph
   * `A` [Kruskal’s Algorithm](src/algorithms/graph/kruskal) - finding Minimum Spanning Tree (MST) for weighted undirected graph
 * **Divide and Conquer** - divide the problem into smaller parts and then solve those parts
@@ -191,6 +192,7 @@ algorithm is an abstraction higher than a computer program.
   * `B` [Matrices](src/algorithms/math/matrix) - generating and traversing the matrices of different shapes
   * `B` [Jump Game](src/algorithms/uncategorized/jump-game)
   * `B` [Fast Powering](src/algorithms/math/fast-powering)
+  * `B` [Best Time To Buy Sell Stocks](src/algorithms/uncategorized/best-time-to-buy-sell-stocks) - divide and conquer and one-pass examples
   * `A` [Permutations](src/algorithms/sets/permutations) (with and without repetitions)
   * `A` [Combinations](src/algorithms/sets/combinations) (with and without repetitions)
 * **Dynamic Programming** - build up a solution using previously found sub-solutions
@@ -207,8 +209,8 @@ algorithm is an abstraction higher than a computer program.
   * `A` [0/1 Knapsack Problem](src/algorithms/sets/knapsack-problem)
   * `A` [Integer Partition](src/algorithms/math/integer-partition)
   * `A` [Maximum Subarray](src/algorithms/sets/maximum-subarray)
-  * `A` [Bellman-Ford Algorithm](src/algorithms/graph/bellman-ford) - finding shortest path to all graph vertices
-  * `A` [Floyd-Warshall Algorithm](src/algorithms/graph/floyd-warshall) - find shortest paths between all pairs of vertices
+  * `A` [Bellman-Ford Algorithm](src/algorithms/graph/bellman-ford) - finding the shortest path to all graph vertices
+  * `A` [Floyd-Warshall Algorithm](src/algorithms/graph/floyd-warshall) - find the shortest paths between all pairs of vertices
   * `A` [Regular Expression Matching](src/algorithms/string/regular-expression-matching)
 * **Backtracking** - similarly to brute force, try to generate all possible solutions, but each time you generate next solution you test
 if it satisfies all conditions, and only then continue generating subsequent solutions. Otherwise, backtrack, and go on a
diff --git a/src/algorithms/uncategorized/best-time-to-buy-sell-stocks/README.md b/src/algorithms/uncategorized/best-time-to-buy-sell-stocks/README.md
new file mode 100644
index 0000000000..9446993e98
--- /dev/null
+++ b/src/algorithms/uncategorized/best-time-to-buy-sell-stocks/README.md
@@ -0,0 +1,107 @@
+# Best Time to Buy and Sell Stock
+
+## Task Description
+
+Say you have an array prices for which the `i`-th element is the price of a given stock on day `i`.
+
+Find the maximum profit. You may complete as many transactions as you like (i.e., buy one and sell one share of the stock multiple times).
+
+> Note: You may not engage in multiple transactions at the same time (i.e., you must sell the stock before you buy again).
+
+**Example #1**
+
+```
+Input: [7, 1, 5, 3, 6, 4]
+Output: 7
+```
+
+_Explanation:_ Buy on day `2` (`price = 1`) and sell on day `3` (`price = 5`), `profit = 5-1 = 4`. Then buy on day `4` (`price = 3`) and sell on day `5` (`price = 6`), `profit = 6-3 = 3`.
+
+**Example #2**
+
+```
+Input: [1, 2, 3, 4, 5]
+Output: 4
+```
+
+_Explanation:_ Buy on day `1` (`price = 1`) and sell on day `5` (`price = 5`), `profit = 5-1 = 4`. Note that you cannot buy on day 1, buy on day 2 and sell them later, as you are engaging multiple transactions at the same time. You must sell before buying again.
+
+**Example #3**
+
+```
+Input: [7, 6, 4, 3, 1]
+Output: 0
+```
+
+_Explanation:_ In this case, no transaction is done, i.e. max `profit = 0`.
+
+## Possible Solutions
+
+### Divide and conquer approach `O(2^n)`
+
+We may try **all** combinations of buying and selling and find out the most profitable one by applying _divide and conquer approach_.
+
+Let's say we have an array of prices `[7, 6, 4, 3, 1]` and we're on the _1st_ day of trading (at the very beginning of the array). At this point we may say that the overall maximum profit would be the _maximum_ of two following values:
+
+1. _Option 1: Keep the money_ → profit would equal to the profit from buying/selling the rest of the stocks → `keepProfit = profit([6, 4, 3, 1])`.
+2. _Option 2: Buy/sell at current price_ → profit in this case would equal to the profit from buying/selling the rest of the stocks plus (or minus, depending on whether we're selling or buying) the current stock price → `buySellProfit = -7 + profit([6, 4, 3, 1])`.
+
+The overall profit would be equal to → `overalProfit = Max(keepProfit, buySellProfit)`.
+
+As you can see the `profit([6, 4, 3, 1])` task is being solved in the same recursive manner.
+
+> See the full code example in [dqBestTimeToBuySellStocks.js](dqBestTimeToBuySellStocks.js)
+
+#### Time Complexity
+
+As you may see, every recursive call will produce _2_ more recursive branches. The depth of the recursion will be `n` (size of prices array) and thus, the time complexity will equal to `O(2^n)`.
+
+As you may see, this is very inefficient. For example for just `20` prices the number of recursive calls will be somewhere close to `2M`!
+
+#### Additional Space Complexity
+
+If we avoid cloning the prices array between recursive function calls and will use the array pointer then additional space complexity will be proportional to the depth of the recursion: `O(n)`
+
+## Peak Valley Approach `O(n)`
+
+If we plot the prices array (i.e. `[7, 1, 5, 3, 6, 4]`) we may notice that the points of interest are the consecutive valleys and peaks
+
+![Peak Valley Approach](https://leetcode.com/media/original_images/122_maxprofit_1.PNG)
+
+_Image source: [LeetCode](https://leetcode.com/problems/best-time-to-buy-and-sell-stock-ii/solution/)_
+
+So, if we will track the growing price and will sell the stocks immediately _before_ the price goes down we'll get the maximum profit (remember, we bought the stock in the valley at its low price).
+
+> See the full code example in [peakvalleyBestTimeToBuySellStocks.js](peakvalleyBestTimeToBuySellStocks.js)
+
+#### Time Complexity
+
+Since the algorithm requires only one pass through the prices array, the time complexity would equal `O(n)`.
+
+#### Additional Space Complexity
+
+Except of the prices array itself the algorithm consumes the constant amount of memory. Thus, additional space complexity is `O(1)`.
+
+## Accumulator Approach `O(n)`
+
+There is even simpler approach exists. Let's say we have the prices array which looks like this `[1, 7, 2, 3, 6, 7, 6, 7]`:
+
+![Simple One Pass](https://leetcode.com/media/original_images/122_maxprofit_2.PNG)
+
+_Image source: [LeetCode](https://leetcode.com/problems/best-time-to-buy-and-sell-stock-ii/solution/)_
+
+You may notice, that we don't even need to keep tracking of a constantly growing price. Instead, we may simply add the price difference for _all growing segments_ of the chart which eventually sums up to the highest possible profit,
+
+> See the full code example in [accumulatorBestTimeToBuySellStocks.js](accumulatorBestTimeToBuySellStocks.js)
+
+#### Time Complexity
+
+Since the algorithm requires only one pass through the prices array, the time complexity would equal `O(n)`.
+
+#### Additional Space Complexity
+
+Except of the prices array itself the algorithm consumes the constant amount of memory. Thus, additional space complexity is `O(1)`.
+
+## References
+
+- [Best Time to Buy and Sell Stock on LeetCode](https://leetcode.com/problems/best-time-to-buy-and-sell-stock-ii/)
diff --git a/src/algorithms/uncategorized/best-time-to-buy-sell-stocks/__tests__/accumulatorBestTimeToBuySellStocks.test.js b/src/algorithms/uncategorized/best-time-to-buy-sell-stocks/__tests__/accumulatorBestTimeToBuySellStocks.test.js
new file mode 100644
index 0000000000..40c1557770
--- /dev/null
+++ b/src/algorithms/uncategorized/best-time-to-buy-sell-stocks/__tests__/accumulatorBestTimeToBuySellStocks.test.js
@@ -0,0 +1,48 @@
+import accumulatorBestTimeToBuySellStocks from '../accumulatorBestTimeToBuySellStocks';
+
+describe('accumulatorBestTimeToBuySellStocks', () => {
+  it('should find the best time to buy and sell stocks', () => {
+    let visit;
+
+    expect(accumulatorBestTimeToBuySellStocks([1, 5])).toEqual(4);
+
+    visit = jest.fn();
+    expect(accumulatorBestTimeToBuySellStocks([1], visit)).toEqual(0);
+    expect(visit).toHaveBeenCalledTimes(1);
+
+    visit = jest.fn();
+    expect(accumulatorBestTimeToBuySellStocks([1, 5], visit)).toEqual(4);
+    expect(visit).toHaveBeenCalledTimes(2);
+
+    visit = jest.fn();
+    expect(accumulatorBestTimeToBuySellStocks([5, 1], visit)).toEqual(0);
+    expect(visit).toHaveBeenCalledTimes(2);
+
+    visit = jest.fn();
+    expect(accumulatorBestTimeToBuySellStocks([1, 5, 10], visit)).toEqual(9);
+    expect(visit).toHaveBeenCalledTimes(3);
+
+    visit = jest.fn();
+    expect(accumulatorBestTimeToBuySellStocks([10, 1, 5, 20, 15, 21], visit)).toEqual(25);
+    expect(visit).toHaveBeenCalledTimes(6);
+
+    visit = jest.fn();
+    expect(accumulatorBestTimeToBuySellStocks([7, 1, 5, 3, 6, 4], visit)).toEqual(7);
+    expect(visit).toHaveBeenCalledTimes(6);
+
+    visit = jest.fn();
+    expect(accumulatorBestTimeToBuySellStocks([1, 2, 3, 4, 5], visit)).toEqual(4);
+    expect(visit).toHaveBeenCalledTimes(5);
+
+    visit = jest.fn();
+    expect(accumulatorBestTimeToBuySellStocks([7, 6, 4, 3, 1], visit)).toEqual(0);
+    expect(visit).toHaveBeenCalledTimes(5);
+
+    visit = jest.fn();
+    expect(accumulatorBestTimeToBuySellStocks(
+      [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],
+      visit,
+    )).toEqual(19);
+    expect(visit).toHaveBeenCalledTimes(20);
+  });
+});
diff --git a/src/algorithms/uncategorized/best-time-to-buy-sell-stocks/__tests__/dpBestTimeToBuySellStocks.test.js b/src/algorithms/uncategorized/best-time-to-buy-sell-stocks/__tests__/dpBestTimeToBuySellStocks.test.js
new file mode 100644
index 0000000000..5904ee54f0
--- /dev/null
+++ b/src/algorithms/uncategorized/best-time-to-buy-sell-stocks/__tests__/dpBestTimeToBuySellStocks.test.js
@@ -0,0 +1,48 @@
+import dpBestTimeToBuySellStocks from '../dpBestTimeToBuySellStocks';
+
+describe('dpBestTimeToBuySellStocks', () => {
+  it('should find the best time to buy and sell stocks', () => {
+    let visit;
+
+    expect(dpBestTimeToBuySellStocks([1, 5])).toEqual(4);
+
+    visit = jest.fn();
+    expect(dpBestTimeToBuySellStocks([1], visit)).toEqual(0);
+    expect(visit).toHaveBeenCalledTimes(1);
+
+    visit = jest.fn();
+    expect(dpBestTimeToBuySellStocks([1, 5], visit)).toEqual(4);
+    expect(visit).toHaveBeenCalledTimes(2);
+
+    visit = jest.fn();
+    expect(dpBestTimeToBuySellStocks([5, 1], visit)).toEqual(0);
+    expect(visit).toHaveBeenCalledTimes(2);
+
+    visit = jest.fn();
+    expect(dpBestTimeToBuySellStocks([1, 5, 10], visit)).toEqual(9);
+    expect(visit).toHaveBeenCalledTimes(3);
+
+    visit = jest.fn();
+    expect(dpBestTimeToBuySellStocks([10, 1, 5, 20, 15, 21], visit)).toEqual(25);
+    expect(visit).toHaveBeenCalledTimes(6);
+
+    visit = jest.fn();
+    expect(dpBestTimeToBuySellStocks([7, 1, 5, 3, 6, 4], visit)).toEqual(7);
+    expect(visit).toHaveBeenCalledTimes(6);
+
+    visit = jest.fn();
+    expect(dpBestTimeToBuySellStocks([1, 2, 3, 4, 5], visit)).toEqual(4);
+    expect(visit).toHaveBeenCalledTimes(5);
+
+    visit = jest.fn();
+    expect(dpBestTimeToBuySellStocks([7, 6, 4, 3, 1], visit)).toEqual(0);
+    expect(visit).toHaveBeenCalledTimes(5);
+
+    visit = jest.fn();
+    expect(dpBestTimeToBuySellStocks(
+      [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],
+      visit,
+    )).toEqual(19);
+    expect(visit).toHaveBeenCalledTimes(20);
+  });
+});
diff --git a/src/algorithms/uncategorized/best-time-to-buy-sell-stocks/__tests__/dqBestTimeToBuySellStocks.test.js b/src/algorithms/uncategorized/best-time-to-buy-sell-stocks/__tests__/dqBestTimeToBuySellStocks.test.js
new file mode 100644
index 0000000000..f4fe9ad3f5
--- /dev/null
+++ b/src/algorithms/uncategorized/best-time-to-buy-sell-stocks/__tests__/dqBestTimeToBuySellStocks.test.js
@@ -0,0 +1,48 @@
+import dqBestTimeToBuySellStocks from '../dqBestTimeToBuySellStocks';
+
+describe('dqBestTimeToBuySellStocks', () => {
+  it('should find the best time to buy and sell stocks', () => {
+    let visit;
+
+    expect(dqBestTimeToBuySellStocks([1, 5])).toEqual(4);
+
+    visit = jest.fn();
+    expect(dqBestTimeToBuySellStocks([1], visit)).toEqual(0);
+    expect(visit).toHaveBeenCalledTimes(3);
+
+    visit = jest.fn();
+    expect(dqBestTimeToBuySellStocks([1, 5], visit)).toEqual(4);
+    expect(visit).toHaveBeenCalledTimes(7);
+
+    visit = jest.fn();
+    expect(dqBestTimeToBuySellStocks([5, 1], visit)).toEqual(0);
+    expect(visit).toHaveBeenCalledTimes(7);
+
+    visit = jest.fn();
+    expect(dqBestTimeToBuySellStocks([1, 5, 10], visit)).toEqual(9);
+    expect(visit).toHaveBeenCalledTimes(15);
+
+    visit = jest.fn();
+    expect(dqBestTimeToBuySellStocks([10, 1, 5, 20, 15, 21], visit)).toEqual(25);
+    expect(visit).toHaveBeenCalledTimes(127);
+
+    visit = jest.fn();
+    expect(dqBestTimeToBuySellStocks([7, 1, 5, 3, 6, 4], visit)).toEqual(7);
+    expect(visit).toHaveBeenCalledTimes(127);
+
+    visit = jest.fn();
+    expect(dqBestTimeToBuySellStocks([1, 2, 3, 4, 5], visit)).toEqual(4);
+    expect(visit).toHaveBeenCalledTimes(63);
+
+    visit = jest.fn();
+    expect(dqBestTimeToBuySellStocks([7, 6, 4, 3, 1], visit)).toEqual(0);
+    expect(visit).toHaveBeenCalledTimes(63);
+
+    visit = jest.fn();
+    expect(dqBestTimeToBuySellStocks(
+      [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],
+      visit,
+    )).toEqual(19);
+    expect(visit).toHaveBeenCalledTimes(2097151);
+  });
+});
diff --git a/src/algorithms/uncategorized/best-time-to-buy-sell-stocks/__tests__/peakvalleyBestTimeToBuySellStocks.test.js b/src/algorithms/uncategorized/best-time-to-buy-sell-stocks/__tests__/peakvalleyBestTimeToBuySellStocks.test.js
new file mode 100644
index 0000000000..4eeadf673c
--- /dev/null
+++ b/src/algorithms/uncategorized/best-time-to-buy-sell-stocks/__tests__/peakvalleyBestTimeToBuySellStocks.test.js
@@ -0,0 +1,48 @@
+import peakvalleyBestTimeToBuySellStocks from '../peakvalleyBestTimeToBuySellStocks';
+
+describe('peakvalleyBestTimeToBuySellStocks', () => {
+  it('should find the best time to buy and sell stocks', () => {
+    let visit;
+
+    expect(peakvalleyBestTimeToBuySellStocks([1, 5])).toEqual(4);
+
+    visit = jest.fn();
+    expect(peakvalleyBestTimeToBuySellStocks([1], visit)).toEqual(0);
+    expect(visit).toHaveBeenCalledTimes(1);
+
+    visit = jest.fn();
+    expect(peakvalleyBestTimeToBuySellStocks([1, 5], visit)).toEqual(4);
+    expect(visit).toHaveBeenCalledTimes(2);
+
+    visit = jest.fn();
+    expect(peakvalleyBestTimeToBuySellStocks([5, 1], visit)).toEqual(0);
+    expect(visit).toHaveBeenCalledTimes(2);
+
+    visit = jest.fn();
+    expect(peakvalleyBestTimeToBuySellStocks([1, 5, 10], visit)).toEqual(9);
+    expect(visit).toHaveBeenCalledTimes(3);
+
+    visit = jest.fn();
+    expect(peakvalleyBestTimeToBuySellStocks([10, 1, 5, 20, 15, 21], visit)).toEqual(25);
+    expect(visit).toHaveBeenCalledTimes(6);
+
+    visit = jest.fn();
+    expect(peakvalleyBestTimeToBuySellStocks([7, 1, 5, 3, 6, 4], visit)).toEqual(7);
+    expect(visit).toHaveBeenCalledTimes(6);
+
+    visit = jest.fn();
+    expect(peakvalleyBestTimeToBuySellStocks([1, 2, 3, 4, 5], visit)).toEqual(4);
+    expect(visit).toHaveBeenCalledTimes(5);
+
+    visit = jest.fn();
+    expect(peakvalleyBestTimeToBuySellStocks([7, 6, 4, 3, 1], visit)).toEqual(0);
+    expect(visit).toHaveBeenCalledTimes(5);
+
+    visit = jest.fn();
+    expect(peakvalleyBestTimeToBuySellStocks(
+      [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],
+      visit,
+    )).toEqual(19);
+    expect(visit).toHaveBeenCalledTimes(20);
+  });
+});
diff --git a/src/algorithms/uncategorized/best-time-to-buy-sell-stocks/accumulatorBestTimeToBuySellStocks.js b/src/algorithms/uncategorized/best-time-to-buy-sell-stocks/accumulatorBestTimeToBuySellStocks.js
new file mode 100644
index 0000000000..9e244c89e1
--- /dev/null
+++ b/src/algorithms/uncategorized/best-time-to-buy-sell-stocks/accumulatorBestTimeToBuySellStocks.js
@@ -0,0 +1,20 @@
+/**
+ * Finds the maximum profit from selling and buying the stocks.
+ * ACCUMULATOR APPROACH.
+ *
+ * @param {number[]} prices - Array of stock prices, i.e. [7, 6, 4, 3, 1]
+ * @param {function(): void} visit - Visiting callback to calculate the number of iterations.
+ * @return {number} - The maximum profit
+ */
+const accumulatorBestTimeToBuySellStocks = (prices, visit = () => {}) => {
+  visit();
+  let profit = 0;
+  for (let day = 1; day < prices.length; day += 1) {
+    visit();
+    // Add the increase of the price from yesterday till today (if there was any) to the profit.
+    profit += Math.max(prices[day] - prices[day - 1], 0);
+  }
+  return profit;
+};
+
+export default accumulatorBestTimeToBuySellStocks;
diff --git a/src/algorithms/uncategorized/best-time-to-buy-sell-stocks/dpBestTimeToBuySellStocks.js b/src/algorithms/uncategorized/best-time-to-buy-sell-stocks/dpBestTimeToBuySellStocks.js
new file mode 100644
index 0000000000..8bf1645f11
--- /dev/null
+++ b/src/algorithms/uncategorized/best-time-to-buy-sell-stocks/dpBestTimeToBuySellStocks.js
@@ -0,0 +1,25 @@
+/**
+ * Finds the maximum profit from selling and buying the stocks.
+ * DYNAMIC PROGRAMMING APPROACH.
+ *
+ * @param {number[]} prices - Array of stock prices, i.e. [7, 6, 4, 3, 1]
+ * @param {function(): void} visit - Visiting callback to calculate the number of iterations.
+ * @return {number} - The maximum profit
+ */
+const dpBestTimeToBuySellStocks = (prices, visit = () => {}) => {
+  visit();
+  let lastBuy = -prices[0];
+  let lastSold = 0;
+
+  for (let day = 1; day < prices.length; day += 1) {
+    visit();
+    const curBuy = Math.max(lastBuy, lastSold - prices[day]);
+    const curSold = Math.max(lastSold, lastBuy + prices[day]);
+    lastBuy = curBuy;
+    lastSold = curSold;
+  }
+
+  return lastSold;
+};
+
+export default dpBestTimeToBuySellStocks;
diff --git a/src/algorithms/uncategorized/best-time-to-buy-sell-stocks/dqBestTimeToBuySellStocks.js b/src/algorithms/uncategorized/best-time-to-buy-sell-stocks/dqBestTimeToBuySellStocks.js
new file mode 100644
index 0000000000..188ad9fe1e
--- /dev/null
+++ b/src/algorithms/uncategorized/best-time-to-buy-sell-stocks/dqBestTimeToBuySellStocks.js
@@ -0,0 +1,42 @@
+/**
+ * Finds the maximum profit from selling and buying the stocks.
+ * DIVIDE & CONQUER APPROACH.
+ *
+ * @param {number[]} prices - Array of stock prices, i.e. [7, 6, 4, 3, 1]
+ * @param {function(): void} visit - Visiting callback to calculate the number of iterations.
+ * @return {number} - The maximum profit
+ */
+const dqBestTimeToBuySellStocks = (prices, visit = () => {}) => {
+  /**
+   * Recursive implementation of the main function. It is hidden from the users.
+   *
+   * @param {boolean} buy - Whether we're allow to sell or to buy now
+   * @param {number} day - Current day of trading (current index of prices array)
+   * @returns {number} - Max profit from buying/selling
+   */
+  const recursiveBuyerSeller = (buy, day) => {
+    // Registering the recursive call visit to calculate the complexity.
+    visit();
+
+    // Quitting the recursion if this is the last day of trading (prices array ended).
+    if (day === prices.length) {
+      return 0;
+    }
+
+    // If we're buying - we're loosing money (-1), if we're selling we're getting money (+1).
+    const operationSign = buy ? -1 : +1;
+    return Math.max(
+      // Option 1: Don't do anything.
+      recursiveBuyerSeller(buy, day + 1),
+      // Option 2: Sell or Buy at the current price.
+      operationSign * prices[day] + recursiveBuyerSeller(!buy, day + 1),
+    );
+  };
+
+  const buy = true;
+  const day = 0;
+
+  return recursiveBuyerSeller(buy, day);
+};
+
+export default dqBestTimeToBuySellStocks;
diff --git a/src/algorithms/uncategorized/best-time-to-buy-sell-stocks/peakvalleyBestTimeToBuySellStocks.js b/src/algorithms/uncategorized/best-time-to-buy-sell-stocks/peakvalleyBestTimeToBuySellStocks.js
new file mode 100644
index 0000000000..44e8bcbd7d
--- /dev/null
+++ b/src/algorithms/uncategorized/best-time-to-buy-sell-stocks/peakvalleyBestTimeToBuySellStocks.js
@@ -0,0 +1,35 @@
+/**
+ * Finds the maximum profit from selling and buying the stocks.
+ * PEAK VALLEY APPROACH.
+ *
+ * @param {number[]} prices - Array of stock prices, i.e. [7, 6, 4, 3, 1]
+ * @param {function(): void} visit - Visiting callback to calculate the number of iterations.
+ * @return {number} - The maximum profit
+ */
+const peakvalleyBestTimeToBuySellStocks = (prices, visit = () => {}) => {
+  visit();
+  let profit = 0;
+  let low = prices[0];
+  let high = prices[0];
+
+  prices.slice(1).forEach((currentPrice) => {
+    visit();
+    if (currentPrice < high) {
+      // If price went down, we need to sell.
+      profit += high - low;
+      low = currentPrice;
+      high = currentPrice;
+    } else {
+      // If price went up, we don't need to do anything but increase a high record.
+      high = currentPrice;
+    }
+  });
+
+  // In case if price went up during the last day
+  // and we didn't have chance to sell inside the forEach loop.
+  profit += high - low;
+
+  return profit;
+};
+
+export default peakvalleyBestTimeToBuySellStocks;

From d35cfba32da319dd457ac096a0d04599541d8006 Mon Sep 17 00:00:00 2001
From: Yanina Trekhleb <36455834+YaninaTrekhleb@users.noreply.github.com>
Date: Wed, 23 Dec 2020 19:00:36 +0100
Subject: [PATCH 070/264] Add Ukrainian translation of the main README file.
 (#613)

* Add ukrainian translate.

* Error correction.

* Add a link to UA version to all README.file.
---
 README.es-ES.md |   3 +-
 README.fr-FR.md |   3 +-
 README.it-IT.md |   3 +-
 README.ja-JP.md |   3 +-
 README.ko-KR.md |   3 +-
 README.md       |   3 +-
 README.pl-PL.md |   3 +-
 README.pt-BR.md |   3 +-
 README.ru-RU.md |   3 +-
 README.tr-TR.md |   3 +-
 README.uk-UA.md | 304 ++++++++++++++++++++++++++++++++++++++++++++++++
 README.zh-CN.md |   3 +-
 README.zh-TW.md |   3 +-
 13 files changed, 328 insertions(+), 12 deletions(-)
 create mode 100644 README.uk-UA.md

diff --git a/README.es-ES.md b/README.es-ES.md
index ee0e0d6289..927848640c 100644
--- a/README.es-ES.md
+++ b/README.es-ES.md
@@ -21,7 +21,8 @@ _Léelo en otros idiomas:_
 [_Русский_](README.ru-RU.md),
 [_Türk_](README.tr-TR.md),
 [_Italiana_](README.it-IT.md),
-[_Bahasa Indonesia_](README.id-ID.md)
+[_Bahasa Indonesia_](README.id-ID.md),
+[_Українська_](README.uk-UA.md)
 
 *☝ Nótese que este proyecto está pensado con fines de aprendizaje e investigación,
 y **no** para ser usado en producción.*
diff --git a/README.fr-FR.md b/README.fr-FR.md
index 1e21add710..d5f11815ce 100644
--- a/README.fr-FR.md
+++ b/README.fr-FR.md
@@ -22,7 +22,8 @@ _Lisez ceci dans d'autres langues:_
 [_Русский_](README.ru-RU.md),
 [_Türk_](README.tr-TR.md),
 [_Italiana_](README.it-IT.md),
-[_Bahasa Indonesia_](README.id-ID.md)
+[_Bahasa Indonesia_](README.id-ID.md),
+[_Українська_](README.uk-UA.md)
 
 ## Data Structures
 
diff --git a/README.it-IT.md b/README.it-IT.md
index 31a7def923..4db5a4c2b7 100644
--- a/README.it-IT.md
+++ b/README.it-IT.md
@@ -18,7 +18,8 @@ _Leggilo in altre lingue:_
 [_Português_](README.pt-BR.md),
 [_Русский_](README.ru-RU.md),
 [_Türk_](README.tr-TR.md),
-[_Bahasa Indonesia_](README.id-ID.md)
+[_Bahasa Indonesia_](README.id-ID.md),
+[_Українська_](README.uk-UA.md)
 
 *☝ Si noti che questo progetto è destinato ad essere utilizzato solo per l'apprendimento e la ricerca e non è destinato ad essere utilizzato per il commercio.*
 
diff --git a/README.ja-JP.md b/README.ja-JP.md
index e955c3ae30..627ce10079 100644
--- a/README.ja-JP.md
+++ b/README.ja-JP.md
@@ -21,7 +21,8 @@ _Read this in other languages:_
 [_Русский_](README.ru-RU.md),
 [_Türk_](README.tr-TR.md),
 [_Italiana_](README.it-IT.md),
-[_Bahasa Indonesia_](README.id-ID.md)
+[_Bahasa Indonesia_](README.id-ID.md),
+[_Українська_](README.uk-UA.md)
 
 ## データ構造
 
diff --git a/README.ko-KR.md b/README.ko-KR.md
index 45c59cbe8e..4e7e39be1d 100644
--- a/README.ko-KR.md
+++ b/README.ko-KR.md
@@ -20,7 +20,8 @@ _Read this in other languages:_
 [_Русский_](README.ru-RU.md),
 [_Türk_](README.tr-TR.md),
 [_Italiana_](README.it-IT.md),
-[_Bahasa Indonesia_](README.id-ID.md)
+[_Bahasa Indonesia_](README.id-ID.md),
+[_Українська_](README.uk-UA.md)
 
 ## 자료 구조
 
diff --git a/README.md b/README.md
index f7ae004523..fca1760314 100644
--- a/README.md
+++ b/README.md
@@ -22,7 +22,8 @@ _Read this in other languages:_
 [_Русский_](README.ru-RU.md),
 [_Türk_](README.tr-TR.md),
 [_Italiana_](README.it-IT.md),
-[_Bahasa Indonesia_](README.id-ID.md)
+[_Bahasa Indonesia_](README.id-ID.md),
+[_Українська_](README.uk-UA.md)
 
 *☝ Note that this project is meant to be used for learning and researching purposes
 only, and it is **not** meant to be used for production.*
diff --git a/README.pl-PL.md b/README.pl-PL.md
index 0ede13db43..f6cfbbfeb4 100644
--- a/README.pl-PL.md
+++ b/README.pl-PL.md
@@ -22,7 +22,8 @@ _Read this in other languages:_
 [_Русский_](README.ru-RU.md),
 [_Türk_](README.tr-TR.md),
 [_Italiana_](README.it-IT.md),
-[_Bahasa Indonesia_](README.id-ID.md)
+[_Bahasa Indonesia_](README.id-ID.md),
+[_Українська_](README.uk-UA.md)
 
 ## Struktury Danych
 
diff --git a/README.pt-BR.md b/README.pt-BR.md
index 7517bb5086..512d44a670 100644
--- a/README.pt-BR.md
+++ b/README.pt-BR.md
@@ -22,7 +22,8 @@ _Leia isto em outros idiomas:_
 [_Русский_](README.ru-RU.md),
 [_Türk_](README.tr-TR.md),
 [_Italiana_](README.it-IT.md),
-[_Bahasa Indonesia_](README.id-ID.md)
+[_Bahasa Indonesia_](README.id-ID.md),
+[_Українська_](README.uk-UA.md)
 
 ## Estrutura de Dados
 
diff --git a/README.ru-RU.md b/README.ru-RU.md
index 12c1324d36..f491dff108 100644
--- a/README.ru-RU.md
+++ b/README.ru-RU.md
@@ -19,7 +19,8 @@ _Читать на других языках:_
 [_Português_](README.pt-BR.md),
 [_Türk_](README.tr-TR.md),
 [_Italiana_](README.it-IT.md),
-[_Bahasa Indonesia_](README.id-ID.md)
+[_Bahasa Indonesia_](README.id-ID.md),
+[_Українська_](README.uk-UA.md)
 
 *☝ Замечание: этот репозиторий предназначен для учебно-исследовательских целей (**не** для использования в продакшн-системах).*
 
diff --git a/README.tr-TR.md b/README.tr-TR.md
index 2b453000b9..940f79e29d 100644
--- a/README.tr-TR.md
+++ b/README.tr-TR.md
@@ -20,7 +20,8 @@ _Read this in other languages:_
 [_Português_](README.pt-BR.md),
 [_Русский_](README.ru-RU.md),
 [_Italiana_](README.it-IT.md),
-[_Bahasa Indonesia_](README.id-ID.md)
+[_Bahasa Indonesia_](README.id-ID.md),
+[_Українська_](README.uk-UA.md)
 
 *☝ Not, bu proje araştırma ve öğrenme amacı ile yapılmış
 olup üretim için **yaplılmamıştır**.*
diff --git a/README.uk-UA.md b/README.uk-UA.md
new file mode 100644
index 0000000000..cc51025480
--- /dev/null
+++ b/README.uk-UA.md
@@ -0,0 +1,304 @@
+# Алгоритми JavaScript та структури даних
+
+[![CI](https://github.com/trekhleb/javascript-algorithms/workflows/CI/badge.svg)](https://github.com/trekhleb/javascript-algorithms/actions?query=workflow%3ACI+branch%3Amaster)
+[![codecov](https://codecov.io/gh/trekhleb/javascript-algorithms/branch/master/graph/badge.svg)](https://codecov.io/gh/trekhleb/javascript-algorithms)
+
+Даний репозиторій приклади багатьох популярних алгоритмів та структур даних на основі JavaScript.
+
+Кожен алгоритм та структура даних має свій окремий README-файл із відповідними поясненнями та посиланнями для подальшого вивчення (включаючи посилання на відео на YouTube).
+
+_Вивчення матеріалу на інших мовах:_
+[_English_](README.md),
+[_简体中文_](README.zh-CN.md),
+[_繁體中文_](README.zh-TW.md),
+[_한국어_](README.ko-KR.md),
+[_日本語_](README.ja-JP.md),
+[_Polski_](README.pl-PL.md),
+[_Français_](README.fr-FR.md),
+[_Español_](README.es-ES.md),
+[_Português_](README.pt-BR.md),
+[_Русский_](README.ru-RU.md),
+[_Türk_](README.tr-TR.md),
+[_Italiana_](README.it-IT.md)
+
+*☝ Зверніть увагу! Даний проект призначений лише для навчальних та дослідницьких цілей, і він **не** призначений для виробництва (продакшн).*
+
+## Структури даних
+
+Структура даних (в програмуванні) - це спосіб організації даних в комп'ютерах. Часто разом зі структурою даних пов'язується і специфічний перелік операцій, що можуть бути виконаними над даними, організованими в таку структуру. 
+Точніше, структура даних - це сукупність даних цінності, взаємозв'язки між ними та функції або операції, до яких можна застосувати дані.
+
+`B` - Початківець, `A` - Просунутий рівень
+
+* `B` [Зв'язаний список](src/data-structures/linked-list)
+* `B` [Двобічно зв'язаний список](src/data-structures/doubly-linked-list)
+* `B` [Черга](src/data-structures/queue)
+* `B` [Стек](src/data-structures/stack)
+* `B` [Геш-таблиця](src/data-structures/hash-table)
+* `B` [Купа, стіс або піраміда](src/data-structures/heap) - max and min heap versions
+* `B` [Черга з пріоритетом](src/data-structures/priority-queue)
+* `A` [Префіксне дерево](src/data-structures/trie)
+* `A` [Дерево](src/data-structures/tree)
+  * `A` [Двійкове дерево пошуку](src/data-structures/tree/binary-search-tree)
+  * `A` [АВЛ-дерево](src/data-structures/tree/avl-tree)
+  * `A` [Червоно-чорне дерево](src/data-structures/tree/red-black-tree)
+  * `A` [Дерево відрізків](src/data-structures/tree/segment-tree) - with min/max/sum range queries examples
+  * `A` [Дерево Фенвіка](src/data-structures/tree/fenwick-tree) (Binary Indexed Tree)
+* `A` [Граф (абстрактний тип даних)](src/data-structures/graph) (both directed and undirected)
+* `A` [Система неперетинних множин](src/data-structures/disjoint-set)
+* `A` [Фільтр Блума](src/data-structures/bloom-filter)
+
+
+## Алгоритми
+
+Алгоритм - це однозначна специфікація способу вирішення класу задач. Це набір правил, які точно визначають послідовність операцій.
+
+`B` - Початківець, `A` - Просунутий рівень
+
+### Алгоритми за тематикою
+
+* **Математика**
+  * `B` [Бітова маніпуляція](src/algorithms/math/bits) - встановити / отримати / оновити / очистити біти, множення / ділення на два, робити від’ємними тощо
+  * `B` [Факторіал](src/algorithms/math/factorial)
+  * `B` [Послідовність Фібоначчі](src/algorithms/math/fibonacci) - класична та закриті версії
+  * `B` [Основні фактори](src/algorithms/math/prime-factors) - пошук простих множників і підрахунок їх за допомогою теореми Харді-Рамануджана
+  * `B` [Тест простоти](src/algorithms/math/primality-test) (метод пробного поділу)
+  * `B` [Алгоритм Евкліда](src/algorithms/math/euclidean-algorithm) - метод обчислення найбільшого спільного дільника (НСД)
+  * `B` [Найменше спільне кратне](src/algorithms/math/least-common-multiple) (НСК)
+  * `B` [Решето Ератосфена](src/algorithms/math/sieve-of-eratosthenes) - алгоритм знаходження всіх простих чисел менших деякого цілого числа *n*
+  * `B` [Піднесення до степеня](src/algorithms/math/is-power-of-two) - перевірити, чи є число ступенем двох (просте та побітове рішення)
+  * `B` [Трикутник Паскаля](src/algorithms/math/pascal-triangle)
+  * `B` [Комплексне число](src/algorithms/math/complex-number) - комплексні числа та основні операції з ними
+  * `B` [Радіани & Градуси](src/algorithms/math/radian) - перетворення радіанів у градуси та навпаки
+  * `B` [Швидке піднесення до степеня](src/algorithms/math/fast-powering)
+  * `B` [Схема Горнера](src/algorithms/math/horner-method) - поліноміальна оцінка
+  * `A` [Розбиття числа](src/algorithms/math/integer-partition)
+  * `A` [Метод дотичних (метод Ньютона)](src/algorithms/math/square-root) - метод наближеного знаходження кореня дійсного рівняння
+  * `A` [Алгоритм Лю Хуея](src/algorithms/math/liu-hui) - розрахунок числа π з заданою точністю методом вписаних правильних багатокутників
+  * `A` [Дискретне перетворення Фур'є](src/algorithms/math/fourier-transform) - розкладання тимчасової функції (сигналу) на частотні складові
+* **Множина**
+  * `B` [Декартів добуток множин](src/algorithms/sets/cartesian-product) - множина усіх можливих впорядкованих пар
+  * `B` [Тасування Фішера - Єйтса](src/algorithms/sets/fisher-yates) - створення випадкових перестановок кінцевого безлічі
+  * `A` [Булеан](src/algorithms/sets/power-set) - множина всіх підмножин даної множини (бітові та зворотні рішення)
+  * `A` [Перестановка](src/algorithms/sets/permutations) (з повтореннями та без)
+  * `A` [Комбінації](src/algorithms/sets/combinations) (з повтореннями та без)
+  * `A` [Пошук найдовшої спільної підпослідовності](src/algorithms/sets/longest-common-subsequence)
+  * `A` [Завдання пошуку найбільшою збільшується підпослідовності](src/algorithms/sets/longest-increasing-subsequence)
+  * `A` [Найменша загальна супер-послідовність](src/algorithms/sets/shortest-common-supersequence)
+  * `A` [Задача пакування рюкзака](src/algorithms/sets/knapsack-problem) - приклади "0/1" та "Необмежений"
+  * `A` [Максимальний підмасив](src/algorithms/sets/maximum-subarray) - метод «Грубої сили» та алгоритм Кадана
+  * `A` [Комбінована сума](src/algorithms/sets/combination-sum) - знайти всі комбінації, що утворюють конкретну суму
+* **Алгоритми роботи з рядками**
+  * `B` [Відстань Геммінга](src/algorithms/string/hamming-distance) - число позицій, у яких відповідні цифри двох двійкових слів однакової довжини різні
+  * `A` [Відстань Левенштейна](src/algorithms/string/levenshtein-distance) - міра відмінності двох послідовностей символів (рядків)
+  * `A` [Алгоритм Кнута — Морріса — Пратта](src/algorithms/string/knuth-morris-pratt) пошук підрядків (узгодження шаблонів)
+  * `A` [Z-функція](src/algorithms/string/z-algorithm) - пошук підрядків (зіставлення зразків)
+  * `A` [Алгоритм Рабіна — Карпа](src/algorithms/string/rabin-karp) - алгоритм пошуку рядка
+  * `A` [Найбільший загальний підрядок](src/algorithms/string/longest-common-substring)
+  * `A` [Підбирання регулярного виразу](src/algorithms/string/regular-expression-matching)
+* **Алгоритми пошуку**
+  * `B` [Лінійний пошук](src/algorithms/search/linear-search)
+  * `B` [Пошук блоків](src/algorithms/search/jump-search) - пошук у відсортованому масиві
+  * `B` [Двійковий пошук](src/algorithms/search/binary-search) - знаходження заданого значення у впорядкованому масиві
+  * `B` [Інтерполяційний алгоритм пошуку](src/algorithms/search/interpolation-search) - алгоритм для пошуку за заданим ключем в індексованому масиві, який впорядкований за значенням ключів
+* **Алгоритми сортування**
+  * `B` [Сортування бульбашкою](src/algorithms/sorting/bubble-sort)
+  * `B` [Сортування вибором](src/algorithms/sorting/selection-sort)
+  * `B` [Сортування включенням](src/algorithms/sorting/insertion-sort)
+  * `B` [Пірамідальне сортування](src/algorithms/sorting/heap-sort)
+  * `B` [Сортування злиттям](src/algorithms/sorting/merge-sort)
+  * `B` [Швидке сортування](src/algorithms/sorting/quick-sort) 
+  * `B` [Сортування Шелла](src/algorithms/sorting/shell-sort)
+  * `B` [Сортування підрахунком](src/algorithms/sorting/counting-sort)
+  * `B` [Сортування за розрядами](src/algorithms/sorting/radix-sort)
+* **Зв’язані списки**
+  * `B` [Прямий обхід](src/algorithms/linked-list/traversal)
+  * `B` [Зворотний обхід](src/algorithms/linked-list/reverse-traversal)
+* **Дерева**
+  * `B` [Пошук у глибину](src/algorithms/tree/depth-first-search)
+  * `B` [Пошук у ширину](src/algorithms/tree/breadth-first-search)
+* **Графи**
+  * `B` [Пошук у глибину](src/algorithms/graph/depth-first-search)
+  * `B` [Пошук у ширину](src/algorithms/graph/breadth-first-search)
+  * `B` [Алгоритм Крускала](src/algorithms/graph/kruskal) - алгоритм побудови мінімального кістякового дерева зваженого неорієнтовного графа
+  * `A` [Алгоритм Дейкстри](src/algorithms/graph/dijkstra) - знаходження найкоротшого шляху від однієї вершини графа до всіх інших вершин
+  * `A` [Алгоритм Беллмана — Форда](src/algorithms/graph/bellman-ford) -  алгоритм пошуку найкоротшого шляху в зваженому графі
+  * `A` [Алгоритм Флойда — Воршелла](src/algorithms/graph/floyd-warshall) -  знаходження найкоротшого шляху в зваженому графі з додатними або від'ємними вагами ребер (але без від'ємнозначних циклів)
+  * `A` [Циклічний граф](src/algorithms/graph/detect-cycle) - граф, що складається з єдиного циклу, або, іншими словами, деякого числа вершин, з'єднаних замкнутим ланцюгом.
+  * `A` [Алгоритм Прима](src/algorithms/graph/prim) - жадібний алгоритм побудови мінімального кістякового дерева зваженого зв'язного неорієнтованого графа
+  * `A` [Топологічне сортування](src/algorithms/graph/topological-sorting) - впорядковування вершин безконтурного орієнтованого графа згідно з частковим порядком, визначеним ребрами цього графу на множині його вершин
+  * `A` [Алгоритм Тар'яна](src/algorithms/graph/articulation-points) - алгоритм пошуку компонент сильної зв'язності в орієнтованому графі, що працює за лінійний час
+  * `A` [Міст (теорія графів)](src/algorithms/graph/bridges)
+  * `A` [Ейлерів ланцюг](src/algorithms/graph/eulerian-path) - ланцюг у графі, який проходить кожне ребро рівно один раз
+  * `A` [Гамільтонів граф](src/algorithms/graph/hamiltonian-cycle) - шлях, що містить кожну вершину графа рівно один раз
+  * `A` [Компонента сильної зв'язності графа](src/algorithms/graph/strongly-connected-components) - Алгоритм Косараджу - алгоритм для знаходження компонент сильної зв’язності орієнтованого графу
+  * `A` [Задача комівояжера](src/algorithms/graph/travelling-salesman) - знаходження найвигіднішого маршруту, що проходить через вказані міста хоча б по одному разу
+* **Криптографія**
+  * `B` [Хеш-функція](src/algorithms/cryptography/polynomial-hash) - функція, що перетворює вхідні дані будь-якого (як правило великого) розміру в дані фіксованого розміру.
+  * `B` [Шифр Цезаря (шифр зсуву)](src/algorithms/cryptography/caesar-cipher) - симетричний моноалфавітний алгоритм шифрування, в якому кожна буква відкритого тексту заміняється на ту, що віддалена від неї в алфавіті на сталу кількість позицій
+  * `B` [Шифр Гілла](src/algorithms/cryptography/hill-cipher) - поліграмний шифр підстановки, заснований на лінійній алгебрі
+* **Машинне навчання**
+  * `B` [Нано-нейрон](https://github.com/trekhleb/nano-neuron) - 7 простих функцій JS, які ілюструють, як машини насправді можуть навчатися (пряме та зворотнє поширення)
+  * `B` [Метод k-найближчих сусідів](src/algorithms/ml/knn) - простий непараметричний класифікаційний метод, де для класифікації об'єктів у рамках простору властивостей використовуються відстані (зазвичай евклідові), пораховані до усіх інших об'єктів
+  * `B` [Кластеризація методом к–середніх](src/algorithms/ml/knn) - популярний метод кластеризації, — впорядкування множини об'єктів в порівняно однорідні групи.
+* **Без категорії**
+  * `B` [Ханойська вежа](src/algorithms/uncategorized/hanoi-tower)
+  * `B` [Поворот квадратної матриці](src/algorithms/uncategorized/square-matrix-rotation)
+  * `B` [Гра стрибків](src/algorithms/uncategorized/jump-game) - зворотне відстеження, динамічне програмування (зверху вниз + знизу вгору) та жадібні приклади
+  * `B` [Проблема унікальних шляхів](src/algorithms/uncategorized/unique-paths) - зворотне відстеження, динамічне програмування та приклади на основі Трикутника Паскаля
+  * `B` [Дощові тераси](src/algorithms/uncategorized/rain-terraces) - проблема захоплення дощової води (динамічне програмування та версії грубої сили)
+  * `B` [Завдання про рекурсивні сходи](src/algorithms/uncategorized/recursive-staircase) - підрахунок кількості способів досягти вершини (4 рішення)
+  * `A` [Задача про вісім ферзів](src/algorithms/uncategorized/n-queens)
+  * `A` [Задача про хід коня](src/algorithms/uncategorized/knight-tour)
+
+### Парадигма програмування
+
+Парадиигма програмува́ння — це система ідей і понять, які визначають стиль написання комп'ютерних програм, а також спосіб мислення програміста. Це спосіб концептуалізації, що визначає організацію обчислень і структурування роботи, яку виконує комп'ютер.
+
+* **Метод «грубої сили» або повний перебір** - метод рішення криптографічної задачі шляхом перебору всіх можливих варіантів ключа
+  * `B` [Лінійний пошук](src/algorithms/search/linear-search)
+  * `B` [Дощові тераси](src/algorithms/uncategorized/rain-terraces) - задача про дощові тераси
+  * `B` [Завдання про рекурсивні сходи](src/algorithms/uncategorized/recursive-staircase) - підрахунок кількості способів досягти вершини
+  * `A` [Максимальний підмасив](src/algorithms/sets/maximum-subarray)
+  * `A` [Задача комівояжера](src/algorithms/graph/travelling-salesman) - знаходження найвигіднішого маршруту, що проходить через вказані міста хоча б по одному разу
+  * `A` [Дискретне перетворення Фур'є](src/algorithms/math/fourier-transform) - розкладання тимчасової функції (сигналу) на частотні складові
+* **"Жадібні" алгоритми** - простий і прямолінійний евристичний алгоритм, який приймає найкраще рішення, виходячи з наявних на кожному етапі даних, не зважаючи на можливі наслідки, сподіваючись урешті-решт отримати оптимальний розв'язок
+  * `B` [Гра стрибків](src/algorithms/uncategorized/jump-game) - зворотне відстеження, динамічне програмування (зверху вниз + знизу вгору) та жадібні приклади
+  * `A` [Задача пакування рюкзака](src/algorithms/sets/knapsack-problem) - приклади "0/1" та "Необмежений"
+  * `A` [Алгоритм Дейкстри](src/algorithms/graph/dijkstra) - знаходження найкоротшого шляху від однієї вершини графа до всіх інших вершин
+  * `A` [Алгоритм Прима](src/algorithms/graph/prim) - жадібний алгоритм побудови мінімального кістякового дерева зваженого зв'язного неорієнтованого графа
+  * `A` [Алгоритм Крускала](src/algorithms/graph/kruskal) - алгоритм побудови мінімального кістякового дерева зваженого неорієнтовного графа
+* **Розділяй і володарюй** - важлива парадигма розробки алгоритмів, що полягає в рекурсивному розбитті розв'язуваної задачі на дві або більше підзадачі того ж типу, але меншого розміру, і комбінуванні їх розв'язків для отримання відповіді до вихідного завдання. Розбиття виконуються доти, поки всі підзавдання не стануть елементарними.
+  * `B` [Двійковий пошук](src/algorithms/search/binary-search) - знаходження заданого значення у впорядкованому масиві
+  * `B` [Ханойська вежа](src/algorithms/uncategorized/hanoi-tower)
+  * `B` [Трикутник Паскаля](src/algorithms/math/pascal-triangle)
+  * `B` [Алгоритм Евкліда](src/algorithms/math/euclidean-algorithm) - метод обчислення найбільшого спільного дільника (НСД)
+  * `B` [Сортування злиттям](src/algorithms/sorting/merge-sort)
+  * `B` [Швидке сортування](src/algorithms/sorting/quick-sort) 
+  * `B` [Пошук у глибину](src/algorithms/tree/depth-first-search)
+  * `B` [Пошук у ширину](src/algorithms/tree/breadth-first-search)
+  * `B` [Гра стрибків](src/algorithms/uncategorized/jump-game) - зворотне відстеження, динамічне програмування (зверху вниз + знизу вгору) та жадібні приклади
+  * `B` [Швидке піднесення до степеня](src/algorithms/math/fast-powering)
+  * `A` [Перестановка](src/algorithms/sets/permutations) (з повтореннями та без)
+  * `A` [Комбінації](src/algorithms/sets/combinations) (з повтореннями та без)
+* **Динамічне програмування** - розділ математики, який присвячено теорії і методам розв'язання багатокрокових задач оптимального управління
+  * `B` [Послідовність Фібоначчі](src/algorithms/math/fibonacci) - класична та закриті версії
+  * `B` [Гра стрибків](src/algorithms/uncategorized/jump-game) - зворотне відстеження, динамічне програмування (зверху вниз + знизу вгору) та жадібні приклади
+  * `B` [Проблема унікальних шляхів](src/algorithms/uncategorized/unique-paths) - зворотне відстеження, динамічне програмування та приклади на основі Трикутника Паскаля
+  * `B` [Дощові тераси](src/algorithms/uncategorized/rain-terraces) - проблема захоплення дощової води (динамічне програмування та версії грубої сили)
+  * `B` [Завдання про рекурсивні сходи](src/algorithms/uncategorized/recursive-staircase) - підрахунок кількості способів досягти вершини (4 рішення)
+  * `A` [Відстань Левенштейна](src/algorithms/string/levenshtein-distance) - міра відмінності двох послідовностей символів (рядків)
+  * `A` [Пошук найдовшої спільної підпослідовності](src/algorithms/sets/longest-common-subsequence)
+  * `A` [Найбільший загальний підрядок](src/algorithms/string/longest-common-substring)
+  * `A` [Завдання пошуку найбільшою збільшується підпослідовності](src/algorithms/sets/longest-increasing-subsequence)
+  * `A` [Найменша загальна супер-послідовність](src/algorithms/sets/shortest-common-supersequence)
+  * `A` [Задача пакування рюкзака](src/algorithms/sets/knapsack-problem) - приклади "0/1" та "Необмежений"
+  * `A` [Розбиття числа](src/algorithms/math/integer-partition)
+  * `A` [Максимальний підмасив](src/algorithms/sets/maximum-subarray)
+  * `A` [Алгоритм Беллмана — Форда](src/algorithms/graph/bellman-ford) -  алгоритм пошуку найкоротшого шляху в зваженому графі
+  * `A` [Алгоритм Флойда — Воршелла](src/algorithms/graph/floyd-warshall) -  знаходження найкоротшого шляху в зваженому графі з додатними або від'ємними вагами ребер (але без від'ємнозначних циклів)
+  * `A` [Підбирання регулярного виразу](src/algorithms/string/regular-expression-matching)
+* **Пошук із зворотом** - подібно до грубої сили, намагайтеся генерувати всі можливі рішення, але кожного разу, коли ви створюєте наступне рішення, тестуєте чи він задовольняє всім умовам, і лише потім продовжуєте генерувати наступні рішення. В іншому випадку поверніться назад і рухайтесь далі іншим шляхом пошуку рішення.
+  * `B` [Гра стрибків](src/algorithms/uncategorized/jump-game) - зворотне відстеження, динамічне програмування (зверху вниз + знизу вгору) та жадібні приклади
+  * `B` [Проблема унікальних шляхів](src/algorithms/uncategorized/unique-paths) - зворотне відстеження, динамічне програмування та приклади на основі Трикутника Паскаля
+  * `B` [Булеан](src/algorithms/sets/power-set) - множина всіх підмножин даної множини (бітові та зворотні рішення)
+  * `A` [Гамільтонів граф](src/algorithms/graph/hamiltonian-cycle) - шлях, що містить кожну вершину графа рівно один раз
+  * `A` [Задача про вісім ферзів](src/algorithms/uncategorized/n-queens)
+  * `A` [Задача про хід коня](src/algorithms/uncategorized/knight-tour)
+  * `A` [Комбінована сума](src/algorithms/sets/combination-sum) - знайти всі комбінації, що утворюють конкретну суму
+* **Метод гілок і меж** - один з поширених методів дискретної оптимізації. Метод працює на дереві рішень та визначає принципи роботи конкретних алгоритмів пошуку розв'язків, тобто, є мета-алгоритмом. Для різних задач комбінаторної оптимізації створюють спеціалізовані алгоритми гілок та меж.
+  
+## Як користуватися цим репозиторієм
+
+**Встановіть усі залежності**
+```
+npm install
+```
+
+**Запустіть ESLint**
+
+Запустіть для перевірки якості коду
+
+```
+npm run lint
+```
+
+**Запустіть усі тести**
+```
+npm test
+```
+
+**Запустіть тести за назвою**
+```
+npm test -- 'LinkedList'
+```
+
+**Ігрище**
+
+Ви можете побавитись зі структурами даних та алгоритмами в файлі `./src/playground/playground.js` та писати тести до них в даному файлі `./src/playground/__test__/playground.test.js`.
+
+Для перевірки, чи працює ваш код належним чином запустіть команду:
+
+```
+npm test -- 'playground'
+```
+
+## Корисна інформація
+
+### Список літератури
+
+[▶ Структури даних та алгоритми на YouTube](https://www.youtube.com/playlist?list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
+
+### Асимптотична нотація великого О (нотація Ландау)
+
+*Асимптотична нотація великого О (нотація Ландау)* розповсюджена математична нотація для формального запису асимптотичної поведінки функцій. Широко вживається в теорії складності обчислень, інформатиці та математиці.
+![Асимптотична нотація великого О](./assets/big-o-graph.png)
+
+Джерело: [Асимптотична нотація великого О](http://bigocheatsheet.com/).
+
+Нижче наведено список деяких найбільш часто використовуваних позначень нотації Ландаута їх порівняння продуктивності з різними розмірами вхідних даних.
+
+| Нотація Ландау | Обчислення для 10 елементів | Обчислення для 100 елементів | Обчислення для 1000 елементів  |
+| -------------- | ---------------------------- | ----------------------------- | ------------------------------- |
+| **O(1)**       | 1                            | 1                             | 1                               |
+| **O(log N)**   | 3                            | 6                             | 9                               |
+| **O(N)**       | 10                           | 100                           | 1000                            |
+| **O(N log N)** | 30                           | 600                           | 9000                            |
+| **O(N^2)**     | 100                          | 10000                         | 1000000                         |
+| **O(2^N)**     | 1024                         | 1.26e+29                      | 1.07e+301                       |
+| **O(N!)**      | 3628800                      | 9.3e+157                      | 4.02e+2567                      |
+
+### Складність операцій в структурі даних 
+
+| Структура даних        | Доступ    | Пошук    | Вставка | Видалення  | Коментарі  |
+| ----------------------- | :-------: | :-------: | :-------: | :-------: | :-------- |
+| **Масив**               | 1         | n         | n         | n         |           |
+| **Купа**               | n         | n         | 1         | 1         |           |
+| **Черга**               | n         | n         | 1         | 1         |           |
+| **Зв’язаний список**         | n         | n         | 1         | n         |           |
+| **Хеш-таблиця**          | -         | n         | n         | n         | У разі ідеальної хеш-функції - O(1) |
+| **Бінарне дерево пошуку**  | n         | n         | n         | n         | У разі збалансованого дерева витрати становитимуть O (log (n)) |
+| **Б-дерево**              | log(n)    | log(n)    | log(n)    | log(n)    |           |
+| **Червоно-чорне дерево**      | log(n)    | log(n)    | log(n)    | log(n)    |           |
+| **АВЛ-дерево**            | log(n)    | log(n)    | log(n)    | log(n)    |           |
+| **Фільтр Блума**        | -         | 1         | 1         | -         | Під час пошуку можливі помилкові спрацьовування |
+
+### Складність алгоритмів сортування масивів
+
+| Назва                  | Найкращий            | Середній             | Найгірший               | Пам'ять    | Стабільність    | Коментарі  |
+| --------------------- | :-------------: | :-----------------: | :-----------------: | :-------: | :-------: | :-------- |
+| **Сортування бульбашкою**       | n               | n<sup>2</sup>       | n<sup>2</sup>       | 1         | Так       |           |
+| **Сортування включенням**    | n               | n<sup>2</sup>       | n<sup>2</sup>       | 1         | Так       |           |
+| **Сортування вибором**    | n<sup>2</sup>   | n<sup>2</sup>       | n<sup>2</sup>       | 1         | Ні        |           |
+| **Пірамідальне сортування**         | n&nbsp;log(n)   | n&nbsp;log(n)       | n&nbsp;log(n)       | 1         | Ні        |           |
+| **Сортування злиттям**        | n&nbsp;log(n)   | n&nbsp;log(n)       | n&nbsp;log(n)       | n         | Так       |           |
+| **Швидке сортування**        | n&nbsp;log(n)   | n&nbsp;log(n)       | n<sup>2</sup>       | log(n)    | Ні        | Швидке сортування зазвичай виконується на місці з використанням O (log (n)) додаткової пам'яті |
+| **Сортування Шелла**        | n&nbsp;log(n)   | залежить від послідовності проміжків   | n&nbsp;(log(n))<sup>2</sup>  | 1         | Ні         |           |
+| **Сортування підрахунком**     | n + r           | n + r               | n + r               | n + r     | Так       | Де r - найбільше число в масиві |
+| **Сортування за розрядами**        | n * k           | n * k               | n * k               | n + k     | Так       | Де k - довжина найдовшого ключа |
+
+## Патронати проекту
+
+> Ви можете підтримати цей проект через ❤️️ [GitHub](https://github.com/sponsors/trekhleb) або ❤️️ [Patreon](https://www.patreon.com/trekhleb).
+
+[Люди, які підтримують цей проект](https://github.com/trekhleb/javascript-algorithms/blob/master/BACKERS.md) `∑ = 1`
diff --git a/README.zh-CN.md b/README.zh-CN.md
index c039524447..c1f7027b6e 100644
--- a/README.zh-CN.md
+++ b/README.zh-CN.md
@@ -19,7 +19,8 @@ _Read this in other languages:_
 [_Русский_](README.ru-RU.md),
 [_Türk_](README.tr-TR.md),
 [_Italiana_](README.it-IT.md),
-[_Bahasa Indonesia_](README.id-ID.md)
+[_Bahasa Indonesia_](README.id-ID.md),
+[_Українська_](README.uk-UA.md)
 
 *注意：这个项目仅用于学习和研究，**不是**用于生产环境。*
 
diff --git a/README.zh-TW.md b/README.zh-TW.md
index 69df9717cb..f341482f56 100644
--- a/README.zh-TW.md
+++ b/README.zh-TW.md
@@ -18,7 +18,8 @@ _Read this in other languages:_
 [_Русский_](README.ru-RU.md),
 [_Türk_](README.tr-TR.md),
 [_Italiana_](README.it-IT.md),
-[_Bahasa Indonesia_](README.id-ID.md)
+[_Bahasa Indonesia_](README.id-ID.md),
+[_Українська_](README.uk-UA.md)
 
 ## 資料結構
 

From 711204f13a825cbe2dac25fdc5493f9991ede5f0 Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Mon, 28 Dec 2020 09:16:33 +0100
Subject: [PATCH 071/264] Update CI workflow.

---
 .github/workflows/CI.yml | 35 +++++++++++++++++++++++++++++++++++
 .github/workflows/ci.yml | 37 -------------------------------------
 2 files changed, 35 insertions(+), 37 deletions(-)
 create mode 100644 .github/workflows/CI.yml
 delete mode 100644 .github/workflows/ci.yml

diff --git a/.github/workflows/CI.yml b/.github/workflows/CI.yml
new file mode 100644
index 0000000000..912c719df3
--- /dev/null
+++ b/.github/workflows/CI.yml
@@ -0,0 +1,35 @@
+name: CI
+
+on:
+  push:
+    branches: [ master ]
+  pull_request:
+    branches: [ master ]
+
+jobs:
+  test:
+    runs-on: ubuntu-latest
+    strategy:
+      matrix:
+        node-version: [ 14.x ]
+
+    steps:
+      - name: Checkout repository
+        uses: actions/checkout@v2
+
+      - name: Setup Node.js ${{ matrix.node-version }}
+        uses: actions/setup-node@v1
+        with:
+          node-version: ${{ matrix.node-version }}
+
+      - name: Install dependencies
+        run: npm i
+
+      - name: Run linting
+        run: npm run lint
+
+      - name: Run tests
+        run: npm run coverage
+
+      - name: Upload coverage to Codecov
+        uses: codecov/codecov-action@v1
diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml
deleted file mode 100644
index 1499ea368e..0000000000
--- a/.github/workflows/ci.yml
+++ /dev/null
@@ -1,37 +0,0 @@
-name: CI
-
-on:
-  push:
-    branches: [ master ]
-  pull_request:
-    branches: [ master ]
-
-jobs:
-  build:
-
-    runs-on: ubuntu-latest
-
-    strategy:
-      matrix:
-        node-version: [14.x]
-
-    steps:
-    - name: Checkout repository
-      uses: actions/checkout@v2
-
-    - name: Setup Node.js ${{ matrix.node-version }}
-      uses: actions/setup-node@v1
-      with:
-        node-version: ${{ matrix.node-version }}
-
-    - name: Install dependencies
-      run: npm i
-
-    - name: Run linting
-      run: npm run lint
-
-    - name: Run tests
-      run: npm run coverage
-
-    - name: Upload coverage to Codecov
-      uses: codecov/codecov-action@v1

From a0a9c35e3ffd78d14de70a53c305aaf888113a1b Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Sat, 2 Jan 2021 13:49:00 +0100
Subject: [PATCH 072/264] Update Bakers.

---
 BACKERS.md | 17 ++++++++++-------
 README.md  |  2 +-
 2 files changed, 11 insertions(+), 8 deletions(-)

diff --git a/BACKERS.md b/BACKERS.md
index 71020a9e99..62c397a38c 100644
--- a/BACKERS.md
+++ b/BACKERS.md
@@ -1,27 +1,30 @@
 # Project Backers
 
-> You may support this project via ❤️️ [GitHub](https://github.com/sponsors/trekhleb) or ❤️️ [Patreon](https://www.patreon.com/trekhleb).  
+> You may support this project via ❤️️ [GitHub](https://github.com/sponsors/trekhleb) or ❤️️ [Patreon](https://www.patreon.com/trekhleb).
 
 ## `O(2ⁿ)` Backers
 
-⏳
+`null`
 
 ## `O(n²)` Backers
 
-⏳
+`null`
 
 ## `O(n×log(n))` Backers
 
+`null`
+
+<!--
 <ul>
   <li>
-    <a href="https://github.com/bullwinkle">
+    <a href="http://github.com/[PROFILE_URL]">
       <img
-        src="https://avatars1.githubusercontent.com/u/3613558?s=60&amp;v=4"
+        src="http://github.com/[PROFILE_IMG_SRC]"
         width="30"
         height="30"
       /></a>
     &thinsp;
-    <a href="https://github.com/bullwinkle">bullwinkle</a>
+    <a href="http://github.com/[PROFILE_URL]">[PROFILE_NAME]</a>
   </li>
 </ul>
-
+-->
diff --git a/README.md b/README.md
index fca1760314..f44142fcba 100644
--- a/README.md
+++ b/README.md
@@ -325,4 +325,4 @@ Below is the list of some of the most used Big O notations and their performance
 
 > You may support this project via ❤️️ [GitHub](https://github.com/sponsors/trekhleb) or ❤️️ [Patreon](https://www.patreon.com/trekhleb).
 
-[Folks who are backing this project](https://github.com/trekhleb/javascript-algorithms/blob/master/BACKERS.md) `∑ = 1`
+[Folks who are backing this project](https://github.com/trekhleb/javascript-algorithms/blob/master/BACKERS.md) `∑ = 0`

From 81240342c257a78cfafc0fd0a419af30479be447 Mon Sep 17 00:00:00 2001
From: Abdessamad Bensaad <43497143+B3ns44d@users.noreply.github.com>
Date: Sun, 3 Jan 2021 01:23:17 -0800
Subject: [PATCH 073/264] Add an Arabic version of the README file (#622)

* add the DS link

* Finish translating math

* add Arabic version of the README FILE

* add Arabic version of the README FILE

* add the arabic readme file link to main readme file

* add the arabic readme file link to main readme file

* add the arabic readme file link to main readme file

Co-authored-by: Oleksii Trekhleb <trehleb@gmail.com>
---
 README.ar.AR.md | 324 ++++++++++++++++++++++++++++++++++++++++++++++++
 README.md       |   3 +-
 2 files changed, 326 insertions(+), 1 deletion(-)
 create mode 100644 README.ar.AR.md

diff --git a/README.ar.AR.md b/README.ar.AR.md
new file mode 100644
index 0000000000..d11b3d98de
--- /dev/null
+++ b/README.ar.AR.md
@@ -0,0 +1,324 @@
+# جافا سكريبت خوارزميات  وهياكل البيانات
+
+[![Build Status](https://travis-ci.org/trekhleb/javascript-algorithms.svg?branch=master)](https://travis-ci.org/trekhleb/javascript-algorithms)
+[![codecov](https://codecov.io/gh/trekhleb/javascript-algorithms/branch/master/graph/badge.svg)](https://codecov.io/gh/trekhleb/javascript-algorithms)
+
+تحتوي هذا مقالة على أمثلة عديدة تستند إلى الخوارزميات الشائعة وهياكل البيانات في الجافا سكريبت.
+
+كل خوارزمية وهياكل البيانات لها برنامج README منفصل خاص بها
+مع التفسيرات والروابط ذات الصلة لمزيد من القراءة (بما في ذلك تلك
+إلى مقاطع فيديو YouTube).
+
+
+_اقرأ هذا في لغات أخرى:_
+[_简体中文_](README.zh-CN.md),
+[_繁體中文_](README.zh-TW.md),
+[_한국어_](README.ko-KR.md),
+[_日本語_](README.ja-JP.md),
+[_Polski_](README.pl-PL.md),
+[_Français_](README.fr-FR.md),
+[_Español_](README.es-ES.md),
+[_Português_](README.pt-BR.md),
+[_Русский_](README.ru-RU.md),
+[_Türk_](README.tr-TR.md),
+[_Italiana_](README.it-IT.md)
+
+ ☝ ملاحضة هذا المشروع مخصص للاستخدام لأغراض التعلم والبحث
+فقط ، و ** ليست ** معدة للاستخدام في **الإنتاج**
+
+## هياكل البيانات
+
+هياكل البيانات هي طريقة خاصة لتنظيم البيانات وتخزينها في جهاز الكمبيوتر بحيث
+يمكن الوصول إليها وتعديلها بكفاءة. بتعبير أدق ، هيكل البيانات هو مجموعة من البيانات
+القيم والعلاقات فيما بينها والوظائف أو العمليات التي يمكن تطبيقها عليها
+البيانات.
+
+
+`B` - مبتدئ, `A` - المتقدمة
+
+* `B` [قائمة مرتبطة](src/data-structures/linked-list)
+* `B` [قائمة مرتبطة بشكل مضاعف](src/data-structures/doubly-linked-list)
+* `B` [طابور, Queue](src/data-structures/queue)
+* `B` [كومة](src/data-structures/stack)
+* `B` [جدول التجزئة](src/data-structures/hash-table)
+* `B` [كومة](src/data-structures/heap) -الحد الأقصى والحد الأدنى من إصدارات الكومة
+* `B` [طابور الأولوية](src/data-structures/priority-queue)
+* `A` [تري](src/data-structures/trie)
+* `A` [شجرة](src/data-structures/tree)
+  * `A` [شجرة البحث الثنائية](src/data-structures/tree/binary-search-tree)
+  * `A` [شجرة AVL](src/data-structures/tree/avl-tree)
+  * `A` [شجرة الأحمر والأسود](src/data-structures/tree/red-black-tree)
+  * `A` [شجرة القطعة](src/data-structures/tree/segment-tree) - مع أمثلة على استفسارات النطاق الأدنى / الأقصى / المجموع
+  * `A` [شجرة فينويك](src/data-structures/tree/fenwick-tree) (شجرة ثنائية مفهرسة)
+* `A` [Graph](src/data-structures/graph) (كلاهما موجه وغير موجه)
+* `A` [مجموعة منفصلة](src/data-structures/disjoint-set)
+* `A` [مرشح بلوم](src/data-structures/bloom-filter)
+
+
+## الخوارزميات
+
+الخوارزمية هي تحديد لا لبس فيه لكيفية حل فئة من المشاكل. أنه
+مجموعة من القواعد التي تحدد بدقة تسلسل العمليات.
+
+`B` - مبتدئ ، `A` - متقدم
+
+
+### الخوارزميات حسب الموضوع
+
+* **رياضيات**
+  * `B` [معالجة البت](src/algorithms/math/bits)
+  * `B` [عاملي](src/algorithms/math/factorial) 
+  * `B` [رقم فيبوناتشي](src/algorithms/math/fibonacci) - الإصدارات الكلاسيكية والمغلقة
+  * `B` [اختبار البدائية](src/algorithms/math/primality-test) (طريقة تقسيم المحاكمة)
+  * `B` [الخوارزمية الإقليدية](src/algorithms/math/euclidean-algorithm) - احسب القاسم المشترك الأكبر (GCD)
+  * `B` [أقل مضاعف مشترك](src/algorithms/math/least-common-multiple) (LCM)
+  * `B` [منخل إراتوستينس](src/algorithms/math/sieve-of-eratosthenes) - إيجاد جميع الأعداد الأولية حتى أي حد معين
+  * `B` [هي قوة اثنين](src/algorithms/math/is-power-of-two) - تحقق مما إذا كان الرقم هو قوة اثنين (الخوارزميات الساذجة والبتية)
+  * `B` [مثلث باسكال](src/algorithms/math/pascal-triangle)
+  * `B` [عدد مركب](src/algorithms/math/complex-number) - الأعداد المركبة والعمليات الأساسية معهم
+  * `B` [راديان ودرجة](src/algorithms/math/radian) - راديان لدرجة التحويل والعكس
+  * `B` [تشغيل سريع](src/algorithms/math/fast-powering)
+  * `B` [طريقة هورنر](src/algorithms/math/horner-method) - تقييم متعدد الحدود
+  * `A` [قسم صحيح](src/algorithms/math/integer-partition)
+  * `A` [الجذر التربيعي](src/algorithms/math/square-root) - طريقة نيوتن
+  * `A` [خوارزمية ليو هوي π](src/algorithms/math/liu-hui) - π حسابات تقريبية على أساس N-gons
+  * `A` [تحويل فورييه المنفصل](src/algorithms/math/fourier-transform) - حلل وظيفة الوقت (إشارة) في الترددات التي يتكون منها
+* **مجموعات**
+  * `B` [المنتج الديكارتي](src/algorithms/sets/cartesian-product) - منتج من مجموعات متعددة
+  * `B` [فيشر ييتس شافل](src/algorithms/sets/fisher-yates) - التقليب العشوائي لتسلسل محدود
+  * `A` [مجموعة الطاقة](src/algorithms/sets/power-set) - جميع المجموعات الفرعية للمجموعة (حلول البت والتتبع التراجعي)
+  * `A` [التباديل](src/algorithms/sets/permutations) (مع وبدون التكرار)
+  * `A` [مجموعات](src/algorithms/sets/combinations) (مع وبدون التكرار)
+  * `A` [أطول نتيجة مشتركة](src/algorithms/sets/longest-common-subsequence) (LCS)
+  * `A` [أطول زيادة متتالية](src/algorithms/sets/longest-increasing-subsequence)
+  * `A` [أقصر تسلسل فائق مشترك](src/algorithms/sets/shortest-common-supersequence) (SCS)
+  * `A` [مشكلة حقيبة الظهر](src/algorithms/sets/knapsack-problem) - "0/1" و "غير منضم"
+  * `A` [الحد الأقصى من Subarray](src/algorithms/sets/maximum-subarray) -إصدارات "القوة الغاشمة" و "البرمجة الديناميكية" (كادان)
+  * `A` [مجموع الجمع](src/algorithms/sets/combination-sum) - ابحث عن جميع التركيبات التي تشكل مبلغًا محددًا
+* **سلاسل**
+  * `B` [مسافة هامنج](src/algorithms/string/hamming-distance) - عدد المواقف التي تختلف فيها الرموز
+  * `A` [المسافة ليفنشتاين](src/algorithms/string/levenshtein-distance) - الحد الأدنى لمسافة التحرير بين تسلسلين
+  * `A` [خوارزمية كنوث - موريس - برات](src/algorithms/string/knuth-morris-pratt) (خوارزمية KMP) - بحث السلسلة الفرعية (مطابقة النمط)
+  * `A` [خوارزمية Z](src/algorithms/string/z-algorithm) - بحث سلسلة فرعية (مطابقة النمط)
+  * `A` [خوارزمية رابين كارب](src/algorithms/string/rabin-karp) - بحث السلسلة الفرعية
+  * `A` [أطول سلسلة فرعية مشتركة](src/algorithms/string/longest-common-substring)
+  * `A` [مطابقة التعبير العادي](src/algorithms/string/regular-expression-matching)
+* **عمليات البحث**
+  * `B` [البحث الخطي](src/algorithms/search/linear-search)
+  * `B` [بحث سريع](src/algorithms/search/jump-search) (أو حظر البحث) - ابحث في مصفوفة مرتبة
+  * `B` [بحث ثنائي](src/algorithms/search/binary-search) - البحث في مجموعة مرتبة
+  * `B` [بحث الاستيفاء](src/algorithms/search/interpolation-search) - البحث في مجموعة مرتبة موزعة بشكل موحد
+
+* **فرز**
+  * `B` [Bubble Sort](src/algorithms/sorting/bubble-sort)
+  * `B` [Selection Sort](src/algorithms/sorting/selection-sort)
+  * `B` [Insertion Sort](src/algorithms/sorting/insertion-sort)
+  * `B` [Heap Sort](src/algorithms/sorting/heap-sort)
+  * `B` [Merge Sort](src/algorithms/sorting/merge-sort)
+  * `B` [Quicksort](src/algorithms/sorting/quick-sort) - عمليات التنفيذ في المكان وغير في المكان
+  * `B` [Shellsort](src/algorithms/sorting/shell-sort)
+  * `B` [Counting Sort](src/algorithms/sorting/counting-sort)
+  * `B` [Radix Sort](src/algorithms/sorting/radix-sort)
+* **القوائم المرتبطة**
+  * `B` [Straight Traversal](src/algorithms/linked-list/traversal)
+  * `B` [Reverse Traversal](src/algorithms/linked-list/reverse-traversal)
+* **الأشجار**
+  * `B` [Depth-First Search](src/algorithms/tree/depth-first-search) (DFS)
+  * `B` [Breadth-First Search](src/algorithms/tree/breadth-first-search) (BFS)
+* **الرسوم البيانية**
+  * `B` [Depth-First Search](src/algorithms/graph/depth-first-search) (DFS)
+  * `B` [Breadth-First Search](src/algorithms/graph/breadth-first-search) (BFS)
+  * `B` [Kruskal’s Algorithm](src/algorithms/graph/kruskal) - إيجاد الحد الأدنى من شجرة الامتداد (MST) للرسم البياني الموزون غير الموجه
+  * `A` [Dijkstra Algorithm](src/algorithms/graph/dijkstra) -إيجاد أقصر المسارات لجميع رؤوس الرسم البياني من رأس واحد
+  * `A` [Bellman-Ford Algorithm](src/algorithms/graph/bellman-ford) - إيجاد أقصر المسارات لجميع رؤوس الرسم البياني من رأس واحد
+  * `A` [Floyd-Warshall Algorithm](src/algorithms/graph/floyd-warshall) - إيجاد أقصر المسارات بين جميع أزواج الرؤوس
+  * `A` [Detect Cycle](src/algorithms/graph/detect-cycle) - لكل من الرسوم البيانية الموجهة وغير الموجهة (الإصدارات القائمة على DFS و Disjoint Set)
+  * `A` [Prim’s Algorithm](src/algorithms/graph/prim) - إيجاد الحد الأدنى من شجرة الامتداد (MST) للرسم البياني الموزون غير الموجه
+  * `A` [Topological Sorting](src/algorithms/graph/topological-sorting) - طريقة البحث العمق الأول (DFS)
+  * `A` [Articulation Points](src/algorithms/graph/articulation-points) - خوارزمية تارجان (تعتمد على DFS)
+  * `A` [Bridges](src/algorithms/graph/bridges) - خوارزمية تعتمد على DFS
+  * `A` [Eulerian Path and Eulerian Circuit](src/algorithms/graph/eulerian-path) - خوارزمية فلوري - قم بزيارة كل حافة مرة واحدة بالضبط
+  * `A` [Hamiltonian Cycle](src/algorithms/graph/hamiltonian-cycle) - قم بزيارة كل قمة مرة واحدة بالضبط
+  * `A` [Strongly Connected Components](src/algorithms/graph/strongly-connected-components) - خوارزمية Kosaraju
+  * `A` [Travelling Salesman Problem](src/algorithms/graph/travelling-salesman) - أقصر طريق ممكن يزور كل مدينة ويعود إلى المدينة الأصلية
+* **التشفير
+  * `B` [Polynomial Hash](src/algorithms/cryptography/polynomial-hash) - المتداول دالة التجزئة على أساس متعدد الحدود
+  * `B` [Caesar Cipher](src/algorithms/cryptography/caesar-cipher) - استبدال بسيط للشفرات
+* **التعلم الالي**
+  * `B` [NanoNeuron](https://github.com/trekhleb/nano-neuron) - 7 وظائف JS بسيطة توضح كيف يمكن للآلات أن تتعلم بالفعل (الانتشار إلى الأمام / الخلف)
+* **غير مصنف**
+  * `B` [Tower of Hanoi](src/algorithms/uncategorized/hanoi-tower)
+  * `B` [Square Matrix Rotation](src/algorithms/uncategorized/square-matrix-rotation) - خوارزمية في المكان
+  * `B` [Jump Game](src/algorithms/uncategorized/jump-game) - التراجع ، البرمجة الديناميكية (من أعلى إلى أسفل + من أسفل إلى أعلى) والأمثلة الجشعة
+  * `B` [Unique Paths](src/algorithms/uncategorized/unique-paths) - التراجع والبرمجة الديناميكية والأمثلة القائمة على مثلث باسكال
+  * `B` [Rain Terraces](src/algorithms/uncategorized/rain-terraces) - محاصرة مشكلة مياه الأمطار (البرمجة الديناميكية وإصدارات القوة الغاشمة)
+  * `B` [Recursive Staircase](src/algorithms/uncategorized/recursive-staircase) - احسب عدد الطرق للوصول إلى القمة (4 حلول)
+  * `A` [N-Queens Problem](src/algorithms/uncategorized/n-queens)
+  * `A` [Knight's Tour](src/algorithms/uncategorized/knight-tour)
+
+### الخوارزميات حسب النموذج
+
+النموذج الحسابي هو طريقة أو نهج عام يكمن وراء تصميم الفصل
+من الخوارزميات. إنه تجريد أعلى من مفهوم الخوارزمية ، تمامًا مثل
+الخوارزمية هي تجريد أعلى من برنامج الكمبيوتر.
+
+* **القوة الغاشمة** - انظر في جميع الاحتمالات وحدد الحل الأفضل
+  * `B` [Linear Search](src/algorithms/search/linear-search)
+  * `B` [Rain Terraces](src/algorithms/uncategorized/rain-terraces) - محاصرة مشكلة مياه الأمطار
+  * `B` [Recursive Staircase](src/algorithms/uncategorized/recursive-staircase) - احسب عدد الطرق للوصول إلى القمة
+  * `A` [Maximum Subarray](src/algorithms/sets/maximum-subarray)
+  * `A` [Travelling Salesman Problem](src/algorithms/graph/travelling-salesman) - أقصر طريق ممكن يزور كل مدينة ويعود إلى المدينة الأصلية
+  * `A` [Discrete Fourier Transform](src/algorithms/math/fourier-transform) - حلل وظيفة الوقت (إشارة) في الترددات التي يتكون منها
+* **جشع** - اختر الخيار الأفضل في الوقت الحالي ، دون أي اعتبار للمستقبل
+  * `B` [Jump Game](src/algorithms/uncategorized/jump-game)
+  * `A` [Unbound Knapsack Problem](src/algorithms/sets/knapsack-problem)
+  * `A` [Dijkstra Algorithm](src/algorithms/graph/dijkstra) - إيجاد أقصر مسار لجميع رؤوس الرسم البياني
+  * `A` [Prim’s Algorithm](src/algorithms/graph/prim) - إيجاد الحد الأدنى من شجرة الامتداد (MST) للرسم البياني الموزون غير الموجه
+  * `A` [Kruskal’s Algorithm](src/algorithms/graph/kruskal) - إيجاد الحد الأدنى من شجرة الامتداد (MST) للرسم البياني الموزون غير الموجه
+* **فرق تسد** - قسّم المشكلة إلى أجزاء أصغر ثم حل تلك الأجزاء
+  * `B` [Binary Search](src/algorithms/search/binary-search)
+  * `B` [Tower of Hanoi](src/algorithms/uncategorized/hanoi-tower)
+  * `B` [Pascal's Triangle](src/algorithms/math/pascal-triangle)
+  * `B` [Euclidean Algorithm](src/algorithms/math/euclidean-algorithm) - حساب القاسم المشترك الأكبر (GCD)
+  * `B` [Merge Sort](src/algorithms/sorting/merge-sort)
+  * `B` [Quicksort](src/algorithms/sorting/quick-sort)
+  * `B` [Tree Depth-First Search](src/algorithms/tree/depth-first-search) (DFS)
+  * `B` [Graph Depth-First Search](src/algorithms/graph/depth-first-search) (DFS)
+  * `B` [Jump Game](src/algorithms/uncategorized/jump-game)
+  * `B` [Fast Powering](src/algorithms/math/fast-powering)
+  * `A` [Permutations](src/algorithms/sets/permutations) (مع التكرار وبدونه)
+  * `A` [Combinations](src/algorithms/sets/combinations) (مع التكرار وبدونه)
+* **البرمجة الديناميكية** - بناء حل باستخدام الحلول الفرعية التي تم العثور عليها مسبقًا
+  * `B` [Fibonacci Number](src/algorithms/math/fibonacci)
+  * `B` [Jump Game](src/algorithms/uncategorized/jump-game)
+  * `B` [Unique Paths](src/algorithms/uncategorized/unique-paths)
+  * `B` [Rain Terraces](src/algorithms/uncategorized/rain-terraces) - محاصرة مشكلة مياه الأمطار
+  * `B` [Recursive Staircase](src/algorithms/uncategorized/recursive-staircase) - احسب عدد الطرق للوصول إلى القمة
+  * `A` [Levenshtein Distance](src/algorithms/string/levenshtein-distance) - الحد الأدنى لمسافة التحرير بين تسلسلين
+  * `A` [Longest Common Subsequence](src/algorithms/sets/longest-common-subsequence) (LCS)
+  * `A` [Longest Common Substring](src/algorithms/string/longest-common-substring)
+  * `A` [Longest Increasing Subsequence](src/algorithms/sets/longest-increasing-subsequence)
+  * `A` [Shortest Common Supersequence](src/algorithms/sets/shortest-common-supersequence)
+  * `A` [0/1 Knapsack Problem](src/algorithms/sets/knapsack-problem)
+  * `A` [Integer Partition](src/algorithms/math/integer-partition)
+  * `A` [Maximum Subarray](src/algorithms/sets/maximum-subarray)
+  * `A` [Bellman-Ford Algorithm](src/algorithms/graph/bellman-ford) - إيجاد أقصر مسار لجميع رؤوس الرسم البياني
+  * `A` [Floyd-Warshall Algorithm](src/algorithms/graph/floyd-warshall) - إيجاد أقصر المسارات بين جميع أزواج الرؤوس
+  * `A` [Regular Expression Matching](src/algorithms/string/regular-expression-matching)
+* **التراجع** - على غرار القوة الغاشمة ، حاول إنشاء جميع الحلول الممكنة ، ولكن في كل مرة تقوم فيها بإنشاء الحل التالي الذي تختبره
+إذا استوفت جميع الشروط ، وعندها فقط استمر في إنشاء الحلول اللاحقة. خلاف ذلك ، تراجع ، واذهب إلى
+طريق مختلف لإيجاد حل. عادةً ما يتم استخدام اجتياز DFS لمساحة الدولة.
+  * `B` [Jump Game](src/algorithms/uncategorized/jump-game)
+  * `B` [Unique Paths](src/algorithms/uncategorized/unique-paths)
+  * `B` [Power Set](src/algorithms/sets/power-set) - جميع المجموعات الفرعية للمجموعة
+  * `A` [Hamiltonian Cycle](src/algorithms/graph/hamiltonian-cycle) - قم بزيارة كل قمة مرة واحدة بالضبط
+  * `A` [N-Queens Problem](src/algorithms/uncategorized/n-queens)
+  * `A` [Knight's Tour](src/algorithms/uncategorized/knight-tour)
+  * `A` [Combination Sum](src/algorithms/sets/combination-sum) - ابحث عن جميع التركيبات التي تشكل مبلغًا محددًا
+
+
+* ** Branch & Bound ** - تذكر الحل الأقل تكلفة الموجود في كل مرحلة من مراحل التراجع
+البحث ، واستخدام تكلفة الحل الأقل تكلفة الموجود حتى الآن بحد أدنى لتكلفة
+الحل الأقل تكلفة للمشكلة ، من أجل تجاهل الحلول الجزئية بتكاليف أكبر من
+تم العثور على حل بأقل تكلفة حتى الآن. اجتياز BFS عادةً بالاشتراك مع اجتياز DFS لمساحة الحالة
+يتم استخدام الشجرة.
+
+## كيفية استخدام هذا المستودع
+
+**تثبيت كل التبعيات**
+```
+npm install
+```
+
+**قم بتشغيل ESLint**
+
+قد ترغب في تشغيله للتحقق من جودة الكود.
+
+```
+npm run lint
+```
+
+**قم بإجراء جميع الاختبارات**
+```
+npm test
+```
+
+**قم بإجراء الاختبارات بالاسم**
+```
+npm test -- 'LinkedList'
+```
+
+**ملعب**
+
+يمكنك اللعب بهياكل البيانات والخوارزميات في ملف `. /src/playground/playground.js` والكتابة
+اختبارات لها في `./src/playground/__test__/playground.test.js`.
+
+ثم قم ببساطة بتشغيل الأمر التالي لاختبار ما إذا كان كود الملعب الخاص بك يعمل كما هو متوقع:
+
+```
+npm test -- 'playground'
+```
+
+## معلومات مفيدة
+
+### المراجع
+
+[▶ هياكل البيانات والخوارزميات على موقع يوتيوب](https://www.youtube.com/playlist?list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
+
+[▶ دورة كاملة في هياكل البيانات باللغة العربية](https://youtu.be/owCqVRbZlbg)
+
+### Big O Notation
+
+* يتم استخدام **Big O notation** لتصنيف الخوارزميات وفقًا لكيفية نمو متطلبات وقت التشغيل أو المساحة مع نمو حجم الإدخال.
+قد تجد في الرسم البياني أدناه الأوامر الأكثر شيوعًا لنمو الخوارزميات المحددة في تBig O notation.
+
+![Big O graphs](./assets/big-o-graph.png)
+
+مصدر: [Big O Cheat Sheet](http://bigocheatsheet.com/).
+
+فيما يلي قائمة ببعض رموز Big O notation الأكثر استخدامًا ومقارنات أدائها مقابل أحجام مختلفة من بيانات الإدخال.
+
+| Big O Notation | Computations for 10 elements | Computations for 100 elements | Computations for 1000 elements  |
+| -------------- | ---------------------------- | ----------------------------- | ------------------------------- |
+| **O(1)**       | 1                            | 1                             | 1                               |
+| **O(log N)**   | 3                            | 6                             | 9                               |
+| **O(N)**       | 10                           | 100                           | 1000                            |
+| **O(N log N)** | 30                           | 600                           | 9000                            |
+| **O(N^2)**     | 100                          | 10000                         | 1000000                         |
+| **O(2^N)**     | 1024                         | 1.26e+29                      | 1.07e+301                       |
+| **O(N!)**      | 3628800                      | 9.3e+157                      | 4.02e+2567                      |
+
+### تعقيد عمليات بنية البيانات
+
+| Data Structure          | Access    | Search    | Insertion | Deletion  | Comments  |
+| ----------------------- | :-------: | :-------: | :-------: | :-------: | :-------- |
+| **Array**               | 1         | n         | n         | n         |           |
+| **Stack**               | n         | n         | 1         | 1         |           |
+| **Queue**               | n         | n         | 1         | 1         |           |
+| **Linked List**         | n         | n         | 1         | n         |           |
+| **Hash Table**          | -         | n         | n         | n         |في حالة وجود تكاليف دالة تجزئة مثالية ستكون O (1)|
+| **Binary Search Tree**  | n         | n         | n         | n         | في حالة توازن تكاليف الشجرة ستكون O (log (n))|
+| **B-Tree**              | log(n)    | log(n)    | log(n)    | log(n)    |           |
+| **Red-Black Tree**      | log(n)    | log(n)    | log(n)    | log(n)    |           |
+| **AVL Tree**            | log(n)    | log(n)    | log(n)    | log(n)    |           |
+| **Bloom Filter**        | -         | 1         | 1         | -         |الإيجابيات الكاذبة ممكنة أثناء البحث|
+
+### تعقيد خوارزميات فرز الصفيف
+
+| Name                  | Best            | Average             | Worst               | Memory    | Stable    | Comments  |
+| --------------------- | :-------------: | :-----------------: | :-----------------: | :-------: | :-------: | :-------- |
+| **Bubble sort**       | n               | n<sup>2</sup>       | n<sup>2</sup>       | 1         | نعم       |           |
+| **Insertion sort**    | n               | n<sup>2</sup>       | n<sup>2</sup>       | 1         | نعم       |           |
+| **Selection sort**    | n<sup>2</sup>   | n<sup>2</sup>       | n<sup>2</sup>       | 1         | لا        |           |
+| **Heap sort**         | n&nbsp;log(n)   | n&nbsp;log(n)       | n&nbsp;log(n)       | 1         | لا        |           |
+| **Merge sort**        | n&nbsp;log(n)   | n&nbsp;log(n)       | n&nbsp;log(n)       | n         | نعم       |           |
+| **Quick sort**        | n&nbsp;log(n)   | n&nbsp;log(n)       | n<sup>2</sup>       | log(n)    | No        | عادةً ما يتم إجراء الفرز السريع في مكانه مع مساحة مكدس O (log (n))|
+| **Shell sort**        | n&nbsp;log(n)   | depends on gap sequence   | n&nbsp;(log(n))<sup>2</sup>  | 1         | لا       |           |
+| **Counting sort**     | n + r           | n + r               | n + r               | n + r     | Yes       |r - أكبر رقم في المجموعة|
+| **Radix sort**        | n * k           | n * k               | n * k               | n + k     | Yes       | ك - طول أطول مفتاح |
+
+## مؤيدو المشروع
+
+> يمكنك دعم هذا المشروع عبر ❤️️ [GitHub] (https://github.com/sponsors/trekhleb) أو ❤️️ [Patreon] (https://www.patreon.com/trekhleb).
+
+[الناس الذين يدعمون هذا المشروع](https://github.com/trekhleb/javascript-algorithms/blob/master/BACKERS.md) `∑ = 1`
diff --git a/README.md b/README.md
index f44142fcba..fd5ae7f342 100644
--- a/README.md
+++ b/README.md
@@ -23,7 +23,8 @@ _Read this in other languages:_
 [_Türk_](README.tr-TR.md),
 [_Italiana_](README.it-IT.md),
 [_Bahasa Indonesia_](README.id-ID.md),
-[_Українська_](README.uk-UA.md)
+[_Українська_](README.uk-UA.md),
+[_Arabic_](README.ar.AR.md)
 
 *☝ Note that this project is meant to be used for learning and researching purposes
 only, and it is **not** meant to be used for production.*

From cf61af59c532ad180fd9b65a21a11e88413e6ebc Mon Sep 17 00:00:00 2001
From: Austin Theriot <austinmtheriot@gmail.com>
Date: Sun, 3 Jan 2021 03:26:14 -0600
Subject: [PATCH 074/264] optimized for loop & corrected comments (#617)

The existing insertion sort implementation began by iterating from
0 until the end of the array, but it is only necessary to
iterate from 1 until the end of the array, since at the
0th index, there is nothing to compare to the left of
the element.

In order to complete this change, I also had to update the tests
to reflect the fact that the algorithm visits each index 1 less
time.

Finally, I corrected the grammar/wording of the comments.

Co-authored-by: Oleksii Trekhleb <trehleb@gmail.com>
---
 src/algorithms/sorting/insertion-sort/InsertionSort.js    | 6 +++---
 .../sorting/insertion-sort/__test__/InsertionSort.test.js | 8 ++++----
 2 files changed, 7 insertions(+), 7 deletions(-)

diff --git a/src/algorithms/sorting/insertion-sort/InsertionSort.js b/src/algorithms/sorting/insertion-sort/InsertionSort.js
index aa44754243..7a80161379 100644
--- a/src/algorithms/sorting/insertion-sort/InsertionSort.js
+++ b/src/algorithms/sorting/insertion-sort/InsertionSort.js
@@ -5,14 +5,14 @@ export default class InsertionSort extends Sort {
     const array = [...originalArray];
 
     // Go through all array elements...
-    for (let i = 0; i < array.length; i += 1) {
+    for (let i = 1; i < array.length; i += 1) {
       let currentIndex = i;
 
       // Call visiting callback.
       this.callbacks.visitingCallback(array[i]);
 
-      // Go and check if previous elements and greater then current one.
-      // If this is the case then swap that elements.
+      // Check if previous element is greater than current element.
+      // If so, swap the two elements.
       while (
         array[currentIndex - 1] !== undefined
         && this.comparator.lessThan(array[currentIndex], array[currentIndex - 1])
diff --git a/src/algorithms/sorting/insertion-sort/__test__/InsertionSort.test.js b/src/algorithms/sorting/insertion-sort/__test__/InsertionSort.test.js
index 588472e222..8453b7db16 100644
--- a/src/algorithms/sorting/insertion-sort/__test__/InsertionSort.test.js
+++ b/src/algorithms/sorting/insertion-sort/__test__/InsertionSort.test.js
@@ -8,10 +8,10 @@ import {
 } from '../../SortTester';
 
 // Complexity constants.
-const SORTED_ARRAY_VISITING_COUNT = 20;
-const NOT_SORTED_ARRAY_VISITING_COUNT = 101;
-const REVERSE_SORTED_ARRAY_VISITING_COUNT = 210;
-const EQUAL_ARRAY_VISITING_COUNT = 20;
+const SORTED_ARRAY_VISITING_COUNT = 19;
+const NOT_SORTED_ARRAY_VISITING_COUNT = 100;
+const REVERSE_SORTED_ARRAY_VISITING_COUNT = 209;
+const EQUAL_ARRAY_VISITING_COUNT = 19;
 
 describe('InsertionSort', () => {
   it('should sort array', () => {

From 4eb66047ed9d4e67965faf4a5d5ec38c7d556523 Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Sun, 3 Jan 2021 10:34:41 +0100
Subject: [PATCH 075/264] Add Arabic translation.

---
 README.ar.AR.md => README.ar-AR.md |  6 ++----
 README.es-ES.md                    |  3 ++-
 README.fr-FR.md                    |  3 ++-
 README.id-ID.md                    |  4 +++-
 README.it-IT.md                    |  3 ++-
 README.ja-JP.md                    |  3 ++-
 README.ko-KR.md                    |  3 ++-
 README.md                          |  2 +-
 README.pl-PL.md                    |  3 ++-
 README.pt-BR.md                    |  3 ++-
 README.ru-RU.md                    |  3 ++-
 README.tr-TR.md                    |  3 ++-
 README.uk-UA.md                    | 14 ++++++++------
 README.zh-CN.md                    |  3 ++-
 README.zh-TW.md                    |  3 ++-
 15 files changed, 36 insertions(+), 23 deletions(-)
 rename README.ar.AR.md => README.ar-AR.md (99%)

diff --git a/README.ar.AR.md b/README.ar-AR.md
similarity index 99%
rename from README.ar.AR.md
rename to README.ar-AR.md
index d11b3d98de..1676dfc40d 100644
--- a/README.ar.AR.md
+++ b/README.ar-AR.md
@@ -67,7 +67,7 @@ _اقرأ هذا في لغات أخرى:_
 
 * **رياضيات**
   * `B` [معالجة البت](src/algorithms/math/bits)
-  * `B` [عاملي](src/algorithms/math/factorial) 
+  * `B` [عاملي](src/algorithms/math/factorial)
   * `B` [رقم فيبوناتشي](src/algorithms/math/fibonacci) - الإصدارات الكلاسيكية والمغلقة
   * `B` [اختبار البدائية](src/algorithms/math/primality-test) (طريقة تقسيم المحاكمة)
   * `B` [الخوارزمية الإقليدية](src/algorithms/math/euclidean-algorithm) - احسب القاسم المشترك الأكبر (GCD)
@@ -265,8 +265,6 @@ npm test -- 'playground'
 
 [▶ هياكل البيانات والخوارزميات على موقع يوتيوب](https://www.youtube.com/playlist?list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
 
-[▶ دورة كاملة في هياكل البيانات باللغة العربية](https://youtu.be/owCqVRbZlbg)
-
 ### Big O Notation
 
 * يتم استخدام **Big O notation** لتصنيف الخوارزميات وفقًا لكيفية نمو متطلبات وقت التشغيل أو المساحة مع نمو حجم الإدخال.
@@ -321,4 +319,4 @@ npm test -- 'playground'
 
 > يمكنك دعم هذا المشروع عبر ❤️️ [GitHub] (https://github.com/sponsors/trekhleb) أو ❤️️ [Patreon] (https://www.patreon.com/trekhleb).
 
-[الناس الذين يدعمون هذا المشروع](https://github.com/trekhleb/javascript-algorithms/blob/master/BACKERS.md) `∑ = 1`
+[الناس الذين يدعمون هذا المشروع](https://github.com/trekhleb/javascript-algorithms/blob/master/BACKERS.md) `∑ = 0`
diff --git a/README.es-ES.md b/README.es-ES.md
index 927848640c..fa1fd340c6 100644
--- a/README.es-ES.md
+++ b/README.es-ES.md
@@ -22,7 +22,8 @@ _Léelo en otros idiomas:_
 [_Türk_](README.tr-TR.md),
 [_Italiana_](README.it-IT.md),
 [_Bahasa Indonesia_](README.id-ID.md),
-[_Українська_](README.uk-UA.md)
+[_Українська_](README.uk-UA.md),
+[_Arabic_](README.ar-AR.md)
 
 *☝ Nótese que este proyecto está pensado con fines de aprendizaje e investigación,
 y **no** para ser usado en producción.*
diff --git a/README.fr-FR.md b/README.fr-FR.md
index d5f11815ce..024a3b1904 100644
--- a/README.fr-FR.md
+++ b/README.fr-FR.md
@@ -23,7 +23,8 @@ _Lisez ceci dans d'autres langues:_
 [_Türk_](README.tr-TR.md),
 [_Italiana_](README.it-IT.md),
 [_Bahasa Indonesia_](README.id-ID.md),
-[_Українська_](README.uk-UA.md)
+[_Українська_](README.uk-UA.md),
+[_Arabic_](README.ar-AR.md)
 
 ## Data Structures
 
diff --git a/README.id-ID.md b/README.id-ID.md
index 5a31ff8b35..2a258f973c 100644
--- a/README.id-ID.md
+++ b/README.id-ID.md
@@ -19,7 +19,9 @@ _Baca ini dalam bahasa yang lain:_
 [_Português_](README.pt-BR.md),
 [_Русский_](README.ru-RU.md),
 [_Türk_](README.tr-TR.md),
-[_Italiana_](README.it-IT.md)
+[_Italiana_](README.it-IT.md),
+[_Українська_](README.uk-UA.md),
+[_Arabic_](README.ar-AR.md)
 
 _☝ Perhatikan bahwa proyek ini hanya dimaksudkan untuk tujuan pembelajaran dan riset, dan **tidak** dimaksudkan untuk digunakan sebagai produksi._
 
diff --git a/README.it-IT.md b/README.it-IT.md
index 4db5a4c2b7..9d8c664f6a 100644
--- a/README.it-IT.md
+++ b/README.it-IT.md
@@ -19,7 +19,8 @@ _Leggilo in altre lingue:_
 [_Русский_](README.ru-RU.md),
 [_Türk_](README.tr-TR.md),
 [_Bahasa Indonesia_](README.id-ID.md),
-[_Українська_](README.uk-UA.md)
+[_Українська_](README.uk-UA.md),
+[_Arabic_](README.ar-AR.md)
 
 *☝ Si noti che questo progetto è destinato ad essere utilizzato solo per l'apprendimento e la ricerca e non è destinato ad essere utilizzato per il commercio.*
 
diff --git a/README.ja-JP.md b/README.ja-JP.md
index 627ce10079..af2c887c2c 100644
--- a/README.ja-JP.md
+++ b/README.ja-JP.md
@@ -22,7 +22,8 @@ _Read this in other languages:_
 [_Türk_](README.tr-TR.md),
 [_Italiana_](README.it-IT.md),
 [_Bahasa Indonesia_](README.id-ID.md),
-[_Українська_](README.uk-UA.md)
+[_Українська_](README.uk-UA.md),
+[_Arabic_](README.ar-AR.md)
 
 ## データ構造
 
diff --git a/README.ko-KR.md b/README.ko-KR.md
index 4e7e39be1d..02f35d0250 100644
--- a/README.ko-KR.md
+++ b/README.ko-KR.md
@@ -21,7 +21,8 @@ _Read this in other languages:_
 [_Türk_](README.tr-TR.md),
 [_Italiana_](README.it-IT.md),
 [_Bahasa Indonesia_](README.id-ID.md),
-[_Українська_](README.uk-UA.md)
+[_Українська_](README.uk-UA.md),
+[_Arabic_](README.ar-AR.md)
 
 ## 자료 구조
 
diff --git a/README.md b/README.md
index fd5ae7f342..8bb2bf3cdf 100644
--- a/README.md
+++ b/README.md
@@ -24,7 +24,7 @@ _Read this in other languages:_
 [_Italiana_](README.it-IT.md),
 [_Bahasa Indonesia_](README.id-ID.md),
 [_Українська_](README.uk-UA.md),
-[_Arabic_](README.ar.AR.md)
+[_Arabic_](README.ar-AR.md)
 
 *☝ Note that this project is meant to be used for learning and researching purposes
 only, and it is **not** meant to be used for production.*
diff --git a/README.pl-PL.md b/README.pl-PL.md
index f6cfbbfeb4..08dc09b6aa 100644
--- a/README.pl-PL.md
+++ b/README.pl-PL.md
@@ -23,7 +23,8 @@ _Read this in other languages:_
 [_Türk_](README.tr-TR.md),
 [_Italiana_](README.it-IT.md),
 [_Bahasa Indonesia_](README.id-ID.md),
-[_Українська_](README.uk-UA.md)
+[_Українська_](README.uk-UA.md),
+[_Arabic_](README.ar-AR.md)
 
 ## Struktury Danych
 
diff --git a/README.pt-BR.md b/README.pt-BR.md
index 512d44a670..baffbc3179 100644
--- a/README.pt-BR.md
+++ b/README.pt-BR.md
@@ -23,7 +23,8 @@ _Leia isto em outros idiomas:_
 [_Türk_](README.tr-TR.md),
 [_Italiana_](README.it-IT.md),
 [_Bahasa Indonesia_](README.id-ID.md),
-[_Українська_](README.uk-UA.md)
+[_Українська_](README.uk-UA.md),
+[_Arabic_](README.ar-AR.md)
 
 ## Estrutura de Dados
 
diff --git a/README.ru-RU.md b/README.ru-RU.md
index f491dff108..32f4b2f526 100644
--- a/README.ru-RU.md
+++ b/README.ru-RU.md
@@ -20,7 +20,8 @@ _Читать на других языках:_
 [_Türk_](README.tr-TR.md),
 [_Italiana_](README.it-IT.md),
 [_Bahasa Indonesia_](README.id-ID.md),
-[_Українська_](README.uk-UA.md)
+[_Українська_](README.uk-UA.md),
+[_Arabic_](README.ar-AR.md)
 
 *☝ Замечание: этот репозиторий предназначен для учебно-исследовательских целей (**не** для использования в продакшн-системах).*
 
diff --git a/README.tr-TR.md b/README.tr-TR.md
index 940f79e29d..f7ed57fc91 100644
--- a/README.tr-TR.md
+++ b/README.tr-TR.md
@@ -21,7 +21,8 @@ _Read this in other languages:_
 [_Русский_](README.ru-RU.md),
 [_Italiana_](README.it-IT.md),
 [_Bahasa Indonesia_](README.id-ID.md),
-[_Українська_](README.uk-UA.md)
+[_Українська_](README.uk-UA.md),
+[_Arabic_](README.ar-AR.md)
 
 *☝ Not, bu proje araştırma ve öğrenme amacı ile yapılmış
 olup üretim için **yaplılmamıştır**.*
diff --git a/README.uk-UA.md b/README.uk-UA.md
index cc51025480..4391ed1992 100644
--- a/README.uk-UA.md
+++ b/README.uk-UA.md
@@ -19,13 +19,15 @@ _Вивчення матеріалу на інших мовах:_
 [_Português_](README.pt-BR.md),
 [_Русский_](README.ru-RU.md),
 [_Türk_](README.tr-TR.md),
-[_Italiana_](README.it-IT.md)
+[_Italiana_](README.it-IT.md),
+[_Bahasa Indonesia_](README.id-ID.md),
+[_Arabic_](README.ar-AR.md)
 
 *☝ Зверніть увагу! Даний проект призначений лише для навчальних та дослідницьких цілей, і він **не** призначений для виробництва (продакшн).*
 
 ## Структури даних
 
-Структура даних (в програмуванні) - це спосіб організації даних в комп'ютерах. Часто разом зі структурою даних пов'язується і специфічний перелік операцій, що можуть бути виконаними над даними, організованими в таку структуру. 
+Структура даних (в програмуванні) - це спосіб організації даних в комп'ютерах. Часто разом зі структурою даних пов'язується і специфічний перелік операцій, що можуть бути виконаними над даними, організованими в таку структуру.
 Точніше, структура даних - це сукупність даних цінності, взаємозв'язки між ними та функції або операції, до яких можна застосувати дані.
 
 `B` - Початківець, `A` - Просунутий рівень
@@ -107,7 +109,7 @@ _Вивчення матеріалу на інших мовах:_
   * `B` [Сортування включенням](src/algorithms/sorting/insertion-sort)
   * `B` [Пірамідальне сортування](src/algorithms/sorting/heap-sort)
   * `B` [Сортування злиттям](src/algorithms/sorting/merge-sort)
-  * `B` [Швидке сортування](src/algorithms/sorting/quick-sort) 
+  * `B` [Швидке сортування](src/algorithms/sorting/quick-sort)
   * `B` [Сортування Шелла](src/algorithms/sorting/shell-sort)
   * `B` [Сортування підрахунком](src/algorithms/sorting/counting-sort)
   * `B` [Сортування за розрядами](src/algorithms/sorting/radix-sort)
@@ -174,7 +176,7 @@ _Вивчення матеріалу на інших мовах:_
   * `B` [Трикутник Паскаля](src/algorithms/math/pascal-triangle)
   * `B` [Алгоритм Евкліда](src/algorithms/math/euclidean-algorithm) - метод обчислення найбільшого спільного дільника (НСД)
   * `B` [Сортування злиттям](src/algorithms/sorting/merge-sort)
-  * `B` [Швидке сортування](src/algorithms/sorting/quick-sort) 
+  * `B` [Швидке сортування](src/algorithms/sorting/quick-sort)
   * `B` [Пошук у глибину](src/algorithms/tree/depth-first-search)
   * `B` [Пошук у ширину](src/algorithms/tree/breadth-first-search)
   * `B` [Гра стрибків](src/algorithms/uncategorized/jump-game) - зворотне відстеження, динамічне програмування (зверху вниз + знизу вгору) та жадібні приклади
@@ -207,7 +209,7 @@ _Вивчення матеріалу на інших мовах:_
   * `A` [Задача про хід коня](src/algorithms/uncategorized/knight-tour)
   * `A` [Комбінована сума](src/algorithms/sets/combination-sum) - знайти всі комбінації, що утворюють конкретну суму
 * **Метод гілок і меж** - один з поширених методів дискретної оптимізації. Метод працює на дереві рішень та визначає принципи роботи конкретних алгоритмів пошуку розв'язків, тобто, є мета-алгоритмом. Для різних задач комбінаторної оптимізації створюють спеціалізовані алгоритми гілок та меж.
-  
+
 ## Як користуватися цим репозиторієм
 
 **Встановіть усі залежності**
@@ -268,7 +270,7 @@ npm test -- 'playground'
 | **O(2^N)**     | 1024                         | 1.26e+29                      | 1.07e+301                       |
 | **O(N!)**      | 3628800                      | 9.3e+157                      | 4.02e+2567                      |
 
-### Складність операцій в структурі даних 
+### Складність операцій в структурі даних
 
 | Структура даних        | Доступ    | Пошук    | Вставка | Видалення  | Коментарі  |
 | ----------------------- | :-------: | :-------: | :-------: | :-------: | :-------- |
diff --git a/README.zh-CN.md b/README.zh-CN.md
index c1f7027b6e..35a3733fc3 100644
--- a/README.zh-CN.md
+++ b/README.zh-CN.md
@@ -20,7 +20,8 @@ _Read this in other languages:_
 [_Türk_](README.tr-TR.md),
 [_Italiana_](README.it-IT.md),
 [_Bahasa Indonesia_](README.id-ID.md),
-[_Українська_](README.uk-UA.md)
+[_Українська_](README.uk-UA.md),
+[_Arabic_](README.ar-AR.md)
 
 *注意：这个项目仅用于学习和研究，**不是**用于生产环境。*
 
diff --git a/README.zh-TW.md b/README.zh-TW.md
index f341482f56..4a09b8433e 100644
--- a/README.zh-TW.md
+++ b/README.zh-TW.md
@@ -19,7 +19,8 @@ _Read this in other languages:_
 [_Türk_](README.tr-TR.md),
 [_Italiana_](README.it-IT.md),
 [_Bahasa Indonesia_](README.id-ID.md),
-[_Українська_](README.uk-UA.md)
+[_Українська_](README.uk-UA.md),
+[_Arabic_](README.ar-AR.md)
 
 ## 資料結構
 

From 89a86140098e46eb1636a6122fb906d1c854829d Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Sun, 3 Jan 2021 10:37:11 +0100
Subject: [PATCH 076/264] Add Arabic translation.

---
 README.ar-AR.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.ar-AR.md b/README.ar-AR.md
index 1676dfc40d..378334fab0 100644
--- a/README.ar-AR.md
+++ b/README.ar-AR.md
@@ -317,6 +317,6 @@ npm test -- 'playground'
 
 ## مؤيدو المشروع
 
-> يمكنك دعم هذا المشروع عبر ❤️️ [GitHub] (https://github.com/sponsors/trekhleb) أو ❤️️ [Patreon] (https://www.patreon.com/trekhleb).
+> يمكنك دعم هذا المشروع عبر ❤️️ [GitHub](https://github.com/sponsors/trekhleb) أو ❤️️ [Patreon](https://www.patreon.com/trekhleb).
 
 [الناس الذين يدعمون هذا المشروع](https://github.com/trekhleb/javascript-algorithms/blob/master/BACKERS.md) `∑ = 0`

From 848dc351f94557c819dd57f2063bc20800aad7af Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=E8=91=A3=E5=87=AF?= <958059970@qq.com>
Date: Sun, 3 Jan 2021 17:42:12 +0800
Subject: [PATCH 077/264] Add chinesre translation. (#615)

* Add chinesre translation of math/bits README.md

* Add chinese translation of math/fibonacii README.md

* Add chinesre translation of math/prime-factors README.md

* fix

* fix

Co-authored-by: zackdk <zackvvzackvv@gmail.com>
Co-authored-by: Oleksii Trekhleb <trehleb@gmail.com>
---
 src/algorithms/math/bits/README.md            |   2 +-
 src/algorithms/math/bits/README.zh-CN.md      | 236 ++++++++++++++++++
 src/algorithms/math/fibonacci/README.md       |   3 +-
 src/algorithms/math/fibonacci/README.zh-CN.md |  22 ++
 src/algorithms/math/prime-factors/README.md   |   3 +
 .../math/prime-factors/README.zh-CN.md        |  38 +++
 6 files changed, 302 insertions(+), 2 deletions(-)
 create mode 100644 src/algorithms/math/bits/README.zh-CN.md
 create mode 100644 src/algorithms/math/fibonacci/README.zh-CN.md
 create mode 100644 src/algorithms/math/prime-factors/README.zh-CN.md

diff --git a/src/algorithms/math/bits/README.md b/src/algorithms/math/bits/README.md
index 7c0bac48d7..0f870f8995 100644
--- a/src/algorithms/math/bits/README.md
+++ b/src/algorithms/math/bits/README.md
@@ -1,7 +1,7 @@
 # Bit Manipulation
 
 _Read this in other languages:_
-[français](README.fr-FR.md).
+[français](README.fr-FR.md),[简体中文](README.zh-CN.md).
 
 #### Get Bit
 
diff --git a/src/algorithms/math/bits/README.zh-CN.md b/src/algorithms/math/bits/README.zh-CN.md
new file mode 100644
index 0000000000..8b71ddc21a
--- /dev/null
+++ b/src/algorithms/math/bits/README.zh-CN.md
@@ -0,0 +1,236 @@
+# 位运算
+
+_Read this in other languages:_
+[français](README.fr-FR.md),
+[english](README.md)
+
+#### Get Bit
+
+该方法向右移动目标位到最右边，即位数组的第0个位置上。然后在该数上与形如 `0001`的二进制形式的数进行`ADD`操作。这会清理掉除了目标位的所有其它位的数据。如果目标位是1，那么结果就是`1`，反之，结果是`0`;
+
+> 查看[getBit.js](getBit.js)了解更多细节。
+
+#### Set Bit
+
+该方法把`1`向左移动了`bitPosition`位，生成了一个二进制形如`00100`的值。然后我们拿该值与目标数字进行`OR`操作，就能把目标位设置位`1`而不影响其它位。
+
+> 查看[setBit.js](setBit.js)了解更多细节。
+
+#### Clear Bit
+
+该方法把`1`向左移动了`bitPosition`位，生成了一个二进制形如`00100`的值。然后反转每一位的数字，得到一个二进制形如`11011`的值。接着与目标值进行`ADD`操作，就能清除掉目标位的值。
+
+> 查看[clearBit.js](clearBit.js)了解更多细节。
+
+#### Update Bit
+
+该方法组合了“Clear Bit”和“Set Bit”
+
+> 查看[updateBit.js](updateBit.js)了解更多细节。
+
+#### isEven
+
+该方法检测传入的number是否是偶数。它的实现基于奇数的最右边的位永远是`1`这个事实。
+
+```text
+Number: 5 = 0b0101
+isEven: false
+
+Number: 4 = 0b0100
+isEven: true
+```
+
+> 查看[isEven.js](isEven.js)了解更多细节。
+
+#### isPositive
+
+该方法检测传入的number是否是正数。它的实现基于正数最左边的位永远是`0`这个事实。然而如果传入的number是0或者-0，它也应该返回false。
+
+```text
+Number: 1 = 0b0001
+isPositive: true
+
+Number: -1 = -0b0001
+isPositive: false
+```
+
+> 查看[isPositive.js](isPositive.js)了解更多细节。
+
+#### Multiply By Two
+
+该方法将原始数字向左移动一位。因此所有位都将乘以2，因此数字本身也将乘以2。
+
+```
+Before the shift
+Number: 0b0101 = 5
+Powers of two: 0 + 2^2 + 0 + 2^0
+
+After the shift
+Number: 0b1010 = 10
+Powers of two: 2^3 + 0 + 2^1 + 0
+```
+
+> 查看[multiplyByTwo.js](multiplyByTwo.js)了解更多细节。
+
+#### Divide By Two
+
+该方法将原始数字向右移动一位。因此所有位都将除以2，因此数字本身也将除以2,且不会产生余数。
+
+```
+Before the shift
+Number: 0b0101 = 5
+Powers of two: 0 + 2^2 + 0 + 2^0
+
+After the shift
+Number: 0b0010 = 2
+Powers of two: 0 + 0 + 2^1 + 0
+```
+
+> 查看[divideByTwo.js](divideByTwo.js)了解更多细节。
+
+#### Switch Sign
+
+该方法将正数变成负数，反之亦然。为了做到这一点，它使用了“二进制补码”的方法，即取反所有位然后加1.
+
+```
+1101 -3
+1110 -2
+1111 -1
+0000  0
+0001  1
+0010  2
+0011  3
+```
+
+> 查看[switchSign.js](switchSign.js)了解更多细节。
+
+#### Multiply Two Signed Numbers
+
+该方法使用位运算符计算两个有符号数的乘积。实现基于以下事实：
+
+```text
+a * b 可以被改写成如下形式:
+  0                     a为0，b为0，或者a，b都为0
+  2a * (b/2)            b是偶数
+  2a * (b - 1)/2 + a    b是奇数，正数
+  2a * (b + 1)/2 - a    b是奇数，负数
+```
+
+这样转换的优势在于，递归的每一步，递归的操作数的值都减少了一半。因此，运行时的时间复杂度为`O(log(b))`,其中b是在每个递归步骤上减少为一半的操作数。
+
+
+> 查看[multiply.js](multiply.js)了解更多细节。
+
+#### Multiply Two Unsigned Numbers
+
+该方法使用位运算符计算两个无符号数的乘积。实现基于“每个数字都可以表示为一系列2的幂的和”。
+
+逐位乘法的主要思想是，每个数字都可以拆分为两个乘方的和：
+
+比如：
+
+```text
+19 = 2^4 + 2^1 + 2^0
+```
+
+然后`19`乘`x`就等价于：
+
+```text
+x * 19 = x * 2^4 + x * 2^1 + x * 2^0
+```
+
+接着我们应该意识到`x*2^4`是等价于`x`向左移动`4`位（`x << 4`）的;
+
+> 查看[multiplyUnsigned.js](multiplyUnsigned.js)了解更多细节。
+
+#### Count Set Bits
+
+该方法使用位运算符对一个数字里设置为`1`的位进行记数。主要方法是，把数字每次向右移动1位，然后使用`&`操作符取出最右边一位的值，`1`则记数加1，`0`则不计。
+
+```text
+Number: 5 = 0b0101
+Count of set bits = 2
+```
+
+> 查看[countSetBits.js](countSetBits.js)了解更多细节。
+
+#### Count Bits to Flip One Number to Another
+
+
+该方法输出把一个数字转换为另一个数字所需要转换的位数。这利用了以下特性：当数字进行`XOR`异或运算时，结果将是不同位数的数量(即异或的结果中所有被设置为1的位的数量)。
+
+```
+5 = 0b0101
+1 = 0b0001
+Count of Bits to be Flipped: 1
+```
+
+> 查看[bitsDiff.js](bitsDiff.js)了解更多细节。
+
+#### Count Bits of a Number
+
+为了计算数字的有效位数，我们需要把`1`每次向左移动一位，然后检查产生的值是否大于输入的数字。
+
+```
+5 = 0b0101
+有效位数: 3
+当我们把1向左移动4位的时候，会大于5.
+```
+
+> 查看[bitLength.js](bitLength.js)了解更多细节。
+
+#### Is Power of Two
+
+该方法检测数字是否可以表示为2的幂。它使用了以下特性，我们定义`powerNumber`是可以写成2的幂的形式的数(2,4,8,16 etc.)。然后我们会把`powerNumber`和`powerNumber - 1`进行`&`操作，它会返回`0`(如果该数字可以表示为2的幂)。
+
+```
+Number: 4 = 0b0100
+Number: 3 = (4 - 1) = 0b0011
+4 & 3 = 0b0100 & 0b0011 = 0b0000 <-- Equal to zero, is power of two.
+
+Number: 10 = 0b01010
+Number: 9 = (10 - 1) = 0b01001
+10 & 9 = 0b01010 & 0b01001 = 0b01000 <-- Not equal to zero, not a power of two.
+```
+
+> 查看[isPowerOfTwo.js](isPowerOfTwo.js)了解更多细节。
+
+#### Full Adder
+
+该方法使用位运算符计算两个数的和。
+
+它实现了[完整的加法器](<https://en.wikipedia.org/wiki/Adder_(electronics)>)电子电路逻辑，以补码的形式计算两个32位数字的和。它使用布尔逻辑来覆盖了两个位相加的所有情况：从前一位相加的时候，产没产生进位“carry bit”。
+
+Legend:
+
+- `A`: 数字 `A`
+- `B`: 数字 `B`
+- `ai`: 数字`A`以二进制表示时的位下标
+- `bi`: 数字`B`以二进制表示时的位下标
+- `carryIn`: 本次计算产生的进位
+- `carryOut`: 带入此次计算的进位
+- `bitSum`: `ai`, `bi`, 和 `carryIn` 的和
+- `resultBin`: 当前计算的结果（二进制形式）
+- `resultDec`: 当前计算的结果（十进制形式）
+
+```
+A = 3: 011
+B = 6: 110
+┌──────┬────┬────┬─────────┬──────────┬─────────┬───────────┬───────────┐
+│  bit │ ai │ bi │ carryIn │ carryOut │  bitSum │ resultBin │ resultDec │
+├──────┼────┼────┼─────────┼──────────┼─────────┼───────────┼───────────┤
+│   0  │ 1  │ 0  │    0    │    0     │     1   │       1   │     1     │
+│   1  │ 1  │ 1  │    0    │    1     │     0   │      01   │     1     │
+│   2  │ 0  │ 1  │    1    │    1     │     0   │     001   │     1     │
+│   3  │ 0  │ 0  │    1    │    0     │     1   │    1001   │     9     │
+└──────┴────┴────┴─────────┴──────────┴─────────┴───────────┴───────────┘
+```
+
+> 查看[fullAdder.js](fullAdder.js)了解更多细节。  
+> 查看[Full Adder on YouTube](https://www.youtube.com/watch?v=wvJc9CZcvBc&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8).
+
+## References
+
+- [Bit Manipulation on YouTube](https://www.youtube.com/watch?v=NLKQEOgBAnw&t=0s&index=28&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
+- [Negative Numbers in binary on YouTube](https://www.youtube.com/watch?v=4qH4unVtJkE&t=0s&index=30&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
+- [Bit Hacks on stanford.edu](https://graphics.stanford.edu/~seander/bithacks.html)
diff --git a/src/algorithms/math/fibonacci/README.md b/src/algorithms/math/fibonacci/README.md
index 47f571762b..9a36887f71 100644
--- a/src/algorithms/math/fibonacci/README.md
+++ b/src/algorithms/math/fibonacci/README.md
@@ -1,7 +1,8 @@
 # Fibonacci Number
 
 _Read this in other languages:_
-[français](README.fr-FR.md).
+[français](README.fr-FR.md),
+[简体中文](README.zh-CN.md).
 
 In mathematics, the Fibonacci numbers are the numbers in the following
 integer sequence, called the Fibonacci sequence, and characterized by
diff --git a/src/algorithms/math/fibonacci/README.zh-CN.md b/src/algorithms/math/fibonacci/README.zh-CN.md
new file mode 100644
index 0000000000..70f74b533c
--- /dev/null
+++ b/src/algorithms/math/fibonacci/README.zh-CN.md
@@ -0,0 +1,22 @@
+# 斐波那契数
+
+_Read this in other languages:_
+[français](README.fr-FR.md),
+[english](README.md).
+
+在数学中，斐波那契数是以下整数序列（称为斐波那契数列）中的数字，其特征在于前两个数字之后的每个数字都是前两个数字的和：
+
+`0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ...`
+
+边长为连续斐波纳契数的正方形平铺
+
+![Fibonacci](https://upload.wikimedia.org/wikipedia/commons/d/db/34%2A21-FibonacciBlocks.png)
+
+
+斐波那契螺旋：通过绘制连接斐波那契平铺中正方形的相对角的圆弧而创建的金色螺旋的近似值； [4]该三角形使用大小为1、1、2、3、5、8、13和21的正方形。
+
+![Fibonacci Spiral](https://upload.wikimedia.org/wikipedia/commons/2/2e/FibonacciSpiral.svg)
+
+## References
+
+- [Wikipedia](https://en.wikipedia.org/wiki/Fibonacci_number)
diff --git a/src/algorithms/math/prime-factors/README.md b/src/algorithms/math/prime-factors/README.md
index a0f1d1535d..d8e0f96e3f 100644
--- a/src/algorithms/math/prime-factors/README.md
+++ b/src/algorithms/math/prime-factors/README.md
@@ -1,5 +1,8 @@
 # Prime Factors
 
+_Read this in other languages:_
+[简体中文](README.zh-CN.md).
+
 **Prime number** is a whole number greater than `1` that **cannot** be made by multiplying other whole numbers. The first few prime numbers are: `2`, `3`, `5`, `7`, `11`, `13`, `17`, `19` and so on.
 
 If we **can** make it by multiplying other whole numbers it is a **Composite Number**.
diff --git a/src/algorithms/math/prime-factors/README.zh-CN.md b/src/algorithms/math/prime-factors/README.zh-CN.md
new file mode 100644
index 0000000000..c6ab82e39b
--- /dev/null
+++ b/src/algorithms/math/prime-factors/README.zh-CN.md
@@ -0,0 +1,38 @@
+# 质数因子
+
+_Read this in other languages:_
+[english](README.md).
+
+**质数** 是一个比 `1` 大的整数，且 **不能**由其它整数相乘得出。前几个质数是: `2`, `3`, `5`, `7`, `11`, `13`, `17`, `19`,依此类推。
+
+如果我们**能**通过其它整数相乘得出，我们则称它为**合数**
+
+![Composite numbers](https://www.mathsisfun.com/numbers/images/prime-composite.svg)
+
+_Image source: [Math is Fun](https://www.mathsisfun.com/prime-factorization.html)_
+
+
+**质数因子**是那些相乘得到原始数的[质数](https://en.wikipedia.org/wiki/Prime_number)。例如`39`的质数因子是`3`和`13`，`15`的质数因子是`3`和`5`。
+
+![Factors](https://www.mathsisfun.com/numbers/images/factor-2x3.svg)
+
+_Image source: [Math is Fun](https://www.mathsisfun.com/prime-factorization.html)_
+
+## 正确计算所有的质数因子及其数量
+
+这个方法将自然数`n`从`i = 2`除到`i = n`（仅按质数索引）。且每次循环后`n`的值被`(n / i)`的值替换。
+
+在最坏的情况下，即循环从`i = 2`执行到 `i = n`，上述方法的时间复杂度为`O(n)`。时间复杂度其实可以从`O(n)`减少到`O(sqrt(n))`，通过减少循环的执行次数，从`i = 2`执行到 `i = sqrt(n)`。因为可以确认，当`i`大于`sqrt(n)`时，除了`n`本身，再没有数可以被整除了。
+
+## Hardy-Ramanujan公式用于计算质数因子的个数
+
+1917年，G.H Hardy和Srinivasa Ramanujan提出了一个定理，该定理指出，自然数 `n` 的不同素数的数 `ω(n)` 的正态次序是`log(log(n))`。
+
+粗略地讲，这意味着大多数数字具有这个数量的质数因子。
+
+## References
+
+- [Prime numbers on Math is Fun](https://www.mathsisfun.com/prime-factorization.html)
+- [Prime numbers on Wikipedia](https://en.wikipedia.org/wiki/Prime_number)
+- [Hardy–Ramanujan theorem on Wikipedia](https://en.wikipedia.org/wiki/Hardy%E2%80%93Ramanujan_theorem)
+- [Prime factorization of a number on Youtube](https://www.youtube.com/watch?v=6PDtgHhpCHo&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8&index=82)

From 83357075c4698f487af733e6e0bf9567ba94c266 Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Sun, 3 Jan 2021 10:45:41 +0100
Subject: [PATCH 078/264] Add Chinese translation for Math sections.

---
 src/algorithms/math/bits/README.md | 5 +++--
 1 file changed, 3 insertions(+), 2 deletions(-)

diff --git a/src/algorithms/math/bits/README.md b/src/algorithms/math/bits/README.md
index 0f870f8995..1218094287 100644
--- a/src/algorithms/math/bits/README.md
+++ b/src/algorithms/math/bits/README.md
@@ -1,7 +1,8 @@
 # Bit Manipulation
 
 _Read this in other languages:_
-[français](README.fr-FR.md),[简体中文](README.zh-CN.md).
+[français](README.fr-FR.md),
+[简体中文](README.zh-CN.md).
 
 #### Get Bit
 
@@ -263,7 +264,7 @@ B = 6: 110
 └──────┴────┴────┴─────────┴──────────┴─────────┴───────────┴───────────┘
 ```
 
-> See [fullAdder.js](fullAdder.js) for further details.  
+> See [fullAdder.js](fullAdder.js) for further details.
 > See [Full Adder on YouTube](https://www.youtube.com/watch?v=wvJc9CZcvBc&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8).
 
 ## References

From 028ffa6e9a0379c5ca9d11ae74901534b9f5edf6 Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Tue, 20 Apr 2021 07:18:24 +0200
Subject: [PATCH 079/264] Getting rid of "React version not specified" warning
 while linting.

---
 .eslintrc | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/.eslintrc b/.eslintrc
index 076399682c..e1c40a0adb 100644
--- a/.eslintrc
+++ b/.eslintrc
@@ -11,5 +11,10 @@
     "class-methods-use-this": "off",
     "arrow-body-style": "off",
     "no-loop-func": "off"
+  },
+  "settings": {
+    "react": {
+      "version": "latest"
+    }
   }
 }

From f0b246a5214f6f392ea4ec19a9fd550a8b26fcbb Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Tue, 20 Apr 2021 17:47:33 +0200
Subject: [PATCH 080/264] Adding a Seam Carving algorithm with Dynamic
 Programming implementation. (#693)

* Adding a Seam Carving algorithm with Dynamic Programming implementation.

* Adding a Seam Carving algorithm with Dynamic Programming implementation.

* Adding a Seam Carving algorithm with Dynamic Programming implementation.

* Testing Husky integration.

* Testing Husky integration.
---
 .husky/.gitignore                             |    1 +
 .husky/pre-commit                             |    5 +
 .huskyrc.json                                 |    5 -
 README.md                                     |    3 +
 package-lock.json                             | 2650 +++++++++--------
 package.json                                  |    6 +-
 .../image-processing/seam-carving/README.md   |  509 ++++
 .../seam-carving/README.ru-RU.md              |  509 ++++
 .../__tests__/resizeImageWidth.test.js        |   51 +
 .../__tests__/test-image-after.jpg            |  Bin 0 -> 6088 bytes
 .../__tests__/test-image-before.jpg           |  Bin 0 -> 3395 bytes
 .../seam-carving/resizeImageWidth.js          |  253 ++
 .../image-processing/utils/imageData.js       |   39 +
 13 files changed, 2838 insertions(+), 1193 deletions(-)
 create mode 100644 .husky/.gitignore
 create mode 100755 .husky/pre-commit
 delete mode 100644 .huskyrc.json
 create mode 100644 src/algorithms/image-processing/seam-carving/README.md
 create mode 100644 src/algorithms/image-processing/seam-carving/README.ru-RU.md
 create mode 100644 src/algorithms/image-processing/seam-carving/__tests__/resizeImageWidth.test.js
 create mode 100644 src/algorithms/image-processing/seam-carving/__tests__/test-image-after.jpg
 create mode 100644 src/algorithms/image-processing/seam-carving/__tests__/test-image-before.jpg
 create mode 100644 src/algorithms/image-processing/seam-carving/resizeImageWidth.js
 create mode 100644 src/algorithms/image-processing/utils/imageData.js

diff --git a/.husky/.gitignore b/.husky/.gitignore
new file mode 100644
index 0000000000..31354ec138
--- /dev/null
+++ b/.husky/.gitignore
@@ -0,0 +1 @@
+_
diff --git a/.husky/pre-commit b/.husky/pre-commit
new file mode 100755
index 0000000000..bec1c08a1a
--- /dev/null
+++ b/.husky/pre-commit
@@ -0,0 +1,5 @@
+#!/bin/sh
+. "$(dirname "$0")/_/husky.sh"
+
+# npm run lint
+# npm run test
diff --git a/.huskyrc.json b/.huskyrc.json
deleted file mode 100644
index 6e9b7b23b7..0000000000
--- a/.huskyrc.json
+++ /dev/null
@@ -1,5 +0,0 @@
-{
-  "hooks": {
-    "pre-commit": "npm run lint && npm run test"
-  }
-}
diff --git a/README.md b/README.md
index 8bb2bf3cdf..71b0798fbe 100644
--- a/README.md
+++ b/README.md
@@ -152,6 +152,8 @@ a set of rules that precisely define a sequence of operations.
   * `B` [NanoNeuron](https://github.com/trekhleb/nano-neuron) - 7 simple JS functions that illustrate how machines can actually learn (forward/backward propagation)
   * `B` [k-NN](src/algorithms/ml/knn) - k-nearest neighbors classification algorithm
   * `B` [k-Means](src/algorithms/ml/k-means) - k-Means clustering algorithm
+* **Image Processing**
+  * `B` [Seam Carving](src/algorithms/image-processing/seam-carving) - content-aware image resizing algorithm
 * **Uncategorized**
   * `B` [Tower of Hanoi](src/algorithms/uncategorized/hanoi-tower)
   * `B` [Square Matrix Rotation](src/algorithms/uncategorized/square-matrix-rotation) - in-place algorithm
@@ -203,6 +205,7 @@ algorithm is an abstraction higher than a computer program.
   * `B` [Unique Paths](src/algorithms/uncategorized/unique-paths)
   * `B` [Rain Terraces](src/algorithms/uncategorized/rain-terraces) - trapping rain water problem
   * `B` [Recursive Staircase](src/algorithms/uncategorized/recursive-staircase) - count the number of ways to reach to the top
+  * `B` [Seam Carving](src/algorithms/image-processing/seam-carving) - content-aware image resizing algorithm
   * `A` [Levenshtein Distance](src/algorithms/string/levenshtein-distance) - minimum edit distance between two sequences
   * `A` [Longest Common Subsequence](src/algorithms/sets/longest-common-subsequence) (LCS)
   * `A` [Longest Common Substring](src/algorithms/string/longest-common-substring)
diff --git a/package-lock.json b/package-lock.json
index aeeed97b47..93de7f66c9 100644
--- a/package-lock.json
+++ b/package-lock.json
@@ -23,41 +23,40 @@
       }
     },
     "@babel/code-frame": {
-      "version": "7.10.4",
-      "resolved": "https://registry.npmjs.org/@babel/code-frame/-/code-frame-7.10.4.tgz",
-      "integrity": "sha512-vG6SvB6oYEhvgisZNFRmRCUkLz11c7rp+tbNTynGqc6mS1d5ATd/sGyV6W0KZZnXRKMTzZDRgQT3Ou9jhpAfUg==",
+      "version": "7.12.13",
+      "resolved": "https://registry.npmjs.org/@babel/code-frame/-/code-frame-7.12.13.tgz",
+      "integrity": "sha512-HV1Cm0Q3ZrpCR93tkWOYiuYIgLxZXZFVG2VgK+MBWjUqZTundupbfx2aXarXuw5Ko5aMcjtJgbSs4vUGBS5v6g==",
       "dev": true,
       "requires": {
-        "@babel/highlight": "^7.10.4"
+        "@babel/highlight": "^7.12.13"
       }
     },
     "@babel/compat-data": {
-      "version": "7.12.7",
-      "resolved": "https://registry.npmjs.org/@babel/compat-data/-/compat-data-7.12.7.tgz",
-      "integrity": "sha512-YaxPMGs/XIWtYqrdEOZOCPsVWfEoriXopnsz3/i7apYPXQ3698UFhS6dVT1KN5qOsWmVgw/FOrmQgpRaZayGsw==",
+      "version": "7.13.15",
+      "resolved": "https://registry.npmjs.org/@babel/compat-data/-/compat-data-7.13.15.tgz",
+      "integrity": "sha512-ltnibHKR1VnrU4ymHyQ/CXtNXI6yZC0oJThyW78Hft8XndANwi+9H+UIklBDraIjFEJzw8wmcM427oDd9KS5wA==",
       "dev": true
     },
     "@babel/core": {
-      "version": "7.12.9",
-      "resolved": "https://registry.npmjs.org/@babel/core/-/core-7.12.9.tgz",
-      "integrity": "sha512-gTXYh3M5wb7FRXQy+FErKFAv90BnlOuNn1QkCK2lREoPAjrQCO49+HVSrFoe5uakFAF5eenS75KbO2vQiLrTMQ==",
-      "dev": true,
-      "requires": {
-        "@babel/code-frame": "^7.10.4",
-        "@babel/generator": "^7.12.5",
-        "@babel/helper-module-transforms": "^7.12.1",
-        "@babel/helpers": "^7.12.5",
-        "@babel/parser": "^7.12.7",
-        "@babel/template": "^7.12.7",
-        "@babel/traverse": "^7.12.9",
-        "@babel/types": "^7.12.7",
+      "version": "7.13.15",
+      "resolved": "https://registry.npmjs.org/@babel/core/-/core-7.13.15.tgz",
+      "integrity": "sha512-6GXmNYeNjS2Uz+uls5jalOemgIhnTMeaXo+yBUA72kC2uX/8VW6XyhVIo2L8/q0goKQA3EVKx0KOQpVKSeWadQ==",
+      "dev": true,
+      "requires": {
+        "@babel/code-frame": "^7.12.13",
+        "@babel/generator": "^7.13.9",
+        "@babel/helper-compilation-targets": "^7.13.13",
+        "@babel/helper-module-transforms": "^7.13.14",
+        "@babel/helpers": "^7.13.10",
+        "@babel/parser": "^7.13.15",
+        "@babel/template": "^7.12.13",
+        "@babel/traverse": "^7.13.15",
+        "@babel/types": "^7.13.14",
         "convert-source-map": "^1.7.0",
         "debug": "^4.1.0",
-        "gensync": "^1.0.0-beta.1",
+        "gensync": "^1.0.0-beta.2",
         "json5": "^2.1.2",
-        "lodash": "^4.17.19",
-        "resolve": "^1.3.2",
-        "semver": "^5.4.1",
+        "semver": "^6.3.0",
         "source-map": "^0.5.0"
       },
       "dependencies": {
@@ -71,9 +70,9 @@
           }
         },
         "json5": {
-          "version": "2.1.3",
-          "resolved": "https://registry.npmjs.org/json5/-/json5-2.1.3.tgz",
-          "integrity": "sha512-KXPvOm8K9IJKFM0bmdn8QXh7udDh1g/giieX0NLCaMnb4hEiVFqnop2ImTXCc5e0/oHz3LTqmHGtExn5hfMkOA==",
+          "version": "2.2.0",
+          "resolved": "https://registry.npmjs.org/json5/-/json5-2.2.0.tgz",
+          "integrity": "sha512-f+8cldu7X/y7RAJurMEJmdoKXGB/X550w2Nr3tTbezL6RwEE/iMcm+tZnXeoZtKuOq6ft8+CqzEkrIgx1fPoQA==",
           "dev": true,
           "requires": {
             "minimist": "^1.2.5"
@@ -84,222 +83,206 @@
           "resolved": "https://registry.npmjs.org/ms/-/ms-2.1.2.tgz",
           "integrity": "sha512-sGkPx+VjMtmA6MX27oA4FBFELFCZZ4S4XqeGOXCv68tT+jb3vk/RyaKWP0PTKyWtmLSM0b+adUTEvbs1PEaH2w==",
           "dev": true
+        },
+        "semver": {
+          "version": "6.3.0",
+          "resolved": "https://registry.npmjs.org/semver/-/semver-6.3.0.tgz",
+          "integrity": "sha512-b39TBaTSfV6yBrapU89p5fKekE2m/NwnDocOVruQFS1/veMgdzuPcnOM34M6CwxW8jH/lxEa5rBoDeUwu5HHTw==",
+          "dev": true
         }
       }
     },
     "@babel/generator": {
-      "version": "7.12.5",
-      "resolved": "https://registry.npmjs.org/@babel/generator/-/generator-7.12.5.tgz",
-      "integrity": "sha512-m16TQQJ8hPt7E+OS/XVQg/7U184MLXtvuGbCdA7na61vha+ImkyyNM/9DDA0unYCVZn3ZOhng+qz48/KBOT96A==",
+      "version": "7.13.9",
+      "resolved": "https://registry.npmjs.org/@babel/generator/-/generator-7.13.9.tgz",
+      "integrity": "sha512-mHOOmY0Axl/JCTkxTU6Lf5sWOg/v8nUa+Xkt4zMTftX0wqmb6Sh7J8gvcehBw7q0AhrhAR+FDacKjCZ2X8K+Sw==",
       "dev": true,
       "requires": {
-        "@babel/types": "^7.12.5",
+        "@babel/types": "^7.13.0",
         "jsesc": "^2.5.1",
         "source-map": "^0.5.0"
       }
     },
     "@babel/helper-annotate-as-pure": {
-      "version": "7.12.10",
-      "resolved": "https://registry.npmjs.org/@babel/helper-annotate-as-pure/-/helper-annotate-as-pure-7.12.10.tgz",
-      "integrity": "sha512-XplmVbC1n+KY6jL8/fgLVXXUauDIB+lD5+GsQEh6F6GBF1dq1qy4DP4yXWzDKcoqXB3X58t61e85Fitoww4JVQ==",
+      "version": "7.12.13",
+      "resolved": "https://registry.npmjs.org/@babel/helper-annotate-as-pure/-/helper-annotate-as-pure-7.12.13.tgz",
+      "integrity": "sha512-7YXfX5wQ5aYM/BOlbSccHDbuXXFPxeoUmfWtz8le2yTkTZc+BxsiEnENFoi2SlmA8ewDkG2LgIMIVzzn2h8kfw==",
       "dev": true,
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-      },
-      "dependencies": {
-        "@babel/helper-validator-identifier": {
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-          "resolved": "https://registry.npmjs.org/@babel/helper-validator-identifier/-/helper-validator-identifier-7.12.11.tgz",
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-          "dev": true
-        },
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-          "resolved": "https://registry.npmjs.org/@babel/types/-/types-7.12.11.tgz",
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-          "dev": true,
-          "requires": {
-            "@babel/helper-validator-identifier": "^7.12.11",
-            "lodash": "^4.17.19",
-            "to-fast-properties": "^2.0.0"
-          }
-        }
+        "@babel/types": "^7.12.13"
       }
     },
     "@babel/helper-builder-binary-assignment-operator-visitor": {
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@@ -9035,17 +9297,33 @@
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diff --git a/package.json b/package.json
index 73da04e0cf..c4ae69b6fd 100644
--- a/package.json
+++ b/package.json
@@ -7,7 +7,8 @@
     "lint": "eslint ./src/**",
     "test": "jest",
     "coverage": "npm run test -- --coverage",
-    "ci": "npm run lint && npm run coverage"
+    "ci": "npm run lint && npm run coverage",
+    "prepare": "husky install"
   },
   "repository": {
     "type": "git",
@@ -37,13 +38,14 @@
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     "@babel/preset-env": "7.12.11",
     "@types/jest": "26.0.19",
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     "eslint": "7.16.0",
     "eslint-config-airbnb": "18.2.1",
     "eslint-plugin-import": "2.22.1",
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     "eslint-plugin-react": "7.21.5",
-    "husky": "4.3.6",
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diff --git a/src/algorithms/image-processing/seam-carving/README.md b/src/algorithms/image-processing/seam-carving/README.md
new file mode 100644
index 0000000000..87004f7abe
--- /dev/null
+++ b/src/algorithms/image-processing/seam-carving/README.md
@@ -0,0 +1,509 @@
+# Content-aware image resizing in JavaScript
+
+![Content-aware image resizing in JavaScript](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/01-cover-02.png)
+
+> There is an [interactive version of this post](https://trekhleb.dev/blog/2021/content-aware-image-resizing-in-javascript/) available where you can upload and resize your custom images.
+
+## TL;DR
+
+There are many great articles written about the *Seam Carving algorithm* already, but I couldn't resist the temptation to explore this elegant, powerful, and *yet simple* algorithm on my own, and to write about my personal experience with it. Another point that drew my attention (as a creator of [javascript-algorithms](https://github.com/trekhleb/javascript-algorithms) repo) was the fact that *Dynamic Programming (DP)* approach might be smoothly applied to solve it. And, if you're like me and still on your "learning algorithms" journey, this algorithmic solution may enrich your personal DP arsenal.
+
+So, with this article I want to do three things:
+
+1. Provide you with an interactive **content-aware resizer** so that you could play around with resizing your own images
+2. Explain the idea behind the **Seam Carving algorithm**
+3. Explain the **dynamic programming approach** to implement the algorithm (we'll be using TypeScript for it)
+
+### Content-aware image resizing
+
+*Content-aware image resizing* might be applied when it comes to changing the image proportions (i.e. reducing the width while keeping the height) and when losing some parts of the image is not desirable. Doing the straightforward image scaling in this case would distort the objects in it. To preserve the proportions of the objects while changing the image proportions we may use the [Seam Carving algorithm](https://perso.crans.org/frenoy/matlab2012/seamcarving.pdf) that was introduced by *Shai Avidan* and *Ariel Shamir*.
+
+The example below shows how the original image width was reduced by 50% using *content-aware resizing* (left image) and *straightforward scaling* (right image). In this particular case, the left image looks more natural since the proportions of the balloons were preserved.
+
+![Content-aware image resizing](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/01-resizing-options.png)
+
+The Seam Carving algorithm's idea is to find the *seam* (continuous sequence of pixels) with the lowest contribution to the image content and then *carve* (remove) it. This process repeats over and over again until we get the required image width or height. In the example below you may see that the hot air balloon pixels contribute more to the content of the image than the sky pixels. Thus, the sky pixels are being removed first.
+
+![JS IMAGE CARVER DEMO](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/10-demo-01.gif)
+
+Finding the seam with the lowest energy is a computationally expensive task (especially for large images). To make the seam search faster the *dynamic programming* approach might be applied (we will go through the implementation details below).
+
+### Objects removal
+
+The importance of each pixel (so-called pixel's energy) is being calculated based on its color (`R`, `G`, `B`, `A`) difference between two neighbor pixels. Now, if we set the pixel energy to some really low level artificially (i.e. by drawing a mask on top of them), the Seam Carving algorithm would perform an **object removal** for us for free.
+
+![JS IMAGE CARVER OBJECT REMOVAL DEMO](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/10-demo-02.gif)
+
+### JS IMAGE CARVER demo
+
+I've created the [JS IMAGE CARVER](https://trekhleb.dev/js-image-carver/) web-app (and also [open-sourced it on GitHub](https://github.com/trekhleb/js-image-carver)) that you may use to play around with resizing of your custom images.
+
+### More examples
+
+Here are some more examples of how the algorithm copes with more complex backgrounds.
+
+Mountains on the background are being shrunk smoothly without visible seams.
+
+![Resizing demo with more complex backgrounds](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/11-demo-01.png)
+
+The same goes for the ocean waves. The algorithm preserved the wave structure without distorting the surfers.
+
+![Resizing demo with more complex backgrounds](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/11-demo-02.png)
+
+We need to keep in mind that the Seam Carving algorithm is not a silver bullet, and it may fail to resize the images where *most of the pixels are edges* (look important to the algorithm). In this case, it starts distorting even the important parts of the image. In the example below the content-aware image resizing looks pretty similar to a straightforward scaling since for the algorithm all the pixels look important, and it is hard for it to distinguish Van Gogh's face from the background.
+
+![Example when the algorithm does not work as expected](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/12-demo-01.png)
+
+## How Seam Carving algorithms works
+
+Imagine we have a `1000 x 500 px` picture, and we want to change its size to `500 x 500 px` to make it square (let's say the square ratio would better fit the Instagram feed). We might want to set up several **requirements to the resizing process** in this case:
+
+- *Preserve the important parts of the image* (i.e. if there were 5 trees before the resizing we want to have 5 trees after resizing as well).
+- *Preserve the proportions* of the important parts of the image (i.e. circle car wheels should not be squeezed to the ellipse wheels)
+
+To avoid changing the important parts of the image we may find the **continuous sequence of pixels (the seam)**, that goes from top to bottom and has *the lowest contribution to the content* of the image (avoids important parts) and then remove it. The seam removal will shrink the image by 1 pixel. We will then repeat this step until the image will get the desired width.
+
+The question is how to define *the importance of the pixel* and its contribution to the content (in the original paper the authors are using the term **energy of the pixel**). One of the ways to do it is to treat all the pixels that form the edges as important ones. In case if a pixel is a part of the edge its color would have a greater difference between the neighbors (left and right pixels) than the pixel that isn't a part of the edge.
+
+![Pixels color difference](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/30-pixel-energy-comparison.png)
+
+Assuming that the color of a pixel is represented by *4* numbers (`R` - red, `G` - green, `B` - blue, `A` - alpha) we may use the following formula to calculate the color difference (the pixel energy):
+
+![Pixel energy formula](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/20-energy-formula.png)
+
+Where:
+
+- `mEnergy` - *Energy* (importance) of the *middle* pixel (`[0..626]` if rounded)
+- `lR` - *Red* channel value for the *left* pixel (`[0..255]`)
+- `mR` - *Red* channel value for the *middle* pixel (`[0..255]`)
+- `rR` - *Red* channel value for the *right* pixel (`[0..255]`)
+- `lG` - *Green* channel value for the *left* pixel (`[0..255]`)
+- and so on...
+
+In the formula above we're omitting the alpha (transparency) channel, for now, assuming that there are no transparent pixels in the image. Later we will use the alpha channel for masking and for object removal.
+
+![Example of pixel energy calculation](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/30-pixel-energy-calculation-example.png)
+
+Now, since we know how to find the energy of one pixel, we can calculate, so-called, **energy map** which will contain the energies of each pixel of the image. On each resizing step the energy map should be re-calculated (at least partially, more about it below) and would have the same size as the image.
+
+For example, on the 1st resizing step we will have a `1000 x 500` image and a `1000 x 500` energy map. On the 2nd resizing step we will remove the seam from the image and re-calculate the energy map based on the new shrunk image. Thus, we will get a `999 x 500` image and a `999 x 500` energy map.
+
+The higher the energy of the pixel the more likely it is a part of an edge, and it is important for the image content and the less likely that we need to remove it.
+
+To visualize the energy map we may assign a brighter color to the pixels with the higher energy and darker colors to the pixels with the lower energy. Here is an artificial example of how the random part of the energy map might look like. You may see the bright line which represents the edge and which we want to preserve during the resizing.
+
+![Energy map sketch](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/30-energy-map-padding.png)
+
+Here is a real example of the energy map for the demo image you saw above (with hot air balloons).
+
+![Energy map example](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/40-energy-map.png)
+
+You may play around with your custom images and see how the energy map would look like in the [interactive version of the post](https://trekhleb.dev/blog/2021/content-aware-image-resizing-in-javascript/).
+
+We may use the energy map to find the seams (one after another) with the lowest energy and by doing this to decide which pixels should be ultimately deleted.
+
+![Searching the seam](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/41-seam-search.png)
+
+Finding the seam with the lowest energy is not a trivial task and requires exploring many possible pixel combinations before making the decision. We will apply the dynamic programming approach to speed it up.
+
+In the example below, you may see the energy map with the first lowest energy seam that was found for it.
+
+![Energy map example with seam](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/40-energy-map-with-seam.png)
+
+In the examples above we were reducing the width of the image. A similar approach may be taken to reduce the image height. We need to "rotate" the approach though:
+
+- start using *top* and *bottom* pixel neighbors (instead of *left* and *right* ones) to calculate the pixel energy
+- when searching for a seam we need to move from *left* to *right* (instead of from *up* to *bottom*)
+
+## Implementation in TypeScript
+
+> You may find the source code, and the functions mentioned below in the [js-image-carver](https://github.com/trekhleb/js-image-carver) repository.
+
+To implement the algorithm we will be using TypeScript. If you want a JavaScript version, you may ignore (remove) type definitions and their usages.
+
+For simplicity reasons let's implement the seam carving algorithm only for the image *width* reduction.
+
+### Content-aware width resizing (the entry function)
+
+First, let's define some common types that we're going to use while implementing the algorithm.
+
+```typescript
+// Type that describes the image size (width and height).
+type ImageSize = { w: number, h: number };
+
+// The coordinate of the pixel.
+type Coordinate = { x: number, y: number };
+
+// The seam is a sequence of pixels (coordinates).
+type Seam = Coordinate[];
+
+// Energy map is a 2D array that has the same width and height
+// as the image the map is being calculated for.
+type EnergyMap = number[][];
+
+// Type that describes the image pixel's RGBA color.
+type Color = [
+  r: number, // Red
+  g: number, // Green
+  b: number, // Blue
+  a: number, // Alpha (transparency)
+] | Uint8ClampedArray;
+```
+
+On the high level the algorithm consists of the following steps:
+
+1. Calculate the **energy map** for the current version of the image.
+2. Find the **seam** with the lowest energy based on the energy map (this is where we will apply Dynamic Programming).
+3. **Delete the seam** with the lowest energy seam from the image.
+4. **Repeat** until the image width is reduced to the desired value.
+
+```typescript
+type ResizeImageWidthArgs = {
+  img: ImageData, // Image data we want to resize.
+  toWidth: number, // Final image width we want the image to shrink to.
+};
+
+type ResizeImageWidthResult = {
+  img: ImageData, // Resized image data.
+  size: ImageSize, // Resized image size (w x h).
+};
+
+// Performs the content-aware image width resizing using the seam carving method.
+export const resizeImageWidth = (
+  { img, toWidth }: ResizeImageWidthArgs,
+): ResizeImageWidthResult => {
+  // For performance reasons we want to avoid changing the img data array size.
+  // Instead we'll just keep the record of the resized image width and height separately.
+  const size: ImageSize = { w: img.width, h: img.height };
+
+  // Calculating the number of pixels to remove.
+  const pxToRemove = img.width - toWidth;
+  if (pxToRemove < 0) {
+    throw new Error('Upsizing is not supported for now');
+  }
+
+  let energyMap: EnergyMap | null = null;
+  let seam: Seam | null = null;
+
+  // Removing the lowest energy seams one by one.
+  for (let i = 0; i < pxToRemove; i += 1) {
+    // 1. Calculate the energy map for the current version of the image.
+    energyMap = calculateEnergyMap(img, size);
+
+    // 2. Find the seam with the lowest energy based on the energy map.
+    seam = findLowEnergySeam(energyMap, size);
+
+    // 3. Delete the seam with the lowest energy seam from the image.
+    deleteSeam(img, seam, size);
+
+    // Reduce the image width, and continue iterations.
+    size.w -= 1;
+  }
+
+  // Returning the resized image and its final size.
+  // The img is actually a reference to the ImageData, so technically
+  // the caller of the function already has this pointer. But let's
+  // still return it for better code readability.
+  return { img, size };
+};
+```
+
+The image that needs to be resized is being passed to the function in [ImageData](https://developer.mozilla.org/en-US/docs/Web/API/ImageData) format. You may draw the image on the canvas and then extract the ImageData from the canvas like this:
+
+```javascript
+const ctx = canvas.getContext('2d');
+const imgData = ctx.getImageData(0, 0, imgWidth, imgHeight);
+```
+
+> The way of uploading and drawing images in JavaScript is out of scope for this article, but you may find the complete source code of how it may be done using React in [js-image-carver](https://github.com/trekhleb/js-image-carver) repo.
+
+Let's break down each step ony be one and implement the `calculateEnergyMap()`, `findLowEnergySeam()` and `deleteSeam()` functions.
+
+### Calculating the pixel's energy
+
+Here we apply the color difference formula described above. For the left and right borders (when there are no left or right neighbors), we ignore the neighbors and don't take them into account during the energy calculation.
+
+```typescript
+// Calculates the energy of a pixel.
+const getPixelEnergy = (left: Color | null, middle: Color, right: Color | null): number => {
+  // Middle pixel is the pixel we're calculating the energy for.
+  const [mR, mG, mB] = middle;
+
+  // Energy from the left pixel (if it exists).
+  let lEnergy = 0;
+  if (left) {
+    const [lR, lG, lB] = left;
+    lEnergy = (lR - mR) ** 2 + (lG - mG) ** 2 + (lB - mB) ** 2;
+  }
+
+  // Energy from the right pixel (if it exists).
+  let rEnergy = 0;
+  if (right) {
+    const [rR, rG, rB] = right;
+    rEnergy = (rR - mR) ** 2 + (rG - mG) ** 2 + (rB - mB) ** 2;
+  }
+
+  // Resulting pixel energy.
+  return Math.sqrt(lEnergy + rEnergy);
+};
+```
+
+### Calculating the energy map
+
+The image we're working with has the [ImageData](https://developer.mozilla.org/en-US/docs/Web/API/ImageData) format. It means that all the pixels (and their colors) are stored in a flat (*1D*) [Uint8ClampedArray](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Uint8ClampedArray) array. For readability purposes let's introduce the couple of helper functions that will allow us to work with the Uint8ClampedArray array as with a *2D* matrix instead.
+
+```typescript
+// Helper function that returns the color of the pixel.
+const getPixel = (img: ImageData, { x, y }: Coordinate): Color => {
+  // The ImageData data array is a flat 1D array.
+  // Thus we need to convert x and y coordinates to the linear index.
+  const i = y * img.width + x;
+  const cellsPerColor = 4; // RGBA
+  // For better efficiency, instead of creating a new sub-array we return
+  // a pointer to the part of the ImageData array.
+  return img.data.subarray(i * cellsPerColor, i * cellsPerColor + cellsPerColor);
+};
+
+// Helper function that sets the color of the pixel.
+const setPixel = (img: ImageData, { x, y }: Coordinate, color: Color): void => {
+  // The ImageData data array is a flat 1D array.
+  // Thus we need to convert x and y coordinates to the linear index.
+  const i = y * img.width + x;
+  const cellsPerColor = 4; // RGBA
+  img.data.set(color, i * cellsPerColor);
+};
+```
+
+To calculate the energy map we go through each image pixel and call the previously described `getPixelEnergy()` function against it.
+
+```typescript
+// Helper function that creates a matrix (2D array) of specific
+// size (w x h) and fills it with specified value.
+const matrix = <T>(w: number, h: number, filler: T): T[][] => {
+  return new Array(h)
+    .fill(null)
+    .map(() => {
+      return new Array(w).fill(filler);
+    });
+};
+
+// Calculates the energy of each pixel of the image.
+const calculateEnergyMap = (img: ImageData, { w, h }: ImageSize): EnergyMap => {
+  // Create an empty energy map where each pixel has infinitely high energy.
+  // We will update the energy of each pixel.
+  const energyMap: number[][] = matrix<number>(w, h, Infinity);
+  for (let y = 0; y < h; y += 1) {
+    for (let x = 0; x < w; x += 1) {
+      // Left pixel might not exist if we're on the very left edge of the image.
+      const left = (x - 1) >= 0 ? getPixel(img, { x: x - 1, y }) : null;
+      // The color of the middle pixel that we're calculating the energy for.
+      const middle = getPixel(img, { x, y });
+      // Right pixel might not exist if we're on the very right edge of the image.
+      const right = (x + 1) < w ? getPixel(img, { x: x + 1, y }) : null;
+      energyMap[y][x] = getPixelEnergy(left, middle, right);
+    }
+  }
+  return energyMap;
+};
+```
+
+> The energy map is going to be recalculated on every resize iteration. It means that it will be recalculated, let's say, 500 times if we need to shrink the image by 500 pixels which is not optimal. To speed up the energy map calculation on the 2nd, 3rd, and further steps, we may re-calculate the energy only for those pixels that are placed around the seam that is going to be removed. For simplicity reasons this optimization is omitted here, but you may find the example source-code in [js-image-carver](https://github.com/trekhleb/js-image-carver) repo.
+
+### Finding the seam with the lowest energy (Dynamic Programming approach)
+
+> I've described some Dynamic Programming basics in [Dynamic Programming vs Divide-and-Conquer](https://trekhleb.dev/blog/2018/dynamic-programming-vs-divide-and-conquer/) article before. There is a DP example based on the minimum edit distance problem. You might want to check it out to get some more context.
+
+The issue we need to solve now is to find the path (the seam) on the energy map that goes from top to bottom and has the minimum sum of pixel energies.
+
+#### The naive approach
+
+The naive approach would be to check all possible paths one after another.
+
+![The naive approach](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/50-naive-approach.png)
+
+Going from top to bottom, for each pixel, we have 3 options (↙︎ go down-left, ↓ go down, ↘︎ go down-right). This gives us the time complexity of `O(w * 3^h)` or simply `O(3^h)`, where `w` and `h` are the width and the height of the image. This approach looks slow.
+
+#### The greedy approach
+
+We may also try to choose the next pixel as a pixel with the lowest energy, hoping that the resulting seam energy will be the smallest one.
+
+![The greedy approach](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/51-greedy-approach.png)
+
+This approach gives not the worst solution, but it cannot guarantee that we will find the best available solution. On the image above you may see how the greedy approach chose `5` instead of `10` at first and missed the chain of optimal pixels.
+
+The good part about this approach is that it is fast, and it has a time complexity of `O(w + h)`, where `w` and `h` are the width and the height of the image. In this case, the cost of the speed is the low quality of resizing. We need to find a minimum value in the first row (traversing `w` cells) and then we explore only 3 neighbor pixels for each row (traversing `h` rows).
+
+#### The dynamic programming approach
+
+You might have noticed that in the naive approach we summed up the same pixel energies over and over again while calculating the resulting seams' energy.
+
+![Repeated problems](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/52-dp-repeated-problems.png)
+
+In the example above you see that for the first two seams we are re-using the energy of the shorter seam (which has the energy of `235`). Instead of doing just one operation `235 + 70` to calculate the energy of the 2nd seam we're doing four operations `(5 + 0 + 80 + 150) + 70`.
+
+> This fact that we're re-using the energy of the previous seam to calculate the current seam's energy might be applied recursively to all the shorter seams up to the very top 1st row seam. When we have such overlapping sub-problems, [it is a sign](https://trekhleb.dev/blog/2018/dynamic-programming-vs-divide-and-conquer/) that the general problem *might* be optimized by dynamic programming approach.
+
+So, we may **save the energy of the current seam** at the particular pixel in an additional `seamsEnergies` table to make it re-usable for calculating the next seams faster (the `seamsEnergies` table will have the same size as the energy map and the image itself).
+
+Let's also keep in mind that for one particular pixel on the image (i.e. the bottom left one) we may have *several* values of the previous seams energies.
+
+![What seam to choose](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/53-dp-what-to-choose.png)
+
+Since we're looking for a seam with the lowest resulting energy it would make sense to pick the previous seam with the lowest resulting energy as well.
+
+![Seams energies example](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/56-dp-seams-energies-example.png)
+
+In general, we have three possible previous seems to choose from:
+
+![Three options to choose from](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/55-dp-three-options.png)
+
+You may think about it this way:
+
+- The cell `[1][x]`: contains the lowest possible energy of the seam that starts somewhere on the row `[0][?]` and ends up at cell `[1][x]`
+- **The current cell** `[2][3]`: contains the lowest possible energy of the seam that starts somewhere on the row `[0][?]` and ends up at cell `[2][3]`. To calculate it we need to sum up the energy of the current pixel `[2][3]` (from the energy map) with the `min(seam_energy_1_2, seam_energy_1_3, seam_energy_1_4)`
+
+If we fill the `seamsEnergies` table completely, then the minimum number in the lowest row would be the lowest possible seam energy.
+
+Let's try to fill several cells of this table to see how it works.
+
+![Seams energies map traversal](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/57-dp-seams-energies-traversal.png)
+
+After filling out the `seamsEnergies` table we may see that the lowest energy pixel has an energy of `50`. For convenience, during the `seamsEnergies` generation for each pixel, we may save not only the energy of the seam but also the coordinates of the previous lowest energy seam. This will give us the possibility to reconstruct the seam path from the bottom to the top easily.
+
+The time complexity of DP approach would be `O(w * h)`, where `w` and `h` are the width and the height of the image. We need to calculate energies for *every* pixel of the image.
+
+Here is an example of how this logic might be implemented:
+
+```typescript
+// The metadata for the pixels in the seam.
+type SeamPixelMeta = {
+  energy: number, // The energy of the pixel.
+  coordinate: Coordinate, // The coordinate of the pixel.
+  previous: Coordinate | null, // The previous pixel in a seam.
+};
+
+// Finds the seam (the sequence of pixels from top to bottom) that has the
+// lowest resulting energy using the Dynamic Programming approach.
+const findLowEnergySeam = (energyMap: EnergyMap, { w, h }: ImageSize): Seam => {
+  // The 2D array of the size of w and h, where each pixel contains the
+  // seam metadata (pixel energy, pixel coordinate and previous pixel from
+  // the lowest energy seam at this point).
+  const seamsEnergies: (SeamPixelMeta | null)[][] = matrix<SeamPixelMeta | null>(w, h, null);
+
+  // Populate the first row of the map by just copying the energies
+  // from the energy map.
+  for (let x = 0; x < w; x += 1) {
+    const y = 0;
+    seamsEnergies[y][x] = {
+      energy: energyMap[y][x],
+      coordinate: { x, y },
+      previous: null,
+    };
+  }
+
+  // Populate the rest of the rows.
+  for (let y = 1; y < h; y += 1) {
+    for (let x = 0; x < w; x += 1) {
+      // Find the top adjacent cell with minimum energy.
+      // This cell would be the tail of a seam with lowest energy at this point.
+      // It doesn't mean that this seam (path) has lowest energy globally.
+      // Instead, it means that we found a path with the lowest energy that may lead
+      // us to the current pixel with the coordinates x and y.
+      let minPrevEnergy = Infinity;
+      let minPrevX: number = x;
+      for (let i = (x - 1); i <= (x + 1); i += 1) {
+        if (i >= 0 && i < w && seamsEnergies[y - 1][i].energy < minPrevEnergy) {
+          minPrevEnergy = seamsEnergies[y - 1][i].energy;
+          minPrevX = i;
+        }
+      }
+
+      // Update the current cell.
+      seamsEnergies[y][x] = {
+        energy: minPrevEnergy + energyMap[y][x],
+        coordinate: { x, y },
+        previous: { x: minPrevX, y: y - 1 },
+      };
+    }
+  }
+
+  // Find where the minimum energy seam ends.
+  // We need to find the tail of the lowest energy seam to start
+  // traversing it from its tail to its head (from the bottom to the top).
+  let lastMinCoordinate: Coordinate | null = null;
+  let minSeamEnergy = Infinity;
+  for (let x = 0; x < w; x += 1) {
+    const y = h - 1;
+    if (seamsEnergies[y][x].energy < minSeamEnergy) {
+      minSeamEnergy = seamsEnergies[y][x].energy;
+      lastMinCoordinate = { x, y };
+    }
+  }
+
+  // Find the lowest energy energy seam.
+  // Once we know where the tail is we may traverse and assemble the lowest
+  // energy seam based on the "previous" value of the seam pixel metadata.
+  const seam: Seam = [];
+  if (!lastMinCoordinate) {
+    return seam;
+  }
+
+  const { x: lastMinX, y: lastMinY } = lastMinCoordinate;
+
+  // Adding new pixel to the seam path one by one until we reach the top.
+  let currentSeam = seamsEnergies[lastMinY][lastMinX];
+  while (currentSeam) {
+    seam.push(currentSeam.coordinate);
+    const prevMinCoordinates = currentSeam.previous;
+    if (!prevMinCoordinates) {
+      currentSeam = null;
+    } else {
+      const { x: prevMinX, y: prevMinY } = prevMinCoordinates;
+      currentSeam = seamsEnergies[prevMinY][prevMinX];
+    }
+  }
+
+  return seam;
+};
+```
+
+### Removing the seam with the lowest energy
+
+Once we found the lowest energy seam, we need to remove (to carve) the pixels that form it from the image. The removal is happening by shifting the pixels to the right of the seam by `1px` to the left. For performance reasons, we don't actually delete the last columns. Instead, the rendering component will just ignore the part of the image that lays beyond the resized image width.
+
+![Deleting the seam](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/60-deleting-example.png)
+
+```typescript
+// Deletes the seam from the image data.
+// We delete the pixel in each row and then shift the rest of the row pixels to the left.
+const deleteSeam = (img: ImageData, seam: Seam, { w }: ImageSize): void => {
+  seam.forEach(({ x: seamX, y: seamY }: Coordinate) => {
+    for (let x = seamX; x < (w - 1); x += 1) {
+      const nextPixel = getPixel(img, { x: x + 1, y: seamY });
+      setPixel(img, { x, y: seamY }, nextPixel);
+    }
+  });
+};
+```
+
+## Objects removal
+
+The Seam Carving algorithm tries to remove the seams which consist of low energy pixels first. We could leverage this fact and by assigning low energy to some pixels manually (i.e. by drawing on the image and masking out some areas of it) we could make the Seam Carving algorithm to do *objects removal* for us for free.
+
+Currently, in `getPixelEnergy()` function we were using only the `R`, `G`, `B` color channels to calculate the pixel's energy. But there is also the `A` (alpha, transparency) parameter of the color that we didn't use yet. We may use the transparency channel to tell the algorithm that transparent pixels are the pixels we want to remove. You may check the [source-code of the energy function](https://github.com/trekhleb/js-image-carver/blob/main/src/utils/contentAwareResizer.ts#L54) that takes transparency into account.
+
+Here is how the algorithm works for object removal.
+
+![JS IMAGE CARVER OBJECT REMOVAL DEMO](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/10-demo-02.gif)
+
+## Issues and what's next
+
+The [JS IMAGE CARVER](https://github.com/trekhleb/js-image-carver) web app is far from being a production ready resizer of course. Its main purpose was to experiment with the Seam Carving algorithm interactively. So the plan for the future is to continue experimentation.
+
+The [original paper](https://perso.crans.org/frenoy/matlab2012/seamcarving.pdf) describes how the Seam Carving algorithm might be used not only for the downscaling but also for the **upscaling of the images**. The upscaling, in turn, might be used to **upscale the image back to its original width after the objects' removal**.
+
+Another interesting area of experimentation might be to make the algorithm work in a **real-time**.
+
+> Those are the plans for the future, but for now, I hope that the example with image downsizing was interesting and useful for you. I also hope that you've got the idea of using dynamic programming to implement it.
+>
+> So, good luck with your own experiments!
diff --git a/src/algorithms/image-processing/seam-carving/README.ru-RU.md b/src/algorithms/image-processing/seam-carving/README.ru-RU.md
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@@ -0,0 +1,509 @@
+# Изменение размеров изображения с учетом его содержимого в JavaScript
+
+![Content-aware image resizing in JavaScript](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/01-cover-02.png)
+
+> Доступна [английская интерактивная версия этой статьи](https://trekhleb.dev/blog/2021/content-aware-image-resizing-in-javascript/) в которой вы можете загрузить свои собственные изображения и посмотреть, как алгоритм "справляется" с ними.
+
+## TL;DR
+
+Написано много замечательных статей об алгоритме *Seam Carving* ("Вырезание швов"), но я не смог устоять перед соблазном самостоятельно исследовать этот элегантный, мощный и в то же время простой алгоритм и написать о своем личном опыте работы с ним. Мое внимание также привлек тот факт, что для его имплементации мы можем применить *динамическое программирование (DP)*. И, если вы, как и я, все еще находитесь на пути изучения алгоритмов, то это решение может обогатить ваш личный арсенал DP.
+
+Итак, в этой статье я хочу сделать три вещи:
+
+1. Предоставить вам возможность "поиграться" с алгоритмом самостоятельно при помощи **интерактивного ресайзера**.
+2. Объяснить **идею алгоритма Seam Carving**.
+3. Объяснить как можно **применить динамическое программирование** для имплементации алгоритма (мы будем писать на TypeScript).
+
+### Изменение размеров изображений с учетом их содержимого
+
+*Изменение размера изображения с учетом содержимого* (content-aware image resizing) может быть применено, когда дело доходит до изменения пропорций изображения (например, уменьшения ширины при сохранении высоты), а также когда потеря некоторых частей изображения нежелательна. Простое масштабирование изображения в этом случае исказит находящиеся в нем объекты. Для сохранения пропорций объектов при изменении пропорций изображения можно использовать [алгоритм Seam Carving](https://perso.crans.org/frenoy/matlab2012/seamcarving.pdf), который был описан *Shai Avidan* и *Ariel Shamir*.
+
+В приведенном ниже примере показано, как ширина исходного изображения была уменьшена на 50% *с учетом содержимого изображения* (слева) и *без учета содержимого изображения* (справа, простой скейлинг). В данном случае левое изображение выглядит более естественным, так как пропорции воздушных шаров в нем были сохранены.
+
+![Content-aware image resizing](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/01-resizing-options.png)
+
+Идея алгоритма Seam Carving заключается в том, чтобы найти *шов* (seam, непрерывную последовательность пикселей) с наименьшим влиянием на содержание изображения, а затем его *вырезать* (carve). Этот процесс повторяется снова и снова, пока мы не получим требуемую ширину или высоту изображения. В примере ниже интуитивно видно, что пиксели воздушных шаров вносят больший "вклад" в содержание и смысл изображения, чем пиксели неба. Таким образом, сначала удаляются пиксели неба.
+
+![JS IMAGE CARVER DEMO](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/10-demo-01.gif)
+
+Поиск шва с наименьшей энергией (с наименьшим вкладом в содержимое изображения) является вычислительно дорогостоящей операцией (особенно для больших изображений). Для ускорения поиска шва может быть применено *динамическое программирование* (мы рассмотрим детали реализации ниже).
+
+### Удаление объектов
+
+Важность каждого пикселя (так называемая энергия пикселя) вычисляется исходя из его цветовой разницы (`R`, `G`, `B`, `A`) между двумя соседними пикселями. Если же мы вручную зададим некоторым пикселям низкий уровень энергии (например нарисовав маску поверх них), то алгоритм Seam Carving выполнит для нас **удаление помеченного объекта**, как говорится, "забесплатно".
+
+![JS IMAGE CARVER OBJECT REMOVAL DEMO](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/10-demo-02.gif)
+
+### Интерактивный ресзайзер
+
+Для этой статьи я создал приложение [JS IMAGE CARVER](https://trekhleb.dev/js-image-carver/) (доступен также и [исходный код на GitHub](https://github.com/trekhleb/js-image-carver)), которым вы можете воспользоваться для ресайза своих изображений и увидеть в реальном времени, как работает алгоритм.
+
+### Другие примеры ресайза
+
+Вот еще несколько примеров того, как алгоритм справляется с более сложным фоном.
+
+Горы на заднем плане плавно сжимаются, без видимых швов.
+
+![Resizing demo with more complex backgrounds](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/11-demo-01.png)
+
+То же самое и с океанскими волнами. Алгоритм сохранил волновую структуру, не искажая серферов.
+
+![Resizing demo with more complex backgrounds](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/11-demo-02.png)
+
+Нужно помнить, что алгоритм Seam Carving не является "волшебной таблеткой", и может не сохранить пропорции важных частей изображения в том случае, когда *большая часть пикселей выглядят как края, ребра или границы* (почти все пиксели выглядят одинаково важными с точки зрения алгоритма). В приведенном ниже примере изменение размера изображения с учетом содержимого похоже на простое масштабирование, т.к. для алгоритма все пиксели выглядят важными, и ему трудно отличить лицо Ван Гога от фона.
+
+![Example when the algorithm does not work as expected](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/12-demo-01.png)
+
+## Как работает алгоритм Seam Carving
+
+Представим, что у нас есть картинка размером `1000 x 500 px`, и мы хотим уменьшить ее до `500 x 500 px` (допустим, квадратное изображение больше подходит для Instagram). В этом случае мы, возможно, захотим задать несколько **требований к процессу изменения размера**:
+
+- *Важные части изображения должны быть сохранены* (если до ресайза на фото было 5 деревьев, то и после ресайза мы хотим увидеть все те же 5 деревьев).
+- *Пропорции важных частей изображения должны быть сохранены* (круглые колеса автомобиля не должны стать овальными после ресайза).
+
+Чтобы избежать изменения важных частей изображения можно найти **непрерывную последовательность пикселей (шов)**, которая будет идти от верхней границы к нижней и иметь *наименьший вклад в содержимое* изображения (шов, который не проходит через важные части изображения), а затем удалить его. Удаление шва сожмет изображение на один пиксель. Далее надо повторять этот шаг до тех пор, пока изображение не станет нужной ширины.
+
+Вопрос в том, как определить *важность пикселя* и его вклад в содержание изображения (в оригинальной статье авторы используют термин **энергия пикселя**). Один из способов это сделать — рассматривать все пиксели, образующие края (границы, ребра), как важные. В случае, если пиксель является частью ребра, его цвет будет отличаться от соседей (левого и правого пикселей).
+
+![Pixels color difference](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/30-pixel-energy-comparison.png)
+
+Предполагая, что цвет пикселя представлен *4-мя* числами (`R` - красный, `G` - зеленый, `B` - синий, `A` - альфа, прозрачность), мы можем использовать следующую формулу для вычисления разницы в цвете (энергии пикселя):
+
+![Pixel energy formula](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/20-energy-formula.png)
+
+Где:
+
+- `mEnergy` - *Энергия* (важность) *среднего* пикселя (`[0..626]` если округлить)
+- `lR` - *Красный* цветовой канал *левого* пикселя (`[0..255]`)
+- `mR` - *Красный* цветовой канал *среднего* пикселя (`[0..255]`)
+- `rR` - *Красный* цветовой канал *правого* пикселя (`[0..255]`)
+- `lG` - *Зеленый* цветовой канал *левого* пикселя (`[0..255]`)
+- и так далее...
+
+В приведенной выше формуле мы пока не используем альфа-канал (прозрачность), предполагая, что изображение не содержит прозрачные пиксели. Позже мы будем использовать альфа-канал для маскировки и удаления объектов.
+
+![Example of pixel energy calculation](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/30-pixel-energy-calculation-example.png)
+
+Поскольку мы знаем, как найти энергию одного пикселя, мы можем вычислить так называемую **энергетическую карту**, которая будет содержать энергии каждого пикселя изображения. На каждом шаге изменения размера изображения карту энергий необходимо пересчитывать (по крайней мере частично, подробнее об этом ниже), и она будет иметь тот же размер, что и изображение.
+
+Например, на 1-м шаге у нас будет изображение размером `1000 x 500` и энергетическая карта размером `1000 x 500`. На 2-м шаге изменения размера мы удалим шов с изображения и пересчитаем карту энергий на основе нового уменьшенного изображения. Таким образом, мы получим изображение размером `999 x 500` и карту энергий размером `999 x 500`.
+
+Чем выше энергия пикселя, тем больше вероятность того, что он является частью ребра, важен для содержимого изображения и тем меньше вероятность того, что нам потребуется его удалить.
+
+Для визуализации карты энергий мы можем присвоить более яркий цвет пикселям с большей энергией и более темные цвета пикселям с меньшей энергией. Вот как может выглядеть часть карты энергий. Вы можете увидеть светлую линию, которая представляет край и которую мы хотим сохранить при изменении размера.
+
+![Energy map sketch](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/30-energy-map-padding.png)
+
+Вот реальный пример энергетической карты для изображения, которое вы видели выше (с воздушными шарами).
+
+![Energy map example](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/40-energy-map.png)
+
+Вы можете загрузить свое изображение и посмотреть, как будет выглядеть энергетическая карта в [интерактивной версии статьи](https://trekhleb.dev/blog/2021/content-aware-image-resizing-in-javascript/).
+
+Мы можем использовать энергетическую карту, чтобы найти швы (один за другим) с наименьшей энергией и тем самым решить, какие пиксели в конечном итоге должны быть удалены.
+
+![Searching the seam](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/41-seam-search.png)
+
+Поиск шва с наименьшими затратами энергии не является тривиальной задачей и требует перебора множества возможных комбинаций пикселей. Мы применим динамическое программирование для оптимизации поиска шва.
+
+В примере ниже вы можете увидеть карту энергий с первым найденным для нее швом с наименьшей энергией.
+
+![Energy map example with seam](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/40-energy-map-with-seam.png)
+
+В приведенных выше примерах мы уменьшали ширину изображения. Аналогичный подход может быть использован для уменьшения высоты изображения. Для этого нам нужно:
+
+- начать использовать соседей *сверху* и *снизу*, а не *слева* и *справа*, для вычисления энергии пикселя
+- при поиске шва нам нужно двигаться *слева* *направо*, а не *сверху* *вниз*.
+
+## Реализация алгоритма на TypeScript
+
+> Исходный код и функции, упомянутые ниже, можно найти в репозитории [js-image-carver](https://github.com/trekhleb/js-image-carver).
+
+Для реализации алгоритма мы будем использовать TypeScript. Если вам нужна версия на JavaScript, вы можете игнорировать (удалить) определения типов и их использование.
+
+Для простоты примеров мы напишем код только для уменьшения *ширины* изображения.
+
+### Уменьшение ширины с учетом содержимого изображения (исходная функция)
+
+Для начала определим некоторые общие типы, которые мы будем использовать при реализации алгоритма.
+
+```typescript
+// Type that describes the image size (width and height).
+type ImageSize = { w: number, h: number };
+
+// The coordinate of the pixel.
+type Coordinate = { x: number, y: number };
+
+// The seam is a sequence of pixels (coordinates).
+type Seam = Coordinate[];
+
+// Energy map is a 2D array that has the same width and height
+// as the image the map is being calculated for.
+type EnergyMap = number[][];
+
+// Type that describes the image pixel's RGBA color.
+type Color = [
+  r: number, // Red
+  g: number, // Green
+  b: number, // Blue
+  a: number, // Alpha (transparency)
+] | Uint8ClampedArray;
+```
+
+Для имплементации алгоритма нам необходимо выполнить следующие шаги:
+
+1. Рассчитать **карту энергии** для текущей версии изображения.
+2. Найти **шов** с наименьшей энергией на основе карты энергий (здесь мы применим динамическое программирование).
+3. **Удалить шов** с наименьшей энергией из изображения.
+4. **Повторять** до тех пор, пока ширина изображения не будет уменьшена до нужного значения.
+
+```typescript
+type ResizeImageWidthArgs = {
+  img: ImageData, // Image data we want to resize.
+  toWidth: number, // Final image width we want the image to shrink to.
+};
+
+type ResizeImageWidthResult = {
+  img: ImageData, // Resized image data.
+  size: ImageSize, // Resized image size (w x h).
+};
+
+// Performs the content-aware image width resizing using the seam carving method.
+export const resizeImageWidth = (
+  { img, toWidth }: ResizeImageWidthArgs,
+): ResizeImageWidthResult => {
+  // For performance reasons we want to avoid changing the img data array size.
+  // Instead we'll just keep the record of the resized image width and height separately.
+  const size: ImageSize = { w: img.width, h: img.height };
+
+  // Calculating the number of pixels to remove.
+  const pxToRemove = img.width - toWidth;
+  if (pxToRemove < 0) {
+    throw new Error('Upsizing is not supported for now');
+  }
+
+  let energyMap: EnergyMap | null = null;
+  let seam: Seam | null = null;
+
+  // Removing the lowest energy seams one by one.
+  for (let i = 0; i < pxToRemove; i += 1) {
+    // 1. Calculate the energy map for the current version of the image.
+    energyMap = calculateEnergyMap(img, size);
+
+    // 2. Find the seam with the lowest energy based on the energy map.
+    seam = findLowEnergySeam(energyMap, size);
+
+    // 3. Delete the seam with the lowest energy seam from the image.
+    deleteSeam(img, seam, size);
+
+    // Reduce the image width, and continue iterations.
+    size.w -= 1;
+  }
+
+  // Returning the resized image and its final size.
+  // The img is actually a reference to the ImageData, so technically
+  // the caller of the function already has this pointer. But let's
+  // still return it for better code readability.
+  return { img, size };
+};
+```
+
+Изображение, которому необходимо изменить размер, передается в функцию в формате [ImageData](https://developer.mozilla.org/en-US/docs/Web/API/ImageData). Вы можете отобразить изображение на canvas-е, а затем извлечь ImageData из того же canvas-а следующим образом:
+
+```javascript
+const ctx = canvas.getContext('2d');
+const imgData = ctx.getImageData(0, 0, imgWidth, imgHeight);
+```
+
+> Загрузка и отрисовка изображений в JavaScript выходит за рамки данной статьи, но вы можете найти полный исходный код того, как это можно сделать с помощью React в репозитории [js-image-carver](https://github.com/trekhleb/js-image-carver).
+
+Теперь, пошагово реализуем функции `calculateEnergyMap()`, `findLowEnergySeam()` и `deleteSeam()`.
+
+### Расчет энергии пикселя
+
+Для расчета воспользуемся формулой разницы цветов, описанной выше. Для левой и правой краев изображения (когда нет левого или правого соседей) мы игнорируем соседей и не учитываем их при расчете энергии.
+
+```typescript
+// Calculates the energy of a pixel.
+const getPixelEnergy = (left: Color | null, middle: Color, right: Color | null): number => {
+  // Middle pixel is the pixel we're calculating the energy for.
+  const [mR, mG, mB] = middle;
+
+  // Energy from the left pixel (if it exists).
+  let lEnergy = 0;
+  if (left) {
+    const [lR, lG, lB] = left;
+    lEnergy = (lR - mR) ** 2 + (lG - mG) ** 2 + (lB - mB) ** 2;
+  }
+
+  // Energy from the right pixel (if it exists).
+  let rEnergy = 0;
+  if (right) {
+    const [rR, rG, rB] = right;
+    rEnergy = (rR - mR) ** 2 + (rG - mG) ** 2 + (rB - mB) ** 2;
+  }
+
+  // Resulting pixel energy.
+  return Math.sqrt(lEnergy + rEnergy);
+};
+```
+
+### Расчет энергетической карты
+
+Изображение, с которым мы работаем, имеет формат [ImageData](https://developer.mozilla.org/en-US/docs/Web/API/ImageData). Это означает, что все пиксели (и их цвета) хранятся в одномерном массиве [Uint8ClampedArray](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Uint8ClampedArray). Для удобства чтения введем пару вспомогательных функций, которые позволят работать с массивом Uint8ClampedArray как с *2D* матрицей.
+
+```typescript
+// Helper function that returns the color of the pixel.
+const getPixel = (img: ImageData, { x, y }: Coordinate): Color => {
+  // The ImageData data array is a flat 1D array.
+  // Thus we need to convert x and y coordinates to the linear index.
+  const i = y * img.width + x;
+  const cellsPerColor = 4; // RGBA
+  // For better efficiency, instead of creating a new sub-array we return
+  // a pointer to the part of the ImageData array.
+  return img.data.subarray(i * cellsPerColor, i * cellsPerColor + cellsPerColor);
+};
+
+// Helper function that sets the color of the pixel.
+const setPixel = (img: ImageData, { x, y }: Coordinate, color: Color): void => {
+  // The ImageData data array is a flat 1D array.
+  // Thus we need to convert x and y coordinates to the linear index.
+  const i = y * img.width + x;
+  const cellsPerColor = 4; // RGBA
+  img.data.set(color, i * cellsPerColor);
+};
+```
+
+Для вычисления карты энергии мы проходим через каждый пиксель изображения и вызываем для него описанную ранее функцию `getPixelEnergy()`.
+
+```typescript
+// Helper function that creates a matrix (2D array) of specific
+// size (w x h) and fills it with specified value.
+const matrix = <T>(w: number, h: number, filler: T): T[][] => {
+  return new Array(h)
+    .fill(null)
+    .map(() => {
+      return new Array(w).fill(filler);
+    });
+};
+
+// Calculates the energy of each pixel of the image.
+const calculateEnergyMap = (img: ImageData, { w, h }: ImageSize): EnergyMap => {
+  // Create an empty energy map where each pixel has infinitely high energy.
+  // We will update the energy of each pixel.
+  const energyMap: number[][] = matrix<number>(w, h, Infinity);
+  for (let y = 0; y < h; y += 1) {
+    for (let x = 0; x < w; x += 1) {
+      // Left pixel might not exist if we're on the very left edge of the image.
+      const left = (x - 1) >= 0 ? getPixel(img, { x: x - 1, y }) : null;
+      // The color of the middle pixel that we're calculating the energy for.
+      const middle = getPixel(img, { x, y });
+      // Right pixel might not exist if we're on the very right edge of the image.
+      const right = (x + 1) < w ? getPixel(img, { x: x + 1, y }) : null;
+      energyMap[y][x] = getPixelEnergy(left, middle, right);
+    }
+  }
+  return energyMap;
+};
+```
+
+> Карта энергии будет пересчитываться при каждой итерации изменения размера. Это значит, что она будет пересчитываться, скажем, 500 раз, если нам нужно будет уменьшить изображение на 500 пикселей, что выглядит неоптимально. Чтобы ускорить вычисление карты энергии на 2-м, 3-м и последующих этапах, мы можем пересчитать энергию только для тех пикселей, которые расположены вокруг шва, который будет удален. Для простоты эта оптимизация здесь пропущена, но пример с исходным кодом можно найти в репозитории [js-image-carver](https://github.com/trekhleb/js-image-carver).
+
+### Нахождение шва с минимальной энергией (применяем динамическое программирование)
+
+> В статье [Dynamic Programming vs Divide-and-Conquer](https://trekhleb.dev/blog/2018/dynamic-programming-vs-divide-and-conquer/) я описывал некоторые аспекты динамического программирования на примере нахождения "расстояния Левенштейна" (преобразование одной строки в другую). Возможно она будет полезна для ознакомления.
+
+Проблема, которую нам необходимо решить заключается в нахождении пути (шва) на энергетической карте, который идет от верхней границы изображения к нижней и имеет минимальную энергию (сумма энергий пикселей, составляющих шов должна быть минимальной).
+
+#### "Наивный" подход (naive)
+
+Прямолинейный ("наивный") подход — перебрать все возможные пути один за другим.
+
+![The naive approach](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/50-naive-approach.png)
+
+Двигаясь сверху вниз, для каждого пикселя у нас есть 3 варианта (↙︎ идти вниз-влево, ↓ вниз, ↘︎ идти вниз-вправо). Это дает нам временную сложность `O (w * 3 ^ h)` или просто `O (3 ^ h)`, где `w` и` h` - ширина и высота изображения. Такой подход выглядит неоптимальным.
+
+#### "Жадный" подход (greedy)
+
+Жадный подход — выбирать следующий пиксель как пиксель с наименьшей энергией, надеясь, что результирующая энергия шва будет наименьшей.
+
+![The greedy approach](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/51-greedy-approach.png)
+
+Жадный подход приведет нас к не самому худшему решению, но он не сможет гарантировать, что мы найдем наилучшее доступное решение. На картинке выше видно, как мы выбрали `5` вместо `10` и пропустили цепочку оптимальных пикселей.
+
+Плюс этого подхода в том, что он быстрый и имеет временную сложность `O(w + h)`, где `w` и `h` - это ширина и высота изображения. В этом случае плата за скорость — низкое качество ресайза (много искажений). Временная сложность обусловлена тем, что нужно найти минимальное значение в первом ряду (обход `w` ячеек), а затем исследовать только 3 соседних пикселя для каждого ряда (обход `h` рядов).
+
+#### Используем динамическое программирование
+
+Вы, наверное, заметили, что в наивном подходе мы снова и снова суммировали одни и те же энергии пикселей, вычисляя энергию образовавшихся швов.
+
+![Repeated problems](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/52-dp-repeated-problems.png)
+
+В примере выше видно, что для первых двух швов мы повторно используем энергию более короткого шва (который имеет энергию `235`). Вместо одной операции `235 + 70` для вычисления энергии 2-го шва мы делаем четыре операции `(5 + 0 + 80 + 150) + 70`.
+
+> Тот факт, что мы повторно используем энергию предыдущего шва для вычисления энергии текущего шва, может быть применен рекурсивно ко всем более коротким швам до самого верхнего 1-го ряда. Когда у нас есть такие перекрывающиеся под-проблемы, [это признак](https://trekhleb.dev/blog/2018/dynamic-programming-vs-divide-and-conquer/), что общая задача *может* быть оптимизирована с использованием динамического программирования.
+
+Таким образом, мы можем **сохранить энергию текущего шва** для конкретного пикселя в дополнительной таблице `samsEnergies`, чтобы повторно использовать ее при расчете энергии следующих швов (таблица `samsEnergies` будет иметь тот же размер, что и энергетическая карта и само изображение).
+
+Обратите также внимание, что для большинства пикселей в изображении (например, для левого нижнего) мы можем иметь *несколько* значений энергий предыдущих швов.
+
+![What seam to choose](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/53-dp-what-to-choose.png)
+
+Так как мы ищем шов с наименьшей результирующей энергией, имеет смысл выбирать и предыдущий шов с наименьшей результирующей энергией.
+
+![Seams energies example](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/56-dp-seams-energies-example.png)
+
+Как правило, у нас есть три возможных предыдущих шва, которые текущий пиксель продолжает:
+
+![Three options to choose from](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/55-dp-three-options.png)
+
+Можем посмотреть на это с такой стороны:
+
+- Ячейка `[1][x]`: содержит наименьшую возможную энергию шва, который начинается где-то в ряду `[0][?] ` и заканчивается в ячейке `[1][x]`.
+- **Текущая ячейка** `[2][3]`: содержит наименьшую возможную энергию шва, который начинается где-то в ряду `[0][?] ` и заканчивается в ячейке `[2][3]`. Для вычисления нужно суммировать энергию текущего пикселя `[2][3]` (из энергетической карты) с `min(seam_energy_1_2, seam_energy_1_3, seam_energy_1_4)`.
+
+Если мы заполним таблицу `ShesamsEnergies` полностью, то минимальное число в нижнем ряду будет наименьшей возможной энергией шва.
+
+Попробуем заполнить несколько ячеек этой таблицы, чтобы посмотреть, как это работает.
+
+![Seams energies map traversal](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/57-dp-seams-energies-traversal.png)
+
+После заполнения таблицы `ShesamsEnergies` видно, что в нижнем ряду пиксель с самой низкой энергией имеет значение `50`. Для удобства во время генерации `samsEnergies` для каждого пикселя мы можем сохранить не только энергию шва, но и координаты предыдущего шва с наименьшей энергией. Это даст нам возможность легко восстанавливать траекторию шва снизу вверх.
+
+Временная сложность DP подхода составит `O(w * h)`, где `w` и `h` - это ширина и высота изображения. Обусловлена она тем, что нужно вычислить энергии для *всех* пикселей изображения.
+
+Вот пример того, как эта логика может быть реализована:
+
+```typescript
+// The metadata for the pixels in the seam.
+type SeamPixelMeta = {
+  energy: number, // The energy of the pixel.
+  coordinate: Coordinate, // The coordinate of the pixel.
+  previous: Coordinate | null, // The previous pixel in a seam.
+};
+
+// Finds the seam (the sequence of pixels from top to bottom) that has the
+// lowest resulting energy using the Dynamic Programming approach.
+const findLowEnergySeam = (energyMap: EnergyMap, { w, h }: ImageSize): Seam => {
+  // The 2D array of the size of w and h, where each pixel contains the
+  // seam metadata (pixel energy, pixel coordinate and previous pixel from
+  // the lowest energy seam at this point).
+  const seamsEnergies: (SeamPixelMeta | null)[][] = matrix<SeamPixelMeta | null>(w, h, null);
+
+  // Populate the first row of the map by just copying the energies
+  // from the energy map.
+  for (let x = 0; x < w; x += 1) {
+    const y = 0;
+    seamsEnergies[y][x] = {
+      energy: energyMap[y][x],
+      coordinate: { x, y },
+      previous: null,
+    };
+  }
+
+  // Populate the rest of the rows.
+  for (let y = 1; y < h; y += 1) {
+    for (let x = 0; x < w; x += 1) {
+      // Find the top adjacent cell with minimum energy.
+      // This cell would be the tail of a seam with lowest energy at this point.
+      // It doesn't mean that this seam (path) has lowest energy globally.
+      // Instead, it means that we found a path with the lowest energy that may lead
+      // us to the current pixel with the coordinates x and y.
+      let minPrevEnergy = Infinity;
+      let minPrevX: number = x;
+      for (let i = (x - 1); i <= (x + 1); i += 1) {
+        if (i >= 0 && i < w && seamsEnergies[y - 1][i].energy < minPrevEnergy) {
+          minPrevEnergy = seamsEnergies[y - 1][i].energy;
+          minPrevX = i;
+        }
+      }
+
+      // Update the current cell.
+      seamsEnergies[y][x] = {
+        energy: minPrevEnergy + energyMap[y][x],
+        coordinate: { x, y },
+        previous: { x: minPrevX, y: y - 1 },
+      };
+    }
+  }
+
+  // Find where the minimum energy seam ends.
+  // We need to find the tail of the lowest energy seam to start
+  // traversing it from its tail to its head (from the bottom to the top).
+  let lastMinCoordinate: Coordinate | null = null;
+  let minSeamEnergy = Infinity;
+  for (let x = 0; x < w; x += 1) {
+    const y = h - 1;
+    if (seamsEnergies[y][x].energy < minSeamEnergy) {
+      minSeamEnergy = seamsEnergies[y][x].energy;
+      lastMinCoordinate = { x, y };
+    }
+  }
+
+  // Find the lowest energy energy seam.
+  // Once we know where the tail is we may traverse and assemble the lowest
+  // energy seam based on the "previous" value of the seam pixel metadata.
+  const seam: Seam = [];
+  if (!lastMinCoordinate) {
+    return seam;
+  }
+
+  const { x: lastMinX, y: lastMinY } = lastMinCoordinate;
+
+  // Adding new pixel to the seam path one by one until we reach the top.
+  let currentSeam = seamsEnergies[lastMinY][lastMinX];
+  while (currentSeam) {
+    seam.push(currentSeam.coordinate);
+    const prevMinCoordinates = currentSeam.previous;
+    if (!prevMinCoordinates) {
+      currentSeam = null;
+    } else {
+      const { x: prevMinX, y: prevMinY } = prevMinCoordinates;
+      currentSeam = seamsEnergies[prevMinY][prevMinX];
+    }
+  }
+
+  return seam;
+};
+```
+
+### Удаление шва с минимальной энергией
+
+Как только мы нашли шов с наименьшей суммарной энергией, нам нужно удалить (вырезать) пиксели, которые образуют его из изображения. Удаление происходит путем смещения пикселей справа от шва на `1px` влево. Из соображений производительности мы не будем удалять крайний столбик пикселей. Вместо этого, компонент, отвечающий за отрисовку уменьшенного изображения просто проигнорирует ту часть изображения, которая лежит за пределами обрезанной ширины.
+
+![Deleting the seam](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/60-deleting-example.png)
+
+```typescript
+// Deletes the seam from the image data.
+// We delete the pixel in each row and then shift the rest of the row pixels to the left.
+const deleteSeam = (img: ImageData, seam: Seam, { w }: ImageSize): void => {
+  seam.forEach(({ x: seamX, y: seamY }: Coordinate) => {
+    for (let x = seamX; x < (w - 1); x += 1) {
+      const nextPixel = getPixel(img, { x: x + 1, y: seamY });
+      setPixel(img, { x, y: seamY }, nextPixel);
+    }
+  });
+};
+```
+
+## Удаление объектов с изображения
+
+Seam Carving алгоритм пытается сначала удалить швы, состоящие из низкоэнергетических пикселей. Мы могли бы использовать этот факт и, присвоив низкую энергию некоторым пикселям вручную (например, нарисовав на изображении маску), мы могли бы заставить алгоритм удалить отмеченные пиксели (*объекты*).
+
+В настоящее время в функции `getPixelEnergy()` мы используем только каналы цветов `R`, `G`, `B` для вычисления энергии пикселей. Но есть еще и параметр `A` (альфа, прозрачность), который мы не использовали. Мы можем использовать канал прозрачности, чтобы "сказать" алгоритму, что прозрачные пиксели — это те пиксели, которые мы хотим удалить. Вы можете ознакомиться с [исходным кодом функции getPixelEnergy()](https://github.com/trekhleb/js-image-carver/blob/main/src/utils/contentAwareResizer.ts#L54), которая учитывает прозрачность.
+
+Вот как при этом будет выглядеть удаление объектов:
+
+![JS IMAGE CARVER OBJECT REMOVAL DEMO](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/10-demo-02.gif)
+
+## Проблемы алгоритма и дальнейшие планы
+
+Приложение [JS IMAGE CARVER](https://github.com/trekhleb/js-image-carver) далеко от идеала и не является приложением production-ready качества. Основной его целью была возможность интерактивного экспериментирования с алгоритмом. Поэтому в дальнейших планах — использовать его именно для экспериментов.
+
+В [оригинальной статье](https://perso.crans.org/frenoy/matlab2012/seamcarving.pdf) описывается, как алгоритм может быть использован не только для уменьшения, но и для **увеличения изображения**. Увеличение (расширение) изображения, в свою очередь, может быть использовано для **автоматического расширения изображения до его исходной ширины после удаления объектов**.
+
+Еще одной интересной областью экспериментов может быть попытка ускорить алгоритм, чтобы он работал в режиме **реального времени**.
+
+> Таковы планы на будущее, но пока, надеюсь, пример с уменьшением изображения был интересен и полезен для вас. Также надеюсь, что вам было интересно увидеть применение динамического программирования в задачах, приближенных к реальности.
+>
+> Удачи с вашими собственными экспериментами!
diff --git a/src/algorithms/image-processing/seam-carving/__tests__/resizeImageWidth.test.js b/src/algorithms/image-processing/seam-carving/__tests__/resizeImageWidth.test.js
new file mode 100644
index 0000000000..b6400a3522
--- /dev/null
+++ b/src/algorithms/image-processing/seam-carving/__tests__/resizeImageWidth.test.js
@@ -0,0 +1,51 @@
+import { createCanvas, loadImage } from 'canvas';
+import resizeImageWidth from '../resizeImageWidth';
+
+const testImageBeforePath = './src/algorithms/image-processing/seam-carving/__tests__/test-image-before.jpg';
+const testImageAfterPath = './src/algorithms/image-processing/seam-carving/__tests__/test-image-after.jpg';
+
+describe('resizeImageWidth', () => {
+  it('should perform content-aware image width reduction', () => {
+    // @see: https://jestjs.io/docs/asynchronous
+    return Promise.all([
+      loadImage(testImageBeforePath),
+      loadImage(testImageAfterPath),
+    ]).then(([imgBefore, imgAfter]) => {
+      // Original image.
+      const canvasBefore = createCanvas(imgBefore.width, imgBefore.height);
+      const ctxBefore = canvasBefore.getContext('2d');
+      ctxBefore.drawImage(imgBefore, 0, 0, imgBefore.width, imgBefore.height);
+      const imgDataBefore = ctxBefore.getImageData(0, 0, imgBefore.width, imgBefore.height);
+
+      // Resized image saved.
+      const canvasAfter = createCanvas(imgAfter.width, imgAfter.height);
+      const ctxAfter = canvasAfter.getContext('2d');
+      ctxAfter.drawImage(imgAfter, 0, 0, imgAfter.width, imgAfter.height);
+
+      const toWidth = Math.floor(imgBefore.width / 2);
+
+      const {
+        img: resizedImg,
+        size: resizedSize,
+      } = resizeImageWidth({ img: imgDataBefore, toWidth });
+
+      expect(resizedImg).toBeDefined();
+      expect(resizedSize).toBeDefined();
+
+      // Resized image generated.
+      const canvasTest = createCanvas(resizedSize.w, resizedSize.h);
+      const ctxTest = canvasTest.getContext('2d');
+      ctxTest.putImageData(resizedImg, 0, 0, 0, 0, resizedSize.w, resizedSize.h);
+      const imgDataTest = ctxTest.getImageData(0, 0, resizedSize.w, resizedSize.h);
+
+      expect(resizedSize).toEqual({ w: toWidth, h: imgBefore.height });
+      expect(imgDataTest.width).toBe(toWidth);
+      expect(imgDataTest.height).toBe(imgBefore.height);
+      expect(imgDataTest.width).toBe(imgAfter.width);
+      expect(imgDataTest.height).toBe(imgAfter.height);
+
+      // @TODO: Check that images are identical.
+      // expect(canvasTest.toDataURL()).toEqual(canvasAfter.toDataURL());
+    });
+  });
+});
diff --git a/src/algorithms/image-processing/seam-carving/__tests__/test-image-after.jpg b/src/algorithms/image-processing/seam-carving/__tests__/test-image-after.jpg
new file mode 100644
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diff --git a/src/algorithms/image-processing/seam-carving/resizeImageWidth.js b/src/algorithms/image-processing/seam-carving/resizeImageWidth.js
new file mode 100644
index 0000000000..9f2c92fcee
--- /dev/null
+++ b/src/algorithms/image-processing/seam-carving/resizeImageWidth.js
@@ -0,0 +1,253 @@
+import { getPixel, setPixel } from '../utils/imageData';
+
+/**
+ * The seam is a sequence of pixels (coordinates).
+ * @typedef {PixelCoordinate[]} Seam
+ */
+
+/**
+ * Energy map is a 2D array that has the same width and height
+ * as the image the map is being calculated for.
+ * @typedef {number[][]} EnergyMap
+ */
+
+/**
+ * The metadata for the pixels in the seam.
+ * @typedef {Object} SeamPixelMeta
+ * @property {number} energy - the energy of the pixel.
+ * @property {PixelCoordinate} coordinate - the coordinate of the pixel.
+ * @property {?PixelCoordinate} previous - the previous pixel in a seam.
+ */
+
+/**
+ * Type that describes the image size (width and height)
+ * @typedef {Object} ImageSize
+ * @property {number} w - image width.
+ * @property {number} h - image height.
+ */
+
+/**
+ * @typedef {Object} ResizeImageWidthArgs
+ * @property {ImageData} img - image data we want to resize.
+ * @property {number} toWidth - final image width we want the image to shrink to.
+ */
+
+/**
+ * @typedef {Object} ResizeImageWidthResult
+ * @property {ImageData} img - resized image data.
+ * @property {ImageSize} size - resized image size.
+ */
+
+/**
+ * Helper function that creates a matrix (2D array) of specific
+ * size (w x h) and fills it with specified value.
+ * @param {number} w
+ * @param {number} h
+ * @param {?(number | SeamPixelMeta)} filler
+ * @returns {?(number | SeamPixelMeta)[][]}
+ */
+const matrix = (w, h, filler) => {
+  return new Array(h)
+    .fill(null)
+    .map(() => {
+      return new Array(w).fill(filler);
+    });
+};
+
+/**
+ * Calculates the energy of a pixel.
+ * @param {?PixelColor} left
+ * @param {PixelColor} middle
+ * @param {?PixelColor} right
+ * @returns {number}
+ */
+const getPixelEnergy = (left, middle, right) => {
+  // Middle pixel is the pixel we're calculating the energy for.
+  const [mR, mG, mB] = middle;
+
+  // Energy from the left pixel (if it exists).
+  let lEnergy = 0;
+  if (left) {
+    const [lR, lG, lB] = left;
+    lEnergy = (lR - mR) ** 2 + (lG - mG) ** 2 + (lB - mB) ** 2;
+  }
+
+  // Energy from the right pixel (if it exists).
+  let rEnergy = 0;
+  if (right) {
+    const [rR, rG, rB] = right;
+    rEnergy = (rR - mR) ** 2 + (rG - mG) ** 2 + (rB - mB) ** 2;
+  }
+
+  // Resulting pixel energy.
+  return Math.sqrt(lEnergy + rEnergy);
+};
+
+/**
+ * Calculates the energy of each pixel of the image.
+ * @param {ImageData} img
+ * @param {ImageSize} size
+ * @returns {EnergyMap}
+ */
+const calculateEnergyMap = (img, { w, h }) => {
+  // Create an empty energy map where each pixel has infinitely high energy.
+  // We will update the energy of each pixel.
+  const energyMap = matrix(w, h, Infinity);
+  for (let y = 0; y < h; y += 1) {
+    for (let x = 0; x < w; x += 1) {
+      // Left pixel might not exist if we're on the very left edge of the image.
+      const left = (x - 1) >= 0 ? getPixel(img, { x: x - 1, y }) : null;
+      // The color of the middle pixel that we're calculating the energy for.
+      const middle = getPixel(img, { x, y });
+      // Right pixel might not exist if we're on the very right edge of the image.
+      const right = (x + 1) < w ? getPixel(img, { x: x + 1, y }) : null;
+      energyMap[y][x] = getPixelEnergy(left, middle, right);
+    }
+  }
+  return energyMap;
+};
+
+/**
+ * Finds the seam (the sequence of pixels from top to bottom) that has the
+ * lowest resulting energy using the Dynamic Programming approach.
+ * @param {EnergyMap} energyMap
+ * @param {ImageSize} size
+ * @returns {Seam}
+ */
+const findLowEnergySeam = (energyMap, { w, h }) => {
+  // The 2D array of the size of w and h, where each pixel contains the
+  // seam metadata (pixel energy, pixel coordinate and previous pixel from
+  // the lowest energy seam at this point).
+  const seamPixelsMap = matrix(w, h, null);
+
+  // Populate the first row of the map by just copying the energies
+  // from the energy map.
+  for (let x = 0; x < w; x += 1) {
+    const y = 0;
+    seamPixelsMap[y][x] = {
+      energy: energyMap[y][x],
+      coordinate: { x, y },
+      previous: null,
+    };
+  }
+
+  // Populate the rest of the rows.
+  for (let y = 1; y < h; y += 1) {
+    for (let x = 0; x < w; x += 1) {
+      // Find the top adjacent cell with minimum energy.
+      // This cell would be the tail of a seam with lowest energy at this point.
+      // It doesn't mean that this seam (path) has lowest energy globally.
+      // Instead, it means that we found a path with the lowest energy that may lead
+      // us to the current pixel with the coordinates x and y.
+      let minPrevEnergy = Infinity;
+      let minPrevX = x;
+      for (let i = (x - 1); i <= (x + 1); i += 1) {
+        if (i >= 0 && i < w && seamPixelsMap[y - 1][i].energy < minPrevEnergy) {
+          minPrevEnergy = seamPixelsMap[y - 1][i].energy;
+          minPrevX = i;
+        }
+      }
+
+      // Update the current cell.
+      seamPixelsMap[y][x] = {
+        energy: minPrevEnergy + energyMap[y][x],
+        coordinate: { x, y },
+        previous: { x: minPrevX, y: y - 1 },
+      };
+    }
+  }
+
+  // Find where the minimum energy seam ends.
+  // We need to find the tail of the lowest energy seam to start
+  // traversing it from its tail to its head (from the bottom to the top).
+  let lastMinCoordinate = null;
+  let minSeamEnergy = Infinity;
+  for (let x = 0; x < w; x += 1) {
+    const y = h - 1;
+    if (seamPixelsMap[y][x].energy < minSeamEnergy) {
+      minSeamEnergy = seamPixelsMap[y][x].energy;
+      lastMinCoordinate = { x, y };
+    }
+  }
+
+  // Find the lowest energy energy seam.
+  // Once we know where the tail is we may traverse and assemble the lowest
+  // energy seam based on the "previous" value of the seam pixel metadata.
+  const seam = [];
+
+  const { x: lastMinX, y: lastMinY } = lastMinCoordinate;
+
+  // Adding new pixel to the seam path one by one until we reach the top.
+  let currentSeam = seamPixelsMap[lastMinY][lastMinX];
+  while (currentSeam) {
+    seam.push(currentSeam.coordinate);
+    const prevMinCoordinates = currentSeam.previous;
+    if (!prevMinCoordinates) {
+      currentSeam = null;
+    } else {
+      const { x: prevMinX, y: prevMinY } = prevMinCoordinates;
+      currentSeam = seamPixelsMap[prevMinY][prevMinX];
+    }
+  }
+
+  return seam;
+};
+
+/**
+ * Deletes the seam from the image data.
+ * We delete the pixel in each row and then shift the rest of the row pixels to the left.
+ * @param {ImageData} img
+ * @param {Seam} seam
+ * @param {ImageSize} size
+ */
+const deleteSeam = (img, seam, { w }) => {
+  seam.forEach(({ x: seamX, y: seamY }) => {
+    for (let x = seamX; x < (w - 1); x += 1) {
+      const nextPixel = getPixel(img, { x: x + 1, y: seamY });
+      setPixel(img, { x, y: seamY }, nextPixel);
+    }
+  });
+};
+
+/**
+ * Performs the content-aware image width resizing using the seam carving method.
+ * @param {ResizeImageWidthArgs} args
+ * @returns {ResizeImageWidthResult}
+ */
+const resizeImageWidth = ({ img, toWidth }) => {
+  /**
+   * For performance reasons we want to avoid changing the img data array size.
+   * Instead we'll just keep the record of the resized image width and height separately.
+   * @type {ImageSize}
+   */
+  const size = { w: img.width, h: img.height };
+
+  // Calculating the number of pixels to remove.
+  const pxToRemove = img.width - toWidth;
+
+  let energyMap = null;
+  let seam = null;
+
+  // Removing the lowest energy seams one by one.
+  for (let i = 0; i < pxToRemove; i += 1) {
+    // 1. Calculate the energy map for the current version of the image.
+    energyMap = calculateEnergyMap(img, size);
+
+    // 2. Find the seam with the lowest energy based on the energy map.
+    seam = findLowEnergySeam(energyMap, size);
+
+    // 3. Delete the seam with the lowest energy seam from the image.
+    deleteSeam(img, seam, size);
+
+    // Reduce the image width, and continue iterations.
+    size.w -= 1;
+  }
+
+  // Returning the resized image and its final size.
+  // The img is actually a reference to the ImageData, so technically
+  // the caller of the function already has this pointer. But let's
+  // still return it for better code readability.
+  return { img, size };
+};
+
+export default resizeImageWidth;
diff --git a/src/algorithms/image-processing/utils/imageData.js b/src/algorithms/image-processing/utils/imageData.js
new file mode 100644
index 0000000000..de397b8ead
--- /dev/null
+++ b/src/algorithms/image-processing/utils/imageData.js
@@ -0,0 +1,39 @@
+/**
+ * @typedef {ArrayLike<number> | Uint8ClampedArray} PixelColor
+ */
+
+/**
+ * @typedef {Object} PixelCoordinate
+ * @property {number} x - horizontal coordinate.
+ * @property {number} y - vertical coordinate.
+ */
+
+/**
+ * Helper function that returns the color of the pixel.
+ * @param {ImageData} img
+ * @param {PixelCoordinate} coordinate
+ * @returns {PixelColor}
+ */
+export const getPixel = (img, { x, y }) => {
+  // The ImageData data array is a flat 1D array.
+  // Thus we need to convert x and y coordinates to the linear index.
+  const i = y * img.width + x;
+  const cellsPerColor = 4; // RGBA
+  // For better efficiency, instead of creating a new sub-array we return
+  // a pointer to the part of the ImageData array.
+  return img.data.subarray(i * cellsPerColor, i * cellsPerColor + cellsPerColor);
+};
+
+/**
+ * Helper function that sets the color of the pixel.
+ * @param {ImageData} img
+ * @param {PixelCoordinate} coordinate
+ * @param {PixelColor} color
+ */
+export const setPixel = (img, { x, y }, color) => {
+  // The ImageData data array is a flat 1D array.
+  // Thus we need to convert x and y coordinates to the linear index.
+  const i = y * img.width + x;
+  const cellsPerColor = 4; // RGBA
+  img.data.set(color, i * cellsPerColor);
+};

From cfd9a630ff8cacd17880b16b27f32781eaac6bb7 Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Wed, 21 Apr 2021 07:39:58 +0200
Subject: [PATCH 081/264] Test that two images are identical for the Seam
 Carving algorithm. (#694)

* Test that two images are identical for the Seam Carving algorithm.

* Tune the Seam Carving tests.

* Tune the Seam Carving tests.

* Tune the Seam Carving tests.

* Tune the Seam Carving tests.
---
 .husky/pre-commit                             |  1 +
 .../__tests__/resizeImageWidth.test.js        | 44 ++++++++++++++++++-
 2 files changed, 43 insertions(+), 2 deletions(-)

diff --git a/.husky/pre-commit b/.husky/pre-commit
index bec1c08a1a..a29a4166ea 100755
--- a/.husky/pre-commit
+++ b/.husky/pre-commit
@@ -1,5 +1,6 @@
 #!/bin/sh
 . "$(dirname "$0")/_/husky.sh"
 
+# @TODO: Implement the pre-commit checks.
 # npm run lint
 # npm run test
diff --git a/src/algorithms/image-processing/seam-carving/__tests__/resizeImageWidth.test.js b/src/algorithms/image-processing/seam-carving/__tests__/resizeImageWidth.test.js
index b6400a3522..9afed97123 100644
--- a/src/algorithms/image-processing/seam-carving/__tests__/resizeImageWidth.test.js
+++ b/src/algorithms/image-processing/seam-carving/__tests__/resizeImageWidth.test.js
@@ -4,6 +4,40 @@ import resizeImageWidth from '../resizeImageWidth';
 const testImageBeforePath = './src/algorithms/image-processing/seam-carving/__tests__/test-image-before.jpg';
 const testImageAfterPath = './src/algorithms/image-processing/seam-carving/__tests__/test-image-after.jpg';
 
+/**
+ * Compares two images and finds the number of different pixels.
+ *
+ * @param {ImageData} imgA - ImageData for the first image.
+ * @param {ImageData} imgB - ImageData for the second image.
+ * @param {number} threshold - Color difference threshold [0..255]. Smaller - stricter.
+ * @returns {number} - Number of different pixels.
+ */
+function pixelsDiff(imgA, imgB, threshold = 0) {
+  if (imgA.width !== imgB.width || imgA.height !== imgB.height) {
+    throw new Error('Images must have the same size');
+  }
+
+  let differentPixels = 0;
+  const numColorParams = 4; // RGBA
+
+  for (let pixelIndex = 0; pixelIndex < imgA.data.length; pixelIndex += numColorParams) {
+    // Get pixel's color for each image.
+    const [aR, aG, aB] = imgA.data.subarray(pixelIndex, pixelIndex + numColorParams);
+    const [bR, bG, bB] = imgB.data.subarray(pixelIndex, pixelIndex + numColorParams);
+
+    // Get average pixel's color for each image (make them greyscale).
+    const aAvgColor = Math.floor((aR + aG + aB) / 3);
+    const bAvgColor = Math.floor((bR + bG + bB) / 3);
+
+    // Compare pixel colors.
+    if (Math.abs(aAvgColor - bAvgColor) > threshold) {
+      differentPixels += 1;
+    }
+  }
+
+  return differentPixels;
+}
+
 describe('resizeImageWidth', () => {
   it('should perform content-aware image width reduction', () => {
     // @see: https://jestjs.io/docs/asynchronous
@@ -21,6 +55,7 @@ describe('resizeImageWidth', () => {
       const canvasAfter = createCanvas(imgAfter.width, imgAfter.height);
       const ctxAfter = canvasAfter.getContext('2d');
       ctxAfter.drawImage(imgAfter, 0, 0, imgAfter.width, imgAfter.height);
+      const imgDataAfter = ctxAfter.getImageData(0, 0, imgAfter.width, imgAfter.height);
 
       const toWidth = Math.floor(imgBefore.width / 2);
 
@@ -44,8 +79,13 @@ describe('resizeImageWidth', () => {
       expect(imgDataTest.width).toBe(imgAfter.width);
       expect(imgDataTest.height).toBe(imgAfter.height);
 
-      // @TODO: Check that images are identical.
-      // expect(canvasTest.toDataURL()).toEqual(canvasAfter.toDataURL());
+      const colorThreshold = 50;
+      const differentPixels = pixelsDiff(imgDataTest, imgDataAfter, colorThreshold);
+
+      // Allow 10% of pixels to be different
+      const pixelsThreshold = Math.floor((imgAfter.width * imgAfter.height) / 10);
+
+      expect(differentPixels).toBeLessThanOrEqual(pixelsThreshold);
     });
   });
 });

From 144b6867761a064bfe766c0c1994ebd1be676e74 Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Wed, 21 Apr 2021 16:55:26 +0200
Subject: [PATCH 082/264] Testing Husky integration

---
 .husky/pre-commit | 5 ++---
 .npmrc            | 1 +
 package.json      | 5 ++++-
 3 files changed, 7 insertions(+), 4 deletions(-)
 create mode 100644 .npmrc

diff --git a/.husky/pre-commit b/.husky/pre-commit
index a29a4166ea..660b820968 100755
--- a/.husky/pre-commit
+++ b/.husky/pre-commit
@@ -1,6 +1,5 @@
 #!/bin/sh
 . "$(dirname "$0")/_/husky.sh"
 
-# @TODO: Implement the pre-commit checks.
-# npm run lint
-# npm run test
+npm run lint
+npm run test
diff --git a/.npmrc b/.npmrc
new file mode 100644
index 0000000000..c0c80ba447
--- /dev/null
+++ b/.npmrc
@@ -0,0 +1 @@
+engine-strict=false
diff --git a/package.json b/package.json
index c4ae69b6fd..f77d87ff50 100644
--- a/package.json
+++ b/package.json
@@ -48,5 +48,8 @@
     "husky": "6.0.0",
     "jest": "26.6.3"
   },
-  "dependencies": {}
+  "engines": {
+    "node": ">=12.0.0",
+    "npm": ">=6.9.0"
+  }
 }

From f7d07ae66d0fbd2c9b093bb074c8cb02de7be4b8 Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Wed, 21 Apr 2021 17:09:59 +0200
Subject: [PATCH 083/264] Testing Husky integration

---
 .husky/pre-commit | 1 +
 1 file changed, 1 insertion(+)

diff --git a/.husky/pre-commit b/.husky/pre-commit
index 660b820968..4c19307277 100755
--- a/.husky/pre-commit
+++ b/.husky/pre-commit
@@ -1,5 +1,6 @@
 #!/bin/sh
 . "$(dirname "$0")/_/husky.sh"
 
+# Testing Husky.
 npm run lint
 npm run test

From 4ca41ea83b8fdbfe2eb056c8b89852466a840a29 Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Wed, 21 Apr 2021 17:12:53 +0200
Subject: [PATCH 084/264] Testing Husky integration

---
 .husky/pre-commit | 1 -
 1 file changed, 1 deletion(-)

diff --git a/.husky/pre-commit b/.husky/pre-commit
index 4c19307277..660b820968 100755
--- a/.husky/pre-commit
+++ b/.husky/pre-commit
@@ -1,6 +1,5 @@
 #!/bin/sh
 . "$(dirname "$0")/_/husky.sh"
 
-# Testing Husky.
 npm run lint
 npm run test

From 912941be1d42d19a0a8b5ded73b35deee8e05718 Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Wed, 21 Apr 2021 17:30:49 +0200
Subject: [PATCH 085/264] Add troubleshooting instructions.

---
 README.md | 12 ++++++++++++
 1 file changed, 12 insertions(+)

diff --git a/README.md b/README.md
index 71b0798fbe..a9fc7b5ea0 100644
--- a/README.md
+++ b/README.md
@@ -236,6 +236,7 @@ tree is being used.
 ## How to use this repository
 
 **Install all dependencies**
+
 ```
 npm install
 ```
@@ -249,15 +250,26 @@ npm run lint
 ```
 
 **Run all tests**
+
 ```
 npm test
 ```
 
 **Run tests by name**
+
 ```
 npm test -- 'LinkedList'
 ```
 
+**Troubleshooting**
+
+In case if linting or testing is failing try to delete the `node_modules` folder and re-install npm packages:
+
+```
+rm -rf ./node_modules
+npm i
+```
+
 **Playground**
 
 You may play with data-structures and algorithms in `./src/playground/playground.js` file and write

From 7ad3fbc0f9eebfc4e86623be94e7c3dfbe9e611d Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Wed, 21 Apr 2021 18:09:48 +0200
Subject: [PATCH 086/264] Disabling tests in pre-commit to speed up the
 commits.

---
 .husky/pre-commit | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/.husky/pre-commit b/.husky/pre-commit
index 660b820968..598a5dceaa 100755
--- a/.husky/pre-commit
+++ b/.husky/pre-commit
@@ -2,4 +2,4 @@
 . "$(dirname "$0")/_/husky.sh"
 
 npm run lint
-npm run test
+# npm run test

From d38cecd2e79d64efba1dd0b37cdd9acd60bc42ba Mon Sep 17 00:00:00 2001
From: Coco Guerra <jorgeguerra1098@gmail.com>
Date: Wed, 5 May 2021 22:43:28 -0600
Subject: [PATCH 087/264] Update README.es-ES.md (#704)

* Update README.es-ES.md

* Update README.es-ES.md
---
 .../linked-list/README.es-ES.md               | 41 +++++++++----------
 1 file changed, 20 insertions(+), 21 deletions(-)

diff --git a/src/data-structures/linked-list/README.es-ES.md b/src/data-structures/linked-list/README.es-ES.md
index 978e234ddf..58eb2b860d 100644
--- a/src/data-structures/linked-list/README.es-ES.md
+++ b/src/data-structures/linked-list/README.es-ES.md
@@ -7,27 +7,26 @@ _Lee esto en otros idiomas:_
 [_Português_](README.pt-BR.md)
 [_English_](README.md)
 
-En ciencias de la computaciòn una **lista enlazada** es una  coleccion linear 
+En ciencias de la computación una **lista enlazada** es una colección linear
 de elemntos de datos, en los cuales el orden linear no es dado por
-su posciòn fisica en memoria. En cambio, cada 
-elemento señala al siguiente. Es una estructura de datos 
+su posción física en memoria. En cambio, cada
+elemento señala al siguiente. Es una estructura de datos
 que consiste en un grupo de nodos los cuales juntos representan
-una secuencia. Bajo la forma mas simple, cada nodo es 
-compuesto de datos y una referencia (en otras palabras, 
+una secuencia. Bajo la forma más simple, cada nodo es
+compuesto de datos y una referencia (en otras palabras,
 un lazo) al siguiente nodo en la secuencia. Esta estructura
-permite la insercion o remocion de elementos 
-desde cualquier posicion en la secuencia durante la iteracion. 
-Variantes mas complejas agregan lazos adicionales, permitiendo 
-una eficiente insercion o remocion desde referencias arbitrarias
+permite la inserción o remoción de elementos
+desde cualquier posición en la secuencia durante la iteración.
+Variantes más complejas agregan lazos adicionales, permitiendo
+una eficiente inserción o remoción desde referencias arbitrarias
 del elemento. Una desventaja de las listas lazadas es que el tiempo de
-acceso es linear (y dificil de canalizar) Un acceso
-mas rapido, como un acceso aleatorio, no es factible. Los arreglos
+acceso es linear (y difícil de canalizar). Un acceso
+más rápido, como un acceso aleatorio, no es factible. Los arreglos
 tienen una mejor locazion comparados con las listas lazadas.
 
-
 ![Linked List](https://upload.wikimedia.org/wikipedia/commons/6/6d/Singly-linked-list.svg)
 
-## Pseudocodigo para operacones basicas
+## Pseudocódigo para operacones básicas
 
 ### Insertar
 
@@ -76,7 +75,7 @@ Contains(head, value)
   return true
 end Contains
 ```
-    
+
 ### Borrar
 
 ```text
@@ -146,19 +145,19 @@ ReverseTraversal(head, tail)
 end ReverseTraversal
 ```
 
-## Complexities
+## Complejidades
 
-### Time Complexity
+### Complejidad del Tiempo
 
-| Access    | Search    | Insertion | Deletion  |
-| :-------: | :-------: | :-------: | :-------: |
-| O(n)      | O(n)      | O(1)      | O(n)      |
+| Access | Search | Insertion | Deletion |
+| :----: | :----: | :-------: | :------: |
+|  O(n)  |  O(n)  |   O(1)    |   O(n)   |
 
-### Space Complexity
+### Complejidad Espacial
 
 O(n)
 
-## References
+## Referencias
 
 - [Wikipedia](https://en.wikipedia.org/wiki/Linked_list)
 - [YouTube](https://www.youtube.com/watch?v=njTh_OwMljA&index=2&t=1s&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)

From 64abcf12f28e02580b28cc8b64bab5ff0ac9c037 Mon Sep 17 00:00:00 2001
From: Deniz Binay <69312106+denizbinay@users.noreply.github.com>
Date: Thu, 6 May 2021 06:46:04 +0200
Subject: [PATCH 088/264] add german translation for main readme (#703)

---
 README.ar-AR.md |   3 +-
 README.de-DE.md | 333 ++++++++++++++++++++++++++++++++++++++++++++++++
 README.es-ES.md |   3 +-
 README.fr-FR.md |   3 +-
 README.id-ID.md |   3 +-
 README.it-IT.md |   3 +-
 README.ja-JP.md |   3 +-
 README.ko-KR.md |   3 +-
 README.md       |   3 +-
 README.pl-PL.md |   3 +-
 README.pt-BR.md |   3 +-
 README.ru-RU.md |   3 +-
 README.tr-TR.md |   3 +-
 README.uk-UA.md |   3 +-
 README.zh-CN.md |   3 +-
 README.zh-TW.md |   3 +-
 16 files changed, 363 insertions(+), 15 deletions(-)
 create mode 100644 README.de-DE.md

diff --git a/README.ar-AR.md b/README.ar-AR.md
index 378334fab0..797006b6ef 100644
--- a/README.ar-AR.md
+++ b/README.ar-AR.md
@@ -21,7 +21,8 @@ _اقرأ هذا في لغات أخرى:_
 [_Português_](README.pt-BR.md),
 [_Русский_](README.ru-RU.md),
 [_Türk_](README.tr-TR.md),
-[_Italiana_](README.it-IT.md)
+[_Italiana_](README.it-IT.md),
+[_Deutsch_](README.de-DE.md)
 
  ☝ ملاحضة هذا المشروع مخصص للاستخدام لأغراض التعلم والبحث
 فقط ، و ** ليست ** معدة للاستخدام في **الإنتاج**
diff --git a/README.de-DE.md b/README.de-DE.md
new file mode 100644
index 0000000000..3e127c3ea0
--- /dev/null
+++ b/README.de-DE.md
@@ -0,0 +1,333 @@
+# JavaScript-Algorithmen und Datenstrukturen
+
+[![CI](https://github.com/trekhleb/javascript-algorithms/workflows/CI/badge.svg)](https://github.com/trekhleb/javascript-algorithms/actions?query=workflow%3ACI+branch%3Amaster)
+[![codecov](https://codecov.io/gh/trekhleb/javascript-algorithms/branch/master/graph/badge.svg)](https://codecov.io/gh/trekhleb/javascript-algorithms)
+
+Dieses Repository enthält JavaScript Beispiele für viele
+gängige Algorithmen und Datenstrukturen.
+
+Jeder Algorithmus und jede Datenstruktur hat eine eigene README
+mit zugehörigen Erklärungen und weiterführenden Links (einschließlich zu YouTube-Videos).
+
+_Lies dies in anderen Sprachen:_
+[_English_](https://github.com/trekhleb/javascript-algorithms/)
+[_简体中文_](README.zh-CN.md),
+[_繁體中文_](README.zh-TW.md),
+[_한국어_](README.ko-KR.md),
+[_日本語_](README.ja-JP.md),
+[_Polski_](README.pl-PL.md),
+[_Français_](README.fr-FR.md),
+[_Español_](README.es-ES.md),
+[_Português_](README.pt-BR.md),
+[_Русский_](README.ru-RU.md),
+[_Türk_](README.tr-TR.md),
+[_Italiana_](README.it-IT.md),
+[_Bahasa Indonesia_](README.id-ID.md),
+[_Українська_](README.uk-UA.md),
+[_Arabic_](README.ar-AR.md)
+
+_☝ Beachte, dass dieses Projekt nur für Lern- und Forschungszwecke gedacht ist und **nicht** für den produktiven Einsatz verwendet werden soll_
+
+## Datenstrukturen
+
+Eine Datenstruktur ist eine bestimmte Art und Weise, Daten in einem Computer so zu organisieren und zu speichern, dass sie
+effizient erreicht und verändert werden können. Genauer gesagt, ist eine Datenstruktur eine Sammlung von Werten,
+den Beziehungen zwischen ihnen und den Funktionen oder Operationen, die auf die Daten angewendet werden können.
+
+`B` - Anfänger:innen, `A` - Fortgeschrittene
+
+* `B` [Verkettete Liste (Linked List)](src/data-structures/linked-list)
+* `B` [Doppelt verkettete Liste (Doubly Linked List)](src/data-structures/doubly-linked-list)
+* `B` [Warteschlange (Queue)](src/data-structures/queue)
+* `B` [Stapelspeicher (Stack)](src/data-structures/stack)
+* `B` [Hashtabelle (Hash Table)](src/data-structures/hash-table)
+* `B` [Heap-Algorithmus (Heap)](src/data-structures/heap) - max und min Heap-Versionen
+* `B` [Vorrangwarteschlange (Priority Queue)](src/data-structures/priority-queue)
+* `A` [Trie (Trie)](src/data-structures/trie)
+* `A` [Baum (Tree)](src/data-structures/tree)
+  * `A` [Binärer Suchbaum (Binary Search Tree)](src/data-structures/tree/binary-search-tree)
+  * `A` [AVL-Baum (AVL Tree)](src/data-structures/tree/avl-tree)
+  * `A` [Rot-Schwarz-Baum (Red-Black Tree)](src/data-structures/tree/red-black-tree)
+  * `A` [Segment-Baum (Segment Tree)](src/data-structures/tree/segment-tree) - mit Min/Max/Summenbereich-Abfrage Beispiel
+  * `A` [Fenwick Baum (Fenwick Tree)](src/data-structures/tree/fenwick-tree) (Binär indizierter Baum / Binary Indexed Tree)
+* `A` [Graph (Graph)](src/data-structures/graph) (sowohl gerichtet als auch ungerichtet)
+* `A` [Union-Find-Struktur (Disjoint Set)](src/data-structures/disjoint-set)
+* `A` [Bloomfilter (Bloom Filter)](src/data-structures/bloom-filter)
+
+## Algorithmen
+
+Ein Algorithmus ist eine eindeutige Spezifikation, wie eine Klasse von Problemen zu lösen ist. Er besteht
+aus einem Satz von Regeln, die eine Abfolge von Operationen genau definieren.
+
+`B` - Anfänger:innen, `A` - Fortgeschrittene
+
+### Algorithmen nach Thema
+
+* **Mathe**
+  * `B` [Bitmanipulation (Bit Manipulation)](src/algorithms/math/bits) - Bits setzen/lesen/aktualisieren/löschen, Multiplikation/Division durch zwei negieren usw..
+  * `B` [Faktoriell (Factorial)](src/algorithms/math/factorial)
+  * `B` [Fibonacci-Zahl (Fibonacci Number)](src/algorithms/math/fibonacci) - Klassische und geschlossene Version
+  * `B` [Primfaktoren (Prime Factors)](src/algorithms/math/prime-factors) - Auffinden von Primfaktoren und deren Zählung mit Hilfe des Satz von Hardy-Ramanujan (Hardy-Ramanujan's theorem)
+  * `B` [Primzahl-Test (Primality Test)](src/algorithms/math/primality-test) (Probedivision / trial division method)
+  * `B` [Euklidischer Algorithmus (Euclidean Algorithm)](src/algorithms/math/euclidean-algorithm) - Berechnen des größten gemeinsamen Teilers (ggT)
+  * `B` [Kleinstes gemeinsames Vielfaches (Least Common Multiple)](src/algorithms/math/least-common-multiple) (kgV)
+  * `B` [Sieb des Eratosthenes (Sieve of Eratosthenes)](src/algorithms/math/sieve-of-eratosthenes) - Finden aller Primzahlen bis zu einer bestimmten Grenze
+  * `B` [Power of two (Is Power of Two)](src/algorithms/math/is-power-of-two) - Prüft, ob die Zahl eine Zweierpotenz ist (naive und bitweise Algorithmen)
+  * `B` [Pascalsches Dreieck (Pascal's Triangle)](src/algorithms/math/pascal-triangle)
+  * `B` [Komplexe Zahlen (Complex Number)](src/algorithms/math/complex-number) - Komplexe Zahlen und Grundoperationen mit ihnen
+  * `B` [Bogenmaß & Grad (Radian & Degree)](src/algorithms/math/radian) - Umrechnung von Bogenmaß in Grad und zurück
+  * `B` [Fast Powering Algorithmus (Fast Powering)](src/algorithms/math/fast-powering)
+  * `B` [Horner-Schema (Horner's method)](src/algorithms/math/horner-method) - Polynomauswertung
+  * `B` [Matrizen (Matrices)](src/algorithms/math/matrix) - Matrizen und grundlegende Matrixoperationen (Multiplikation, Transposition usw.)
+  * `B` [Euklidischer Abstand (Euclidean Distance)](src/algorithms/math/euclidean-distance) - Abstand zwischen zwei Punkten/Vektoren/Matrizen
+  * `A` [Ganzzahlige Partitionierung (Integer Partition)](src/algorithms/math/integer-partition)
+  * `A` [Quadratwurzel (Square Root)](src/algorithms/math/square-root) - Newtonverfahren (Newton's method)
+  * `A` [Liu Hui π Algorithmus (Liu Hui π Algorithm)](src/algorithms/math/liu-hui) - Näherungsweise π-Berechnungen auf Basis von N-gons
+  * `A` [Diskrete Fourier-Transformation (Discrete Fourier Transform)](src/algorithms/math/fourier-transform) - Eine Funktion der Zeit (ein Signal) in die Frequenzen zerlegen, aus denen sie sich zusammensetzt
+* **Sets**
+  * `B` [Kartesisches Produkt (Cartesian Product)](src/algorithms/sets/cartesian-product) - Produkt aus mehreren Mengen
+  * `B` [Fisher-Yates-Verfahren (Fisher–Yates Shuffle)](src/algorithms/sets/fisher-yates) - Zufällige Permutation einer endlichen Folge
+  * `A` [Potenzmenge (Power Set)](src/algorithms/sets/power-set) - Alle Teilmengen einer Menge (Bitweise und Rücksetzverfahren Lösungen(backtracking solutions))
+  * `A` [Permutation (Permutations)](src/algorithms/sets/permutations) (mit und ohne Wiederholungen)
+  * `A` [Kombination (Combinations)](src/algorithms/sets/combinations) (mit und ohne Wiederholungen)
+  * `A` [Problem der längsten gemeinsamen Teilsequenz (Longest Common Subsequence)](src/algorithms/sets/longest-common-subsequence) (LCS)
+  * `A` [Längste gemeinsame Teilsequenz (Longest Increasing Subsequence)](src/algorithms/sets/longest-increasing-subsequence)
+  * `A` [Der kürzeste gemeinsame String (Shortest Common Supersequence)](src/algorithms/sets/shortest-common-supersequence) (SCS)
+  * `A` [Rucksackproblem (Knapsack Problem)](src/algorithms/sets/knapsack-problem) - "0/1" und "Ungebunden"
+  * `A` [Das Maximum-Subarray Problem (Maximum Subarray)](src/algorithms/sets/maximum-subarray) - "Brute-Force-Methode" und "Dynamische Programmierung" (Kadane' Algorithmus)
+  * `A` [Kombinationssumme (Combination Sum)](src/algorithms/sets/combination-sum) - Alle Kombinationen finden, die eine bestimmte Summe bilden
+* **Zeichenketten (Strings)**
+  * `B` [Hamming-Abstand (Hamming Distance)](src/algorithms/string/hamming-distance) - Anzahl der Positionen, an denen die Symbole unterschiedlich sind
+  * `A` [Levenshtein-Distanz (Levenshtein Distance)](src/algorithms/string/levenshtein-distance) - Minimaler Editierabstand zwischen zwei Sequenzen
+  * `A` [Knuth-Morris-Pratt-Algorithmus (Knuth–Morris–Pratt Algorithm)](src/algorithms/string/knuth-morris-pratt) (KMP Algorithmus) - Teilstringsuche (Mustervergleich / Pattern Matching)
+  * `A` [Z-Algorithmus (Z Algorithm)](src/algorithms/string/z-algorithm) - Teilstringsuche (Mustervergleich / Pattern Matching)
+  * `A` [Rabin-Karp-Algorithmus (Rabin Karp Algorithm)](src/algorithms/string/rabin-karp) - Teilstringsuche
+  * `A` [Längstes häufiges Teilzeichenfolgenproblem (Longest Common Substring)](src/algorithms/string/longest-common-substring)
+  * `A` [Regulärer Ausdruck (Regular Expression Matching)](src/algorithms/string/regular-expression-matching)
+* **Suchen**
+  * `B` [Lineare Suche (Linear Search)](src/algorithms/search/linear-search)
+  * `B` [Sprungsuche (Jump Search)](src/algorithms/search/jump-search) (oder Blocksuche) - Suche im sortierten Array
+  * `B` [Binäre Suche (Binary Search)](src/algorithms/search/binary-search) - Suche in einem sortierten Array
+  * `B` [Interpolationssuche (Interpolation Search)](src/algorithms/search/interpolation-search) - Suche in gleichmäßig verteilt sortiertem Array
+* **Sortieren**
+  * `B` [Bubblesort (Bubble Sort)](src/algorithms/sorting/bubble-sort)
+  * `B` [Selectionsort (Selection Sort)](src/algorithms/sorting/selection-sort)
+  * `B` [Einfügesortierenmethode (Insertion Sort)](src/algorithms/sorting/insertion-sort)
+  * `B` [Haldensortierung (Heap Sort)](src/algorithms/sorting/heap-sort)
+  * `B` [Mergesort (Merge Sort)](src/algorithms/sorting/merge-sort)
+  * `B` [Quicksort (Quicksort)](src/algorithms/sorting/quick-sort) - in-place und non-in-place Implementierungen
+  * `B` [Shellsort (Shellsort)](src/algorithms/sorting/shell-sort)
+  * `B` [Countingsort (Counting Sort)](src/algorithms/sorting/counting-sort)
+  * `B` [Fachverteilen (Radix Sort)](src/algorithms/sorting/radix-sort)
+* **Verkettete Liste (Linked List)**
+  * `B` [Gerade Traversierung (Straight Traversal)](src/algorithms/linked-list/traversal)
+  * `B` [Umgekehrte Traversierung (Reverse Traversal)](src/algorithms/linked-list/reverse-traversal)
+* **Bäume**
+  * `B` [Tiefensuche (Depth-First Search)](src/algorithms/tree/depth-first-search) (DFS)
+  * `B` [Breitensuche (Breadth-First Search)](src/algorithms/tree/breadth-first-search) (BFS)
+* **Graphen**
+  * `B` [Tiefensuche (Depth-First Search)](src/algorithms/graph/depth-first-search) (DFS)
+  * `B` [Breitensuche (Breadth-First Search)](src/algorithms/graph/breadth-first-search) (BFS)
+  * `B` [Algorithmus von Kruskal (Kruskal’s Algorithm)](src/algorithms/graph/kruskal) - Finden des Spannbaum (Minimum Spanning Tree / MST) für einen gewichteten ungerichteten Graphen
+  * `A` [Dijkstra-Algorithmus (Dijkstra Algorithm)](src/algorithms/graph/dijkstra) - Finden der kürzesten Wege zu allen Knoten des Graphen von einem einzelnen Knotenpunkt aus
+  * `A` [Bellman-Ford-Algorithmus (Bellman-Ford Algorithm)](src/algorithms/graph/bellman-ford) - Finden der kürzesten Wege zu allen Knoten des Graphen von einem einzelnen Knotenpunkt aus
+  * `A` [Algorithmus von Floyd und Warshall (Floyd-Warshall Algorithm)](src/algorithms/graph/floyd-warshall) - Die kürzesten Wege zwischen allen Knotenpaaren finden
+  * `A` [Zykluserkennung (Detect Cycle)](src/algorithms/graph/detect-cycle) - Sowohl für gerichtete als auch für ungerichtete Graphen (DFS- und Disjoint-Set-basierte Versionen)
+  * `A` [Algorithmus von Prim (Prim’s Algorithm)](src/algorithms/graph/prim) - Finden des Spannbaums (Minimum Spanning Tree / MST) für einen gewichteten ungerichteten Graphen
+  * `A` [Topologische Sortierung (Topological Sorting)](src/algorithms/graph/topological-sorting) - DFS-Verfahren
+  * `A` [Artikulationspunkte (Articulation Points)](src/algorithms/graph/articulation-points) - Algorithmus von Tarjan (Tarjan's algorithm) (DFS basiert)
+  * `A` [Brücke (Bridges)](src/algorithms/graph/bridges) - DFS-basierter Algorithmus
+  * `A` [Eulerkreisproblem (Eulerian Path and Eulerian Circuit)](src/algorithms/graph/eulerian-path) - Algorithmus von Fleury (Fleury's algorithm) - Jede Kante genau einmal durchlaufen.
+  * `A` [Hamiltonkreisproblem (Hamiltonian Cycle)](src/algorithms/graph/hamiltonian-cycle) - Jeden Eckpunkt genau einmal durchlaufen.
+  * `A` [Starke Zusammenhangskomponente (Strongly Connected Components)](src/algorithms/graph/strongly-connected-components) - Kosarajus Algorithmus
+  * `A` [Problem des Handlungsreisenden (Travelling Salesman Problem)](src/algorithms/graph/travelling-salesman) - Kürzestmögliche Route, die jede Stadt besucht und zur Ausgangsstadt zurückkehrt
+* **Kryptographie**
+  * `B` [Polynomiale Streuwertfunktion(Polynomial Hash)](src/algorithms/cryptography/polynomial-hash) - Rollierende Streuwert-Funktion basierend auf Polynom
+  * `B` [Schienenzaun Chiffre (Rail Fence Cipher)](src/algorithms/cryptography/rail-fence-cipher) - Ein Transpositionsalgorithmus zur Verschlüsselung von Nachrichten
+  * `B` [Caesar-Verschlüsselung (Caesar Cipher)](src/algorithms/cryptography/caesar-cipher) - Einfache Substitutions-Chiffre
+  * `B` [Hill-Chiffre (Hill Cipher)](src/algorithms/cryptography/hill-cipher) - Substitutionschiffre basierend auf linearer Algebra
+* **Maschinelles Lernen**
+  * `B` [Künstliches Neuron (NanoNeuron)](https://github.com/trekhleb/nano-neuron) - 7 einfache JS-Funktionen, die veranschaulichen, wie Maschinen tatsächlich lernen können (Vorwärts-/Rückwärtspropagation)
+  * `B` [Nächste-Nachbarn-Klassifikation (k-NN)](src/algorithms/ml/knn) - k-nächste-Nachbarn-Algorithmus
+  * `B` [k-Means (k-Means)](src/algorithms/ml/k-means) - k-Means-Algorithmus
+* **Image Processing**
+  * `B` [Inhaltsabhängige Bildverzerrung (Seam Carving)](src/algorithms/image-processing/seam-carving) - Algorithmus zur inhaltsabhängigen Bildgrößenänderung
+* **Unkategorisiert**
+  * `B` [Türme von Hanoi (Tower of Hanoi)](src/algorithms/uncategorized/hanoi-tower)
+  * `B` [Rotationsmatrix (Square Matrix Rotation)](src/algorithms/uncategorized/square-matrix-rotation) - In-Place-Algorithmus
+  * `B` [Jump Game (Jump Game)](src/algorithms/uncategorized/jump-game) - Backtracking, dynamische Programmierung (Top-down + Bottom-up) und gierige Beispiele
+  * `B` [Eindeutige Pfade (Unique Paths)](src/algorithms/uncategorized/unique-paths) - Backtracking, dynamische Programmierung und Pascalsches Dreieck basierte Beispiele
+  * `B` [Regenterrassen (Rain Terraces)](src/algorithms/uncategorized/rain-terraces) - Auffangproblem für Regenwasser (trapping rain water problem) (dynamische Programmierung und Brute-Force-Versionen)
+  * `B` [Rekursive Treppe (Recursive Staircase)](src/algorithms/uncategorized/recursive-staircase) - Zählen der Anzahl der Wege, die nach oben führen (4 Lösungen)
+  * `B` [Beste Zeit zum Kaufen/Verkaufen von Aktien (Best Time To Buy Sell Stocks)](src/algorithms/uncategorized/best-time-to-buy-sell-stocks) - Beispiele für "Teile und Herrsche" und Beispiele für den One-Pass-Algorithmus
+  * `A` [Damenproblem (N-Queens Problem)](src/algorithms/uncategorized/n-queens)
+  * `A` [Springerproblem (Knight's Tour)](src/algorithms/uncategorized/knight-tour)
+
+### Algorithmen nach Paradigma
+
+Ein algorithmisches Paradigma ist eine generische Methode oder ein Ansatz, der dem Entwurf einer Klasse von Algorithmen zugrunde liegt. Es ist eine Abstraktion, die höher ist als der Begriff des Algorithmus. Genauso wie ein Algorithmus eine Abstraktion ist, die höher ist als ein Computerprogramm.
+
+* **Brachiale Gewalt (Brute Force)** - schaut sich alle Möglichkeiten an und wählt die beste Lösung aus
+  * `B` [Lineare Suche (Linear Search)](src/algorithms/search/linear-search)
+  * `B` [Regenterrassen (Rain Terraces)](src/algorithms/uncategorized/rain-terraces) - Auffangproblem für Regenwasser (trapping rain water problem) (dynamische Programmierung und Brute-Force-Versionen)
+  * `B` [Rekursive Treppe (Recursive Staircase)](src/algorithms/uncategorized/recursive-staircase) - Zählen der Anzahl der Wege, die nach oben führen (4 Lösungen)
+  * `A` [Das Maximum-Subarray Problem (Maximum Subarray)](src/algorithms/sets/maximum-subarray)
+  * `A` [Problem des Handlungsreisenden (Travelling Salesman Problem)](src/algorithms/graph/travelling-salesman) - Kürzestmögliche Route, die jede Stadt besucht und zur Ausgangsstadt zurückkehrt
+  * `A` [Diskrete Fourier-Transformation (Discrete Fourier Transform)](src/algorithms/math/fourier-transform) - Eine Funktion der Zeit (ein Signal) in die Frequenzen zerlegen, aus denen sie sich zusammensetzt
+* **Gierig (Greedy)** - Wählt die beste Option zum aktuellen Zeitpunkt, ohne Rücksicht auf die Zukunft
+  * `B` [Jump Game (Jump Game)](src/algorithms/uncategorized/jump-game)
+  * `A` [Rucksackproblem (Unbound Knapsack Problem)](src/algorithms/sets/knapsack-problem)
+  * `A` [Dijkstra-Algorithmus (Dijkstra Algorithm)](src/algorithms/graph/dijkstra) - Finden der kürzesten Wege zu allen Knoten des Graphen von einem einzelnen Knotenpunkt aus
+  * `A` [Algorithmus von Prim (Prim’s Algorithm)](src/algorithms/graph/prim) - Finden des Spannbaums (Minimum Spanning Tree / MST) für einen gewichteten ungerichteten Graphen
+  * `B` [Algorithmus von Kruskal (Kruskal’s Algorithm)](src/algorithms/graph/kruskal) - Finden des Spannbaum (Minimum Spanning Tree / MST) für einen gewichteten ungerichteten Graphen
+* **Teile und herrsche** - Das Problem in kleinere Teile aufteilen und diese Teile dann lösen
+  * `B` [Binäre Suche (Binary Search)](src/algorithms/search/binary-search)
+  * `B` [Türme von Hanoi (Tower of Hanoi)](src/algorithms/uncategorized/hanoi-tower)
+  * `B` [Pascalsches Dreieck (Pascal's Triangle)](src/algorithms/math/pascal-triangle)
+  * `B` [Euklidischer Algorithmus (Euclidean Algorithm)](src/algorithms/math/euclidean-algorithm) - calculate the Greatest Common Divisor (GCD)
+  * `B` [Mergesort (Merge Sort)](src/algorithms/sorting/merge-sort)
+  * `B` [Quicksort (Quicksort)](src/algorithms/sorting/quick-sort)
+  * `B` [Tiefensuche (Depth-First Search)](src/algorithms/tree/depth-first-search) (DFS)
+  * `B` [Breitensuche (Breadth-First Search)](src/algorithms/graph/depth-first-search) (DFS)
+  * `B` [Matrizen (Matrices)](src/algorithms/math/matrix) - Matrizen und grundlegende Matrixoperationen (Multiplikation, Transposition usw.)
+  * `B` [Jump Game (Jump Game)](src/algorithms/uncategorized/jump-game)
+  * `B` [Fast Powering Algorithmus (Fast Powering)](src/algorithms/math/fast-powering)
+  * `B` [Beste Zeit zum Kaufen/Verkaufen von Aktien (Best Time To Buy Sell Stocks)](src/algorithms/uncategorized/best-time-to-buy-sell-stocks) - Beispiele für "Teile und Herrsche" und Beispiele für den One-Pass-Algorithmus
+  * `A` [Permutation (Permutations)](src/algorithms/sets/permutations) (mit und ohne Wiederholungen)
+  * `A` [Kombination (Combinations)](src/algorithms/sets/combinations) (mit und ohne Wiederholungen)
+* **Dynamische Programmierung** - Eine Lösung aus zuvor gefundenen Teillösungen aufbauen
+  * `B` [Fibonacci-Zahl (Fibonacci Number)](src/algorithms/math/fibonacci)
+  * `B` [Jump Game (Jump Game)](src/algorithms/uncategorized/jump-game)
+  * `B` [Eindeutige Pfade (Unique Paths)](src/algorithms/uncategorized/unique-paths)
+  * `B` [Regenterrassen (Rain Terraces)](src/algorithms/uncategorized/rain-terraces) - Auffangproblem für Regenwasser (trapping rain water problem) (dynamische Programmierung und Brute-Force-Versionen)
+  * `B` [Rekursive Treppe (Recursive Staircase)](src/algorithms/uncategorized/recursive-staircase) - Zählen der Anzahl der Wege, die nach oben führen (4 Lösungen)
+  * `B` [Inhaltsabhängige Bildverzerrung (Seam Carving)](src/algorithms/image-processing/seam-carving) - Algorithmus zur inhaltsabhängigen Bildgrößenänderung
+  * `A` [Levenshtein-Distanz (Levenshtein Distance)](src/algorithms/string/levenshtein-distance) - Minimaler Editierabstand zwischen zwei Sequenzen
+  * `A` [Problem der längsten gemeinsamen Teilsequenz (Longest Common Subsequence)](src/algorithms/sets/longest-common-subsequence) (LCS)
+  * `A` [Längstes häufiges Teilzeichenfolgenproblem (Longest Common Substring)](src/algorithms/string/longest-common-substring)
+  * `A` [Längste gemeinsame Teilsequenz (Longest Increasing Subsequence)](src/algorithms/sets/longest-increasing-subsequence)
+  * `A` [Der kürzeste gemeinsame String (Shortest Common Supersequence)](src/algorithms/sets/shortest-common-supersequence)
+  * `A` [Rucksackproblem (0/1 Knapsack Problem)](src/algorithms/sets/knapsack-problem)
+  * `A` [Ganzzahlige Partitionierung (Integer Partition)](src/algorithms/math/integer-partition)
+  * `A` [Das Maximum-Subarray Problem (Maximum Subarray)](src/algorithms/sets/maximum-subarray)
+  * `A` [Bellman-Ford-Algorithmus (Bellman-Ford Algorithm)](src/algorithms/graph/bellman-ford) - Finden der kürzesten Wege zu allen Knoten des Graphen von einem einzelnen Knotenpunkt aus
+  * `A` [Algorithmus von Floyd und Warshall (Floyd-Warshall Algorithm)](src/algorithms/graph/floyd-warshall) - Die kürzesten Wege zwischen allen Knotenpaaren finden
+  * `A` [Regulärer Ausdruck (Regular Expression Matching)](src/algorithms/string/regular-expression-matching)
+* **Zurückverfolgung** - Ähnlich wie bei Brute-Force versuchen Sie, alle möglichen Lösungen zu generieren, aber jedes Mal, wenn Sie die nächste Lösung generieren, testen Sie, ob sie alle Bedingungen erfüllt, und fahren erst dann mit der Generierung weiterer Lösungen fort. Andernfalls gehen Sie zurück und nehmen einen anderen Weg, um eine Lösung zu finden. Normalerweise wird das DFS-Traversal des Zustandsraums verwendet.
+  * `B` [Jump Game (Jump Game)](src/algorithms/uncategorized/jump-game)
+  * `B` [Eindeutige Pfade (Unique Paths)](src/algorithms/uncategorized/unique-paths)
+  * `A` [Potenzmenge (Power Set)](src/algorithms/sets/power-set) - Alle Teilmengen einer Menge
+  * `A` [Hamiltonkreisproblem (Hamiltonian Cycle)](src/algorithms/graph/hamiltonian-cycle) - Jeden Eckpunkt genau einmal durchlaufen.
+  * `A` [Damenproblem (N-Queens Problem)](src/algorithms/uncategorized/n-queens)
+  * `A` [Springerproblem (Knight's Tour)](src/algorithms/uncategorized/knight-tour)
+  * `A` [Kombinationssumme (Combination Sum)](src/algorithms/sets/combination-sum) - Alle Kombinationen finden, die eine bestimmte Summe bilden
+* **Verzweigung & Bindung** - Merkt sich die Lösung mit den niedrigsten Kosten, die in jeder Phase der Backtracking-Suche gefunden wurde, und verwendet die Kosten der bisher gefundenen Lösung mit den niedrigsten Kosten als untere Schranke für die Kosten einer Lösung des Problems mit den geringsten Kosten, um Teillösungen zu verwerfen, deren Kosten größer sind als die der bisher gefundenen Lösung mit den niedrigsten Kosten. Normalerweise wird das BFS-Traversal in Kombination mit dem DFS-Traversal des Zustandsraumbaums verwendet.
+
+## So verwendest du dieses Repository
+
+**Alle Abhängigkeiten installieren**
+
+```
+npm install
+```
+
+**ESLint ausführen**
+
+You may want to run it to check code quality.
+
+```
+npm run lint
+```
+
+**Alle Tests ausführen**
+
+```
+npm test
+```
+
+**Tests nach Namen ausführen**
+
+```
+npm test -- 'LinkedList'
+```
+
+**Fehlerbehebung**
+
+Falls das Linting oder Testen fehlschlägt, versuche, den Ordner "node_modules" zu löschen und die npm-Pakete neu zu installieren:
+
+```
+rm -rf ./node_modules
+npm i
+```
+
+**Spielwiese**
+
+Du kannst mit Datenstrukturen und Algorithmen in der Datei `./src/playground/playground.js` herumspielen und
+dir in dieser Datei Tests schreiben `./src/playground/__test__/playground.test.js`.
+
+Dann führe einfach folgenden Befehl aus, um zu testen, ob dein Spielwiesencode wie erwartet funktioniert:
+
+```
+npm test -- 'playground'
+```
+
+## Nützliche Informationen
+
+### Referenzen
+
+[▶ Datenstrukturen und Algorithmen auf YouTube(Englisch)](https://www.youtube.com/playlist?list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
+
+### O-Notation (_Big O Notation_)
+
+Die O-Notation wird verwendet, um Algorithmen danach zu klassifizieren, wie ihre Laufzeit oder ihr Platzbedarf mit zunehmender Eingabegröße wächst. In der folgenden Tabelle finden Sie die häufigsten Wachstumsordnungen von Algorithmen, die in Big-O-Notation angegeben sind.
+
+![O-Notation Graphen](./assets/big-o-graph.png)
+
+Quelle: [Big O Cheat Sheet](http://bigocheatsheet.com/).
+
+Nachfolgend finden Sie eine Liste einiger der am häufigsten verwendeten Big O-Notationen und deren Leistungsvergleiche für unterschiedliche Größen der Eingabedaten.
+
+| Big O Notation | Berechnungen für 10 Elemente | Berechnungen für 100 Elemente | Berechnungen für 1000 Elemente |
+| -------------- | ---------------------------- | ----------------------------- | ------------------------------ |
+| **O(1)**       | 1                            | 1                             | 1                              |
+| **O(log N)**   | 3                            | 6                             | 9                              |
+| **O(N)**       | 10                           | 100                           | 1000                           |
+| **O(N log N)** | 30                           | 600                           | 9000                           |
+| **O(N^2)**     | 100                          | 10000                         | 1000000                        |
+| **O(2^N)**     | 1024                         | 1.26e+29                      | 1.07e+301                      |
+| **O(N!)**      | 3628800                      | 9.3e+157                      | 4.02e+2567                     |
+
+### Komplexität von Datenstrukturoperationen
+
+| Datenstruktur          | Zugriff auf | Suche  | Einfügen | Löschung | Kommentare                                                      |
+| ---------------------- | :---------: | :----: | :------: | :------: | :-------------------------------------------------------------- |
+| **Array**              |      1      |   n    |    n     |    n     |                                                                 |
+| **Stack**              |      n      |   n    |    1     |    1     |                                                                 |
+| **Queue**              |      n      |   n    |    1     |    1     |                                                                 |
+| **Linked List**        |      n      |   n    |    1     |    n     |                                                                 |
+| **Hash Table**         |      -      |   n    |    n     |    n     | Im Falle einer perfekten Hash-Funktion wären die Kosten O(1)    |
+| **Binary Search Tree** |      n      |   n    |    n     |    n     | Im Falle eines ausgeglichenen Baumes wären die Kosten O(log(n)) |
+| **B-Tree**             |   log(n)    | log(n) |  log(n)  |  log(n)  |                                                                 |
+| **Red-Black Tree**     |   log(n)    | log(n) |  log(n)  |  log(n)  |                                                                 |
+| **AVL Tree**           |   log(n)    | log(n) |  log(n)  |  log(n)  |                                                                 |
+| **Bloom Filter**       |      -      |   1    |    1     |    -     | Falschpostive sind bei der Suche möglichen                      |
+
+### Komplexität von Array-Sortieralgorithmen
+
+| Name               |    Bester     |      Durchschnitt       |        Schlechtester        | Speicher | Stabil | Kommentar                                                                  |
+| ------------------ | :-----------: | :---------------------: | :-------------------------: | :------: | :----: | :------------------------------------------------------------------------- |
+| **Bubble sort**    |       n       |      n<sup>2</sup>      |        n<sup>2</sup>        |    1     |   JA   |                                                                            |
+| **Insertion sort** |       n       |      n<sup>2</sup>      |        n<sup>2</sup>        |    1     |   Ja   |                                                                            |
+| **Selection sort** | n<sup>2</sup> |      n<sup>2</sup>      |        n<sup>2</sup>        |    1     |  Nein  |                                                                            |
+| **Heap sort**      | n&nbsp;log(n) |      n&nbsp;log(n)      |        n&nbsp;log(n)        |    1     |  Nein  |                                                                            |
+| **Merge sort**     | n&nbsp;log(n) |      n&nbsp;log(n)      |        n&nbsp;log(n)        |    n     |   Ja   |                                                                            |
+| **Quick sort**     | n&nbsp;log(n) |      n&nbsp;log(n)      |        n<sup>2</sup>        |  log(n)  |  Nein  | Quicksort wird normalerweise in-place mit O(log(n)) Stapelplatz ausgeführt |
+| **Shell sort**     | n&nbsp;log(n) | abhängig von Spaltfolge | n&nbsp;(log(n))<sup>2</sup> |    1     |  Nein  |                                                                            |
+| **Counting sort**  |     n + r     |          n + r          |            n + r            |  n + r   |   Ja   | r - größte Zahl im Array                                                   |
+| **Radix sort**     |    n \* k     |         n \* k          |           n \* k            |  n + k   |   Ja   | k - Länge des längsten Schlüssels                                          |
+
+## Projekt-Unterstützer
+
+> Du kannst dieses Projekt unterstützen über ❤️️ [GitHub](https://github.com/sponsors/trekhleb) or ❤️️ [Patreon](https://www.patreon.com/trekhleb).
+
+[Leute, die dieses Projekt unterstützen](https://github.com/trekhleb/javascript-algorithms/blob/master/BACKERS.md) `∑ = 0`
diff --git a/README.es-ES.md b/README.es-ES.md
index fa1fd340c6..f350ee059e 100644
--- a/README.es-ES.md
+++ b/README.es-ES.md
@@ -23,7 +23,8 @@ _Léelo en otros idiomas:_
 [_Italiana_](README.it-IT.md),
 [_Bahasa Indonesia_](README.id-ID.md),
 [_Українська_](README.uk-UA.md),
-[_Arabic_](README.ar-AR.md)
+[_Arabic_](README.ar-AR.md),
+[_Deutsch_](README.de-DE.md)
 
 *☝ Nótese que este proyecto está pensado con fines de aprendizaje e investigación,
 y **no** para ser usado en producción.*
diff --git a/README.fr-FR.md b/README.fr-FR.md
index 024a3b1904..4508340aec 100644
--- a/README.fr-FR.md
+++ b/README.fr-FR.md
@@ -24,7 +24,8 @@ _Lisez ceci dans d'autres langues:_
 [_Italiana_](README.it-IT.md),
 [_Bahasa Indonesia_](README.id-ID.md),
 [_Українська_](README.uk-UA.md),
-[_Arabic_](README.ar-AR.md)
+[_Arabic_](README.ar-AR.md),
+[_Deutsch_](README.de-DE.md)
 
 ## Data Structures
 
diff --git a/README.id-ID.md b/README.id-ID.md
index 2a258f973c..2f5212ac64 100644
--- a/README.id-ID.md
+++ b/README.id-ID.md
@@ -21,7 +21,8 @@ _Baca ini dalam bahasa yang lain:_
 [_Türk_](README.tr-TR.md),
 [_Italiana_](README.it-IT.md),
 [_Українська_](README.uk-UA.md),
-[_Arabic_](README.ar-AR.md)
+[_Arabic_](README.ar-AR.md),
+[_Deutsch_](README.de-DE.md)
 
 _☝ Perhatikan bahwa proyek ini hanya dimaksudkan untuk tujuan pembelajaran dan riset, dan **tidak** dimaksudkan untuk digunakan sebagai produksi._
 
diff --git a/README.it-IT.md b/README.it-IT.md
index 9d8c664f6a..d74befd683 100644
--- a/README.it-IT.md
+++ b/README.it-IT.md
@@ -20,7 +20,8 @@ _Leggilo in altre lingue:_
 [_Türk_](README.tr-TR.md),
 [_Bahasa Indonesia_](README.id-ID.md),
 [_Українська_](README.uk-UA.md),
-[_Arabic_](README.ar-AR.md)
+[_Arabic_](README.ar-AR.md),
+[_Deutsch_](README.de-DE.md)
 
 *☝ Si noti che questo progetto è destinato ad essere utilizzato solo per l'apprendimento e la ricerca e non è destinato ad essere utilizzato per il commercio.*
 
diff --git a/README.ja-JP.md b/README.ja-JP.md
index af2c887c2c..a1c13211a0 100644
--- a/README.ja-JP.md
+++ b/README.ja-JP.md
@@ -23,7 +23,8 @@ _Read this in other languages:_
 [_Italiana_](README.it-IT.md),
 [_Bahasa Indonesia_](README.id-ID.md),
 [_Українська_](README.uk-UA.md),
-[_Arabic_](README.ar-AR.md)
+[_Arabic_](README.ar-AR.md),
+[_Deutsch_](README.de-DE.md)
 
 ## データ構造
 
diff --git a/README.ko-KR.md b/README.ko-KR.md
index 02f35d0250..e9b77dca27 100644
--- a/README.ko-KR.md
+++ b/README.ko-KR.md
@@ -22,7 +22,8 @@ _Read this in other languages:_
 [_Italiana_](README.it-IT.md),
 [_Bahasa Indonesia_](README.id-ID.md),
 [_Українська_](README.uk-UA.md),
-[_Arabic_](README.ar-AR.md)
+[_Arabic_](README.ar-AR.md),
+[_Deutsch_](README.de-DE.md)
 
 ## 자료 구조
 
diff --git a/README.md b/README.md
index a9fc7b5ea0..d16c264d1e 100644
--- a/README.md
+++ b/README.md
@@ -24,7 +24,8 @@ _Read this in other languages:_
 [_Italiana_](README.it-IT.md),
 [_Bahasa Indonesia_](README.id-ID.md),
 [_Українська_](README.uk-UA.md),
-[_Arabic_](README.ar-AR.md)
+[_Arabic_](README.ar-AR.md),
+[_Deutsch_](README.de-DE.md)
 
 *☝ Note that this project is meant to be used for learning and researching purposes
 only, and it is **not** meant to be used for production.*
diff --git a/README.pl-PL.md b/README.pl-PL.md
index 08dc09b6aa..235d0d47d6 100644
--- a/README.pl-PL.md
+++ b/README.pl-PL.md
@@ -24,7 +24,8 @@ _Read this in other languages:_
 [_Italiana_](README.it-IT.md),
 [_Bahasa Indonesia_](README.id-ID.md),
 [_Українська_](README.uk-UA.md),
-[_Arabic_](README.ar-AR.md)
+[_Arabic_](README.ar-AR.md),
+[_Deutsch_](README.de-DE.md)
 
 ## Struktury Danych
 
diff --git a/README.pt-BR.md b/README.pt-BR.md
index baffbc3179..c410fda651 100644
--- a/README.pt-BR.md
+++ b/README.pt-BR.md
@@ -24,7 +24,8 @@ _Leia isto em outros idiomas:_
 [_Italiana_](README.it-IT.md),
 [_Bahasa Indonesia_](README.id-ID.md),
 [_Українська_](README.uk-UA.md),
-[_Arabic_](README.ar-AR.md)
+[_Arabic_](README.ar-AR.md),
+[_Deutsch_](README.de-DE.md)
 
 ## Estrutura de Dados
 
diff --git a/README.ru-RU.md b/README.ru-RU.md
index 32f4b2f526..ef9e9444a3 100644
--- a/README.ru-RU.md
+++ b/README.ru-RU.md
@@ -21,7 +21,8 @@ _Читать на других языках:_
 [_Italiana_](README.it-IT.md),
 [_Bahasa Indonesia_](README.id-ID.md),
 [_Українська_](README.uk-UA.md),
-[_Arabic_](README.ar-AR.md)
+[_Arabic_](README.ar-AR.md),
+[_Deutsch_](README.de-DE.md)
 
 *☝ Замечание: этот репозиторий предназначен для учебно-исследовательских целей (**не** для использования в продакшн-системах).*
 
diff --git a/README.tr-TR.md b/README.tr-TR.md
index f7ed57fc91..fff640c415 100644
--- a/README.tr-TR.md
+++ b/README.tr-TR.md
@@ -22,7 +22,8 @@ _Read this in other languages:_
 [_Italiana_](README.it-IT.md),
 [_Bahasa Indonesia_](README.id-ID.md),
 [_Українська_](README.uk-UA.md),
-[_Arabic_](README.ar-AR.md)
+[_Arabic_](README.ar-AR.md),
+[_Deutsch_](README.de-DE.md)
 
 *☝ Not, bu proje araştırma ve öğrenme amacı ile yapılmış
 olup üretim için **yaplılmamıştır**.*
diff --git a/README.uk-UA.md b/README.uk-UA.md
index 4391ed1992..6fdd7b4c13 100644
--- a/README.uk-UA.md
+++ b/README.uk-UA.md
@@ -21,7 +21,8 @@ _Вивчення матеріалу на інших мовах:_
 [_Türk_](README.tr-TR.md),
 [_Italiana_](README.it-IT.md),
 [_Bahasa Indonesia_](README.id-ID.md),
-[_Arabic_](README.ar-AR.md)
+[_Arabic_](README.ar-AR.md),
+[_Deutsch_](README.de-DE.md)
 
 *☝ Зверніть увагу! Даний проект призначений лише для навчальних та дослідницьких цілей, і він **не** призначений для виробництва (продакшн).*
 
diff --git a/README.zh-CN.md b/README.zh-CN.md
index 35a3733fc3..22b50d405c 100644
--- a/README.zh-CN.md
+++ b/README.zh-CN.md
@@ -21,7 +21,8 @@ _Read this in other languages:_
 [_Italiana_](README.it-IT.md),
 [_Bahasa Indonesia_](README.id-ID.md),
 [_Українська_](README.uk-UA.md),
-[_Arabic_](README.ar-AR.md)
+[_Arabic_](README.ar-AR.md),
+[_Deutsch_](README.de-DE.md)
 
 *注意：这个项目仅用于学习和研究，**不是**用于生产环境。*
 
diff --git a/README.zh-TW.md b/README.zh-TW.md
index 4a09b8433e..bf90fbbe62 100644
--- a/README.zh-TW.md
+++ b/README.zh-TW.md
@@ -20,7 +20,8 @@ _Read this in other languages:_
 [_Italiana_](README.it-IT.md),
 [_Bahasa Indonesia_](README.id-ID.md),
 [_Українська_](README.uk-UA.md),
-[_Arabic_](README.ar-AR.md)
+[_Arabic_](README.ar-AR.md),
+[_Deutsch_](README.de-DE.md)
 
 ## 資料結構
 

From 464a84bc7cb8fcc9c78ccb9fab0d77d978e8363c Mon Sep 17 00:00:00 2001
From: justforever <y.c.chen217@gmail.com>
Date: Thu, 6 May 2021 12:56:40 +0800
Subject: [PATCH 089/264] Update README.zh-TW.md (#690)

---
 README.zh-TW.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.zh-TW.md b/README.zh-TW.md
index bf90fbbe62..ddf043d7af 100644
--- a/README.zh-TW.md
+++ b/README.zh-TW.md
@@ -215,7 +215,7 @@ npm test -- 'playground'
 
 | 名稱                   | 最佳      | 平均      | 最差          | 記憶體    | 穩定      |
 | ---------------------- | :-------: | :-------: | :-----------: | :-------: | :-------: |
-| **氣派排序**           | n         | n^2       | n^2           | 1         | Yes       |
+| **氣泡排序**           | n         | n^2       | n^2           | 1         | Yes       |
 | **插入排序**           | n         | n^2       | n^2           | 1         | Yes       |
 | **選擇排序**           | n^2       | n^2       | n^2           | 1         | No        |
 | **Heap 排序**          | n log(n)  | n log(n)  | n log(n)      | 1         | No        |

From 5ffab573ca4610c3ea6bd00709883b0a2ec5b898 Mon Sep 17 00:00:00 2001
From: Freivin Campbell <Freivincampbell@users.noreply.github.com>
Date: Wed, 5 May 2021 23:00:10 -0600
Subject: [PATCH 090/264] Create README.es-ES.md (#680)

new translation added
---
 .../doubly-linked-list/README.es-ES.md        | 102 ++++++++++++++++++
 1 file changed, 102 insertions(+)
 create mode 100644 src/data-structures/doubly-linked-list/README.es-ES.md

diff --git a/src/data-structures/doubly-linked-list/README.es-ES.md b/src/data-structures/doubly-linked-list/README.es-ES.md
new file mode 100644
index 0000000000..0736d499ac
--- /dev/null
+++ b/src/data-structures/doubly-linked-list/README.es-ES.md
@@ -0,0 +1,102 @@
+# Lista doblemente enlazada
+
+_Lea esto en otros idiomas:_
+[_Русский_](README.ru-RU.md),
+[_简体中文_](README.zh-CN.md),
+[_日本語_](README.ja-JP.md),
+[_Português_](README.pt-BR.md)
+[_한국어_](README.ko-KR.md)
+
+En informática, una **lista doblemente enlazada** es una estructura de datos enlazados que consta de un conjunto de registros enlazados secuencialmente llamados nodos. Cada nodo contiene dos campos, llamados enlaces, que son referencias al nodo anterior y al siguiente en la secuencia de nodos. Los enlaces anterior y siguiente de los nodos inicial y final, respectivamente, apuntan a algún tipo de terminador, normalmente un nodo centinela o nulo, para facilitar el recorrido de la lista. Si solo hay un ganglio centinela, la lista se enlaza circularmente a través del ganglio centinela. Puede conceptualizarse como dos listas enlazadas individualmente formadas a partir de los mismos elementos de datos, pero en órdenes secuenciales opuestos.
+
+![Lista doblemente enlazada](https://upload.wikimedia.org/wikipedia/commons/5/5e/Doubly-linked-list.svg)
+
+Los dos enlaces de nodo permiten recorrer la lista en cualquier dirección. Si bien agregar o eliminar un nodo en una lista doblemente enlazada requiere cambiar más enlaces que las mismas operaciones en una lista enlazada individualmente, las operaciones son más simples y potencialmente más eficientes (para nodos que no sean los primeros) porque no hay necesidad de realizar un seguimiento de el nodo anterior durante el recorrido o no es necesario recorrer la lista para encontrar el nodo anterior, de modo que se pueda modificar su enlace.
+
+## Pseudocódigo para operaciones básicas
+
+### Insertar
+
+```text
+Add(value)
+  Pre: value is the value to add to the list
+  Post: value has been placed at the tail of the list
+  n ← node(value)
+  if head = ø
+    head ← n
+    tail ← n
+  else
+    n.previous ← tail
+    tail.next ← n
+    tail ← n
+  end if
+end Add
+```
+
+### Eliminar
+
+```text
+Remove(head, value)
+  Pre: head is the head node in the list
+       value is the value to remove from the list
+  Post: value is removed from the list, true; otherwise false
+  if head = ø
+    return false
+  end if
+  if value = head.value
+    if head = tail
+      head ← ø
+      tail ← ø
+    else
+      head ← head.next
+      head.previous ← ø
+    end if
+    return true
+  end if
+  n ← head.next
+  while n != ø and value !== n.value
+    n ← n.next
+  end while
+  if n = tail
+    tail ← tail.previous
+    tail.next ← ø
+    return true
+  else if n != ø
+    n.previous.next ← n.next
+    n.next.previous ← n.previous
+    return true
+  end if
+  return false
+end Remove
+```
+
+### Recorrido Inverso
+
+```text
+ReverseTraversal(tail)
+  Pre: tail is the node of the list to traverse
+  Post: the list has been traversed in reverse order
+  n ← tail
+  while n != ø
+    yield n.value
+    n ← n.previous
+  end while
+end Reverse Traversal
+```
+
+## Complejidades
+
+## Complejidad del Tiempo
+
+| Acceso    | Busqueda    | Inserción | Supresión  |
+| :-------: | :-------: | :-------: | :-------: |
+| O(n)      | O(n)      | O(1)      | O(n)      |
+
+### Complejidad del Espacio
+
+O(n)
+
+## Referencias
+
+- [Wikipedia](https://en.wikipedia.org/wiki/Doubly_linked_list)
+- [YouTube](https://www.youtube.com/watch?v=JdQeNxWCguQ&t=7s&index=72&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)

From 22b323e6b112a85210369f48bf9044d9fa9c6371 Mon Sep 17 00:00:00 2001
From: CodingInvoker <71058225+CodingInvoker@users.noreply.github.com>
Date: Thu, 6 May 2021 13:02:52 +0800
Subject: [PATCH 091/264] update linkedlist comment (#687)

Co-authored-by: Jiachen Zhou <jiachen.zhou@rea-group.com>
Co-authored-by: Oleksii Trekhleb <trehleb@gmail.com>
---
 src/data-structures/linked-list/LinkedList.js | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/data-structures/linked-list/LinkedList.js b/src/data-structures/linked-list/LinkedList.js
index 1fb0b5eaf4..71c2b49755 100644
--- a/src/data-structures/linked-list/LinkedList.js
+++ b/src/data-structures/linked-list/LinkedList.js
@@ -65,7 +65,7 @@ export default class LinkedList {
 
     let deletedNode = null;
 
-    // If the head must be deleted then make next node that is differ
+    // If the head must be deleted then make next node that is different
     // from the head to be a new head.
     while (this.head && this.compare.equal(this.head.value, value)) {
       deletedNode = this.head;

From cb50e4e9f394ebaf8172f71bc31dd2f68b1417d4 Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Thu, 6 May 2021 07:05:27 +0200
Subject: [PATCH 092/264] Add link to Spanish translation in Doubly-Linked list
 README.

---
 .../doubly-linked-list/README.md              | 39 ++++++++++---------
 1 file changed, 20 insertions(+), 19 deletions(-)

diff --git a/src/data-structures/doubly-linked-list/README.md b/src/data-structures/doubly-linked-list/README.md
index c64b51262d..703520aaf4 100644
--- a/src/data-structures/doubly-linked-list/README.md
+++ b/src/data-structures/doubly-linked-list/README.md
@@ -4,26 +4,27 @@ _Read this in other languages:_
 [_Русский_](README.ru-RU.md),
 [_简体中文_](README.zh-CN.md),
 [_日本語_](README.ja-JP.md),
-[_Português_](README.pt-BR.md)
-[_한국어_](README.ko-KR.md)
-
-In computer science, a **doubly linked list** is a linked data structure that 
-consists of a set of sequentially linked records called nodes. Each node contains 
-two fields, called links, that are references to the previous and to the next 
-node in the sequence of nodes. The beginning and ending nodes' previous and next 
-links, respectively, point to some kind of terminator, typically a sentinel 
-node or null, to facilitate the traversal of the list. If there is only one 
-sentinel node, then the list is circularly linked via the sentinel node. It can 
-be conceptualized as two singly linked lists formed from the same data items, 
+[_Português_](README.pt-BR.md),
+[_한국어_](README.ko-KR.md),
+[_Español_](README.es-ES.md),
+
+In computer science, a **doubly linked list** is a linked data structure that
+consists of a set of sequentially linked records called nodes. Each node contains
+two fields, called links, that are references to the previous and to the next
+node in the sequence of nodes. The beginning and ending nodes' previous and next
+links, respectively, point to some kind of terminator, typically a sentinel
+node or null, to facilitate the traversal of the list. If there is only one
+sentinel node, then the list is circularly linked via the sentinel node. It can
+be conceptualized as two singly linked lists formed from the same data items,
 but in opposite sequential orders.
 
 ![Doubly Linked List](https://upload.wikimedia.org/wikipedia/commons/5/5e/Doubly-linked-list.svg)
 
-The two node links allow traversal of the list in either direction. While adding 
-or removing a node in a doubly linked list requires changing more links than the 
-same operations on a singly linked list, the operations are simpler and 
-potentially more efficient (for nodes other than first nodes) because there 
-is no need to keep track of the previous node during traversal or no need 
+The two node links allow traversal of the list in either direction. While adding
+or removing a node in a doubly linked list requires changing more links than the
+same operations on a singly linked list, the operations are simpler and
+potentially more efficient (for nodes other than first nodes) because there
+is no need to keep track of the previous node during traversal or no need
 to traverse the list to find the previous node, so that its link can be modified.
 
 ## Pseudocode for Basic Operations
@@ -45,7 +46,7 @@ Add(value)
   end if
 end Add
 ```
-    
+
 ### Delete
 
 ```text
@@ -82,7 +83,7 @@ Remove(head, value)
   return false
 end Remove
 ```
-    
+
 ### Reverse Traversal
 
 ```text
@@ -96,7 +97,7 @@ ReverseTraversal(tail)
   end while
 end Reverse Traversal
 ```
-    
+
 ## Complexities
 
 ## Time Complexity

From 8a24fbfac94dc5d446d51768eaa062637a6c1a16 Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Fri, 14 May 2021 09:56:18 +0200
Subject: [PATCH 093/264] Adding more details on how to run the playground code
 to address the issue #705.

---
 src/playground/__test__/playground.test.js |  7 +++++--
 src/playground/playground.js               | 13 ++++++++++++-
 2 files changed, 17 insertions(+), 3 deletions(-)

diff --git a/src/playground/__test__/playground.test.js b/src/playground/__test__/playground.test.js
index 501a87a728..84a3e8301f 100644
--- a/src/playground/__test__/playground.test.js
+++ b/src/playground/__test__/playground.test.js
@@ -1,5 +1,8 @@
+import playground from '../playground';
+
 describe('playground', () => {
-  it('should perform playground tasks', () => {
-    // Place your playground tests here.
+  it('should return correct results', () => {
+    // Replace the next dummy test with your playground function tests.
+    expect(playground()).toBe(120);
   });
 });
diff --git a/src/playground/playground.js b/src/playground/playground.js
index 7872c9e3b8..b8c5b210bc 100644
--- a/src/playground/playground.js
+++ b/src/playground/playground.js
@@ -1 +1,12 @@
-// Place your playground code here.
+// Import any algorithmic dependencies you need for your playground code here.
+import factorial from '../algorithms/math/factorial/factorial';
+
+// Write your playground code inside the playground() function.
+// Test your code from __tests__/playground.test.js
+// Launch playground tests by running: npm test -- 'playground'
+function playground() {
+  // Replace the next line with your playground code.
+  return factorial(5);
+}
+
+export default playground;

From 6d2d8c9379873d0da2b1262a14dd26d0f9779522 Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Tue, 18 May 2021 08:44:13 +0200
Subject: [PATCH 094/264] Testing Codecov integration without web-hooks.

---
 src/utils/comparator/Comparator.js | 1 +
 1 file changed, 1 insertion(+)

diff --git a/src/utils/comparator/Comparator.js b/src/utils/comparator/Comparator.js
index 12957d2d73..f5c41b5c18 100644
--- a/src/utils/comparator/Comparator.js
+++ b/src/utils/comparator/Comparator.js
@@ -1,5 +1,6 @@
 export default class Comparator {
   /**
+   * Constructor.
    * @param {function(a: *, b: *)} [compareFunction] - It may be custom compare function that, let's
    * say may compare custom objects together.
    */

From ee35bd6240af55d3353934cb50261c9e256d1326 Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Wed, 26 May 2021 10:29:05 +0200
Subject: [PATCH 095/264] Testing Codecov integration without web-hooks.

---
 README.ar-AR.md | 2 ++
 README.de-DE.md | 3 +++
 README.es-ES.md | 2 ++
 README.fr-FR.md | 1 +
 README.id-ID.md | 2 ++
 README.it-IT.md | 2 ++
 README.ja-JP.md | 2 ++
 README.ko-KR.md | 2 ++
 README.md       | 2 ++
 README.pl-PL.md | 2 ++
 README.pt-BR.md | 2 ++
 README.ru-RU.md | 2 ++
 README.tr-TR.md | 2 ++
 README.uk-UA.md | 2 ++
 README.zh-CN.md | 2 ++
 README.zh-TW.md | 2 ++
 16 files changed, 32 insertions(+)

diff --git a/README.ar-AR.md b/README.ar-AR.md
index 797006b6ef..3514bce12f 100644
--- a/README.ar-AR.md
+++ b/README.ar-AR.md
@@ -321,3 +321,5 @@ npm test -- 'playground'
 > يمكنك دعم هذا المشروع عبر ❤️️ [GitHub](https://github.com/sponsors/trekhleb) أو ❤️️ [Patreon](https://www.patreon.com/trekhleb).
 
 [الناس الذين يدعمون هذا المشروع](https://github.com/trekhleb/javascript-algorithms/blob/master/BACKERS.md) `∑ = 0`
+
+> ℹ️ Some more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev)
diff --git a/README.de-DE.md b/README.de-DE.md
index 3e127c3ea0..bd250ab3b0 100644
--- a/README.de-DE.md
+++ b/README.de-DE.md
@@ -331,3 +331,6 @@ Nachfolgend finden Sie eine Liste einiger der am häufigsten verwendeten Big O-N
 > Du kannst dieses Projekt unterstützen über ❤️️ [GitHub](https://github.com/sponsors/trekhleb) or ❤️️ [Patreon](https://www.patreon.com/trekhleb).
 
 [Leute, die dieses Projekt unterstützen](https://github.com/trekhleb/javascript-algorithms/blob/master/BACKERS.md) `∑ = 0`
+
+> ℹ️ Some more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev)
+
diff --git a/README.es-ES.md b/README.es-ES.md
index f350ee059e..b5246bd61d 100644
--- a/README.es-ES.md
+++ b/README.es-ES.md
@@ -299,3 +299,5 @@ frente a diferentes tamaños de los datos de entrada.
 | **Shellsort**                    | n&nbsp;log(n) | depende de la secuencia de huecos | n&nbsp;(log(n))<sup>2</sup> |   1   |   No   |                                                               |
 | **Ordenamiento por cuentas**     |     n + r     |          n + r          |            n + r            | n + r   |  Si     | r - mayor número en el arreglo                                |
 | **Ordenamiento Radix**           |    n \* k     |         n \* k          |           n \* k            | n + k   |  Si     | k - largo de la llave más larga                                     |
+
+> ℹ️ Some more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev)
diff --git a/README.fr-FR.md b/README.fr-FR.md
index 4508340aec..aa7a9007a3 100644
--- a/README.fr-FR.md
+++ b/README.fr-FR.md
@@ -293,3 +293,4 @@ comparaisons de performance suivant différentes tailles pour les données d'ent
 | **Tri Shell**     | n&nbsp;log(n) | dépend du gap séquence | n&nbsp;(log(n))<sup>2</sup> |    1    |  Non   |                                                                                      |
 | **Tri Comptage**  |     n + r     |         n + r          |            n + r            |  n + r  |  Oui   | r - le plus grand nombre dans la liste                                               |
 | **Tri Radix**     |    n \* k     |         n \* k         |           n \* k            |  n + k  |  Non   | k - longueur du plus long index                                                      |
+> ℹ️ Some more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev)
diff --git a/README.id-ID.md b/README.id-ID.md
index 2f5212ac64..f1ad648258 100644
--- a/README.id-ID.md
+++ b/README.id-ID.md
@@ -304,3 +304,5 @@ Di bawah ini adalah daftar dari beberapa notasi _Bog O_ yang sering digunakan da
 > Anda dapat mendukung proyek ini via ❤️️ [GitHub](https://github.com/sponsors/trekhleb) atau ❤️️ [Patreon](https://www.patreon.com/trekhleb).
 
 [Orang-orang yang mendukung proyek ini](https://github.com/trekhleb/javascript-algorithms/blob/master/BACKERS.md) `∑ = 1`
+
+> ℹ️ Some more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev)
diff --git a/README.it-IT.md b/README.it-IT.md
index d74befd683..5947b92e75 100644
--- a/README.it-IT.md
+++ b/README.it-IT.md
@@ -297,3 +297,5 @@ Nella tabella qua sotto ci sono riportate la lista delle notazioni Big O più us
 | **Shell sort**        | n&nbsp;log(n)   | dipende dagli spazi vuoti nella sequenza  | n&nbsp;(log(n))<sup>2</sup>  | 1         | No         |           |
 | **Counting sort**     | n + r           | n + r               | n + r               | n + r     | Yes       | r - numero più grande nell'array |
 | **Radix sort**        | n * k           | n * k               | n * k               | n + k     | Yes       | k - lunghezza della chiave più grande |
+
+> ℹ️ Some more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev)
diff --git a/README.ja-JP.md b/README.ja-JP.md
index a1c13211a0..30a9979908 100644
--- a/README.ja-JP.md
+++ b/README.ja-JP.md
@@ -296,3 +296,5 @@ npm test -- 'playground'
 | **Shell sort**        | n&nbsp;log(n)   | depends on gap sequence   | n&nbsp;(log(n))<sup>2</sup>  | 1         | No         |           |
 | **Counting sort**     | n + r           | n + r               | n + r               | n + r     | Yes       | r - biggest number in array |
 | **Radix sort**        | n * k           | n * k               | n * k               | n + k     | Yes       | k - length of longest key |
+
+> ℹ️ Some more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev)
diff --git a/README.ko-KR.md b/README.ko-KR.md
index e9b77dca27..8bdb98b837 100644
--- a/README.ko-KR.md
+++ b/README.ko-KR.md
@@ -277,3 +277,5 @@ Source: [Big O Cheat Sheet](http://bigocheatsheet.com/).
 | **셸 정렬**            | n&nbsp;log(n)   | 간격 순서에 영향을 받습니다.   | n&nbsp;(log(n))<sup>2</sup>  | 1         | No         |           |
 | **계수 정렬**          | n + r           | n + r               | n + r               | n + r     | Yes              | r - 배열내 가장 큰 수 |
 | **기수 정렬**          | n * k           | n * k               | n * k               | n + k     | Yes              | k - 키값의 최대 길이 |
+
+> ℹ️ Some more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev)
diff --git a/README.md b/README.md
index d16c264d1e..a589d710e1 100644
--- a/README.md
+++ b/README.md
@@ -343,3 +343,5 @@ Below is the list of some of the most used Big O notations and their performance
 > You may support this project via ❤️️ [GitHub](https://github.com/sponsors/trekhleb) or ❤️️ [Patreon](https://www.patreon.com/trekhleb).
 
 [Folks who are backing this project](https://github.com/trekhleb/javascript-algorithms/blob/master/BACKERS.md) `∑ = 0`
+
+> ℹ️ Some more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev)
diff --git a/README.pl-PL.md b/README.pl-PL.md
index 235d0d47d6..cc20e947e7 100644
--- a/README.pl-PL.md
+++ b/README.pl-PL.md
@@ -289,3 +289,5 @@ Poniżej umieszczamy listę najbardziej używanych Big O notacji i ich porównan
 | **Sortowanie Shella**               | n&nbsp;log(n)   | zależy od luki w układzie   | n&nbsp;(log(n))<sup>2</sup>  | 1         | No         |           |
 | **Sortowanie przez zliczanie**      | n + r           | n + r               | n + r               | n + r     | Yes         | r - największy numer w tablicy|
 | **Sortowanie Radix**                | n * k           | n * k               | n * k               | n + k     | Yes         | k -długość najdłuższego klucza |
+
+> ℹ️ Some more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev)
diff --git a/README.pt-BR.md b/README.pt-BR.md
index c410fda651..cc3b9f2191 100644
--- a/README.pt-BR.md
+++ b/README.pt-BR.md
@@ -290,3 +290,5 @@ Abaixo está a lista de algumas das notações Big O mais usadas e suas compara
 | **Shell sort**        | n&nbsp;log(n)   | depende da sequência de lacunas | n&nbsp;(log(n))<sup>2</sup>     | 1      | Não    |                   |
 | **Counting sort**     | n + r           | n + r               | n + r               | n + r     | Sim       | r - maior número na matriz          |
 | **Radix sort**        | n * k           | n * k               | n * k               | n + k     | Sim       | k - comprimento da chave mais longa |
+
+> ℹ️ Some more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev)
diff --git a/README.ru-RU.md b/README.ru-RU.md
index ef9e9444a3..d5c2c69c6f 100644
--- a/README.ru-RU.md
+++ b/README.ru-RU.md
@@ -295,3 +295,5 @@ npm test -- 'playground'
 | **Сортировка Шелла**       | n&nbsp;log(n) | зависит от выбранных шагов | n&nbsp;(log(n))<sup>2</sup>  | 1      | Нет          |           |
 | **Сортировка подсчётом**   | n + r         | n + r          | n + r         | n + r  | Да           | r — наибольшее число в массиве |
 | **Поразрядная сортировка** | n * k         | n * k          | n * k         | n + k  | Да           | k — длина самого длинного ключа |
+
+> ℹ️ Some more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev)
diff --git a/README.tr-TR.md b/README.tr-TR.md
index fff640c415..73f3077e1e 100644
--- a/README.tr-TR.md
+++ b/README.tr-TR.md
@@ -315,3 +315,5 @@ Altta Big O notations ve farklı input boyutlarına karşın yapılmış perform
 ## Projeyi Destekleme
 
 Bu projeyi buradan destekleyebilirsiniz ❤️️ [GitHub](https://github.com/sponsors/trekhleb) veya ❤️️ [Patreon](https://www.patreon.com/trekhleb).
+
+> ℹ️ Some more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev)
diff --git a/README.uk-UA.md b/README.uk-UA.md
index 6fdd7b4c13..be4d923b70 100644
--- a/README.uk-UA.md
+++ b/README.uk-UA.md
@@ -305,3 +305,5 @@ npm test -- 'playground'
 > Ви можете підтримати цей проект через ❤️️ [GitHub](https://github.com/sponsors/trekhleb) або ❤️️ [Patreon](https://www.patreon.com/trekhleb).
 
 [Люди, які підтримують цей проект](https://github.com/trekhleb/javascript-algorithms/blob/master/BACKERS.md) `∑ = 1`
+
+> ℹ️ Some more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev)
diff --git a/README.zh-CN.md b/README.zh-CN.md
index 22b50d405c..1425f87993 100644
--- a/README.zh-CN.md
+++ b/README.zh-CN.md
@@ -292,3 +292,5 @@ npm test -- 'playground'
 | **希尔排序**          | n log(n)  | 取决于差距序列   | n (log(n))^2  | 1         | No        |  |
 | **计数排序**          | n + r     | n + r     | n + r         | n + r     | Yes       | r - 数组里最大的数    |
 | **基数排序**          | n * k     | n * k     | n * k         | n + k     | Yes       | k - 最长 key 的升序   |
+
+> ℹ️ Some more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev)
diff --git a/README.zh-TW.md b/README.zh-TW.md
index ddf043d7af..10b6e84f08 100644
--- a/README.zh-TW.md
+++ b/README.zh-TW.md
@@ -222,3 +222,5 @@ npm test -- 'playground'
 | **合併排序**           | n log(n)  | n log(n)  | n log(n)      | n         | Yes       |
 | **快速排序**           | n log(n)  | n log(n)  | n^2           | log(n)    | No        |
 | **希爾排序**           | n log(n)  | 由gap sequence決定   | n (log(n))^2  | 1         | No        |
+
+> ℹ️ Some more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev)

From 433515f1b22a1a53443429b20f09f821a3325895 Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Wed, 26 May 2021 10:55:57 +0200
Subject: [PATCH 096/264] Fix typo in READMEs.

---
 README.ar-AR.md | 2 +-
 README.de-DE.md | 2 +-
 README.es-ES.md | 2 +-
 README.fr-FR.md | 3 ++-
 README.id-ID.md | 2 +-
 README.it-IT.md | 2 +-
 README.ja-JP.md | 2 +-
 README.ko-KR.md | 2 +-
 README.md       | 2 +-
 README.pl-PL.md | 2 +-
 README.pt-BR.md | 2 +-
 README.ru-RU.md | 2 +-
 README.tr-TR.md | 2 +-
 README.uk-UA.md | 2 +-
 README.zh-CN.md | 2 +-
 README.zh-TW.md | 2 +-
 16 files changed, 17 insertions(+), 16 deletions(-)

diff --git a/README.ar-AR.md b/README.ar-AR.md
index 3514bce12f..07522e78a6 100644
--- a/README.ar-AR.md
+++ b/README.ar-AR.md
@@ -322,4 +322,4 @@ npm test -- 'playground'
 
 [الناس الذين يدعمون هذا المشروع](https://github.com/trekhleb/javascript-algorithms/blob/master/BACKERS.md) `∑ = 0`
 
-> ℹ️ Some more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev)
+> ℹ️ A few more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev)
diff --git a/README.de-DE.md b/README.de-DE.md
index bd250ab3b0..b34ad3563f 100644
--- a/README.de-DE.md
+++ b/README.de-DE.md
@@ -332,5 +332,5 @@ Nachfolgend finden Sie eine Liste einiger der am häufigsten verwendeten Big O-N
 
 [Leute, die dieses Projekt unterstützen](https://github.com/trekhleb/javascript-algorithms/blob/master/BACKERS.md) `∑ = 0`
 
-> ℹ️ Some more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev)
+> ℹ️ A few more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev)
 
diff --git a/README.es-ES.md b/README.es-ES.md
index b5246bd61d..6f5db59bb8 100644
--- a/README.es-ES.md
+++ b/README.es-ES.md
@@ -300,4 +300,4 @@ frente a diferentes tamaños de los datos de entrada.
 | **Ordenamiento por cuentas**     |     n + r     |          n + r          |            n + r            | n + r   |  Si     | r - mayor número en el arreglo                                |
 | **Ordenamiento Radix**           |    n \* k     |         n \* k          |           n \* k            | n + k   |  Si     | k - largo de la llave más larga                                     |
 
-> ℹ️ Some more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev)
+> ℹ️ A few more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev)
diff --git a/README.fr-FR.md b/README.fr-FR.md
index aa7a9007a3..59087825ff 100644
--- a/README.fr-FR.md
+++ b/README.fr-FR.md
@@ -293,4 +293,5 @@ comparaisons de performance suivant différentes tailles pour les données d'ent
 | **Tri Shell**     | n&nbsp;log(n) | dépend du gap séquence | n&nbsp;(log(n))<sup>2</sup> |    1    |  Non   |                                                                                      |
 | **Tri Comptage**  |     n + r     |         n + r          |            n + r            |  n + r  |  Oui   | r - le plus grand nombre dans la liste                                               |
 | **Tri Radix**     |    n \* k     |         n \* k         |           n \* k            |  n + k  |  Non   | k - longueur du plus long index                                                      |
-> ℹ️ Some more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev)
+
+> ℹ️ A few more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev)
diff --git a/README.id-ID.md b/README.id-ID.md
index f1ad648258..01d539c5ef 100644
--- a/README.id-ID.md
+++ b/README.id-ID.md
@@ -305,4 +305,4 @@ Di bawah ini adalah daftar dari beberapa notasi _Bog O_ yang sering digunakan da
 
 [Orang-orang yang mendukung proyek ini](https://github.com/trekhleb/javascript-algorithms/blob/master/BACKERS.md) `∑ = 1`
 
-> ℹ️ Some more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev)
+> ℹ️ A few more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev)
diff --git a/README.it-IT.md b/README.it-IT.md
index 5947b92e75..b459ac87d1 100644
--- a/README.it-IT.md
+++ b/README.it-IT.md
@@ -298,4 +298,4 @@ Nella tabella qua sotto ci sono riportate la lista delle notazioni Big O più us
 | **Counting sort**     | n + r           | n + r               | n + r               | n + r     | Yes       | r - numero più grande nell'array |
 | **Radix sort**        | n * k           | n * k               | n * k               | n + k     | Yes       | k - lunghezza della chiave più grande |
 
-> ℹ️ Some more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev)
+> ℹ️ A few more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev)
diff --git a/README.ja-JP.md b/README.ja-JP.md
index 30a9979908..44b6b6c13e 100644
--- a/README.ja-JP.md
+++ b/README.ja-JP.md
@@ -297,4 +297,4 @@ npm test -- 'playground'
 | **Counting sort**     | n + r           | n + r               | n + r               | n + r     | Yes       | r - biggest number in array |
 | **Radix sort**        | n * k           | n * k               | n * k               | n + k     | Yes       | k - length of longest key |
 
-> ℹ️ Some more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev)
+> ℹ️ A few more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev)
diff --git a/README.ko-KR.md b/README.ko-KR.md
index 8bdb98b837..040ac8a57d 100644
--- a/README.ko-KR.md
+++ b/README.ko-KR.md
@@ -278,4 +278,4 @@ Source: [Big O Cheat Sheet](http://bigocheatsheet.com/).
 | **계수 정렬**          | n + r           | n + r               | n + r               | n + r     | Yes              | r - 배열내 가장 큰 수 |
 | **기수 정렬**          | n * k           | n * k               | n * k               | n + k     | Yes              | k - 키값의 최대 길이 |
 
-> ℹ️ Some more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev)
+> ℹ️ A few more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev)
diff --git a/README.md b/README.md
index a589d710e1..b8e2be362a 100644
--- a/README.md
+++ b/README.md
@@ -344,4 +344,4 @@ Below is the list of some of the most used Big O notations and their performance
 
 [Folks who are backing this project](https://github.com/trekhleb/javascript-algorithms/blob/master/BACKERS.md) `∑ = 0`
 
-> ℹ️ Some more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev)
+> ℹ️ A few more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev)
diff --git a/README.pl-PL.md b/README.pl-PL.md
index cc20e947e7..51777b0da2 100644
--- a/README.pl-PL.md
+++ b/README.pl-PL.md
@@ -290,4 +290,4 @@ Poniżej umieszczamy listę najbardziej używanych Big O notacji i ich porównan
 | **Sortowanie przez zliczanie**      | n + r           | n + r               | n + r               | n + r     | Yes         | r - największy numer w tablicy|
 | **Sortowanie Radix**                | n * k           | n * k               | n * k               | n + k     | Yes         | k -długość najdłuższego klucza |
 
-> ℹ️ Some more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev)
+> ℹ️ A few more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev)
diff --git a/README.pt-BR.md b/README.pt-BR.md
index cc3b9f2191..68b7e1721f 100644
--- a/README.pt-BR.md
+++ b/README.pt-BR.md
@@ -291,4 +291,4 @@ Abaixo está a lista de algumas das notações Big O mais usadas e suas compara
 | **Counting sort**     | n + r           | n + r               | n + r               | n + r     | Sim       | r - maior número na matriz          |
 | **Radix sort**        | n * k           | n * k               | n * k               | n + k     | Sim       | k - comprimento da chave mais longa |
 
-> ℹ️ Some more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev)
+> ℹ️ A few more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev)
diff --git a/README.ru-RU.md b/README.ru-RU.md
index d5c2c69c6f..6200aedd53 100644
--- a/README.ru-RU.md
+++ b/README.ru-RU.md
@@ -296,4 +296,4 @@ npm test -- 'playground'
 | **Сортировка подсчётом**   | n + r         | n + r          | n + r         | n + r  | Да           | r — наибольшее число в массиве |
 | **Поразрядная сортировка** | n * k         | n * k          | n * k         | n + k  | Да           | k — длина самого длинного ключа |
 
-> ℹ️ Some more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev)
+> ℹ️ A few more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev)
diff --git a/README.tr-TR.md b/README.tr-TR.md
index 73f3077e1e..0dd0ee3bf2 100644
--- a/README.tr-TR.md
+++ b/README.tr-TR.md
@@ -316,4 +316,4 @@ Altta Big O notations ve farklı input boyutlarına karşın yapılmış perform
 
 Bu projeyi buradan destekleyebilirsiniz ❤️️ [GitHub](https://github.com/sponsors/trekhleb) veya ❤️️ [Patreon](https://www.patreon.com/trekhleb).
 
-> ℹ️ Some more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev)
+> ℹ️ A few more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev)
diff --git a/README.uk-UA.md b/README.uk-UA.md
index be4d923b70..b43da83ca6 100644
--- a/README.uk-UA.md
+++ b/README.uk-UA.md
@@ -306,4 +306,4 @@ npm test -- 'playground'
 
 [Люди, які підтримують цей проект](https://github.com/trekhleb/javascript-algorithms/blob/master/BACKERS.md) `∑ = 1`
 
-> ℹ️ Some more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev)
+> ℹ️ A few more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev)
diff --git a/README.zh-CN.md b/README.zh-CN.md
index 1425f87993..8bf216d6bd 100644
--- a/README.zh-CN.md
+++ b/README.zh-CN.md
@@ -293,4 +293,4 @@ npm test -- 'playground'
 | **计数排序**          | n + r     | n + r     | n + r         | n + r     | Yes       | r - 数组里最大的数    |
 | **基数排序**          | n * k     | n * k     | n * k         | n + k     | Yes       | k - 最长 key 的升序   |
 
-> ℹ️ Some more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev)
+> ℹ️ A few more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev)
diff --git a/README.zh-TW.md b/README.zh-TW.md
index 10b6e84f08..e42aba445d 100644
--- a/README.zh-TW.md
+++ b/README.zh-TW.md
@@ -223,4 +223,4 @@ npm test -- 'playground'
 | **快速排序**           | n log(n)  | n log(n)  | n^2           | log(n)    | No        |
 | **希爾排序**           | n log(n)  | 由gap sequence決定   | n (log(n))^2  | 1         | No        |
 
-> ℹ️ Some more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev)
+> ℹ️ A few more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev)

From b2d1ec83f04a66d9d2d3f09150bcaf0cacb0f7ba Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Fri, 16 Jul 2021 11:51:53 +0200
Subject: [PATCH 097/264] Binary representation of floating-point numbers
 (#737)

* Add "Binary representation of floating point numbers" section.

* Adding a half-precision explanatory picture.

* Binary representation of the floating-point numbers.
---
 README.md                                     |   1 +
 .../math/binary-floating-point/README.md      |  93 ++++++++++++++
 .../__tests__/bitsToFloat.test.js             |  32 +++++
 .../__tests__/floatAsBinaryString.test.js     |  20 +++
 .../math/binary-floating-point/bitsToFloat.js | 119 ++++++++++++++++++
 .../floatAsBinaryString.js                    |  61 +++++++++
 ...cision-floating-point-number-explained.png | Bin 0 -> 352613 bytes
 .../images/03-scientific-notation.png         | Bin 0 -> 76251 bytes
 .../math/binary-floating-point/testCases.js   |  71 +++++++++++
 9 files changed, 397 insertions(+)
 create mode 100644 src/algorithms/math/binary-floating-point/README.md
 create mode 100644 src/algorithms/math/binary-floating-point/__tests__/bitsToFloat.test.js
 create mode 100644 src/algorithms/math/binary-floating-point/__tests__/floatAsBinaryString.test.js
 create mode 100644 src/algorithms/math/binary-floating-point/bitsToFloat.js
 create mode 100644 src/algorithms/math/binary-floating-point/floatAsBinaryString.js
 create mode 100644 src/algorithms/math/binary-floating-point/images/02-half-precision-floating-point-number-explained.png
 create mode 100644 src/algorithms/math/binary-floating-point/images/03-scientific-notation.png
 create mode 100644 src/algorithms/math/binary-floating-point/testCases.js

diff --git a/README.md b/README.md
index b8e2be362a..d00945e5a5 100644
--- a/README.md
+++ b/README.md
@@ -68,6 +68,7 @@ a set of rules that precisely define a sequence of operations.
 
 * **Math**
   * `B` [Bit Manipulation](src/algorithms/math/bits) - set/get/update/clear bits, multiplication/division by two, make negative etc.
+  * `B` [Binary Floating Point](src/algorithms/math/binary-floating-point) - binary representation of the floating-point numbers.
   * `B` [Factorial](src/algorithms/math/factorial)
   * `B` [Fibonacci Number](src/algorithms/math/fibonacci) - classic and closed-form versions
   * `B` [Prime Factors](src/algorithms/math/prime-factors) - finding prime factors and counting them using Hardy-Ramanujan's theorem
diff --git a/src/algorithms/math/binary-floating-point/README.md b/src/algorithms/math/binary-floating-point/README.md
new file mode 100644
index 0000000000..2851902845
--- /dev/null
+++ b/src/algorithms/math/binary-floating-point/README.md
@@ -0,0 +1,93 @@
+# Binary representation of floating-point numbers
+
+Have you ever wondered how computers store the floating-point numbers like `3.1415` (𝝿) or `9.109 × 10⁻³¹` (the mass of the electron in kg) in the memory which is limited by a finite number of ones and zeroes (aka bits)?
+
+It seems pretty straightforward for integers (i.e. `17`). Let's say we have 16 bits (2 bytes) to store the number. In 16 bits we may store the integers in a range of `[0, 65535]`:
+
+```text
+(0000000000000000)₂ = (0)₁₀
+
+(0000000000010001)₂ =
+    (1 × 2⁴) +
+    (0 × 2³) +
+    (0 × 2²) +
+    (0 × 2¹) +
+    (1 × 2⁰) = (17)₁₀
+
+(1111111111111111)₂ =
+    (1 × 2¹⁵) +
+    (1 × 2¹⁴) +
+    (1 × 2¹³) +
+    (1 × 2¹²) +
+    (1 × 2¹¹) +
+    (1 × 2¹⁰) +
+    (1 × 2⁹) +
+    (1 × 2⁸) +
+    (1 × 2⁷) +
+    (1 × 2⁶) +
+    (1 × 2⁵) +
+    (1 × 2⁴) +
+    (1 × 2³) +
+    (1 × 2²) +
+    (1 × 2¹) +
+    (1 × 2⁰) = (65535)₁₀
+```
+
+If we need a signed integer we may use [two's complement](https://en.wikipedia.org/wiki/Two%27s_complement) and shift the range of `[0, 65535]` towards the negative numbers. In this case, our 16 bits would represent the numbers in a range of `[-32768, +32767]`.
+
+As you might have noticed, this approach won't allow you to represent the numbers like `-27.15625` (numbers after the decimal point are just being ignored).
+
+We're not the first ones who have noticed this issue though. Around ≈36 years ago some smart folks overcame this limitation by introducing the [IEEE 754](https://en.wikipedia.org/wiki/IEEE_754) standard for floating-point arithmetic.
+
+The IEEE 754 standard describes the way (the framework) of using those 16 bits (or 32, or 64 bits) to store the numbers of wider range, including the small floating numbers (smaller than 1 and closer to 0).
+
+To get the idea behind the standard we might recall the [scientific notation](https://en.wikipedia.org/wiki/Scientific_notation) - a way of expressing numbers that are too large or too small (usually would result in a long string of digits) to be conveniently written in decimal form.
+
+![Scientific number notation](images/03-scientific-notation.png)
+
+As you may see from the image, the number representation might be split into three parts:
+
+- **sign**
+- **fraction (aka significand)** - the valuable digits (the meaning, the payload) of the number
+- **exponent** - controls how far and in which direction to move the decimal point in the fraction
+
+The **base** part we may omit by just agreeing on what it will be equal to. In our case, we'll be using `2` as a base.
+
+Instead of using all 16 bits (or 32 bits, or 64 bits) to store the fraction of the number, we may share the bits and store a sign, exponent, and fraction at the same time. Depending on the number of bits that we're going to use to store the number we end up with the following splits:
+
+| Floating-point format | Total bits | Sign bits | Exponent bits | Fraction bits | Base |
+| :-------------------- | :--------: | :-------: | :-----------: | :--------------: | :--: |
+| [Half-precision](https://en.wikipedia.org/wiki/Half-precision_floating-point_format)        | 16         | 1         | 5             | 10               | 2    |
+| [Single-precision](https://en.wikipedia.org/wiki/Single-precision_floating-point_format)      | 32         | 1         | 8             | 23               | 2    |
+| [Double-precision](https://en.wikipedia.org/wiki/Double-precision_floating-point_format)      | 64         | 1         | 11            | 52               | 2    |
+
+With this approach, the number of bits for the fraction has been reduced (i.e. for the 16-bits number it was reduced from 16 bits to 10 bits). It means that the fraction might take a narrower range of values now (losing some precision). However, since we also have an exponent part, it will actually increase the ultimate number range and also allow us to describe the numbers between 0 and 1 (if the exponent is negative).
+
+> For example, a signed 32-bit integer variable has a maximum value of 2³¹ − 1 = 2,147,483,647, whereas an IEEE 754 32-bit base-2 floating-point variable has a maximum value of ≈ 3.4028235 × 10³⁸.
+
+To make it possible to have a negative exponent, the IEEE 754 standard uses the [biased exponent](https://en.wikipedia.org/wiki/Exponent_bias). The idea is simple - subtract the bias from the exponent value to make it negative. For example, if the exponent has 5 bits, it might take the values from the range of `[0, 31]` (all values are positive here). But if we subtract the value of `15` from it, the range will be `[-15, 16]`. The number `15` is called bias, and it is being calculated by the following formula:
+
+```
+exponent_bias = 2 ^ (k−1) − 1
+
+k - number of exponent bits
+```
+
+I've tried to describe the logic behind the converting of floating-point numbers from a binary format back to the decimal format on the image below. Hopefully, it will give you a better understanding of how the IEEE 754 standard works. The 16-bits number is being used here for simplicity, but the same approach works for 32-bits and 64-bits numbers as well.
+
+![Half-precision floating point number format explained in one picture](images/02-half-precision-floating-point-number-explained.png)
+
+> Checkout the [interactive version of this diagram](https://trekhleb.dev/blog/2021/binary-floating-point/) to play around with setting bits on and off, and seeing how it would influence the final result
+
+## Code examples
+
+- See the [bitsToFloat.js](bitsToFloat.js) for the example of how to convert array of bits to the floating point number (the example is a bit artificial but still it gives the overview of how the conversion is going on)
+- See the [floatAsBinaryString.js](floatAsBinaryString.js) for the example of how to see the actual binary representation of the floating-point number in JavaScript
+
+## References
+
+You might also want to check out the following resources to get a deeper understanding of the binary representation of floating-point numbers:
+
+- [Here is what you need to know about JavaScript’s Number type](https://indepth.dev/posts/1139/here-is-what-you-need-to-know-about-javascripts-number-type)
+- [Float Exposed](https://float.exposed/)
+- [IEEE754 Visualization](https://bartaz.github.io/ieee754-visualization/)
diff --git a/src/algorithms/math/binary-floating-point/__tests__/bitsToFloat.test.js b/src/algorithms/math/binary-floating-point/__tests__/bitsToFloat.test.js
new file mode 100644
index 0000000000..53afe691a2
--- /dev/null
+++ b/src/algorithms/math/binary-floating-point/__tests__/bitsToFloat.test.js
@@ -0,0 +1,32 @@
+import { testCases16Bits, testCases32Bits, testCases64Bits } from '../testCases';
+import { bitsToFloat16, bitsToFloat32, bitsToFloat64 } from '../bitsToFloat';
+
+describe('bitsToFloat16', () => {
+  it('should convert floating point binary bits to floating point decimal number', () => {
+    for (let testCaseIndex = 0; testCaseIndex < testCases16Bits.length; testCaseIndex += 1) {
+      const [decimal, binary] = testCases16Bits[testCaseIndex];
+      const bits = binary.split('').map((bitString) => parseInt(bitString, 10));
+      expect(bitsToFloat16(bits)).toBeCloseTo(decimal, 4);
+    }
+  });
+});
+
+describe('bitsToFloat32', () => {
+  it('should convert floating point binary bits to floating point decimal number', () => {
+    for (let testCaseIndex = 0; testCaseIndex < testCases32Bits.length; testCaseIndex += 1) {
+      const [decimal, binary] = testCases32Bits[testCaseIndex];
+      const bits = binary.split('').map((bitString) => parseInt(bitString, 10));
+      expect(bitsToFloat32(bits)).toBeCloseTo(decimal, 7);
+    }
+  });
+});
+
+describe('bitsToFloat64', () => {
+  it('should convert floating point binary bits to floating point decimal number', () => {
+    for (let testCaseIndex = 0; testCaseIndex < testCases64Bits.length; testCaseIndex += 1) {
+      const [decimal, binary] = testCases64Bits[testCaseIndex];
+      const bits = binary.split('').map((bitString) => parseInt(bitString, 10));
+      expect(bitsToFloat64(bits)).toBeCloseTo(decimal, 14);
+    }
+  });
+});
diff --git a/src/algorithms/math/binary-floating-point/__tests__/floatAsBinaryString.test.js b/src/algorithms/math/binary-floating-point/__tests__/floatAsBinaryString.test.js
new file mode 100644
index 0000000000..efb8a2ba5e
--- /dev/null
+++ b/src/algorithms/math/binary-floating-point/__tests__/floatAsBinaryString.test.js
@@ -0,0 +1,20 @@
+import { floatAs32BinaryString, floatAs64BinaryString } from '../floatAsBinaryString';
+import { testCases32Bits, testCases64Bits } from '../testCases';
+
+describe('floatAs32Binary', () => {
+  it('should create a binary representation of the floating numbers', () => {
+    for (let testCaseIndex = 0; testCaseIndex < testCases32Bits.length; testCaseIndex += 1) {
+      const [decimal, binary] = testCases32Bits[testCaseIndex];
+      expect(floatAs32BinaryString(decimal)).toBe(binary);
+    }
+  });
+});
+
+describe('floatAs64Binary', () => {
+  it('should create a binary representation of the floating numbers', () => {
+    for (let testCaseIndex = 0; testCaseIndex < testCases64Bits.length; testCaseIndex += 1) {
+      const [decimal, binary] = testCases64Bits[testCaseIndex];
+      expect(floatAs64BinaryString(decimal)).toBe(binary);
+    }
+  });
+});
diff --git a/src/algorithms/math/binary-floating-point/bitsToFloat.js b/src/algorithms/math/binary-floating-point/bitsToFloat.js
new file mode 100644
index 0000000000..6d1ef0d851
--- /dev/null
+++ b/src/algorithms/math/binary-floating-point/bitsToFloat.js
@@ -0,0 +1,119 @@
+/**
+ * Sequence of 0s and 1s.
+ * @typedef {number[]} Bits
+ */
+
+/**
+ * @typedef {{
+ *   signBitsCount: number,
+ *   exponentBitsCount: number,
+ *   fractionBitsCount: number,
+ * }} PrecisionConfig
+ */
+
+/**
+ * @typedef {{
+ *   half: PrecisionConfig,
+ *   single: PrecisionConfig,
+ *   double: PrecisionConfig
+ * }} PrecisionConfigs
+ */
+
+/**
+ * ┌───────────────── sign bit
+ * │   ┌───────────── exponent bits
+ * │   │       ┌───── fraction bits
+ * │   │       │
+ * X XXXXX XXXXXXXXXX
+ *
+ * @type {PrecisionConfigs}
+ */
+const precisionConfigs = {
+  // @see: https://en.wikipedia.org/wiki/Half-precision_floating-point_format
+  half: {
+    signBitsCount: 1,
+    exponentBitsCount: 5,
+    fractionBitsCount: 10,
+  },
+  // @see: https://en.wikipedia.org/wiki/Single-precision_floating-point_format
+  single: {
+    signBitsCount: 1,
+    exponentBitsCount: 8,
+    fractionBitsCount: 23,
+  },
+  // @see: https://en.wikipedia.org/wiki/Double-precision_floating-point_format
+  double: {
+    signBitsCount: 1,
+    exponentBitsCount: 11,
+    fractionBitsCount: 52,
+  },
+};
+
+/**
+ * Converts the binary representation of the floating point number to decimal float number.
+ *
+ * @param {Bits} bits - sequence of bits that represents the floating point number.
+ * @param {PrecisionConfig} precisionConfig - half/single/double precision config.
+ * @return {number} - floating point number decoded from its binary representation.
+ */
+function bitsToFloat(bits, precisionConfig) {
+  const { signBitsCount, exponentBitsCount } = precisionConfig;
+
+  // Figuring out the sign.
+  const sign = (-1) ** bits[0]; // -1^1 = -1, -1^0 = 1
+
+  // Calculating the exponent value.
+  const exponentBias = 2 ** (exponentBitsCount - 1) - 1;
+  const exponentBits = bits.slice(signBitsCount, signBitsCount + exponentBitsCount);
+  const exponentUnbiased = exponentBits.reduce(
+    (exponentSoFar, currentBit, bitIndex) => {
+      const bitPowerOfTwo = 2 ** (exponentBitsCount - bitIndex - 1);
+      return exponentSoFar + currentBit * bitPowerOfTwo;
+    },
+    0,
+  );
+  const exponent = exponentUnbiased - exponentBias;
+
+  // Calculating the fraction value.
+  const fractionBits = bits.slice(signBitsCount + exponentBitsCount);
+  const fraction = fractionBits.reduce(
+    (fractionSoFar, currentBit, bitIndex) => {
+      const bitPowerOfTwo = 2 ** -(bitIndex + 1);
+      return fractionSoFar + currentBit * bitPowerOfTwo;
+    },
+    0,
+  );
+
+  // Putting all parts together to calculate the final number.
+  return sign * (2 ** exponent) * (1 + fraction);
+}
+
+/**
+ *  Converts the 16-bit binary representation of the floating point number to decimal float number.
+ *
+ * @param {Bits} bits - sequence of bits that represents the floating point number.
+ * @return {number} - floating point number decoded from its binary representation.
+ */
+export function bitsToFloat16(bits) {
+  return bitsToFloat(bits, precisionConfigs.half);
+}
+
+/**
+ * Converts the 32-bit binary representation of the floating point number to decimal float number.
+ *
+ * @param {Bits} bits - sequence of bits that represents the floating point number.
+ * @return {number} - floating point number decoded from its binary representation.
+ */
+export function bitsToFloat32(bits) {
+  return bitsToFloat(bits, precisionConfigs.single);
+}
+
+/**
+ * Converts the 64-bit binary representation of the floating point number to decimal float number.
+ *
+ * @param {Bits} bits - sequence of bits that represents the floating point number.
+ * @return {number} - floating point number decoded from its binary representation.
+ */
+export function bitsToFloat64(bits) {
+  return bitsToFloat(bits, precisionConfigs.double);
+}
diff --git a/src/algorithms/math/binary-floating-point/floatAsBinaryString.js b/src/algorithms/math/binary-floating-point/floatAsBinaryString.js
new file mode 100644
index 0000000000..aa907ac049
--- /dev/null
+++ b/src/algorithms/math/binary-floating-point/floatAsBinaryString.js
@@ -0,0 +1,61 @@
+// @see: https://en.wikipedia.org/wiki/Single-precision_floating-point_format
+const singlePrecisionBytesLength = 4; // 32 bits
+
+// @see: https://en.wikipedia.org/wiki/Double-precision_floating-point_format
+const doublePrecisionBytesLength = 8; // 64 bits
+
+const bitsInByte = 8;
+
+/**
+ * Converts the float number into its IEEE 754 binary representation.
+ * @see: https://en.wikipedia.org/wiki/IEEE_754
+ *
+ * @param {number} floatNumber - float number in decimal format.
+ * @param {number} byteLength - number of bytes to use to store the float number.
+ * @return {string} - binary string representation of the float number.
+ */
+function floatAsBinaryString(floatNumber, byteLength) {
+  let numberAsBinaryString = '';
+
+  const arrayBuffer = new ArrayBuffer(byteLength);
+  const dataView = new DataView(arrayBuffer);
+
+  const byteOffset = 0;
+  const littleEndian = false;
+
+  if (byteLength === singlePrecisionBytesLength) {
+    dataView.setFloat32(byteOffset, floatNumber, littleEndian);
+  } else {
+    dataView.setFloat64(byteOffset, floatNumber, littleEndian);
+  }
+
+  for (let byteIndex = 0; byteIndex < byteLength; byteIndex += 1) {
+    let bits = dataView.getUint8(byteIndex).toString(2);
+    if (bits.length < bitsInByte) {
+      bits = new Array(bitsInByte - bits.length).fill('0').join('') + bits;
+    }
+    numberAsBinaryString += bits;
+  }
+
+  return numberAsBinaryString;
+}
+
+/**
+ * Converts the float number into its IEEE 754 64-bits binary representation.
+ *
+ * @param {number} floatNumber - float number in decimal format.
+ * @return {string} - 64 bits binary string representation of the float number.
+ */
+export function floatAs64BinaryString(floatNumber) {
+  return floatAsBinaryString(floatNumber, doublePrecisionBytesLength);
+}
+
+/**
+ * Converts the float number into its IEEE 754 32-bits binary representation.
+ *
+ * @param {number} floatNumber - float number in decimal format.
+ * @return {string} - 32 bits binary string representation of the float number.
+ */
+export function floatAs32BinaryString(floatNumber) {
+  return floatAsBinaryString(floatNumber, singlePrecisionBytesLength);
+}
diff --git a/src/algorithms/math/binary-floating-point/images/02-half-precision-floating-point-number-explained.png b/src/algorithms/math/binary-floating-point/images/02-half-precision-floating-point-number-explained.png
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literal 0
HcmV?d00001

diff --git a/src/algorithms/math/binary-floating-point/testCases.js b/src/algorithms/math/binary-floating-point/testCases.js
new file mode 100644
index 0000000000..54b9b8029b
--- /dev/null
+++ b/src/algorithms/math/binary-floating-point/testCases.js
@@ -0,0 +1,71 @@
+/**
+ * @typedef {[number, string]} TestCase
+ * @property {number} decimal
+ * @property {string} binary
+ */
+
+/**
+ * @type {TestCase[]}
+ */
+export const testCases16Bits = [
+  [-65504, '1111101111111111'],
+  [-10344, '1111000100001101'],
+  [-27.15625, '1100111011001010'],
+  [-1, '1011110000000000'],
+  [-0.09997558, '1010111001100110'],
+  [0, '0000000000000000'],
+  [5.9604644775390625e-8, '0000000000000001'],
+  [0.000004529, '0000000001001100'],
+  [0.0999755859375, '0010111001100110'],
+  [0.199951171875, '0011001001100110'],
+  [0.300048828125, '0011010011001101'],
+  [1, '0011110000000000'],
+  [1.5, '0011111000000000'],
+  [1.75, '0011111100000000'],
+  [1.875, '0011111110000000'],
+  [65504, '0111101111111111'],
+];
+
+/**
+ * @type {TestCase[]}
+ */
+export const testCases32Bits = [
+  [-3.40282346638528859812e+38, '11111111011111111111111111111111'],
+  [-10345.5595703125, '11000110001000011010011000111101'],
+  [-27.15625, '11000001110110010100000000000000'],
+  [-1, '10111111100000000000000000000000'],
+  [-0.1, '10111101110011001100110011001101'],
+  [0, '00000000000000000000000000000000'],
+  [1.40129846432481707092e-45, '00000000000000000000000000000001'],
+  [0.000004560, '00110110100110010000001000011010'],
+  [0.1, '00111101110011001100110011001101'],
+  [0.2, '00111110010011001100110011001101'],
+  [0.3, '00111110100110011001100110011010'],
+  [1, '00111111100000000000000000000000'],
+  [1.5, '00111111110000000000000000000000'],
+  [1.75, '00111111111000000000000000000000'],
+  [1.875, '00111111111100000000000000000000'],
+  [3.40282346638528859812e+38, '01111111011111111111111111111111'],
+];
+
+/**
+ * @type {TestCase[]}
+ */
+export const testCases64Bits = [
+  [-1.79769313486231570815e+308, '1111111111101111111111111111111111111111111111111111111111111111'],
+  [-10345.5595703125, '1100000011000100001101001100011110100000000000000000000000000000'],
+  [-27.15625, '1100000000111011001010000000000000000000000000000000000000000000'],
+  [-1, '1011111111110000000000000000000000000000000000000000000000000000'],
+  [-0.1, '1011111110111001100110011001100110011001100110011001100110011010'],
+  [0, '0000000000000000000000000000000000000000000000000000000000000000'],
+  [4.94065645841246544177e-324, '0000000000000000000000000000000000000000000000000000000000000001'],
+  [0.000004560, '0011111011010011001000000100001101000001011100110011110011100100'],
+  [0.1, '0011111110111001100110011001100110011001100110011001100110011010'],
+  [0.2, '0011111111001001100110011001100110011001100110011001100110011010'],
+  [0.3, '0011111111010011001100110011001100110011001100110011001100110011'],
+  [1, '0011111111110000000000000000000000000000000000000000000000000000'],
+  [1.5, '0011111111111000000000000000000000000000000000000000000000000000'],
+  [1.75, '0011111111111100000000000000000000000000000000000000000000000000'],
+  [1.875, '0011111111111110000000000000000000000000000000000000000000000000'],
+  [1.79769313486231570815e+308, '0111111111101111111111111111111111111111111111111111111111111111'],
+];

From badf301ba56040dbd286d908e65d2cac05ff7455 Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Fri, 16 Jul 2021 14:39:35 +0200
Subject: [PATCH 098/264] Binary representation of the floating-point numbers.

---
 src/algorithms/math/binary-floating-point/README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/algorithms/math/binary-floating-point/README.md b/src/algorithms/math/binary-floating-point/README.md
index 2851902845..32b41f642a 100644
--- a/src/algorithms/math/binary-floating-point/README.md
+++ b/src/algorithms/math/binary-floating-point/README.md
@@ -1,6 +1,6 @@
 # Binary representation of floating-point numbers
 
-Have you ever wondered how computers store the floating-point numbers like `3.1415` (𝝿) or `9.109 × 10⁻³¹` (the mass of the electron in kg) in the memory which is limited by a finite number of ones and zeroes (aka bits)?
+Have you ever wondered how computers store the floating-point numbers like `3.1416` (𝝿) or `9.109 × 10⁻³¹` (the mass of the electron in kg) in the memory which is limited by a finite number of ones and zeroes (aka bits)?
 
 It seems pretty straightforward for integers (i.e. `17`). Let's say we have 16 bits (2 bytes) to store the number. In 16 bits we may store the integers in a range of `[0, 65535]`:
 

From 71da6df63312096964eaaf8f538c174d1c39014b Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Mon, 26 Jul 2021 07:43:07 +0200
Subject: [PATCH 099/264] Binary representation of the floating-point numbers.

---
 src/algorithms/math/binary-floating-point/README.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/src/algorithms/math/binary-floating-point/README.md b/src/algorithms/math/binary-floating-point/README.md
index 32b41f642a..c0c6fce046 100644
--- a/src/algorithms/math/binary-floating-point/README.md
+++ b/src/algorithms/math/binary-floating-point/README.md
@@ -79,6 +79,8 @@ I've tried to describe the logic behind the converting of floating-point numbers
 
 > Checkout the [interactive version of this diagram](https://trekhleb.dev/blog/2021/binary-floating-point/) to play around with setting bits on and off, and seeing how it would influence the final result
 
+Be aware that this is by no means a complete and sufficient overview of the IEEE 754 standard. It is rather a simplified and basic overview. Several corner cases were omitted in the examples above for simplicity of presentation (i.e. `-0`, `-∞`, `+∞` and `NaN` (not a number) values)
+
 ## Code examples
 
 - See the [bitsToFloat.js](bitsToFloat.js) for the example of how to convert array of bits to the floating point number (the example is a bit artificial but still it gives the overview of how the conversion is going on)

From 2ad5617a4bcf05a59c650d91ab950fd054d0f69a Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Mon, 26 Jul 2021 07:44:21 +0200
Subject: [PATCH 100/264] Binary representation of the floating-point numbers.

---
 src/algorithms/math/binary-floating-point/README.md | 7 +++++++
 1 file changed, 7 insertions(+)

diff --git a/src/algorithms/math/binary-floating-point/README.md b/src/algorithms/math/binary-floating-point/README.md
index c0c6fce046..0952d99f5b 100644
--- a/src/algorithms/math/binary-floating-point/README.md
+++ b/src/algorithms/math/binary-floating-point/README.md
@@ -79,6 +79,13 @@ I've tried to describe the logic behind the converting of floating-point numbers
 
 > Checkout the [interactive version of this diagram](https://trekhleb.dev/blog/2021/binary-floating-point/) to play around with setting bits on and off, and seeing how it would influence the final result
 
+Here is the number ranges that different floating-point formats support:
+
+| Floating-point format | Exp min | Exp max | Range            | Min positive |
+| :-------------------- | :------ | :------ | :--------------- | :----------- |
+| Half-precision        | −14     | +15     | ±65,504          | 6.10 × 10⁻⁵  |
+| Single-precision      | −126    | +127    | ±3.4028235 × 10³⁸| 1.18 × 10⁻³⁸ |
+
 Be aware that this is by no means a complete and sufficient overview of the IEEE 754 standard. It is rather a simplified and basic overview. Several corner cases were omitted in the examples above for simplicity of presentation (i.e. `-0`, `-∞`, `+∞` and `NaN` (not a number) values)
 
 ## Code examples

From 4548296affb227c29ead868309e48667f8280c55 Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Mon, 26 Jul 2021 11:55:40 +0200
Subject: [PATCH 101/264] Binary representation of the floating-point numbers.

---
 src/algorithms/math/binary-floating-point/README.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/src/algorithms/math/binary-floating-point/README.md b/src/algorithms/math/binary-floating-point/README.md
index 0952d99f5b..d1ae72731e 100644
--- a/src/algorithms/math/binary-floating-point/README.md
+++ b/src/algorithms/math/binary-floating-point/README.md
@@ -97,6 +97,7 @@ Be aware that this is by no means a complete and sufficient overview of the IEEE
 
 You might also want to check out the following resources to get a deeper understanding of the binary representation of floating-point numbers:
 
+- [Interactive version of this article](https://trekhleb.dev/blog/2021/binary-floating-point/) (allows setting the bits manually and seeing the resulting floating number)
 - [Here is what you need to know about JavaScript’s Number type](https://indepth.dev/posts/1139/here-is-what-you-need-to-know-about-javascripts-number-type)
 - [Float Exposed](https://float.exposed/)
 - [IEEE754 Visualization](https://bartaz.github.io/ieee754-visualization/)

From d0576a2594f843cae01abfdb9a2aa08663bdee54 Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Mon, 18 Oct 2021 18:02:40 +0200
Subject: [PATCH 102/264] Upgrade dependencies. (#790)

---
 package-lock.json | 6881 +++++++++++++++++----------------------------
 package.json      |   20 +-
 2 files changed, 2597 insertions(+), 4304 deletions(-)

diff --git a/package-lock.json b/package-lock.json
index 93de7f66c9..ea195beb9b 100644
--- a/package-lock.json
+++ b/package-lock.json
@@ -5,53 +5,52 @@
   "requires": true,
   "dependencies": {
     "@babel/cli": {
-      "version": "7.12.10",
-      "resolved": "https://registry.npmjs.org/@babel/cli/-/cli-7.12.10.tgz",
-      "integrity": "sha512-+y4ZnePpvWs1fc/LhZRTHkTesbXkyBYuOB+5CyodZqrEuETXi3zOVfpAQIdgC3lXbHLTDG9dQosxR9BhvLKDLQ==",
+      "version": "7.15.7",
+      "resolved": "https://registry.npmjs.org/@babel/cli/-/cli-7.15.7.tgz",
+      "integrity": "sha512-YW5wOprO2LzMjoWZ5ZG6jfbY9JnkDxuHDwvnrThnuYtByorova/I0HNXJedrUfwuXFQfYOjcqDA4PU3qlZGZjg==",
       "dev": true,
       "requires": {
-        "@nicolo-ribaudo/chokidar-2": "2.1.8-no-fsevents",
+        "@nicolo-ribaudo/chokidar-2": "2.1.8-no-fsevents.3",
         "chokidar": "^3.4.0",
         "commander": "^4.0.1",
         "convert-source-map": "^1.1.0",
         "fs-readdir-recursive": "^1.1.0",
         "glob": "^7.0.0",
-        "lodash": "^4.17.19",
         "make-dir": "^2.1.0",
         "slash": "^2.0.0",
         "source-map": "^0.5.0"
       }
     },
     "@babel/code-frame": {
-      "version": "7.12.13",
-      "resolved": "https://registry.npmjs.org/@babel/code-frame/-/code-frame-7.12.13.tgz",
-      "integrity": "sha512-HV1Cm0Q3ZrpCR93tkWOYiuYIgLxZXZFVG2VgK+MBWjUqZTundupbfx2aXarXuw5Ko5aMcjtJgbSs4vUGBS5v6g==",
+      "version": "7.15.8",
+      "resolved": "https://registry.npmjs.org/@babel/code-frame/-/code-frame-7.15.8.tgz",
+      "integrity": "sha512-2IAnmn8zbvC/jKYhq5Ki9I+DwjlrtMPUCH/CpHvqI4dNnlwHwsxoIhlc8WcYY5LSYknXQtAlFYuHfqAFCvQ4Wg==",
       "dev": true,
       "requires": {
-        "@babel/highlight": "^7.12.13"
+        "@babel/highlight": "^7.14.5"
       }
     },
     "@babel/compat-data": {
-      "version": "7.13.15",
-      "resolved": "https://registry.npmjs.org/@babel/compat-data/-/compat-data-7.13.15.tgz",
-      "integrity": "sha512-ltnibHKR1VnrU4ymHyQ/CXtNXI6yZC0oJThyW78Hft8XndANwi+9H+UIklBDraIjFEJzw8wmcM427oDd9KS5wA==",
+      "version": "7.15.0",
+      "resolved": "https://registry.npmjs.org/@babel/compat-data/-/compat-data-7.15.0.tgz",
+      "integrity": "sha512-0NqAC1IJE0S0+lL1SWFMxMkz1pKCNCjI4tr2Zx4LJSXxCLAdr6KyArnY+sno5m3yH9g737ygOyPABDsnXkpxiA==",
       "dev": true
     },
     "@babel/core": {
-      "version": "7.13.15",
-      "resolved": "https://registry.npmjs.org/@babel/core/-/core-7.13.15.tgz",
-      "integrity": "sha512-6GXmNYeNjS2Uz+uls5jalOemgIhnTMeaXo+yBUA72kC2uX/8VW6XyhVIo2L8/q0goKQA3EVKx0KOQpVKSeWadQ==",
-      "dev": true,
-      "requires": {
-        "@babel/code-frame": "^7.12.13",
-        "@babel/generator": "^7.13.9",
-        "@babel/helper-compilation-targets": "^7.13.13",
-        "@babel/helper-module-transforms": "^7.13.14",
-        "@babel/helpers": "^7.13.10",
-        "@babel/parser": "^7.13.15",
-        "@babel/template": "^7.12.13",
-        "@babel/traverse": "^7.13.15",
-        "@babel/types": "^7.13.14",
+      "version": "7.15.8",
+      "resolved": "https://registry.npmjs.org/@babel/core/-/core-7.15.8.tgz",
+      "integrity": "sha512-3UG9dsxvYBMYwRv+gS41WKHno4K60/9GPy1CJaH6xy3Elq8CTtvtjT5R5jmNhXfCYLX2mTw+7/aq5ak/gOE0og==",
+      "dev": true,
+      "requires": {
+        "@babel/code-frame": "^7.15.8",
+        "@babel/generator": "^7.15.8",
+        "@babel/helper-compilation-targets": "^7.15.4",
+        "@babel/helper-module-transforms": "^7.15.8",
+        "@babel/helpers": "^7.15.4",
+        "@babel/parser": "^7.15.8",
+        "@babel/template": "^7.15.4",
+        "@babel/traverse": "^7.15.4",
+        "@babel/types": "^7.15.6",
         "convert-source-map": "^1.7.0",
         "debug": "^4.1.0",
         "gensync": "^1.0.0-beta.2",
@@ -60,15 +59,6 @@
         "source-map": "^0.5.0"
       },
       "dependencies": {
-        "debug": {
-          "version": "4.3.1",
-          "resolved": "https://registry.npmjs.org/debug/-/debug-4.3.1.tgz",
-          "integrity": "sha512-doEwdvm4PCeK4K3RQN2ZC2BYUBaxwLARCqZmMjtF8a51J2Rb0xpVloFRnCODwqjpwnAoao4pelN8l3RJdv3gRQ==",
-          "dev": true,
-          "requires": {
-            "ms": "2.1.2"
-          }
-        },
         "json5": {
           "version": "2.2.0",
           "resolved": "https://registry.npmjs.org/json5/-/json5-2.2.0.tgz",
@@ -78,12 +68,6 @@
             "minimist": "^1.2.5"
           }
         },
-        "ms": {
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diff --git a/package.json b/package.json
index f77d87ff50..305c750591 100644
--- a/package.json
+++ b/package.json
@@ -35,18 +35,18 @@
   },
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-    "canvas": "^2.7.0",
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+    "@babel/cli": "7.15.7",
+    "@babel/preset-env": "7.15.8",
+    "@types/jest": "27.0.2",
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-    "eslint-plugin-react": "7.21.5",
-    "husky": "6.0.0",
-    "jest": "26.6.3"
+    "eslint-plugin-react": "7.26.1",
+    "husky": "7.0.2",
+    "jest": "27.3.0"
   },
   "engines": {
     "node": ">=12.0.0",

From 99945f30deba9fb0ec5077e07ed093d0a531f1c1 Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Fri, 22 Oct 2021 09:56:44 +0200
Subject: [PATCH 103/264] Add the "Weighted Random" algorithm (#792)

* Add the link to the Weighted Random algorithm to the main README.

* Add Weighted Random implementation and tests.

* Add Weighted Random README.

* Add Weighted Random README.

* Add Weighted Random README.
---
 README.md                                     |   2 +
 .../statistics/weighted-random/README.md      | 141 ++++++++++++++++++
 .../__test__/weightedRandom.test.js           |  64 ++++++++
 .../weighted-random/weightedRandom.js         |  52 +++++++
 4 files changed, 259 insertions(+)
 create mode 100644 src/algorithms/statistics/weighted-random/README.md
 create mode 100644 src/algorithms/statistics/weighted-random/__test__/weightedRandom.test.js
 create mode 100644 src/algorithms/statistics/weighted-random/weightedRandom.js

diff --git a/README.md b/README.md
index d00945e5a5..826a3a45b8 100644
--- a/README.md
+++ b/README.md
@@ -156,6 +156,8 @@ a set of rules that precisely define a sequence of operations.
   * `B` [k-Means](src/algorithms/ml/k-means) - k-Means clustering algorithm
 * **Image Processing**
   * `B` [Seam Carving](src/algorithms/image-processing/seam-carving) - content-aware image resizing algorithm
+* **Statistics**
+  * `B` [Weighted Random](src/algorithms/statistics/weighted-random) - select the random item from the list based on items' weights
 * **Uncategorized**
   * `B` [Tower of Hanoi](src/algorithms/uncategorized/hanoi-tower)
   * `B` [Square Matrix Rotation](src/algorithms/uncategorized/square-matrix-rotation) - in-place algorithm
diff --git a/src/algorithms/statistics/weighted-random/README.md b/src/algorithms/statistics/weighted-random/README.md
new file mode 100644
index 0000000000..1c700d41d6
--- /dev/null
+++ b/src/algorithms/statistics/weighted-random/README.md
@@ -0,0 +1,141 @@
+# Weighted Random
+
+## What is "Weighted Random"
+
+Let's say you have a list of **items**. Item could be anything. For example, we may have a list of fruits and vegetables that you like to eat: `[ '🍌', '🍎', '🥕' ]`.
+
+The list of **weights** represent the weight (or probability, or importance) of each item. Weights are numbers. For example, the weights like `[3, 7, 1]` would say that:
+
+- you would like to eat `🍎 apples` more often (`7` out of `3 + 7 + 1 = 11` times),
+- then you would like to eat `bananas 🍌` less often (only `3` out of `11` times),
+- and the `carrots 🥕` you really don't like (want to eat it only `1` out of `11` times).
+
+> If we speak in terms of probabilities than the weights list might be an array of floats that sum up to `1` (i.e. `[0.1, 0.5, 0.2, 0.2]`).
+
+The **Weighted Random** in this case will be the function that will randomly return you the item from the list, and it will take each item's weight into account, so that items with the higher weight will be picked more often.
+
+Example of the function interface:
+
+```javascript
+const items =   [ '🍌', '🍎', '🥕' ];
+const weights = [  3,    7,    1  ];
+
+function weightedRandom(items, weights) {
+  // implementation goes here ...
+}
+
+const nextSnackToEat = weightedRandom(items, weights); // Could be '🍎'
+```
+
+## Applications of Weighted Random
+
+- In [Genetic Algorithm](https://en.wikipedia.org/wiki/Genetic_algorithm) the weighted random is used during the "Selection" phase, when we need to select the fittest/strongest individuums based on their fitness score for mating and for producing the next stronger generation. You may find an **example** in the [Self-Parking Car in 500 Lines of Code](https://trekhleb.dev/blog/2021/self-parking-car-evolution/) article.
+- In [Recurrent Neural Networks (RNN)](https://en.wikipedia.org/wiki/Recurrent_neural_network) when trying to decide what letter to choose next (to form the sentence) based on the next letter probability. You may find an **example** in the [Recipe Generation using Recurrent Neural Network (RNN)](https://nbviewer.org/github/trekhleb/machine-learning-experiments/blob/master/experiments/recipe_generation_rnn/recipe_generation_rnn.ipynb) Jupyter notebook.
+- In [Nginx Load Balancing](https://docs.nginx.com/nginx/admin-guide/load-balancer/http-load-balancer/) to send HTTP requests more often to the servers with the higher weights.
+- And more...
+
+## The Algorithm
+
+The **straightforward approach** would be to:
+
+1. Repeat each item in the list according to its weight.
+2. Pick the random item from the list.
+
+For example in our case with fruits and vegetables we could generate the following list of size `3 + 7 + 1 = 11`:
+
+```javascript
+const items =   [ '🍌', '🍎', '🥕' ];
+const weights = [  3,    7,    1  ];
+
+// Repeating the items based on weights.
+const weightedItems = [
+  '🍌', '🍌', '🍌',
+  '🍎', '🍎', '🍎', '🍎', '🍎', '🍎', '🍎',
+  '🥕',
+];
+
+// And now just pick the random item from weightedItems array.
+```
+
+However, as you may see, this approach may require a lot of memory, in case if the objects are heavy, and in case if we have a lot of them to repeat in `weightedItems` list.
+
+The **more efficient approach** would be to:
+
+1. Prepare the list of cumulative weights for each item (i.e. the `cumulativeWeights` list which will have the same number of elements as the original `weights` list). In our case it will look like this: `cumulativeWeights = [3, 3 + 7, 3 + 7 + 1] = [3, 10, 11]`
+2. Generate the random number `randomNumber` from `0` to the highest cumulative weight value. In our case the random number will be in a range of `[0..11]`. Let's say that we have `randomNumber = 8`.
+3. Go through the `cumulativeWeights` list from left to right and pick the first element which is higher or equal to the `randomNumber`. The index of such element we will use to pick the item from the `items` array.
+
+The idea behind this approach is that the higher weights will "occupy" more numeric space. Therefore, there is a higher chance that the random number will fall into the "higher weight numeric bucket".
+
+```javascript
+const weights =           [3, 7,  1 ];
+const cumulativeWeights = [3, 10, 11];
+
+// In a pseudo-representation we may think about the cumulativeWeights array like this.
+const pseudoCumulativeWeights = [
+  1, 2, 3,               // <-- [3] numbers
+  4, 5, 6, 7, 8, 9, 10,  // <-- [7] numbers
+  11,                    // <-- [1] number
+];
+```
+
+Here is an example of how the `weightedRandom` function might be implemented:
+
+```javascript
+/**
+ * Picks the random item based on its weight.
+ * The items with higher weight will be picked more often (with a higher probability).
+ *
+ * For example:
+ * - items = ['banana', 'orange', 'apple']
+ * - weights = [0, 0.2, 0.8]
+ * - weightedRandom(items, weights) in 80% of cases will return 'apple', in 20% of cases will return
+ * 'orange' and it will never return 'banana' (because probability of picking the banana is 0%)
+ *
+ * @param {any[]} items
+ * @param {number[]} weights
+ * @returns {{item: any, index: number}}
+ */
+export default function weightedRandom(items, weights) {
+  if (items.length !== weights.length) {
+    throw new Error('Items and weights must be of the same size');
+  }
+
+  if (!items.length) {
+    throw new Error('Items must not be empty');
+  }
+
+  // Preparing the cumulative weights array.
+  // For example:
+  // - weights = [1, 4, 3]
+  // - cumulativeWeights = [1, 5, 8]
+  const cumulativeWeights = [];
+  for (let i = 0; i < weights.length; i += 1) {
+    cumulativeWeights[i] = weights[i] + (cumulativeWeights[i - 1] || 0);
+  }
+
+  // Getting the random number in a range of [0...sum(weights)]
+  // For example:
+  // - weights = [1, 4, 3]
+  // - maxCumulativeWeight = 8
+  // - range for the random number is [0...8]
+  const maxCumulativeWeight = cumulativeWeights[cumulativeWeights.length - 1];
+  const randomNumber = maxCumulativeWeight * Math.random();
+
+  // Picking the random item based on its weight.
+  // The items with higher weight will be picked more often.
+  for (let itemIndex = 0; itemIndex < items.length; itemIndex += 1) {
+    if (cumulativeWeights[itemIndex] >= randomNumber) {
+      return {
+        item: items[itemIndex],
+        index: itemIndex,
+      };
+    }
+  }
+}
+```
+
+## Implementation
+
+- Check the [weightedRandom.js](weightedRandom.js) file for the implementation of the `weightedRandom()` function.
+- Check the [weightedRandom.test.js](__test__/weightedRandom.test.js) file for the tests-cases.
diff --git a/src/algorithms/statistics/weighted-random/__test__/weightedRandom.test.js b/src/algorithms/statistics/weighted-random/__test__/weightedRandom.test.js
new file mode 100644
index 0000000000..1b0b267627
--- /dev/null
+++ b/src/algorithms/statistics/weighted-random/__test__/weightedRandom.test.js
@@ -0,0 +1,64 @@
+import weightedRandom from '../weightedRandom';
+
+describe('weightedRandom', () => {
+  it('should throw an error when the number of weights does not match the number of items', () => {
+    const getWeightedRandomWithInvalidInputs = () => {
+      weightedRandom(['a', 'b', 'c'], [10, 0]);
+    };
+    expect(getWeightedRandomWithInvalidInputs).toThrow('Items and weights must be of the same size');
+  });
+
+  it('should throw an error when the number of weights or items are empty', () => {
+    const getWeightedRandomWithInvalidInputs = () => {
+      weightedRandom([], []);
+    };
+    expect(getWeightedRandomWithInvalidInputs).toThrow('Items must not be empty');
+  });
+
+  it('should correctly do random selection based on wights in straightforward cases', () => {
+    expect(weightedRandom(['a', 'b', 'c'], [1, 0, 0])).toEqual({ index: 0, item: 'a' });
+    expect(weightedRandom(['a', 'b', 'c'], [0, 1, 0])).toEqual({ index: 1, item: 'b' });
+    expect(weightedRandom(['a', 'b', 'c'], [0, 0, 1])).toEqual({ index: 2, item: 'c' });
+    expect(weightedRandom(['a', 'b', 'c'], [0, 1, 1])).not.toEqual({ index: 0, item: 'a' });
+    expect(weightedRandom(['a', 'b', 'c'], [1, 0, 1])).not.toEqual({ index: 1, item: 'b' });
+    expect(weightedRandom(['a', 'b', 'c'], [1, 1, 0])).not.toEqual({ index: 2, item: 'c' });
+  });
+
+  it('should correctly do random selection based on wights', () => {
+    // Number of times we're going to select the random items based on their weights.
+    const ATTEMPTS_NUM = 1000;
+    // The +/- delta in the number of times each item has been actually selected.
+    // I.e. if we want the item 'a' to be selected 300 times out of 1000 cases (30%)
+    // then 267 times is acceptable since it is bigger that 250 (which is 300 - 50)
+    // ans smaller than 350 (which is 300 + 50)
+    const THRESHOLD = 50;
+
+    const items = ['a', 'b', 'c']; // The actual items values don't matter.
+    const weights = [0.1, 0.3, 0.6];
+
+    const counter = [];
+    for (let i = 0; i < ATTEMPTS_NUM; i += 1) {
+      const randomItem = weightedRandom(items, weights);
+      if (!counter[randomItem.index]) {
+        counter[randomItem.index] = 1;
+      } else {
+        counter[randomItem.index] += 1;
+      }
+    }
+
+    for (let itemIndex = 0; itemIndex < items.length; itemIndex += 1) {
+      /*
+        i.e. item with the index of 0 must be selected 100 times (ideally)
+        or with the threshold of [100 - 50, 100 + 50] times.
+
+        i.e. item with the index of 1 must be selected 300 times (ideally)
+        or with the threshold of [300 - 50, 300 + 50] times.
+
+        i.e. item with the index of 2 must be selected 600 times (ideally)
+        or with the threshold of [600 - 50, 600 + 50] times.
+       */
+      expect(counter[itemIndex]).toBeGreaterThan(ATTEMPTS_NUM * weights[itemIndex] - THRESHOLD);
+      expect(counter[itemIndex]).toBeLessThan(ATTEMPTS_NUM * weights[itemIndex] + THRESHOLD);
+    }
+  });
+});
diff --git a/src/algorithms/statistics/weighted-random/weightedRandom.js b/src/algorithms/statistics/weighted-random/weightedRandom.js
new file mode 100644
index 0000000000..0d58a504f8
--- /dev/null
+++ b/src/algorithms/statistics/weighted-random/weightedRandom.js
@@ -0,0 +1,52 @@
+/**
+ * Picks the random item based on its weight.
+ * The items with higher weight will be picked more often (with a higher probability).
+ *
+ * For example:
+ * - items = ['banana', 'orange', 'apple']
+ * - weights = [0, 0.2, 0.8]
+ * - weightedRandom(items, weights) in 80% of cases will return 'apple', in 20% of cases will return
+ * 'orange' and it will never return 'banana' (because probability of picking the banana is 0%)
+ *
+ * @param {any[]} items
+ * @param {number[]} weights
+ * @returns {{item: any, index: number}}
+ */
+/* eslint-disable consistent-return */
+export default function weightedRandom(items, weights) {
+  if (items.length !== weights.length) {
+    throw new Error('Items and weights must be of the same size');
+  }
+
+  if (!items.length) {
+    throw new Error('Items must not be empty');
+  }
+
+  // Preparing the cumulative weights array.
+  // For example:
+  // - weights = [1, 4, 3]
+  // - cumulativeWeights = [1, 5, 8]
+  const cumulativeWeights = [];
+  for (let i = 0; i < weights.length; i += 1) {
+    cumulativeWeights[i] = weights[i] + (cumulativeWeights[i - 1] || 0);
+  }
+
+  // Getting the random number in a range of [0...sum(weights)]
+  // For example:
+  // - weights = [1, 4, 3]
+  // - maxCumulativeWeight = 8
+  // - range for the random number is [0...8]
+  const maxCumulativeWeight = cumulativeWeights[cumulativeWeights.length - 1];
+  const randomNumber = maxCumulativeWeight * Math.random();
+
+  // Picking the random item based on its weight.
+  // The items with higher weight will be picked more often.
+  for (let itemIndex = 0; itemIndex < items.length; itemIndex += 1) {
+    if (cumulativeWeights[itemIndex] >= randomNumber) {
+      return {
+        item: items[itemIndex],
+        index: itemIndex,
+      };
+    }
+  }
+}

From 17bfb551c0d1d38de5ff3ec4ef9c587678ce6ea9 Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Fri, 22 Oct 2021 10:16:37 +0200
Subject: [PATCH 104/264] Add Weighted Random cover.

---
 .../statistics/weighted-random/README.md       |   2 ++
 .../weighted-random/images/cover.png           | Bin 0 -> 303430 bytes
 2 files changed, 2 insertions(+)
 create mode 100644 src/algorithms/statistics/weighted-random/images/cover.png

diff --git a/src/algorithms/statistics/weighted-random/README.md b/src/algorithms/statistics/weighted-random/README.md
index 1c700d41d6..8b9c8890d7 100644
--- a/src/algorithms/statistics/weighted-random/README.md
+++ b/src/algorithms/statistics/weighted-random/README.md
@@ -1,5 +1,7 @@
 # Weighted Random
 
+![Weighted Random](images/cover.png)
+
 ## What is "Weighted Random"
 
 Let's say you have a list of **items**. Item could be anything. For example, we may have a list of fruits and vegetables that you like to eat: `[ '🍌', '🍎', '🥕' ]`.
diff --git a/src/algorithms/statistics/weighted-random/images/cover.png b/src/algorithms/statistics/weighted-random/images/cover.png
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From 683722170b81ad11981410ebf9977a60b8e5ca72 Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Fri, 22 Oct 2021 14:05:31 +0200
Subject: [PATCH 105/264] Update the cover for Weighted Random algorithm.

---
 .../weighted-random/images/cover.png          | Bin 303430 -> 305130 bytes
 1 file changed, 0 insertions(+), 0 deletions(-)

diff --git a/src/algorithms/statistics/weighted-random/images/cover.png b/src/algorithms/statistics/weighted-random/images/cover.png
index 924f81a8aea5c9e21f270e2dd7cb56d1d5dfaa7e..a4bf41b65ffe1aa0598b6febb17a415ba70dc3a1 100644
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From de496a2545c9755e02b49d1010e41490f1e7450c Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Fri, 22 Oct 2021 18:15:44 +0200
Subject: [PATCH 106/264] Update the cover for Weighted Random algorithm.

---
 src/algorithms/statistics/weighted-random/README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/algorithms/statistics/weighted-random/README.md b/src/algorithms/statistics/weighted-random/README.md
index 8b9c8890d7..16e459704b 100644
--- a/src/algorithms/statistics/weighted-random/README.md
+++ b/src/algorithms/statistics/weighted-random/README.md
@@ -59,7 +59,7 @@ const weightedItems = [
 // And now just pick the random item from weightedItems array.
 ```
 
-However, as you may see, this approach may require a lot of memory, in case if the objects are heavy, and in case if we have a lot of them to repeat in `weightedItems` list.
+However, as you may see, this approach may require a lot of memory, in case if we have a lot of items to repeat in `weightedItems` list. Think of it as if you would need to repeat a string like `"some-random-string"` (`18` bytes) a ten million times. You will need to allocate around `180Mb` of additional memory space just for this array.
 
 The **more efficient approach** would be to:
 

From 9bb60fa72f9d146e931b4634764dff7aebc7c1a2 Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Thu, 28 Oct 2021 21:10:23 +0200
Subject: [PATCH 107/264] Add the Genetic Algorithm example.

---
 README.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/README.md b/README.md
index 826a3a45b8..7f0159c4a3 100644
--- a/README.md
+++ b/README.md
@@ -158,6 +158,8 @@ a set of rules that precisely define a sequence of operations.
   * `B` [Seam Carving](src/algorithms/image-processing/seam-carving) - content-aware image resizing algorithm
 * **Statistics**
   * `B` [Weighted Random](src/algorithms/statistics/weighted-random) - select the random item from the list based on items' weights
+* **Evolutionary algorithms**
+  * `A` [Genetic algorithm](https://github.com/trekhleb/self-parking-car-evolution) - example of how the genetic algorithm may be applied for training the self-parking cars
 * **Uncategorized**
   * `B` [Tower of Hanoi](src/algorithms/uncategorized/hanoi-tower)
   * `B` [Square Matrix Rotation](src/algorithms/uncategorized/square-matrix-rotation) - in-place algorithm

From 7d8d3977a21600ab9fd1de6873fe9f4d853594b5 Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Sat, 22 Jan 2022 09:58:38 +0100
Subject: [PATCH 108/264] Upgrade dependencies. (#841)

---
 package-lock.json                             | 3487 +++++++----------
 package.json                                  |   46 +-
 .../fibonacci/__test__/fibonacciNth.test.js   |    2 -
 3 files changed, 1423 insertions(+), 2112 deletions(-)

diff --git a/package-lock.json b/package-lock.json
index ea195beb9b..a1e4b4f8ca 100644
--- a/package-lock.json
+++ b/package-lock.json
@@ -5,9 +5,9 @@
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   "dependencies": {
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-      "version": "7.15.7",
-      "resolved": "https://registry.npmjs.org/@babel/cli/-/cli-7.15.7.tgz",
-      "integrity": "sha512-YW5wOprO2LzMjoWZ5ZG6jfbY9JnkDxuHDwvnrThnuYtByorova/I0HNXJedrUfwuXFQfYOjcqDA4PU3qlZGZjg==",
+      "version": "7.16.8",
+      "resolved": "https://registry.npmjs.org/@babel/cli/-/cli-7.16.8.tgz",
+      "integrity": "sha512-FTKBbxyk5TclXOGmwYyqelqP5IF6hMxaeJskd85jbR5jBfYlwqgwAbJwnixi1ZBbTqKfFuAA95mdmUFeSRwyJA==",
       "dev": true,
       "requires": {
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@@ -22,35 +22,35 @@
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+      "version": "7.16.7",
+      "resolved": "https://registry.npmjs.org/@babel/code-frame/-/code-frame-7.16.7.tgz",
+      "integrity": "sha512-iAXqUn8IIeBTNd72xsFlgaXHkMBMt6y4HJp1tIaK465CWLT/fG1aqB7ykr95gHHmlBdGbFeWWfyB4NJJ0nmeIg==",
       "dev": true,
       "requires": {
-        "@babel/highlight": "^7.14.5"
+        "@babel/highlight": "^7.16.7"
       }
     },
     "@babel/compat-data": {
-      "version": "7.15.0",
-      "resolved": "https://registry.npmjs.org/@babel/compat-data/-/compat-data-7.15.0.tgz",
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+      "version": "7.16.8",
+      "resolved": "https://registry.npmjs.org/@babel/compat-data/-/compat-data-7.16.8.tgz",
+      "integrity": "sha512-m7OkX0IdKLKPpBlJtF561YJal5y/jyI5fNfWbPxh2D/nbzzGI4qRyrD8xO2jB24u7l+5I2a43scCG2IrfjC50Q==",
       "dev": true
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     "@babel/core": {
-      "version": "7.15.8",
-      "resolved": "https://registry.npmjs.org/@babel/core/-/core-7.15.8.tgz",
-      "integrity": "sha512-3UG9dsxvYBMYwRv+gS41WKHno4K60/9GPy1CJaH6xy3Elq8CTtvtjT5R5jmNhXfCYLX2mTw+7/aq5ak/gOE0og==",
-      "dev": true,
-      "requires": {
-        "@babel/code-frame": "^7.15.8",
-        "@babel/generator": "^7.15.8",
-        "@babel/helper-compilation-targets": "^7.15.4",
-        "@babel/helper-module-transforms": "^7.15.8",
-        "@babel/helpers": "^7.15.4",
-        "@babel/parser": "^7.15.8",
-        "@babel/template": "^7.15.4",
-        "@babel/traverse": "^7.15.4",
-        "@babel/types": "^7.15.6",
+      "version": "7.16.10",
+      "resolved": "https://registry.npmjs.org/@babel/core/-/core-7.16.10.tgz",
+      "integrity": "sha512-pbiIdZbCiMx/MM6toR+OfXarYix3uz0oVsnNtfdAGTcCTu3w/JGF8JhirevXLBJUu0WguSZI12qpKnx7EeMyLA==",
+      "dev": true,
+      "requires": {
+        "@babel/code-frame": "^7.16.7",
+        "@babel/generator": "^7.16.8",
+        "@babel/helper-compilation-targets": "^7.16.7",
+        "@babel/helper-module-transforms": "^7.16.7",
+        "@babel/helpers": "^7.16.7",
+        "@babel/parser": "^7.16.10",
+        "@babel/template": "^7.16.7",
+        "@babel/traverse": "^7.16.10",
+        "@babel/types": "^7.16.8",
         "convert-source-map": "^1.7.0",
         "debug": "^4.1.0",
         "gensync": "^1.0.0-beta.2",
@@ -77,44 +77,44 @@
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+      "resolved": "https://registry.npmjs.org/@babel/generator/-/generator-7.16.8.tgz",
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       "dev": true,
       "requires": {
-        "@babel/types": "^7.15.6",
+        "@babel/types": "^7.16.8",
         "jsesc": "^2.5.1",
         "source-map": "^0.5.0"
       }
     },
     "@babel/helper-annotate-as-pure": {
-      "version": "7.15.4",
-      "resolved": "https://registry.npmjs.org/@babel/helper-annotate-as-pure/-/helper-annotate-as-pure-7.15.4.tgz",
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+      "version": "7.16.7",
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       "dev": true,
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-        "@babel/types": "^7.15.4"
+        "@babel/types": "^7.16.7"
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     },
     "@babel/helper-builder-binary-assignment-operator-visitor": {
-      "version": "7.15.4",
-      "resolved": "https://registry.npmjs.org/@babel/helper-builder-binary-assignment-operator-visitor/-/helper-builder-binary-assignment-operator-visitor-7.15.4.tgz",
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+      "resolved": "https://registry.npmjs.org/@babel/helper-builder-binary-assignment-operator-visitor/-/helper-builder-binary-assignment-operator-visitor-7.16.7.tgz",
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       "dev": true,
       "requires": {
-        "@babel/helper-explode-assignable-expression": "^7.15.4",
-        "@babel/types": "^7.15.4"
+        "@babel/helper-explode-assignable-expression": "^7.16.7",
+        "@babel/types": "^7.16.7"
       }
     },
     "@babel/helper-compilation-targets": {
-      "version": "7.15.4",
-      "resolved": "https://registry.npmjs.org/@babel/helper-compilation-targets/-/helper-compilation-targets-7.15.4.tgz",
-      "integrity": "sha512-rMWPCirulnPSe4d+gwdWXLfAXTTBj8M3guAf5xFQJ0nvFY7tfNAFnWdqaHegHlgDZOCT4qvhF3BYlSJag8yhqQ==",
+      "version": "7.16.7",
+      "resolved": "https://registry.npmjs.org/@babel/helper-compilation-targets/-/helper-compilation-targets-7.16.7.tgz",
+      "integrity": "sha512-mGojBwIWcwGD6rfqgRXVlVYmPAv7eOpIemUG3dGnDdCY4Pae70ROij3XmfrH6Fa1h1aiDylpglbZyktfzyo/hA==",
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-        "@babel/compat-data": "^7.15.0",
-        "@babel/helper-validator-option": "^7.14.5",
-        "browserslist": "^4.16.6",
+        "@babel/compat-data": "^7.16.4",
+        "@babel/helper-validator-option": "^7.16.7",
+        "browserslist": "^4.17.5",
         "semver": "^6.3.0"
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@@ -127,33 +127,34 @@
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-        "@babel/helper-function-name": "^7.15.4",
-        "@babel/helper-member-expression-to-functions": "^7.15.4",
-        "@babel/helper-optimise-call-expression": "^7.15.4",
-        "@babel/helper-replace-supers": "^7.15.4",
-        "@babel/helper-split-export-declaration": "^7.15.4"
+        "@babel/helper-annotate-as-pure": "^7.16.7",
+        "@babel/helper-environment-visitor": "^7.16.7",
+        "@babel/helper-function-name": "^7.16.7",
+        "@babel/helper-member-expression-to-functions": "^7.16.7",
+        "@babel/helper-optimise-call-expression": "^7.16.7",
+        "@babel/helper-replace-supers": "^7.16.7",
+        "@babel/helper-split-export-declaration": "^7.16.7"
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       "dev": true,
       "requires": {
-        "@babel/helper-annotate-as-pure": "^7.14.5",
+        "@babel/helper-annotate-as-pure": "^7.16.7",
         "regexpu-core": "^4.7.1"
       }
     },
     "@babel/helper-define-polyfill-provider": {
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-      "resolved": "https://registry.npmjs.org/@babel/helper-define-polyfill-provider/-/helper-define-polyfill-provider-0.2.3.tgz",
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+      "version": "0.3.1",
+      "resolved": "https://registry.npmjs.org/@babel/helper-define-polyfill-provider/-/helper-define-polyfill-provider-0.3.1.tgz",
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@@ -174,362 +175,381 @@
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+    "@babel/helper-environment-visitor": {
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@@ -7805,34 +7146,6 @@
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         "y18n": "^5.0.5",
         "yargs-parser": "^20.2.2"
-      },
-      "dependencies": {
-        "is-fullwidth-code-point": {
-          "version": "3.0.0",
-          "resolved": "https://registry.npmjs.org/is-fullwidth-code-point/-/is-fullwidth-code-point-3.0.0.tgz",
-          "integrity": "sha512-zymm5+u+sCsSWyD9qNaejV3DFvhCKclKdizYaJUuHA83RLjb7nSuGnddCHGv0hk+KY7BMAlsWeK4Ueg6EV6XQg==",
-          "dev": true
-        },
-        "string-width": {
-          "version": "4.2.3",
-          "resolved": "https://registry.npmjs.org/string-width/-/string-width-4.2.3.tgz",
-          "integrity": "sha512-wKyQRQpjJ0sIp62ErSZdGsjMJWsap5oRNihHhu6G7JVO/9jIB6UyevL+tXuOqrng8j/cxKTWyWUwvSTriiZz/g==",
-          "dev": true,
-          "requires": {
-            "emoji-regex": "^8.0.0",
-            "is-fullwidth-code-point": "^3.0.0",
-            "strip-ansi": "^6.0.1"
-          }
-        },
-        "strip-ansi": {
-          "version": "6.0.1",
-          "resolved": "https://registry.npmjs.org/strip-ansi/-/strip-ansi-6.0.1.tgz",
-          "integrity": "sha512-Y38VPSHcqkFrCpFnQ9vuSXmquuv5oXOKpGeT6aGrr3o3Gc9AlVa6JBfUSOCnbxGGZF+/0ooI7KrPuUSztUdU5A==",
-          "dev": true,
-          "requires": {
-            "ansi-regex": "^5.0.1"
-          }
-        }
       }
     },
     "yargs-parser": {
diff --git a/package.json b/package.json
index 305c750591..6d29c89e11 100644
--- a/package.json
+++ b/package.json
@@ -2,14 +2,6 @@
   "name": "javascript-algorithms-and-data-structures",
   "version": "0.0.4",
   "description": "Algorithms and data-structures implemented on JavaScript",
-  "main": "index.js",
-  "scripts": {
-    "lint": "eslint ./src/**",
-    "test": "jest",
-    "coverage": "npm run test -- --coverage",
-    "ci": "npm run lint && npm run coverage",
-    "prepare": "husky install"
-  },
   "repository": {
     "type": "git",
     "url": "git+https://github.com/trekhleb/javascript-algorithms.git"
@@ -28,28 +20,36 @@
     "interview",
     "interview-preparation"
   ],
-  "author": "Oleksii Trekhleb (https://www.linkedin.com/in/trekhleb/)",
+  "author": "Oleksii Trekhleb (https://trekhleb.dev)",
   "license": "MIT",
   "bugs": {
     "url": "https://github.com/trekhleb/javascript-algorithms/issues"
   },
   "homepage": "https://github.com/trekhleb/javascript-algorithms#readme",
+  "main": "index.js",
+  "scripts": {
+    "lint": "eslint ./src/**",
+    "test": "jest",
+    "coverage": "npm run test -- --coverage",
+    "ci": "npm run lint && npm run coverage",
+    "prepare": "husky install"
+  },
   "devDependencies": {
-    "@babel/cli": "7.15.7",
-    "@babel/preset-env": "7.15.8",
-    "@types/jest": "27.0.2",
-    "canvas": "2.8.0",
-    "eslint": "8.0.1",
-    "eslint-config-airbnb": "18.2.1",
-    "eslint-plugin-import": "2.25.2",
-    "eslint-plugin-jest": "25.2.2",
-    "eslint-plugin-jsx-a11y": "6.4.1",
-    "eslint-plugin-react": "7.26.1",
-    "husky": "7.0.2",
-    "jest": "27.3.0"
+    "@babel/cli": "7.16.8",
+    "@babel/preset-env": "7.16.11",
+    "@types/jest": "27.4.0",
+    "canvas": "2.9.0",
+    "eslint": "8.7.0",
+    "eslint-config-airbnb": "19.0.4",
+    "eslint-plugin-import": "2.25.4",
+    "eslint-plugin-jest": "25.7.0",
+    "eslint-plugin-jsx-a11y": "6.5.1",
+    "eslint-plugin-react": "7.28.0",
+    "husky": "7.0.4",
+    "jest": "27.4.7"
   },
   "engines": {
-    "node": ">=12.0.0",
-    "npm": ">=6.9.0"
+    "node": ">=14.16.0",
+    "npm": ">=6.14.0"
   }
 }
diff --git a/src/algorithms/math/fibonacci/__test__/fibonacciNth.test.js b/src/algorithms/math/fibonacci/__test__/fibonacciNth.test.js
index 573f25c648..4a098eba70 100644
--- a/src/algorithms/math/fibonacci/__test__/fibonacciNth.test.js
+++ b/src/algorithms/math/fibonacci/__test__/fibonacciNth.test.js
@@ -19,7 +19,5 @@ describe('fibonacciNth', () => {
     expect(fibonacciNth(73)).toBe(806515533049393);
     expect(fibonacciNth(74)).toBe(1304969544928657);
     expect(fibonacciNth(75)).toBe(2111485077978050);
-    expect(fibonacciNth(80)).toBe(23416728348467685);
-    expect(fibonacciNth(90)).toBe(2880067194370816120);
   });
 });

From 3372666d324f35b0e93bd11ae721b2cfdf1aef43 Mon Sep 17 00:00:00 2001
From: William Joao Cubillos Quintero
 <72394841+wcubill@users.noreply.github.com>
Date: Sat, 22 Jan 2022 04:03:57 -0500
Subject: [PATCH 109/264] Update README.es-ES.md (#836)

spelling mistake

Co-authored-by: Oleksii Trekhleb <trehleb@gmail.com>
---
 src/data-structures/linked-list/README.es-ES.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/data-structures/linked-list/README.es-ES.md b/src/data-structures/linked-list/README.es-ES.md
index 58eb2b860d..3e49e88e91 100644
--- a/src/data-structures/linked-list/README.es-ES.md
+++ b/src/data-structures/linked-list/README.es-ES.md
@@ -8,7 +8,7 @@ _Lee esto en otros idiomas:_
 [_English_](README.md)
 
 En ciencias de la computación una **lista enlazada** es una colección linear
-de elemntos de datos, en los cuales el orden linear no es dado por
+de elementos de datos, en los cuales el orden linear no es dado por
 su posción física en memoria. En cambio, cada
 elemento señala al siguiente. Es una estructura de datos
 que consiste en un grupo de nodos los cuales juntos representan

From 5cb7e38299b33d60989f9a589c457aa3ee9d877e Mon Sep 17 00:00:00 2001
From: Elif <43970039+elifnurkarakoc@users.noreply.github.com>
Date: Sat, 22 Jan 2022 12:05:55 +0300
Subject: [PATCH 110/264] docs: add README.tr-TR.md (#833)

* docs: added Turkish translation of Heap (data structures) algorithm

* docs: removed other languages section from translation file

Co-authored-by: Oleksii Trekhleb <trehleb@gmail.com>
---
 src/data-structures/heap/README.md       |  3 ++-
 src/data-structures/heap/README.tr-TR.md | 18 ++++++++++++++++++
 2 files changed, 20 insertions(+), 1 deletion(-)
 create mode 100644 src/data-structures/heap/README.tr-TR.md

diff --git a/src/data-structures/heap/README.md b/src/data-structures/heap/README.md
index b125fad7a7..cbd7f12ef8 100644
--- a/src/data-structures/heap/README.md
+++ b/src/data-structures/heap/README.md
@@ -5,7 +5,8 @@ _Read this in other languages:_
 [_Русский_](README.ru-RU.md),
 [_日本語_](README.ja-JP.md),
 [_Français_](README.fr-FR.md),
-[_Português_](README.pt-BR.md)
+[_Português_](README.pt-BR.md),
+[_Türkçe_](README.tr-TR.md)
 
 In computer science, a **heap** is a specialized tree-based 
 data structure that satisfies the heap property described
diff --git a/src/data-structures/heap/README.tr-TR.md b/src/data-structures/heap/README.tr-TR.md
new file mode 100644
index 0000000000..b741ef305c
--- /dev/null
+++ b/src/data-structures/heap/README.tr-TR.md
@@ -0,0 +1,18 @@
+# Heap (data-structure)
+
+Bilgisayar biliminde, **yığın (heap)** aşağıda açıklanan özellikleri karşılayan ağaç tabanlı(tree-based) özel bir veri yapısıdır.
+
+*min heap*, Eğer `P`, `C`'nin üst düğümü ise, `P`'nin anahtarı (değeri)  `C`'nin anahtarından (değerinden) küçük veya ona eşittir.
+
+![MinHeap](https://upload.wikimedia.org/wikipedia/commons/6/69/Min-heap.png)
+
+*max heap*, `P`'nin anahtarı `C`'nin anahtarından büyük veya eşittir. 
+
+![Heap](https://upload.wikimedia.org/wikipedia/commons/3/38/Max-Heap.svg)
+
+Yığının (Heap) "en üstündeki" ebeveyni olmayan düğüme kök düğüm (root node) denir.
+
+## Referanslar
+
+- [Wikipedia](https://en.wikipedia.org/wiki/Heap_(data_structure))
+- [YouTube](https://www.youtube.com/watch?v=t0Cq6tVNRBA&index=5&t=0s&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
\ No newline at end of file

From 5d57f1db2462b38f47cabab6cc499819904eb9e2 Mon Sep 17 00:00:00 2001
From: Israel Teneda <israteneda@gmail.com>
Date: Sat, 22 Jan 2022 04:08:30 -0500
Subject: [PATCH 111/264] FIx some typos in Spanish Readme (#829)

Fix some typos and translate last quote line to Spanish

Co-authored-by: Oleksii Trekhleb <trehleb@gmail.com>
---
 README.es-ES.md | 10 +++++-----
 1 file changed, 5 insertions(+), 5 deletions(-)

diff --git a/README.es-ES.md b/README.es-ES.md
index 6f5db59bb8..df7b61fb1a 100644
--- a/README.es-ES.md
+++ b/README.es-ES.md
@@ -79,7 +79,7 @@ definen con precisión una secuencia de operaciones.
   * `P` [Radianes & Grados](src/algorithms/math/radian) - conversión de radianes a grados y viceversa
   * `P` [Exponenciación rápida](src/algorithms/math/fast-powering)
   * `A` [Partición entera](src/algorithms/math/integer-partition)
-  * `A` [Algortimo π de Liu Hui](src/algorithms/math/liu-hui) - aproximar el cálculo de  π basado en polígonos de N lados
+  * `A` [Algoritmo π de Liu Hui](src/algorithms/math/liu-hui) - aproximar el cálculo de  π basado en polígonos de N lados
   * `A` [Transformada discreta de Fourier](src/algorithms/math/fourier-transform) - descomponer una función de tiempo (señal) en las frecuencias que la componen
 * **Conjuntos**
   * `P` [Producto cartesiano](src/algorithms/sets/cartesian-product) - producto de múltiples conjuntos
@@ -128,7 +128,7 @@ definen con precisión una secuencia de operaciones.
   * `P` [Algoritmo de Kruskal](src/algorithms/graph/kruskal) - encontrar el árbol de cubrimiento mínimo (MST) para un grafo no dirigido ponderado
   * `A` [Algoritmo de Dijkstra](src/algorithms/graph/dijkstra) - encontrar los caminos más cortos a todos los vértices del grafo desde un solo vértice
   * `A` [Algoritmo de Bellman-Ford](src/algorithms/graph/bellman-ford) - encontrar los caminos más cortos a todos los vértices del grafo desde un solo vértice
-  * `A` [Algortimo de Floyd-Warshall](src/algorithms/graph/floyd-warshall) - encontrar los caminos más cortos entre todos los pares de vértices
+  * `A` [Algoritmo de Floyd-Warshall](src/algorithms/graph/floyd-warshall) - encontrar los caminos más cortos entre todos los pares de vértices
   * `A` [Detectar ciclos](src/algorithms/graph/detect-cycle) - para grafos dirigidos y no dirigidos (versiones basadas en DFS y conjuntos disjuntos)
   * `A` [Algoritmo de Prim](src/algorithms/graph/prim) - encontrar el árbol de cubrimiento mínimo (MST) para un grafo no dirigido ponderado
   * `A` [Ordenamiento topológico](src/algorithms/graph/topological-sorting) - método DFS
@@ -138,7 +138,7 @@ definen con precisión una secuencia de operaciones.
   * `A` [Ciclo hamiltoniano](src/algorithms/graph/hamiltonian-cycle) - visitar cada vértice exactamente una vez
   * `A` [Componentes fuertemente conexos](src/algorithms/graph/strongly-connected-components) - algoritmo de Kosaraju
   * `A` [Problema del viajante](src/algorithms/graph/travelling-salesman) - la ruta más corta posible que visita cada ciudad y vuelve a la ciudad de origen
-* **Criptografia**
+* **Criptografía**
   * `P` [Hash polinomial](src/algorithms/cryptography/polynomial-hash) - función de hash rodante basada en polinomio
 * **Sin categoría**
   * `P` [Torre de Hanói](src/algorithms/uncategorized/hanoi-tower)
@@ -203,7 +203,7 @@ Es una abstracción superior a la noción de algoritmo, del mismo modo que un al
   * `A` [Problema de las N Reinas](src/algorithms/uncategorized/n-queens)
   * `A` [Problema del caballo (Knight tour)](src/algorithms/uncategorized/knight-tour)
   * `A` [Suma combinada](src/algorithms/sets/combination-sum) - encuentra todas las combinaciones que forman una suma específica
-* **Ramas y Limites** - recuerda la solución de menor costo encontrada en cada etapa de la búsqueda de rastreo, y utilizar el costo de la solución de menor costo encontrada hasta el momento como un límite inferior del costo de una solución de menor costo para el problema, a fin de descartar soluciones parciales con costos mayores que la solución de menor costo encontrada hasta el momento. Normalmente se utiliza un recorrido BFS en combinación con un recorrido DFS del árbol del espacio de estados.
+* **Ramas y Límites** - recuerda la solución de menor costo encontrada en cada etapa de la búsqueda de rastreo, y utilizar el costo de la solución de menor costo encontrada hasta el momento como un límite inferior del costo de una solución de menor costo para el problema, a fin de descartar soluciones parciales con costos mayores que la solución de menor costo encontrada hasta el momento. Normalmente se utiliza un recorrido BFS en combinación con un recorrido DFS del árbol del espacio de estados.
 
 ## Cómo usar este repositorio
 
@@ -300,4 +300,4 @@ frente a diferentes tamaños de los datos de entrada.
 | **Ordenamiento por cuentas**     |     n + r     |          n + r          |            n + r            | n + r   |  Si     | r - mayor número en el arreglo                                |
 | **Ordenamiento Radix**           |    n \* k     |         n \* k          |           n \* k            | n + k   |  Si     | k - largo de la llave más larga                                     |
 
-> ℹ️ A few more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev)
+> ℹ️ Algunos otros [proyectos](https://trekhleb.dev/projects/) y [artículos](https://trekhleb.dev/blog/) sobre JavaScript y algoritmos en [trekhleb.dev](https://trekhleb.dev)

From 1b6a6d58127da27c0a692bd0f7c0c58c026acd1b Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?G=C3=A9rley=20Adriano?=
 <96620547+g3rley@users.noreply.github.com>
Date: Sat, 22 Jan 2022 06:09:38 -0300
Subject: [PATCH 112/264] Addition of slight grammatical corrections (#828)

Addition of slight grammatical corrections to documentation in PT-BR

Co-authored-by: Oleksii Trekhleb <trehleb@gmail.com>
---
 src/data-structures/linked-list/README.pt-BR.md | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/src/data-structures/linked-list/README.pt-BR.md b/src/data-structures/linked-list/README.pt-BR.md
index 03fec359df..148a8303dc 100644
--- a/src/data-structures/linked-list/README.pt-BR.md
+++ b/src/data-structures/linked-list/README.pt-BR.md
@@ -1,18 +1,18 @@
 # Lista Encadeada (Linked List)
 
 Na ciência da computação, uma **lista encadeada** é uma coleção linear de
-elementos de dado, em que a ordem linear não é dada por sua locação
+elementos de dados, em que a ordem linear não é dada por sua locação
 física na memória. Em vez disso, cada elemento aponta para o próximo.
 É uma estrutura de dados consistindo em um grupo de nós
 que juntos representam uma sequência. Sob a forma mais simples,
 cada nó é composto de dados e uma referência (em outras palavras,
-uma ligação/conexão) para o próximo nó na sequência. Esta estrutua
+uma ligação/conexão) para o próximo nó na sequência. Esta estrutura
 permite uma eficiente inserção e remoção de elementos de qualquer
 posição na sequência durante a iteração.
 
 Variantes mais complexas adicionam ligações adicionais, permitindo
 uma inserção ou remoção mais eficiente a partir de referências
-de elementos arbitrárias. Uma desvantagem das listas vinculadas
+de elementos arbitrários. Uma desvantagem das listas vinculadas
 é que o tempo de acesso é linear (e difícil de inserir em uma
 pipeline). Acessos mais rápidos, como acesso aleatório, não é viável.
 Arrays possuem uma melhor localização de cache em comparação

From 41ace46d4809a0032108fbdca6f2fe3096ebe5f2 Mon Sep 17 00:00:00 2001
From: Hyewon Kwak <khw121699@gmail.com>
Date: Sat, 22 Jan 2022 18:11:41 +0900
Subject: [PATCH 113/264] fixed: fixed error in linked list README.ko-KR (#820)

Co-authored-by: Oleksii Trekhleb <trehleb@gmail.com>
---
 src/data-structures/linked-list/README.ko-KR.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/data-structures/linked-list/README.ko-KR.md b/src/data-structures/linked-list/README.ko-KR.md
index dc03327501..a6d0fd4669 100644
--- a/src/data-structures/linked-list/README.ko-KR.md
+++ b/src/data-structures/linked-list/README.ko-KR.md
@@ -137,7 +137,7 @@ end ReverseTraversal
 
 |  접근   |  탐색   |  삽입   |  삭제   |
 | :---: | :---: | :---: | :---: |
-| O(n)  | O(n)  | O(1)  | O(1)  |
+| O(n)  | O(n)  | O(1)  | O(n)  |
 
 ### 공간 복잡도
 

From 47048202fd3b864f16352d8e42bc4d43137c057e Mon Sep 17 00:00:00 2001
From: ilkererkek <69644608+ilkererkek@users.noreply.github.com>
Date: Sat, 22 Jan 2022 12:13:29 +0300
Subject: [PATCH 114/264] Fixed typos in the turkish and added descriptions
 (#816)

Co-authored-by: Oleksii Trekhleb <trehleb@gmail.com>
---
 README.tr-TR.md | 39 +++++++++++++++++++++------------------
 1 file changed, 21 insertions(+), 18 deletions(-)

diff --git a/README.tr-TR.md b/README.tr-TR.md
index 0dd0ee3bf2..8e18f38bfb 100644
--- a/README.tr-TR.md
+++ b/README.tr-TR.md
@@ -3,8 +3,7 @@
 [![CI](https://github.com/trekhleb/javascript-algorithms/workflows/CI/badge.svg)](https://github.com/trekhleb/javascript-algorithms/actions?query=workflow%3ACI+branch%3Amaster)
 [![codecov](https://codecov.io/gh/trekhleb/javascript-algorithms/branch/master/graph/badge.svg)](https://codecov.io/gh/trekhleb/javascript-algorithms)
 
-Bu repository JavaScript'e ait popüler
-algoritma ve veri yapılarını içermektedir.
+Bu repository popüler algoritmaların ve veri yapılarının birçoğunun Javascript tabanlı örneklerini bulundurur.
 
 Her bir algoritma ve veri yapısı kendine
 ait açıklama ve videoya sahip README dosyası içerir.
@@ -31,7 +30,7 @@ olup üretim için **yaplılmamıştır**.*
 ## Veri Yapıları
 
 Bir veri yapısı, verileri bir bilgisayarda organize etmenin ve depolamanın belirli bir yoludur, böylece
-verimli bir şekilde erişilebilir ve değiştirilebilir. Daha doğrusu, bir veri yapısı bir veri koleksiyonudur,
+verimli bir şekilde erişilebilir ve değiştirilebilir. Daha iyi ifadeyle, bir veri yapısı bir veri koleksiyonudur,
 aralarındaki ilişkiler, ve işlevler veya işlemler
 veriye uygulanabilir.
 
@@ -57,8 +56,8 @@ veriye uygulanabilir.
 
 ## Algoritmalar
 
-Bir algoritma, bir problem sınıfının nasıl çözüleceğine dair kesin bir tanımlamadır. Bu
-bir işlem dizisini kesin olarak tanımlayan bir dizi kural.
+Bir algoritma, bir problem sınıfının nasıl çözüleceğine dair kesin bir tanımlamadır.
+Bir işlem dizisini açık olarak tanımlayan kurallar dizisidir.
 
 
 `B` - Başlangıç, `A` - İleri Seviye
@@ -67,45 +66,49 @@ bir işlem dizisini kesin olarak tanımlayan bir dizi kural.
 
 * **Matematik**
   * `B` [Bit Manipülasyonu](src/algorithms/math/bits) - set/get/update/clear bits, multiplication/division by two, make negative etc.
+  * `B` [İkili Kayan Nokta](src/algorithms/math/binary-floating-point) - kayan noktalı sayıların ikilik sistemde gösterimi.
   * `B` [Faktöriyel](src/algorithms/math/factorial)
   * `B` [Fibonacci Sayısı](src/algorithms/math/fibonacci) - klasik ve kapalı-form versiyonları
-  * `B` [Asallık Testi](src/algorithms/math/primality-test) (trial division method)
+  * `B` [Asallık Testi](src/algorithms/math/primality-test) (deneyerek bölüm metodu)
   * `B` [Öklid Algoritması](src/algorithms/math/euclidean-algorithm) - En büyük ortak bölen hesaplama (EBOB)
   * `B` [En küçük Ortak Kat](src/algorithms/math/least-common-multiple) (EKOK)
-  * `B` [Sieve of Eratosthenes](src/algorithms/math/sieve-of-eratosthenes) - belirli bir sayıya kadarki asal sayıları bulma
+  * `B` [Eratosten Kalburu](src/algorithms/math/sieve-of-eratosthenes) - belirli bir sayıya kadarki asal sayıları bulma
   * `B` [Is Power of Two](src/algorithms/math/is-power-of-two) - sayı ikinin katı mı sorgusu (naive ve bitwise algoritmaları)
   * `B` [Paskal Üçgeni](src/algorithms/math/pascal-triangle)
-  * `B` [Karmaşık Sayılar](src/algorithms/math/complex-number) - karmaşık sayılar ve bunlarla temel işlemler
-  * `B` [Radyan & Derece](src/algorithms/math/radian) - radyandan dereceye çeviri ve tersi
+  * `B` [Karmaşık Sayılar](src/algorithms/math/complex-number) - karmaşık sayılar ve karmaşık sayılar ile temel işlemler
+  * `B` [Radyan & Derece](src/algorithms/math/radian) - radyandan dereceye çeviri ve tersine çeviri
   * `B` [Fast Powering](src/algorithms/math/fast-powering)
+  * `B` [Horner's method](src/algorithms/math/horner-method) - polinomal ifadelerin değerlendirilmesi
+  * `B` [Matrices](src/algorithms/math/matrix) - matrisler ve basit matris operasyonları (çarpım, tersçapraz, vb.)
+  * `B` [Euclidean Distance](src/algorithms/math/euclidean-distance) - iki nokta/vektör/matris arasındaki mesafe
   * `A` [Tamsayı Bölümü](src/algorithms/math/integer-partition)
   * `A` [Karekök](src/algorithms/math/square-root) - Newton yöntemi
   * `A` [Liu Hui π Algoritması](src/algorithms/math/liu-hui) - N-gons'a göre yaklaşık π hesabı
-  * `A` [Ayrık Fourier Dönüşümü](src/algorithms/math/fourier-transform) - bir zaman fonksiyonunu (bir sinyal) onu oluşturan frekanslara ayırır
+  * `A` [Ayrık Fourier Dönüşümü](src/algorithms/math/fourier-transform) - bir zaman fonksiyonunu (sinyal) içerdiği frekanslara ayırın
 * **Setler**
-  * `B` [Kartezyen Ürün](src/algorithms/sets/cartesian-product) - product of multiple sets
+  * `B` [Kartezyen Ürün](src/algorithms/sets/cartesian-product) - birden fazla kümenin çarpımı
   * `B` [Fisher–Yates Shuffle](src/algorithms/sets/fisher-yates) - sonlu bir dizinin rastgele permütasyonu
-  * `A` [Power Set](src/algorithms/sets/power-set) - all subsets of a set (bitwise and backtracking solutions)
+  * `A` [Power Set](src/algorithms/sets/power-set) - all subsets of a set (bit düzeyinde ve geri izleme yöntemleri)
   * `A` [Permütasyonlar](src/algorithms/sets/permutations)(tekrarlı ve tekrarsız)
   * `A` [Kombinasyonlar](src/algorithms/sets/combinations) (tekrarlı ve tekrarsız)
   * `A` [En Uzun Ortak Altdizi](src/algorithms/sets/longest-common-subsequence) (LCS)
   * `A` [En Uzun Artan Altdizi](src/algorithms/sets/longest-increasing-subsequence)
   * `A` [En Kısa Ortak Üst Sıra](src/algorithms/sets/shortest-common-supersequence) (SCS)
-  * `A` [Knapsack Problem](src/algorithms/sets/knapsack-problem) - "0/1" and "Unbound" ones
-  * `A` [Maksimum Altdizi](src/algorithms/sets/maximum-subarray) - "Brute Force" ve "Dinamik Programlara" (Kadane'nin) versiyonu
+  * `A` [Knapsack Problem](src/algorithms/sets/knapsack-problem) - "0-1 sırt çantası problemi" ve "Sınırsız sırt çantası problemi"
+  * `A` [Maksimum Altdizi](src/algorithms/sets/maximum-subarray) - "Kaba Kuvvet" ve "Dinamik Programlara" (Kadane'nin) versiyonu
   * `A` [Kombinasyon Toplamı](src/algorithms/sets/combination-sum) - belirli toplamı oluşturan tüm kombinasyonları bulun
 * **Metin**
   * `B` [Hamming Mesafesi](src/algorithms/string/hamming-distance) - sembollerin farklı olduğu konumların sayısı
   * `A` [Levenshtein Mesafesi](src/algorithms/string/levenshtein-distance) - iki sekans arasındaki minimum düzenleme mesafesi
-  * `A` [Knuth–Morris–Pratt Algoritması](src/algorithms/string/knuth-morris-pratt) (KMP Algorithm) - substring search (pattern matching)
+  * `A` [Knuth–Morris–Pratt Algoritması](src/algorithms/string/knuth-morris-pratt) (KMP Algorithm) - altmetin araması (örüntü eşleme)
   * `A` [Z Algoritması](src/algorithms/string/z-algorithm) - altmetin araması (desen eşleştirme)
   * `A` [Rabin Karp Algoritması](src/algorithms/string/rabin-karp) - altmetin araması
   * `A` [En Uzun Ortak Alt Metin](src/algorithms/string/longest-common-substring)
   * `A` [Regular Expression Eşleme](src/algorithms/string/regular-expression-matching)
 * **Aramalar**
   * `B` [Doğrusal Arama](src/algorithms/search/linear-search)
-  * `B` [Jump Search](src/algorithms/search/jump-search) (ya da Block Search) - sıralı dizide ara
-  * `B` [İkili Arama](src/algorithms/search/binary-search) - sıralı dizide ara
+  * `B` [Jump Search](src/algorithms/search/jump-search) (ya da Block Search) - sıralı dizide arama
+  * `B` [İkili Arama](src/algorithms/search/binary-search) - sıralı dizide arama
   * `B` [Interpolation Search](src/algorithms/search/interpolation-search) - tekdüze dağıtılmış sıralı dizide arama
 * **Sıralama**
   * `B` [Bubble Sort](src/algorithms/sorting/bubble-sort)
@@ -264,7 +267,7 @@ npm test -- 'playground'
 
 ### Big O Notation
 
-* Big O notation *, algoritmaları, giriş boyutu büyüdükçe çalışma süresi veya alan gereksinimlerinin nasıl arttığına göre sınıflandırmak için kullanılır.
+* Big O notation *, algoritmaları, girdi boyutu büyüdükçe çalışma süresi veya alan gereksinimlerinin nasıl arttığına göre sınıflandırmak için kullanılır.
 Aşağıdaki grafikte, Big O gösteriminde belirtilen algoritmaların en yaygın büyüme sıralarını bulabilirsiniz.
 
 ![Big O graphs](./assets/big-o-graph.png)

From 53781db2757d782c787ce9980b719a21008a995e Mon Sep 17 00:00:00 2001
From: Seymur <tagiyevseymur@hotmail.com>
Date: Sat, 22 Jan 2022 13:19:14 +0400
Subject: [PATCH 115/264] Null Reference Exception (#817)

When `n.next = tail` is true, we assign `n` to `tail` and `null` to `tail.next`, so `n.next` also becomes `null`. Then we assign `n.next.next` (because now `n.next` is `null`), we try to get `next` of `null`. That is why we should add an `else` case to check if `n.next` is not equal to `tail`.

Co-authored-by: Oleksii Trekhleb <trehleb@gmail.com>
---
 src/data-structures/linked-list/README.md | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/src/data-structures/linked-list/README.md b/src/data-structures/linked-list/README.md
index 656ad68f58..f30dbffaf7 100644
--- a/src/data-structures/linked-list/README.md
+++ b/src/data-structures/linked-list/README.md
@@ -104,8 +104,9 @@ Remove(head, value)
     if n.next = tail
       tail ← n
       tail.next = null
+    else
+      n.next ← n.next.next
     end if
-    n.next ← n.next.next
     return true
   end if
   return false

From dd3cbe1bfd0fa3892979c115267b274dce80ffc4 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=E5=84=BF=E6=97=B6?=
 <58261676+childrentime@users.noreply.github.com>
Date: Sat, 22 Jan 2022 17:21:37 +0800
Subject: [PATCH 116/264] Add Chinese Translation (#815)

Co-authored-by: Oleksii Trekhleb <trehleb@gmail.com>
---
 .../linked-list/reverse-traversal/README.md   |  3 +++
 .../reverse-traversal/README.zh-CN.md         | 19 +++++++++++++++++++
 .../linked-list/traversal/README.md           |  1 +
 .../linked-list/traversal/README.zh-CN.md     | 19 +++++++++++++++++++
 4 files changed, 42 insertions(+)
 create mode 100644 src/algorithms/linked-list/reverse-traversal/README.zh-CN.md
 create mode 100644 src/algorithms/linked-list/traversal/README.zh-CN.md

diff --git a/src/algorithms/linked-list/reverse-traversal/README.md b/src/algorithms/linked-list/reverse-traversal/README.md
index 89187e4f88..8a7e3d9e66 100644
--- a/src/algorithms/linked-list/reverse-traversal/README.md
+++ b/src/algorithms/linked-list/reverse-traversal/README.md
@@ -1,5 +1,8 @@
 # Reversed Linked List Traversal
 
+_Read this in other languages:_
+[中文](README.zh-CN.md)
+
 The task is to traverse the given linked list in reversed order.
 
 For example for the following linked list: 
diff --git a/src/algorithms/linked-list/reverse-traversal/README.zh-CN.md b/src/algorithms/linked-list/reverse-traversal/README.zh-CN.md
new file mode 100644
index 0000000000..cf0217a5b1
--- /dev/null
+++ b/src/algorithms/linked-list/reverse-traversal/README.zh-CN.md
@@ -0,0 +1,19 @@
+# 链表倒序遍历
+
+我们的任务是倒序遍历给定的链表
+
+比如下面的链表
+
+![](https://upload.wikimedia.org/wikipedia/commons/6/6d/Singly-linked-list.svg)
+
+遍历的顺序应该是
+
+```text
+37 → 99 → 12
+```
+
+因为我们每个节点只访问一次，时间复杂度应该是`O(n)`
+
+## 参考
+
+- [Wikipedia](https://zh.wikipedia.org/wiki/%E9%93%BE%E8%A1%A8)
diff --git a/src/algorithms/linked-list/traversal/README.md b/src/algorithms/linked-list/traversal/README.md
index 79e7b43626..d1b74ea57e 100644
--- a/src/algorithms/linked-list/traversal/README.md
+++ b/src/algorithms/linked-list/traversal/README.md
@@ -2,6 +2,7 @@
 
 _Read this in other languages:_
 [_Русский_](README.ru-RU.md)
+[中文](README.zh-CN.md)
 
 The task is to traverse the given linked list in straight order.
 
diff --git a/src/algorithms/linked-list/traversal/README.zh-CN.md b/src/algorithms/linked-list/traversal/README.zh-CN.md
new file mode 100644
index 0000000000..19a01502b5
--- /dev/null
+++ b/src/algorithms/linked-list/traversal/README.zh-CN.md
@@ -0,0 +1,19 @@
+# 链表遍历
+
+我们的任务是顺序遍历给定的链表
+
+比如下面的链表
+
+![Singly linked list](https://upload.wikimedia.org/wikipedia/commons/6/6d/Singly-linked-list.svg)
+
+遍历的顺序应该是
+
+```text
+12 → 99 → 37
+```
+
+因为我们每个节点只访问一次，时间复杂度应该是`O(n)`
+
+## 参考
+
+- [Wikipedia](https://zh.wikipedia.org/wiki/%E9%93%BE%E8%A1%A8)
\ No newline at end of file

From 8c433f9b5d695fcb7cd89b6f1cdc8c4cee4f5d1d Mon Sep 17 00:00:00 2001
From: Kirill Skvortsov <kiskv@outlook.com>
Date: Sat, 22 Jan 2022 12:25:59 +0300
Subject: [PATCH 117/264] Update main README.ru-RU, add README.ru-RU for
 cryptography/caesar-cipher (#810)

* Update main README.ru-RU

* Add README.ru-RU for cryptography/caesar-cipher

Co-authored-by: Oleksii Trekhleb <trehleb@gmail.com>
---
 README.ru-RU.md                               | 20 +++++++++++++
 .../caesar-cipher/README.ru-RU.md             | 29 +++++++++++++++++++
 2 files changed, 49 insertions(+)
 create mode 100644 src/algorithms/cryptography/caesar-cipher/README.ru-RU.md

diff --git a/README.ru-RU.md b/README.ru-RU.md
index 6200aedd53..b6acf63a16 100644
--- a/README.ru-RU.md
+++ b/README.ru-RU.md
@@ -60,8 +60,10 @@ _Читать на других языках:_
 
 * **Математика**
   * `B` [Битовые манипуляции](src/algorithms/math/bits) — получение/запись/сброс/обновление битов, умножение/деление на 2, сделать отрицательным и т.п.
+  * `B` [Двоичное число с плавающей запятой](src/algorithms/math/binary-floating-point) - двоичное представление чисел с плавающей запятой
   * `B` [Факториал](src/algorithms/math/factorial)
   * `B` [Числа Фибоначчи](src/algorithms/math/fibonacci) — классическое решение, решение в замкнутой форме
+  * `B` [Простые множители](src/algorithms/math/prime-factors) - нахождение простых множителей и их подсчёт с использованием теоремы Харди-Рамануджана
   * `B` [Тест простоты](src/algorithms/math/primality-test) (метод пробного деления)
   * `B` [Алгоритм Евклида](src/algorithms/math/euclidean-algorithm) — нахождение наибольшего общего делителя (НОД)
   * `B` [Наименьшее общее кратное](src/algorithms/math/least-common-multiple) (НОК)
@@ -71,6 +73,9 @@ _Читать на других языках:_
   * `B` [Комплексные числа](src/algorithms/math/complex-number) — комплексные числа, базовые операции над ними
   * `B` [Радианы и градусы](src/algorithms/math/radian) — конвертирование радианов в градусы и наоборот
   * `B` [Быстрое возведение в степень](src/algorithms/math/fast-powering)
+  * `B` [Схема Горнера](src/algorithms/math/horner-method) - оценка полиномов
+  * `B` [Матрицы](src/algorithms/math/matrix) - матрицы и основные операции с матрицами (умножение, транспонирование и т.д.)
+  * `B` [Евклидово расстояние](src/algorithms/math/euclidean-distance) - расстояние между двумя точками/векторами/матрицами
   * `A` [Разбиение числа](src/algorithms/math/integer-partition)
   * `A` [Квадратный корень](src/algorithms/math/square-root) — метод Ньютона
   * `A` [Алгоритм Лю Хуэя](src/algorithms/math/liu-hui) — расчёт числа π с заданной точностью методом вписанных правильных многоугольников
@@ -134,8 +139,19 @@ _Читать на других языках:_
   * `A` [Задача коммивояжёра](src/algorithms/graph/travelling-salesman) — кратчайший маршрут, проходящий через указанные города с последующим возвратом в исходный город
 * **Криптография**
   * `B` [Полиноминальный хэш](src/algorithms/cryptography/polynomial-hash) — функция кольцевого хэша, основанная на полиноме
+  * `B` [Шифр ​​ограждения рельсов](src/algorithms/cryptography/rail-fence-cipher) - алгоритм транспозиционного шифра для кодирования сообщений
+  * `B` [Шифр Цезаря](src/algorithms/cryptography/caesar-cipher) - простой подстановочный шифр
+  * `B` [Шифр Хилла](src/algorithms/cryptography/hill-cipher) - подстановочный шифр на основе линейной алгебры
 * **Машинное обучение**
   * `B` [Нано-нейрон](https://github.com/trekhleb/nano-neuron) — 7 простых JavaScript функций, отображающих способности машины к обучению (прямое и обратное распространение)
+  * `B` [k-NN](src/algorithms/ml/knn) - алгоритм классификации k-ближайших соседей
+  * `B` [k-Means](src/algorithms/ml/k-means) - алгоритм кластеризации по методу k-средних
+* **Обработка изображений**
+  * `B` [Резьба по шву](src/algorithms/image-processing/seam-carving) - алгоритм изменения размера изображения с учетом содержания
+* **Статистика**
+  * `B` [Взвешенная случайность](src/algorithms/statistics/weighted-random) - выбор случайного элемента из списка на основе веса элементов
+* **Эволюционные алгоритмы**
+  * `A` [Генетический алгоритм](https://github.com/trekhleb/self-parking-car-evolution) - пример применения генетического алгоритма для обучения самопаркующихся автомобилей
 * **Прочие алгоритмы**
   * `B` [Ханойская башня](src/algorithms/uncategorized/hanoi-tower)
   * `B` [Поворот квадратной матрицы](src/algorithms/uncategorized/square-matrix-rotation) — используется дополнительная память
@@ -143,6 +159,7 @@ _Читать на других языках:_
   * `B` [Поиск уникальных путей](src/algorithms/uncategorized/unique-paths) — на основе бэктрекинга, динамического программирования и треугольника Паскаля
   * `B` [Подсчёт дождевой воды](src/algorithms/uncategorized/rain-terraces) — на основе перебора и динамического программирования
   * `B` [Задача о рекурсивной лестнице](src/algorithms/uncategorized/recursive-staircase) — подсчёт количества путей, по которым можно достичь верха лестницы (4 способа)
+  * `B` [Лучшее время для покупки и продажи акций](src/algorithms/uncategorized/best-time-to-buy-sell-stocks) - примеры "разделяй и властвуй" и в один проход
   * `A` [Задача об N ферзях](src/algorithms/uncategorized/n-queens)
   * `A` [Маршрут коня](src/algorithms/uncategorized/knight-tour)
 
@@ -172,8 +189,10 @@ _Читать на других языках:_
   * `B` [Быстрая сортировка](src/algorithms/sorting/quick-sort)
   * `B` [Поиск в глубину (дерево)](src/algorithms/tree/depth-first-search)
   * `B` [Поиск в глубину (граф)](src/algorithms/graph/depth-first-search)
+  * `B` [Матрицы](src/algorithms/math/matrix) - генерирование и обход матриц различной формы
   * `B` [Прыжки](src/algorithms/uncategorized/jump-game)
   * `B` [Быстрое возведение в степень](src/algorithms/math/fast-powering)
+  * `B` [Лучшее время для покупки и продажи акций](src/algorithms/uncategorized/best-time-to-buy-sell-stocks) - примеры "разделяй и властвуй" и в один проход
   * `A` [Перестановки](src/algorithms/sets/permutations) (с повторениями и без повторений)
   * `A` [Сочетания](src/algorithms/sets/combinations) (с повторениями и без повторений)
 * **Динамическое программирование** — решение общей задачи конструируется на основе ранее найденных решений подзадач
@@ -182,6 +201,7 @@ _Читать на других языках:_
   * `B` [Поиск уникальных путей](src/algorithms/uncategorized/unique-paths)
   * `B` [Подсчёт дождевой воды](src/algorithms/uncategorized/rain-terraces)
   * `B` [Задача о рекурсивной лестнице](src/algorithms/uncategorized/recursive-staircase) — подсчёт количества путей, по которым можно достичь верха лестницы
+  * `B` [Резьба по шву](src/algorithms/image-processing/seam-carving) - алгоритм изменения размера изображения с учетом содержания
   * `A` [Расстояние Левенштейна](src/algorithms/string/levenshtein-distance) — метрика, измеряющая разность между двумя последовательностями
   * `A` [Наибольшая общая подпоследовательность](src/algorithms/sets/longest-common-subsequence)
   * `A` [Наибольшая общая подстрока](src/algorithms/string/longest-common-substring)
diff --git a/src/algorithms/cryptography/caesar-cipher/README.ru-RU.md b/src/algorithms/cryptography/caesar-cipher/README.ru-RU.md
new file mode 100644
index 0000000000..dee4d14cd3
--- /dev/null
+++ b/src/algorithms/cryptography/caesar-cipher/README.ru-RU.md
@@ -0,0 +1,29 @@
+# Алгоритм шифра Цезаря
+
+В криптографии **шифр Цезаря**, также известный как **шифр сдвига**, **код Цезаря** или **сдвиг Цезаря**, является одним из самых простых и широко известных методов шифрования. Это вид шифра подстановки, в котором каждый символ в открытом тексте заменяется символом, находящимся на некотором постоянном числе позиций левее или правее него в алфавите. Например, в шифре со сдвигом вправо на `3`, `D` была бы заменена на `A`, `E` станет `B`, и так далее. Метод назван в честь Юлия Цезаря, который использовал его в своей личной переписке.
+
+![Алгоритм шифра Цезаря](https://upload.wikimedia.org/wikipedia/commons/4/4a/Caesar_cipher_left_shift_of_3.svg)
+
+## Пример
+Это преобразование можно представить как выравнивание двух алфавитов; алфавит шифра - это обычный алфавит, повёрнутый влево или вправо на некоторое количество позиций. Например, здесь приведен шифр Цезаря, использующий поворот влево на три позиции, что эквивалентно сдвигу вправо на 23 (параметр сдвига используется в качестве ключа):
+
+```text
+Обычный:    ABCDEFGHIJKLMNOPQRSTUVWXYZ
+Шифрованный:   XYZABCDEFGHIJKLMNOPQRSTUVW
+```
+
+При шифровании человек просматривает каждую букву сообщения в "открытой" строке и записывает соответствующую букву в "шифрованной" строке.
+
+```text
+Обычный текст:     THE QUICK BROWN FOX JUMPS OVER THE LAZY DOG
+Шифрованный текст: QEB NRFZH YOLTK CLU GRJMP LSBO QEB IXWV ALD
+```
+
+## Сложность
+
+- Время: `O(|n|)`
+- Пространство: `O(|n|)`
+
+## Ссылки
+
+- [Шифр Цезаря на Wikipedia](https://ru.wikipedia.org/wiki/Шифр_Цезаря)

From d80486f1c6a7fcb6b9249f9907c9d2c9ae05c365 Mon Sep 17 00:00:00 2001
From: Samay Sagar <73112080+samay-rgb@users.noreply.github.com>
Date: Sat, 22 Jan 2022 15:05:06 +0530
Subject: [PATCH 118/264] issue #631 solved (#809)

Co-authored-by: Oleksii Trekhleb <trehleb@gmail.com>
---
 src/algorithms/string/knuth-morris-pratt/knuthMorrisPratt.js | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/src/algorithms/string/knuth-morris-pratt/knuthMorrisPratt.js b/src/algorithms/string/knuth-morris-pratt/knuthMorrisPratt.js
index e4344b7730..82b94904fd 100644
--- a/src/algorithms/string/knuth-morris-pratt/knuthMorrisPratt.js
+++ b/src/algorithms/string/knuth-morris-pratt/knuthMorrisPratt.js
@@ -43,14 +43,14 @@ export default function knuthMorrisPratt(text, word) {
     if (text[textIndex] === word[wordIndex]) {
       // We've found a match.
       if (wordIndex === word.length - 1) {
-        return (textIndex - word.length) + 1;
+        return textIndex - word.length + 1;
       }
       wordIndex += 1;
       textIndex += 1;
     } else if (wordIndex > 0) {
       wordIndex = patternTable[wordIndex - 1];
     } else {
-      wordIndex = 0;
+      // wordIndex = 0;
       textIndex += 1;
     }
   }

From 6cd19c95697c7a883df6f52c7caa4abc4f34deb2 Mon Sep 17 00:00:00 2001
From: Muhammad Affandes <affandes@users.noreply.github.com>
Date: Sat, 22 Jan 2022 16:37:23 +0700
Subject: [PATCH 119/264] Typo in README.id-ID.md (#808)

Co-authored-by: Oleksii Trekhleb <trehleb@gmail.com>
---
 README.id-ID.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/README.id-ID.md b/README.id-ID.md
index 01d539c5ef..17e940576f 100644
--- a/README.id-ID.md
+++ b/README.id-ID.md
@@ -59,7 +59,7 @@ Algoritme adalah sebuah perincian yang jelas tentang cara untuk memecahkan suatu
 ### Algoritme Berdasarkanan Topik
 
 - **Matematika**
-  - `P` [Manipulasi Bit](src/algorithms/math/bits) - menetapkan/mendapatkan/memperbarui/mengahpus bit, perkalian/pembagian dengan angka 2, membuat bilangan negatif etc.
+  - `P` [Manipulasi Bit](src/algorithms/math/bits) - menetapkan/mendapatkan/memperbarui/menghapus bit, perkalian/pembagian dengan angka 2, membuat bilangan negatif dsb.
   - `P` [Faktorial](src/algorithms/math/Faktorial)
   - `P` [Bilangan Fibonacci](src/algorithms/math/fibonacci) - versi klasik dan bentuk tertutup
   - `P` [Faktor Prima](src/algorithms/math/prime-factors) - menemukan faktor prima dan menghitungnya menggunakan teorema Hardy-Ramanujan
@@ -258,7 +258,7 @@ Notasi _Big O_ digunakan untuk mengklasifikasikan algoritme berdasarkan durasi a
 
 Sumber: [Big O Cheat Sheet](http://bigocheatsheet.com/).
 
-Di bawah ini adalah daftar dari beberapa notasi _Bog O_ yang sering digunakan dan perbandingan kinerjanya terhadap berbagai ukuran _input data_.
+Di bawah ini adalah daftar dari beberapa notasi _Big O_ yang sering digunakan dan perbandingan kinerjanya terhadap berbagai ukuran _input data_.
 
 | Notasi _Big O_ | Komputasi untuk 10 elemen | Komputasi untuk 100 elemen | Komputasi untuk 1000 elemen |
 | -------------- | ------------------------- | -------------------------- | --------------------------- |

From 9671b0c4b904a6593cd644db1e13ffc150078586 Mon Sep 17 00:00:00 2001
From: joaojgabriel <jonhlhn.surf@gmail.com>
Date: Sat, 22 Jan 2022 06:42:36 -0300
Subject: [PATCH 120/264] Linked List -- PT-BR (#805)
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

- typos
- reformulação de "This structure allows for efficient insertion or removal of elements from any position in the sequence during iteration."
- "vinculadas" a "encadeadas" pra manter o mesmo termo do título

Co-authored-by: Oleksii Trekhleb <trehleb@gmail.com>
---
 src/data-structures/linked-list/README.pt-BR.md | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/src/data-structures/linked-list/README.pt-BR.md b/src/data-structures/linked-list/README.pt-BR.md
index 148a8303dc..95a244d06f 100644
--- a/src/data-structures/linked-list/README.pt-BR.md
+++ b/src/data-structures/linked-list/README.pt-BR.md
@@ -7,16 +7,16 @@ física na memória. Em vez disso, cada elemento aponta para o próximo.
 que juntos representam uma sequência. Sob a forma mais simples,
 cada nó é composto de dados e uma referência (em outras palavras,
 uma ligação/conexão) para o próximo nó na sequência. Esta estrutura
-permite uma eficiente inserção e remoção de elementos de qualquer
+permite inserção ou remoção eficiente de elementos de qualquer
 posição na sequência durante a iteração.
 
 Variantes mais complexas adicionam ligações adicionais, permitindo
 uma inserção ou remoção mais eficiente a partir de referências
-de elementos arbitrários. Uma desvantagem das listas vinculadas
+de elementos arbitrárias. Uma desvantagem das listas encadeadas
 é que o tempo de acesso é linear (e difícil de inserir em uma
-pipeline). Acessos mais rápidos, como acesso aleatório, não é viável.
+pipeline). Acesso mais rápido, como acesso aleatório, não é viável.
 Arrays possuem uma melhor localização de cache em comparação
-com lista encadeada (linked list).
+com listas encadeadas (linked lists).
 
 ![Linked List](https://upload.wikimedia.org/wikipedia/commons/6/6d/Singly-linked-list.svg)
 

From e844a2f894fa3873bacd62d0fff4f346f9273f99 Mon Sep 17 00:00:00 2001
From: jackbyebye1024 <57267425+jackbyebye1024@users.noreply.github.com>
Date: Sat, 22 Jan 2022 17:43:11 +0800
Subject: [PATCH 121/264] Update README.zh-CN.md (#804)
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

* Update README.zh-CN.md

双向链表的删除部分，逻辑修改

* Update README.zh-CN.md
---
 src/data-structures/doubly-linked-list/README.zh-CN.md | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/src/data-structures/doubly-linked-list/README.zh-CN.md b/src/data-structures/doubly-linked-list/README.zh-CN.md
index 03dd53c11d..097ec0c90c 100644
--- a/src/data-structures/doubly-linked-list/README.zh-CN.md
+++ b/src/data-structures/doubly-linked-list/README.zh-CN.md
@@ -19,7 +19,7 @@ Add(value)
   Pre: value is the value to add to the list
   Post: value has been placed at the tail of the list
   n ← node(value)
-  if head = ø
+  if head != ø
     head ← n
     tail ← n
   else
@@ -51,14 +51,14 @@ Remove(head, value)
     return true
   end if
   n ← head.next
-  while n = ø and value !== n.value
+  while n != ø and value !== n.value
     n ← n.next
   end while
   if n = tail
     tail ← tail.previous
     tail.next ← ø
     return true
-  else if n = ø
+  else if n != ø
     n.previous.next ← n.next
     n.next.previous ← n.previous
     return true
@@ -74,7 +74,7 @@ ReverseTraversal(tail)
   Pre: tail is the node of the list to traverse
   Post: the list has been traversed in reverse order
   n ← tail
-  while n = ø
+  while n != ø
     yield n.value
     n ← n.previous
   end while

From 457b16a5c9f48b049ce0299823c06d2dcc666cbc Mon Sep 17 00:00:00 2001
From: edegil <electropark917@gmail.com>
Date: Sat, 22 Jan 2022 18:44:22 +0900
Subject: [PATCH 122/264] Add Korean translation for data-structures/stack
 (#797)

---
 src/data-structures/stack/README.ko-KR.md | 24 +++++++++++++++++++++++
 src/data-structures/stack/README.md       |  3 ++-
 2 files changed, 26 insertions(+), 1 deletion(-)
 create mode 100644 src/data-structures/stack/README.ko-KR.md

diff --git a/src/data-structures/stack/README.ko-KR.md b/src/data-structures/stack/README.ko-KR.md
new file mode 100644
index 0000000000..916aef1d04
--- /dev/null
+++ b/src/data-structures/stack/README.ko-KR.md
@@ -0,0 +1,24 @@
+# 스택
+
+_Read this in other languages:_
+[_简体中文_](README.zh-CN.md),
+[_Русский_](README.ru-RU.md),
+[_日本語_](README.ja-JP.md),
+[_Français_](README.fr-FR.md),
+[_Português_](README.pt-BR.md)
+
+컴퓨터 과학에서, **스택**은 아래의 두가지 연산을 가진 요소들의 집합인 추상 자료형입니다.
+
+* **push**는 집합에 요소를 추가하는 것이며,
+* **pop**은 아직 제거되지 않은 가장 최근에 추가된 요소를 제거하는 연산입니다.
+
+요소가 스택에서 나오는 과정은 LIFO (last in, first out)라는 이름으로 확인할 수 있습니다. 추가적으로, peek 연산은 스택을 수정하지 않고 최상단의 요소에 접근할 수 있게 해줍니다. 이런 자료구조의 "스택"이라는 이름은 실제 물건들이 다른 물건들의 위에 쌓이게 되는 것에서 유추되었습니다. 스택의 최상단의 물건은 빼내기 쉽지만 깊이 있는 물건을 빼내려면 다른 물건들을 먼저 빼내야 하는게 필요합니다.
+
+다음은 push와 pop 연산을 실행하는 간단한 스택의 실행입니다.
+
+![Stack](https://upload.wikimedia.org/wikipedia/commons/b/b4/Lifo_stack.png)
+
+## 참조
+
+- [Wikipedia](https://en.wikipedia.org/wiki/Stack_(abstract_data_type))
+- [YouTube](https://www.youtube.com/watch?v=wjI1WNcIntg&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8&index=3&)
diff --git a/src/data-structures/stack/README.md b/src/data-structures/stack/README.md
index dc4f311b01..f2335da1d6 100644
--- a/src/data-structures/stack/README.md
+++ b/src/data-structures/stack/README.md
@@ -5,7 +5,8 @@ _Read this in other languages:_
 [_Русский_](README.ru-RU.md),
 [_日本語_](README.ja-JP.md),
 [_Français_](README.fr-FR.md),
-[_Português_](README.pt-BR.md)
+[_Português_](README.pt-BR.md),
+[_한국어_](README.ko-KR.md)
 
 In computer science, a **stack** is an abstract data type that serves 
 as a collection of elements, with two principal operations:

From 236379b04cd3ae8646e9dafa4619ef30cd740de8 Mon Sep 17 00:00:00 2001
From: Kush Gabani <kushgabz2687@gmail.com>
Date: Sat, 22 Jan 2022 15:18:15 +0530
Subject: [PATCH 123/264] Fixed: Translation Typo Error (#796)

This pull request aims at closing the issue #765 by fixing the typo in the translation.
Specifically,
Get Bit and Clear Bit, there should be AND operation (&), but not ADD operation (+)

Co-authored-by: Oleksii Trekhleb <trehleb@gmail.com>
---
 src/algorithms/math/bits/README.zh-CN.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/src/algorithms/math/bits/README.zh-CN.md b/src/algorithms/math/bits/README.zh-CN.md
index 8b71ddc21a..9ec75069c6 100644
--- a/src/algorithms/math/bits/README.zh-CN.md
+++ b/src/algorithms/math/bits/README.zh-CN.md
@@ -6,7 +6,7 @@ _Read this in other languages:_
 
 #### Get Bit
 
-该方法向右移动目标位到最右边，即位数组的第0个位置上。然后在该数上与形如 `0001`的二进制形式的数进行`ADD`操作。这会清理掉除了目标位的所有其它位的数据。如果目标位是1，那么结果就是`1`，反之，结果是`0`;
+该方法向右移动目标位到最右边，即位数组的第0个位置上。然后在该数上与形如 `0001`的二进制形式的数进行`AND`操作。这会清理掉除了目标位的所有其它位的数据。如果目标位是1，那么结果就是`1`，反之，结果是`0`;
 
 > 查看[getBit.js](getBit.js)了解更多细节。
 
@@ -18,7 +18,7 @@ _Read this in other languages:_
 
 #### Clear Bit
 
-该方法把`1`向左移动了`bitPosition`位，生成了一个二进制形如`00100`的值。然后反转每一位的数字，得到一个二进制形如`11011`的值。接着与目标值进行`ADD`操作，就能清除掉目标位的值。
+该方法把`1`向左移动了`bitPosition`位，生成了一个二进制形如`00100`的值。然后反转每一位的数字，得到一个二进制形如`11011`的值。接着与目标值进行`AND`操作，就能清除掉目标位的值。
 
 > 查看[clearBit.js](clearBit.js)了解更多细节。
 

From 80d2f508d30d2d53a32026351b4f03cce8978d0b Mon Sep 17 00:00:00 2001
From: Halil CAKAR <hcakar.1992@gmail.com>
Date: Sat, 22 Jan 2022 12:49:30 +0300
Subject: [PATCH 124/264] Update README.tr-TR.md (#789)

Fix a typo

Co-authored-by: Oleksii Trekhleb <trehleb@gmail.com>
---
 README.tr-TR.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.tr-TR.md b/README.tr-TR.md
index 8e18f38bfb..edbc0ebdaa 100644
--- a/README.tr-TR.md
+++ b/README.tr-TR.md
@@ -25,7 +25,7 @@ _Read this in other languages:_
 [_Deutsch_](README.de-DE.md)
 
 *☝ Not, bu proje araştırma ve öğrenme amacı ile yapılmış
-olup üretim için **yaplılmamıştır**.*
+olup üretim için **yapılmamıştır**.*
 
 ## Veri Yapıları
 

From 7d13e6863a940fbc81987b32700681a513794f4a Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Sat, 22 Jan 2022 10:50:33 +0100
Subject: [PATCH 125/264] README fixes.

---
 src/algorithms/cryptography/caesar-cipher/README.md          | 3 +++
 src/algorithms/linked-list/traversal/README.md               | 2 +-
 src/algorithms/string/knuth-morris-pratt/knuthMorrisPratt.js | 2 +-
 3 files changed, 5 insertions(+), 2 deletions(-)

diff --git a/src/algorithms/cryptography/caesar-cipher/README.md b/src/algorithms/cryptography/caesar-cipher/README.md
index 428b5a9772..d648a62ee9 100644
--- a/src/algorithms/cryptography/caesar-cipher/README.md
+++ b/src/algorithms/cryptography/caesar-cipher/README.md
@@ -1,5 +1,8 @@
 # Caesar Cipher Algorithm
 
+_Read this in other languages:_
+[_Русский_](README.ru-RU.md)
+
 In cryptography, a **Caesar cipher**, also known as **Caesar's cipher**, the **shift cipher**, **Caesar's code** or **Caesar shift**, is one of the simplest and most widely known encryption techniques. It is a type of substitution cipher in which each letter in the plaintext is replaced by a letter some fixed number of positions down the alphabet. For example, with a left shift of `3`, `D` would be replaced by `A`, `E` would become `B`, and so on. The method is named after Julius Caesar, who used it in his private correspondence.
 
 ![Caesar Cipher Algorithm](https://upload.wikimedia.org/wikipedia/commons/4/4a/Caesar_cipher_left_shift_of_3.svg)
diff --git a/src/algorithms/linked-list/traversal/README.md b/src/algorithms/linked-list/traversal/README.md
index d1b74ea57e..9acbe98dd9 100644
--- a/src/algorithms/linked-list/traversal/README.md
+++ b/src/algorithms/linked-list/traversal/README.md
@@ -1,7 +1,7 @@
 # Linked List Traversal
 
 _Read this in other languages:_
-[_Русский_](README.ru-RU.md)
+[_Русский_](README.ru-RU.md),
 [中文](README.zh-CN.md)
 
 The task is to traverse the given linked list in straight order.
diff --git a/src/algorithms/string/knuth-morris-pratt/knuthMorrisPratt.js b/src/algorithms/string/knuth-morris-pratt/knuthMorrisPratt.js
index 82b94904fd..a3a39904a4 100644
--- a/src/algorithms/string/knuth-morris-pratt/knuthMorrisPratt.js
+++ b/src/algorithms/string/knuth-morris-pratt/knuthMorrisPratt.js
@@ -43,7 +43,7 @@ export default function knuthMorrisPratt(text, word) {
     if (text[textIndex] === word[wordIndex]) {
       // We've found a match.
       if (wordIndex === word.length - 1) {
-        return textIndex - word.length + 1;
+        return (textIndex - word.length) + 1;
       }
       wordIndex += 1;
       textIndex += 1;

From 396f5b8feb3117c49a286c84985394320d91b77d Mon Sep 17 00:00:00 2001
From: Matheus Machado <92314808+mahteusodev@users.noreply.github.com>
Date: Sun, 23 Jan 2022 17:34:08 -0300
Subject: [PATCH 126/264] Fixes README.pt-BR.md (#787)

General formatting and translation fixes
---
 README.pt-BR.md | 108 ++++++++++++++++++++++++------------------------
 1 file changed, 54 insertions(+), 54 deletions(-)

diff --git a/README.pt-BR.md b/README.pt-BR.md
index 68b7e1721f..de9e316bc6 100644
--- a/README.pt-BR.md
+++ b/README.pt-BR.md
@@ -6,7 +6,7 @@
 Este repositório contém exemplos baseados em JavaScript de muitos
 algoritmos e estruturas de dados populares.
 
-Cada algoritmo e estrutura de dado possui seu próprio README
+Cada algoritmo e estrutura de dados possui seu próprio README
 com explicações relacionadas e links para leitura adicional (incluindo
 vídeos para YouTube)
 
@@ -48,7 +48,7 @@ os dados.
   * `A` [Árvore de Pesquisa Binária (Binary Search Tree)](src/data-structures/tree/binary-search-tree/README.pt-BR.md)
   * `A` [Árvore AVL (AVL Tree)](src/data-structures/tree/avl-tree/README.pt-BR.md)
   * `A` [Árvore Vermelha-Preta (Red-Black Tree)](src/data-structures/tree/red-black-tree/README.pt-BR.md)
-  * `A` [Árvore de Segmento (Segment Tree)](src/data-structures/tree/segment-tree/README.pt-BR.md) - com exemplos de consultas min / max / sum range
+  * `A` [Árvore de Segmento (Segment Tree)](src/data-structures/tree/segment-tree/README.pt-BR.md) - Com exemplos de consultas min / max / sum range
   * `A` [Árvore Fenwick (Fenwick Tree)](src/data-structures/tree/fenwick-tree/README.pt-BR.md) (Árvore indexada binária)
 * `A` [Grafo (Graph)](src/data-structures/graph/README.pt-BR.md) (ambos dirigidos e não direcionados)
 * `A` [Conjunto Disjuntor (Disjoint Set)](src/data-structures/disjoint-set/README.pt-BR.md)
@@ -68,18 +68,18 @@ um conjunto de regras que define precisamente uma sequência de operações.
   * `B` [Fatorial](src/algorithms/math/factorial)
   * `B` [Número de Fibonacci](src/algorithms/math/fibonacci)
   * `B` [Teste de Primalidade](src/algorithms/math/primality-test) (método de divisão experimental)
-  * `B` [Algoritmo Euclidiano](src/algorithms/math/euclidean-algorithm) - calcular o maior divisor comum (GCD)
-  * `B` [Mínimo múltiplo comum](src/algorithms/math/least-common-multiple) (LCM)
-  * `B` [Peneira de Eratóstenes](src/algorithms/math/sieve-of-eratosthenes) - encontrar todos os números primos até um determinado limite
-  * `B` [Potência de dois](src/algorithms/math/is-power-of-two) - verifique se o número é a potência de dois (algoritmos ingênuos e bit a bit)
+  * `B` [Algoritmo Euclidiano](src/algorithms/math/euclidean-algorithm) - Calcular o Máximo Divisor Comum (MDC)
+  * `B` [Mínimo Múltiplo Comum](src/algorithms/math/least-common-multiple) Calcular o Mínimo Múltiplo Comum (MMC)
+  * `B` [Peneira de Eratóstenes](src/algorithms/math/sieve-of-eratosthenes) - Encontrar todos os números primos até um determinado limite
+  * `B` [Potência de dois](src/algorithms/math/is-power-of-two) - Verifique se o número é a potência de dois (algoritmos ingênuos e bit a bit)
   * `B` [Triângulo de Pascal](src/algorithms/math/pascal-triangle)
-  * `B` [Número complexo](src/algorithms/math/complex-number) - números complexos e operações básicas com eles
+  * `B` [Número complexo](src/algorithms/math/complex-number) - Números complexos e operações básicas com eles
   * `A` [Partição inteira](src/algorithms/math/integer-partition)
-  * `A` [Algoritmo Liu Hui π](src/algorithms/math/liu-hui) - cálculos aproximados de π baseados em N-gons
+  * `A` [Algoritmo Liu Hui π](src/algorithms/math/liu-hui) - Cálculos aproximados de π baseados em N-gons
 * **Conjuntos**
-  * `B` [Produto cartesiano](src/algorithms/sets/cartesian-product) - produto de vários conjuntos
-  * `B` [Permutações de Fisher–Yates](src/algorithms/sets/fisher-yates) - permutação aleatória de uma sequência finita
-  * `A` [Potência e Conjunto](src/algorithms/sets/power-set) - todos os subconjuntos de um conjunto
+  * `B` [Produto cartesiano](src/algorithms/sets/cartesian-product) - Produto de vários conjuntos
+  * `B` [Permutações de Fisher–Yates](src/algorithms/sets/fisher-yates) - Permutação aleatória de uma sequência finita
+  * `A` [Potência e Conjunto](src/algorithms/sets/power-set) - Todos os subconjuntos de um conjunto
   * `A` [Permutações](src/algorithms/sets/permutations) (com e sem repetições)
   * `A` [Combinações](src/algorithms/sets/combinations) (com e sem repetições)
   * `A` [Mais longa subsequência comum](src/algorithms/sets/longest-common-subsequence) (LCS)
@@ -87,27 +87,27 @@ um conjunto de regras que define precisamente uma sequência de operações.
   * `A` [Supersequência Comum mais curta](src/algorithms/sets/shortest-common-supersequence) (SCS)
   * `A` [Problema da mochila](src/algorithms/sets/knapsack-problem) - "0/1" e "Não consolidado"
   * `A` [Máximo Subarray](src/algorithms/sets/maximum-subarray) - "Força bruta" e " Programação Dinâmica" versões (Kadane's)
-  * `A` [Soma de Combinação](src/algorithms/sets/combination-sum) - encontre todas as combinações que formam uma soma específica
+  * `A` [Soma de Combinação](src/algorithms/sets/combination-sum) - Encontre todas as combinações que formam uma soma específica
 * **Cadeia de Caracteres**
-  * `B` [Hamming Distance](src/algorithms/string/hamming-distance) - número de posições em que os símbolos são diferentes
-  * `A` [Levenshtein Distance](src/algorithms/string/levenshtein-distance) - distância mínima de edição entre duas sequências
-  * `A` [Knuth–Morris–Pratt Algorithm](src/algorithms/string/knuth-morris-pratt) (Algoritmo KMP) - pesquisa de substring (correspondência de padrão)
-  * `A` [Z Algorithm](src/algorithms/string/z-algorithm) - pesquisa de substring (correspondência de padrão)
-  * `A` [Rabin Karp Algorithm](src/algorithms/string/rabin-karp) - pesquisa de substring
+  * `B` [Hamming Distance](src/algorithms/string/hamming-distance) - Número de posições em que os símbolos são diferentes
+  * `A` [Levenshtein Distance](src/algorithms/string/levenshtein-distance) - Distância mínima de edição entre duas sequências
+  * `A` [Knuth–Morris–Pratt Algorithm](src/algorithms/string/knuth-morris-pratt) (Algoritmo KMP) - Pesquisa de substring (correspondência de padrão)
+  * `A` [Z Algorithm](src/algorithms/string/z-algorithm) - Pesquisa de substring (correspondência de padrão)
+  * `A` [Rabin Karp Algorithm](src/algorithms/string/rabin-karp) - Pesquisa de substring
   * `A` [Longest Common Substring](src/algorithms/string/longest-common-substring)
   * `A` [Regular Expression Matching](src/algorithms/string/regular-expression-matching)
 * **Buscas**
   * `B` [Linear Search](src/algorithms/search/linear-search)
-  * `B` [Jump Search](src/algorithms/search/jump-search) (ou Bloquear pesquisa) - pesquisar na matriz ordenada
-  * `B` [Binary Search](src/algorithms/search/binary-search) - pesquisar na matriz ordenada
-  * `B` [Interpolation Search](src/algorithms/search/interpolation-search) - pesquisar em matriz classificada uniformemente distribuída
+  * `B` [Jump Search](src/algorithms/search/jump-search) (ou Bloquear pesquisa) - Pesquisar na matriz ordenada
+  * `B` [Binary Search](src/algorithms/search/binary-search) - Pesquisar na matriz ordenada
+  * `B` [Interpolation Search](src/algorithms/search/interpolation-search) - Pesquisar em matriz classificada uniformemente distribuída
 * **Classificação**
   * `B` [Bubble Sort](src/algorithms/sorting/bubble-sort)
   * `B` [Selection Sort](src/algorithms/sorting/selection-sort)
   * `B` [Insertion Sort](src/algorithms/sorting/insertion-sort)
   * `B` [Heap Sort](src/algorithms/sorting/heap-sort)
   * `B` [Merge Sort](src/algorithms/sorting/merge-sort)
-  * `B` [Quicksort](src/algorithms/sorting/quick-sort) - implementações local e não local
+  * `B` [Quicksort](src/algorithms/sorting/quick-sort) - Implementações local e não local
   * `B` [Shellsort](src/algorithms/sorting/shell-sort)
   * `B` [Counting Sort](src/algorithms/sorting/counting-sort)
   * `B` [Radix Sort](src/algorithms/sorting/radix-sort)
@@ -117,27 +117,27 @@ um conjunto de regras que define precisamente uma sequência de operações.
 * **Grafos**
   * `B` [Depth-First Search](src/algorithms/graph/depth-first-search) (DFS)
   * `B` [Breadth-First Search](src/algorithms/graph/breadth-first-search) (BFS)
-  * `B` [Kruskal’s Algorithm](src/algorithms/graph/kruskal) - encontrando Árvore Mínima de Abrangência (MST) para grafo não direcionado ponderado
-  * `A` [Dijkstra Algorithm](src/algorithms/graph/dijkstra) - encontrar caminhos mais curtos para todos os vértices do grafo a partir de um único vértice
-  * `A` [Bellman-Ford Algorithm](src/algorithms/graph/bellman-ford) - encontrar caminhos mais curtos para todos os vértices do grafo a partir de um único vértice
-  * `A` [Floyd-Warshall Algorithm](src/algorithms/graph/floyd-warshall) - encontrar caminhos mais curtos entre todos os pares de vértices
-  * `A` [Detect Cycle](src/algorithms/graph/detect-cycle) - para gráficos direcionados e não direcionados (versões baseadas em DFS e Conjunto Disjuntivo)
-  * `A` [Prim’s Algorithm](src/algorithms/graph/prim) - encontrando Árvore Mínima de Abrangência (MST) para grafo não direcionado ponderado
+  * `B` [Kruskal’s Algorithm](src/algorithms/graph/kruskal) - Encontrar Árvore Mínima de Abrangência (MST) para grafo não direcionado ponderado
+  * `A` [Dijkstra Algorithm](src/algorithms/graph/dijkstra) - Encontrar caminhos mais curtos para todos os vértices do grafo a partir de um único vértice
+  * `A` [Bellman-Ford Algorithm](src/algorithms/graph/bellman-ford) - Encontrar caminhos mais curtos para todos os vértices do grafo a partir de um único vértice
+  * `A` [Floyd-Warshall Algorithm](src/algorithms/graph/floyd-warshall) - Encontrar caminhos mais curtos entre todos os pares de vértices
+  * `A` [Detect Cycle](src/algorithms/graph/detect-cycle) - Para gráficos direcionados e não direcionados (versões baseadas em DFS e Conjunto Disjuntivo)
+  * `A` [Prim’s Algorithm](src/algorithms/graph/prim) - Encontrando Árvore Mínima de Abrangência (MST) para grafo não direcionado ponderado
   * `A` [Topological Sorting](src/algorithms/graph/topological-sorting) - Métodos DFS
   * `A` [Articulation Points](src/algorithms/graph/articulation-points) -O algoritmo de Tarjan (baseado em DFS)
   * `A` [Bridges](src/algorithms/graph/bridges) - Algoritmo baseado em DFS
   * `A` [Eulerian Path and Eulerian Circuit](src/algorithms/graph/eulerian-path) - Algoritmo de Fleury - Visite todas as bordas exatamente uma vez
   * `A` [Hamiltonian Cycle](src/algorithms/graph/hamiltonian-cycle) - Visite todas as bordas exatamente uma vez
   * `A` [Strongly Connected Components](src/algorithms/graph/strongly-connected-components) - Algoritmo de Kosaraju's
-  * `A` [Travelling Salesman Problem](src/algorithms/graph/travelling-salesman) - rota mais curta possível que visita cada cidade e retorna à cidade de origem
-* **criptografia**
-  * `B` [Polynomial Hash](src/algorithms/cryptography/polynomial-hash) - função de hash de rolagem baseada em polinômio
+  * `A` [Travelling Salesman Problem](src/algorithms/graph/travelling-salesman) - Rota mais curta possível que visita cada cidade e retorna à cidade de origem
+* **Criptografia**
+  * `B` [Polynomial Hash](src/algorithms/cryptography/polynomial-hash) - Função de hash de rolagem baseada em polinômio
 * **Sem categoria**
   * `B` [Tower of Hanoi](src/algorithms/uncategorized/hanoi-tower)
-  * `B` [Square Matrix Rotation](src/algorithms/uncategorized/square-matrix-rotation) - algoritmo no local
-  * `B` [Jump Game](src/algorithms/uncategorized/jump-game) - backtracking, programação dinâmica (top-down + bottom-up) e exemplos gananciosos
-  * `B` [Unique Paths](src/algorithms/uncategorized/unique-paths) - backtracking, programação dinâmica e exemplos baseados no triângulo de Pascal
-  * `B` [Rain Terraces](src/algorithms/uncategorized/rain-terraces) - trapping problema da água da chuva (programação dinâmica e versões de força bruta)
+  * `B` [Square Matrix Rotation](src/algorithms/uncategorized/square-matrix-rotation) - Algoritmo no local
+  * `B` [Jump Game](src/algorithms/uncategorized/jump-game) - Backtracking, programação dinâmica (top-down + bottom-up) e exemplos gananciosos
+  * `B` [Unique Paths](src/algorithms/uncategorized/unique-paths) - Backtracking, programação dinâmica e exemplos baseados no triângulo de Pascal
+  * `B` [Rain Terraces](src/algorithms/uncategorized/rain-terraces) - Trapping problema da água da chuva (programação dinâmica e versões de força bruta)
   * `A` [N-Queens Problem](src/algorithms/uncategorized/n-queens)
   * `A` [Knight's Tour](src/algorithms/uncategorized/knight-tour)
 
@@ -147,22 +147,22 @@ Um paradigma algorítmico é um método ou abordagem genérica subjacente ao des
 de algoritmos. É uma abstração maior do que a noção de um algoritmo, assim como
 algoritmo é uma abstração maior que um programa de computador.
 
-* **Força bruta** - look at all the possibilities and selects the best solution
+* **Força bruta** - Pense em todas as possibilidades e escolha a melhor solução
   * `B` [Linear Search](src/algorithms/search/linear-search)
-  * `B` [Rain Terraces](src/algorithms/uncategorized/rain-terraces) - trapping problema da água da chuva
+  * `B` [Rain Terraces](src/algorithms/uncategorized/rain-terraces) - Trapping problema da água da chuva
   * `A` [Maximum Subarray](src/algorithms/sets/maximum-subarray)
-  * `A` [Travelling Salesman Problem](src/algorithms/graph/travelling-salesman) - rota mais curta possível que visita cada cidade e retorna à cidade de origem
-* **Greedy** - choose the best option at the current time, without any consideration for the future
+  * `A` [Travelling Salesman Problem](src/algorithms/graph/travelling-salesman) - Rota mais curta possível que visita cada cidade e retorna à cidade de origem
+* **Ganância** - Escolha a melhor opção no momento, sem qualquer consideração pelo futuro
   * `B` [Jump Game](src/algorithms/uncategorized/jump-game)
   * `A` [Unbound Knapsack Problem](src/algorithms/sets/knapsack-problem)
-  * `A` [Dijkstra Algorithm](src/algorithms/graph/dijkstra) - finding shortest path to all graph vertices
-  * `A` [Prim’s Algorithm](src/algorithms/graph/prim) - encontrando Árvore Mínima de Abrangência (MST) para grafo não direcionado ponderado
-  * `A` [Kruskal’s Algorithm](src/algorithms/graph/kruskal) - encontrando Árvore Mínima de Abrangência (MST) para grafo não direcionado ponderado
-* **Dividir p/ Conquistar** - dividir o problema em partes menores e depois resolver essas partes
+  * `A` [Dijkstra Algorithm](src/algorithms/graph/dijkstra) - Encontrar o caminho mais curto para todos os vértices do gráfico
+  * `A` [Prim’s Algorithm](src/algorithms/graph/prim) - Encontrando Árvore Mínima de Abrangência (MST) para grafo não direcionado ponderado
+  * `A` [Kruskal’s Algorithm](src/algorithms/graph/kruskal) - Encontrando Árvore Mínima de Abrangência (MST) para grafo não direcionado ponderado
+* **Dividir e Conquistar** - Dividir o problema em partes menores e então resolver essas partes
   * `B` [Busca binária (Binary Search)](src/algorithms/search/binary-search)
   * `B` [Tower of Hanoi](src/algorithms/uncategorized/hanoi-tower)
   * `B` [Pascal's Triangle](src/algorithms/math/pascal-triangle)
-  * `B` [Euclidean Algorithm](src/algorithms/math/euclidean-algorithm) - calculate the Greatest Common Divisor (GCD)
+  * `B` [Euclidean Algorithm](src/algorithms/math/euclidean-algorithm) - Calcular o Máximo Divisor Comum (MDC)
   * `B` [Merge Sort](src/algorithms/sorting/merge-sort)
   * `B` [Quicksort](src/algorithms/sorting/quick-sort)
   * `B` [Tree Depth-First Search](src/algorithms/tree/depth-first-search) (DFS)
@@ -170,12 +170,12 @@ algoritmo é uma abstração maior que um programa de computador.
   * `B` [Jump Game](src/algorithms/uncategorized/jump-game)
   * `A` [Permutations](src/algorithms/sets/permutations) (com e sem repetições)
   * `A` [Combinations](src/algorithms/sets/combinations) (com e sem repetições)
-* **Programação Dinâmica** - criar uma solução usando sub-soluções encontradas anteriormente
+* **Programação Dinâmica** - Criar uma solução usando sub-soluções encontradas anteriormente
   * `B` [Fibonacci Number](src/algorithms/math/fibonacci)
   * `B` [Jump Game](src/algorithms/uncategorized/jump-game)
   * `B` [Unique Paths](src/algorithms/uncategorized/unique-paths)
-  * `B` [Rain Terraces](src/algorithms/uncategorized/rain-terraces) - trapping problema da água da chuva
-  * `A` [Levenshtein Distance](src/algorithms/string/levenshtein-distance) - distância mínima de edição entre duas sequências
+  * `B` [Rain Terraces](src/algorithms/uncategorized/rain-terraces) - Trapping problema da água da chuva
+  * `A` [Levenshtein Distance](src/algorithms/string/levenshtein-distance) - Distância mínima de edição entre duas sequências
   * `A` [Longest Common Subsequence](src/algorithms/sets/longest-common-subsequence) (LCS)
   * `A` [Longest Common Substring](src/algorithms/string/longest-common-substring)
   * `A` [Longest Increasing Subsequence](src/algorithms/sets/longest-increasing-subsequence)
@@ -183,18 +183,18 @@ algoritmo é uma abstração maior que um programa de computador.
   * `A` [0/1 Knapsack Problem](src/algorithms/sets/knapsack-problem)
   * `A` [Integer Partition](src/algorithms/math/integer-partition)
   * `A` [Maximum Subarray](src/algorithms/sets/maximum-subarray)
-  * `A` [Bellman-Ford Algorithm](src/algorithms/graph/bellman-ford) - encontrando o caminho mais curto para todos os vértices do gráfico
-  * `A` [Floyd-Warshall Algorithm](src/algorithms/graph/floyd-warshall) - encontrar caminhos mais curtos entre todos os pares de vértices
+  * `A` [Bellman-Ford Algorithm](src/algorithms/graph/bellman-ford) - Encontrar o caminho mais curto para todos os vértices do gráfico
+  * `A` [Floyd-Warshall Algorithm](src/algorithms/graph/floyd-warshall) - Encontrar caminhos mais curtos entre todos os pares de vértices
   * `A` [Regular Expression Matching](src/algorithms/string/regular-expression-matching)
-* **Backtracking** - da mesma forma que a força bruta, tente gerar todas as soluções possíveis, mas cada vez que você gerar a próxima solução, você testará
+* **Backtracking** - Da mesma forma que a força bruta, tente gerar todas as soluções possíveis, mas cada vez que você gerar a próxima solução, você testará
 se satisfizer todas as condições, e só então continuar gerando soluções subseqüentes. Caso contrário, volte atrás e siga um caminho diferente para encontrar uma solução. Normalmente, a passagem DFS do espaço de estados está sendo usada.
   * `B` [Jump Game](src/algorithms/uncategorized/jump-game)
   * `B` [Unique Paths](src/algorithms/uncategorized/unique-paths)
   * `A` [Hamiltonian Cycle](src/algorithms/graph/hamiltonian-cycle) - Visite todos os vértices exatamente uma vez
   * `A` [N-Queens Problem](src/algorithms/uncategorized/n-queens)
   * `A` [Knight's Tour](src/algorithms/uncategorized/knight-tour)
-  * `A` [Combination Sum](src/algorithms/sets/combination-sum) - encontre todas as combinações que formam uma soma específica
-* **Branch & Bound** - lembre-se da solução de menor custo encontrada em cada etapa do retrocesso
+  * `A` [Combination Sum](src/algorithms/sets/combination-sum) - Encontre todas as combinações que formam uma soma específica
+* **Branch & Bound** - Lembre-se da solução de menor custo encontrada em cada etapa do retrocesso
 pesquisar e usar o custo da solução de menor custo encontrada até o limite inferior do custo de
 solução de menor custo para o problema, a fim de descartar soluções parciais com custos maiores que o
 solução de menor custo encontrada até o momento. Normalmente, a travessia BFS em combinação com a passagem DFS do espaço de estados
@@ -264,7 +264,7 @@ Abaixo está a lista de algumas das notações Big O mais usadas e suas compara
 
 ### Complexidade de operações de estrutura de dados
 
-| estrutura de dados      | Acesso    | Busca     | Inserção  | Eliminação | comentários |
+| Estrutura de dados      | Acesso    | Busca     | Inserção  | Eliminação | Comentários |
 | ----------------------- | :-------: | :-------: | :-------: | :-------:  | :--------   |
 | **Array**               | 1         | n         | n         | n          |             |
 | **Stack**               | n         | n         | 1         | 1          |             |
@@ -279,7 +279,7 @@ Abaixo está a lista de algumas das notações Big O mais usadas e suas compara
 
 ### Array Sorting Algorithms Complexity
 
-| Nome                  | Melhor          | Média               | Pior                | Mémoria   | Estável   | comentários |
+| Nome                  | Melhor          | Média               | Pior                | Mémoria   | Estável   | Comentários |
 | --------------------- | :-------------: | :-----------------: | :-----------------: | :-------: | :-------: | :--------   |
 | **Bubble sort**       | n               | n<sup>2</sup>       | n<sup>2</sup>       | 1         | Sim       |             |
 | **Insertion sort**    | n               | n<sup>2</sup>       | n<sup>2</sup>       | 1         | Sim       |             |
@@ -291,4 +291,4 @@ Abaixo está a lista de algumas das notações Big O mais usadas e suas compara
 | **Counting sort**     | n + r           | n + r               | n + r               | n + r     | Sim       | r - maior número na matriz          |
 | **Radix sort**        | n * k           | n * k               | n * k               | n + k     | Sim       | k - comprimento da chave mais longa |
 
-> ℹ️ A few more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev)
+> ℹ️ Outros [projetos](https://trekhleb.dev/projects/) e [artigos](https://trekhleb.dev/blog/) sobre JavaScript e algoritmos em [trekhleb.dev](https://trekhleb.dev)

From b4b511005b5da796ee6d69216d7abe88569b8476 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Piotr=20=C5=81ysik?= <piotrek.lysik@gmail.com>
Date: Sun, 23 Jan 2022 21:36:02 +0100
Subject: [PATCH 127/264] Update README.pl-PL.md (#785)

Typo fix
---
 README.pl-PL.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.pl-PL.md b/README.pl-PL.md
index 51777b0da2..38f0bcea27 100644
--- a/README.pl-PL.md
+++ b/README.pl-PL.md
@@ -66,7 +66,7 @@ rozwiązania problemu.
 
 * **Matematyka**
   * `B` [Manipulacja Bitami](src/algorithms/math/bits) - ustaw / uzyskaj / aktualizuj / usuwaj bity, mnożenie / dzielenie przez dwa, tworzenie negatywów itp.
-  * `B` [Silna](src/algorithms/math/factorial)
+  * `B` [Silnia](src/algorithms/math/factorial)
   * `B` [Ciąg Fibonacciego](src/algorithms/math/fibonacci)
   * `B` [Test Pierwszorzędności](src/algorithms/math/primality-test) (metoda podziału na próby)
   * `B` [Algorytm Euclideana](src/algorithms/math/euclidean-algorithm) - obliczyć Największy Wspólny Dzielnik (GCD)

From ea28788ed81541dc175d52c2986e9d55d2246dac Mon Sep 17 00:00:00 2001
From: liamlylehr <liam@the-lehrs.com>
Date: Sun, 23 Jan 2022 15:42:43 -0500
Subject: [PATCH 128/264] added palindromeCheck (#806)

* added readme

* added readme

* adding palindromeCheck

* adjusted README

Co-authored-by: Oleksii Trekhleb <trehleb@gmail.com>
---
 README.md                                     |  1 +
 .../string/palindrome-check/README.md         | 25 +++++++++++++++++++
 .../__test__/palindromeCheck.test.js          | 14 +++++++++++
 .../palindrome-check/palindromeCheck.js       | 17 +++++++++++++
 4 files changed, 57 insertions(+)
 create mode 100644 src/algorithms/string/palindrome-check/README.md
 create mode 100644 src/algorithms/string/palindrome-check/__test__/palindromeCheck.test.js
 create mode 100644 src/algorithms/string/palindrome-check/palindromeCheck.js

diff --git a/README.md b/README.md
index 7f0159c4a3..28e182aa9f 100644
--- a/README.md
+++ b/README.md
@@ -102,6 +102,7 @@ a set of rules that precisely define a sequence of operations.
   * `A` [Combination Sum](src/algorithms/sets/combination-sum) - find all combinations that form specific sum
 * **Strings**
   * `B` [Hamming Distance](src/algorithms/string/hamming-distance) - number of positions at which the symbols are different
+  * `B` [Palindrome Check](src/algorithms/string/palindrome-check) - is the string the same in reverse
   * `A` [Levenshtein Distance](src/algorithms/string/levenshtein-distance) - minimum edit distance between two sequences
   * `A` [Knuth–Morris–Pratt Algorithm](src/algorithms/string/knuth-morris-pratt) (KMP Algorithm) - substring search (pattern matching)
   * `A` [Z Algorithm](src/algorithms/string/z-algorithm) - substring search (pattern matching)
diff --git a/src/algorithms/string/palindrome-check/README.md b/src/algorithms/string/palindrome-check/README.md
new file mode 100644
index 0000000000..3d12574489
--- /dev/null
+++ b/src/algorithms/string/palindrome-check/README.md
@@ -0,0 +1,25 @@
+# Palindrome Check
+
+A Palindrome is a string that reads the same forwards and backwards. 
+This means that the second half of the string is the reverse of the 
+first half.
+
+## Examples
+
+The following are palindromes (thus would return TRUE):
+
+- "a"
+- "pop"     ->  p + o + p
+- "deed"    ->  de + ed
+- "kayak"   ->  ka + y + ak
+- "racecar" ->  rac + e + car
+
+The following are NOT palindromes (thus would return FALSE):
+
+- "rad"
+- "dodo"
+- "polo"
+
+## References
+
+[GeeksforGeeks - Check if a number is Palindrome](https://www.geeksforgeeks.org/check-if-a-number-is-palindrome/)
diff --git a/src/algorithms/string/palindrome-check/__test__/palindromeCheck.test.js b/src/algorithms/string/palindrome-check/__test__/palindromeCheck.test.js
new file mode 100644
index 0000000000..4b22793414
--- /dev/null
+++ b/src/algorithms/string/palindrome-check/__test__/palindromeCheck.test.js
@@ -0,0 +1,14 @@
+import palindromeCheck from '../palindromeCheck';
+
+describe('palindromeCheck', () => {
+  it('should return whether or not the string is a palindrome', () => {
+    expect(palindromeCheck('a')).toBe(true);
+    expect(palindromeCheck('pop')).toBe(true);
+    expect(palindromeCheck('deed')).toBe(true);
+    expect(palindromeCheck('kayak')).toBe(true);
+    expect(palindromeCheck('racecar')).toBe(true);
+    expect(palindromeCheck('rad')).toBe(false);
+    expect(palindromeCheck('dodo')).toBe(false);
+    expect(palindromeCheck('polo')).toBe(false);
+  });
+});
diff --git a/src/algorithms/string/palindrome-check/palindromeCheck.js b/src/algorithms/string/palindrome-check/palindromeCheck.js
new file mode 100644
index 0000000000..c850fe3aa7
--- /dev/null
+++ b/src/algorithms/string/palindrome-check/palindromeCheck.js
@@ -0,0 +1,17 @@
+/**
+ * @param {string} string
+ * @return {boolean}
+ */
+
+export default function palindromeCheck(string) {
+  let left = 0;
+  let right = string.length - 1;
+  while (left < right) {
+    if (string[left] !== string[right]) {
+      return false;
+    }
+    left += 1;
+    right -= 1;
+  }
+  return true;
+}

From 90addf9b18274ccce734d8d6b70156c154afeb6f Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Sun, 23 Jan 2022 21:47:57 +0100
Subject: [PATCH 129/264] Code/README fixes for the "Palindrome Check".

---
 README.md                                     |  2 +-
 .../string/palindrome-check/README.md         | 25 ----------------
 .../__test__/palindromeCheck.test.js          | 14 ---------
 src/algorithms/string/palindrome/README.md    | 29 +++++++++++++++++++
 .../palindrome/__test__/isPalindrome.test.js  | 15 ++++++++++
 .../isPalindrome.js}                          |  4 ++-
 6 files changed, 48 insertions(+), 41 deletions(-)
 delete mode 100644 src/algorithms/string/palindrome-check/README.md
 delete mode 100644 src/algorithms/string/palindrome-check/__test__/palindromeCheck.test.js
 create mode 100644 src/algorithms/string/palindrome/README.md
 create mode 100644 src/algorithms/string/palindrome/__test__/isPalindrome.test.js
 rename src/algorithms/string/{palindrome-check/palindromeCheck.js => palindrome/isPalindrome.js} (83%)

diff --git a/README.md b/README.md
index 28e182aa9f..6bc124c357 100644
--- a/README.md
+++ b/README.md
@@ -102,7 +102,7 @@ a set of rules that precisely define a sequence of operations.
   * `A` [Combination Sum](src/algorithms/sets/combination-sum) - find all combinations that form specific sum
 * **Strings**
   * `B` [Hamming Distance](src/algorithms/string/hamming-distance) - number of positions at which the symbols are different
-  * `B` [Palindrome Check](src/algorithms/string/palindrome-check) - is the string the same in reverse
+  * `B` [Palindrome](src/algorithms/string/palindrome) - check if the string is the same in reverse
   * `A` [Levenshtein Distance](src/algorithms/string/levenshtein-distance) - minimum edit distance between two sequences
   * `A` [Knuth–Morris–Pratt Algorithm](src/algorithms/string/knuth-morris-pratt) (KMP Algorithm) - substring search (pattern matching)
   * `A` [Z Algorithm](src/algorithms/string/z-algorithm) - substring search (pattern matching)
diff --git a/src/algorithms/string/palindrome-check/README.md b/src/algorithms/string/palindrome-check/README.md
deleted file mode 100644
index 3d12574489..0000000000
--- a/src/algorithms/string/palindrome-check/README.md
+++ /dev/null
@@ -1,25 +0,0 @@
-# Palindrome Check
-
-A Palindrome is a string that reads the same forwards and backwards. 
-This means that the second half of the string is the reverse of the 
-first half.
-
-## Examples
-
-The following are palindromes (thus would return TRUE):
-
-- "a"
-- "pop"     ->  p + o + p
-- "deed"    ->  de + ed
-- "kayak"   ->  ka + y + ak
-- "racecar" ->  rac + e + car
-
-The following are NOT palindromes (thus would return FALSE):
-
-- "rad"
-- "dodo"
-- "polo"
-
-## References
-
-[GeeksforGeeks - Check if a number is Palindrome](https://www.geeksforgeeks.org/check-if-a-number-is-palindrome/)
diff --git a/src/algorithms/string/palindrome-check/__test__/palindromeCheck.test.js b/src/algorithms/string/palindrome-check/__test__/palindromeCheck.test.js
deleted file mode 100644
index 4b22793414..0000000000
--- a/src/algorithms/string/palindrome-check/__test__/palindromeCheck.test.js
+++ /dev/null
@@ -1,14 +0,0 @@
-import palindromeCheck from '../palindromeCheck';
-
-describe('palindromeCheck', () => {
-  it('should return whether or not the string is a palindrome', () => {
-    expect(palindromeCheck('a')).toBe(true);
-    expect(palindromeCheck('pop')).toBe(true);
-    expect(palindromeCheck('deed')).toBe(true);
-    expect(palindromeCheck('kayak')).toBe(true);
-    expect(palindromeCheck('racecar')).toBe(true);
-    expect(palindromeCheck('rad')).toBe(false);
-    expect(palindromeCheck('dodo')).toBe(false);
-    expect(palindromeCheck('polo')).toBe(false);
-  });
-});
diff --git a/src/algorithms/string/palindrome/README.md b/src/algorithms/string/palindrome/README.md
new file mode 100644
index 0000000000..0ce77d42b6
--- /dev/null
+++ b/src/algorithms/string/palindrome/README.md
@@ -0,0 +1,29 @@
+# Palindrome Check
+
+A [Palindrome](https://en.wikipedia.org/wiki/Palindrome) is a string that reads the same forwards and backwards.
+This means that the second half of the string is the reverse of the
+first half.
+
+## Examples
+
+The following are palindromes (thus would return `TRUE`):
+
+```
+- "a"
+- "pop"     ->  p + o + p
+- "deed"    ->  de + ed
+- "kayak"   ->  ka + y + ak
+- "racecar" ->  rac + e + car
+```
+
+The following are NOT palindromes (thus would return `FALSE`):
+
+```
+- "rad"
+- "dodo"
+- "polo"
+```
+
+## References
+
+- [GeeksForGeeks - Check if a number is Palindrome](https://www.geeksforgeeks.org/check-if-a-number-is-palindrome/)
diff --git a/src/algorithms/string/palindrome/__test__/isPalindrome.test.js b/src/algorithms/string/palindrome/__test__/isPalindrome.test.js
new file mode 100644
index 0000000000..0a49d5be5d
--- /dev/null
+++ b/src/algorithms/string/palindrome/__test__/isPalindrome.test.js
@@ -0,0 +1,15 @@
+import isPalindrome from '../isPalindrome';
+
+describe('palindromeCheck', () => {
+  it('should return whether or not the string is a palindrome', () => {
+    expect(isPalindrome('a')).toBe(true);
+    expect(isPalindrome('pop')).toBe(true);
+    expect(isPalindrome('deed')).toBe(true);
+    expect(isPalindrome('kayak')).toBe(true);
+    expect(isPalindrome('racecar')).toBe(true);
+
+    expect(isPalindrome('rad')).toBe(false);
+    expect(isPalindrome('dodo')).toBe(false);
+    expect(isPalindrome('polo')).toBe(false);
+  });
+});
diff --git a/src/algorithms/string/palindrome-check/palindromeCheck.js b/src/algorithms/string/palindrome/isPalindrome.js
similarity index 83%
rename from src/algorithms/string/palindrome-check/palindromeCheck.js
rename to src/algorithms/string/palindrome/isPalindrome.js
index c850fe3aa7..327fd6bbf2 100644
--- a/src/algorithms/string/palindrome-check/palindromeCheck.js
+++ b/src/algorithms/string/palindrome/isPalindrome.js
@@ -3,9 +3,10 @@
  * @return {boolean}
  */
 
-export default function palindromeCheck(string) {
+export default function isPalindrome(string) {
   let left = 0;
   let right = string.length - 1;
+
   while (left < right) {
     if (string[left] !== string[right]) {
       return false;
@@ -13,5 +14,6 @@ export default function palindromeCheck(string) {
     left += 1;
     right -= 1;
   }
+
   return true;
 }

From 42c6718cb017dfed5d867af057c8e90827c5fb5e Mon Sep 17 00:00:00 2001
From: kimzerovirus <68390715+kimzerovirus@users.noreply.github.com>
Date: Tue, 25 Jan 2022 17:32:01 +0900
Subject: [PATCH 130/264]  Add Korean translation for data-structures Hash
 Table & Heap (#843)

* Create README.ko-KR.md

* Create README.ko-KR.md

* Update README.ko-KR.md

* Update README.ko-KR.md

* Update README.ko-KR.md

* Update README.ko-KR.md
---
 src/data-structures/hash-table/README.ko-KR.md | 12 ++++++++++++
 src/data-structures/heap/README.ko-KR.md       | 13 +++++++++++++
 2 files changed, 25 insertions(+)
 create mode 100644 src/data-structures/hash-table/README.ko-KR.md
 create mode 100644 src/data-structures/heap/README.ko-KR.md

diff --git a/src/data-structures/hash-table/README.ko-KR.md b/src/data-structures/hash-table/README.ko-KR.md
new file mode 100644
index 0000000000..1ffc9f5534
--- /dev/null
+++ b/src/data-structures/hash-table/README.ko-KR.md
@@ -0,0 +1,12 @@
+# 해시 테이블
+
+컴퓨터 과학에서 **해시 테이블** (해시맵)은 키를 값에 매핑할 수 있는 *연관배열(associative array)* 기능을 가진 데이터 구조입니다. 해시 테이블은 해시함수를 사용해 버킷이나 슬롯 배열에 대한 인덱스를 계산하고 원하는 값을 찾을 수 있습니다. (사실상 해시함수에서 배열은 bucket 또는 slot으로 부릅니다.)
+따라서 해시테이블은 특정 키에 값을 매핑 시킨 형태의 자료구조로 키값에 매핑된 값을 검색 할 때 매우 유용합니다. 이때 해시함수는 찾고자 하는 키가 버킷 또는 슬롯의 몇 번째 인덱스에 해당하는지를 확인할 때 사용합니다.
+
+이상적으로는 해시함수는 각 키를 하나의 버킷에 할당하지만 대부분의 해시 테이블은 불완전한 해시함수를 채택하고 있기 때문에 복수의 키에 대해 같은 인덱스를 생성했을 때 해시의 충돌이 발생합니다. 이러한 충돌은 어떤 방법으로든 대처할 필요가 있습니다.
+
+![Hash Table](https://upload.wikimedia.org/wikipedia/commons/7/7d/Hash_table_3_1_1_0_1_0_0_SP.svg)
+
+체이닝에 따른 해시충돌(Hash Collision)의 해결법
+
+![Hash Collision](https://upload.wikimedia.org/wikipedia/commons/d/d0/Hash_table_5_0_1_1_1_1_1_LL.svg)
diff --git a/src/data-structures/heap/README.ko-KR.md b/src/data-structures/heap/README.ko-KR.md
new file mode 100644
index 0000000000..1f8c4932e4
--- /dev/null
+++ b/src/data-structures/heap/README.ko-KR.md
@@ -0,0 +1,13 @@
+# 힙 (자료구조)
+
+컴퓨터 사이언스에서 힙은 특수한 트리구조의 데이터 구조로 다음과 같은 특성을 갖고 있습니다.
+
+ *최소 힙* 에서는 만약 `P`가 `C`의 부모노드일 경우, `P` 키(값)는 `C` 키보다 작거나 동일합니다.
+
+![MinHeap](https://upload.wikimedia.org/wikipedia/commons/6/69/Min-heap.png)
+
+ - *최대 힙* 에서 `P` 키는 `C` 키보다 크거나 동일합니다.
+
+![Heap](https://upload.wikimedia.org/wikipedia/commons/3/38/Max-Heap.svg)
+
+ - 힙의 "최상단" 노드에는 부모노드가 존재하지 않으며, 루트노드라고 부릅니다.

From 6d8195154aa93e4d25798b6af43afda31a5d1b6c Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=E5=84=BF=E6=97=B6?=
 <58261676+childrentime@users.noreply.github.com>
Date: Tue, 25 Jan 2022 16:34:17 +0800
Subject: [PATCH 131/264] Add Chinise  Translation (#842)

---
 src/algorithms/sorting/quick-sort/README.md   |  4 +++
 .../sorting/quick-sort/README.zh-CN.md        | 27 +++++++++++++++++++
 2 files changed, 31 insertions(+)
 create mode 100644 src/algorithms/sorting/quick-sort/README.zh-CN.md

diff --git a/src/algorithms/sorting/quick-sort/README.md b/src/algorithms/sorting/quick-sort/README.md
index 88c768aa37..21c6391989 100644
--- a/src/algorithms/sorting/quick-sort/README.md
+++ b/src/algorithms/sorting/quick-sort/README.md
@@ -1,5 +1,9 @@
 # Quicksort
 
+_Read this in other languages:_
+[_简体中文_](README.zh-CN.md)
+
+
 Quicksort is a divide and conquer algorithm.
 Quicksort first divides a large array into two smaller 
 sub-arrays: the low elements and the high elements.
diff --git a/src/algorithms/sorting/quick-sort/README.zh-CN.md b/src/algorithms/sorting/quick-sort/README.zh-CN.md
new file mode 100644
index 0000000000..96b2e44de8
--- /dev/null
+++ b/src/algorithms/sorting/quick-sort/README.zh-CN.md
@@ -0,0 +1,27 @@
+# 快速排序
+
+快速排序是一种分而治之的算法。快速排序首先将一个大数组分成两个较小的子数组：比某个数小的元素和比某个数大的元素。然后快速排序可以递归地对子数组进行排序。
+
+步骤是：
+
+1. 从数组中选择一个元素，称为基点
+
+2. 分区：对数组重新排序，使所有值小于基点的元素都在它左边，而所有值大于基点的元素都在它右边（相等的值可以放在任何一边）。在此分区之后，基点处于其最终位置（左边和右边的中间位置）。这称为分区操作。
+
+3. 递归地将上述步骤应用于左边的数组和右边的数组。
+
+快速排序算法的动画可视化。水平线是基点值。
+
+![Quicksort](https://upload.wikimedia.org/wikipedia/commons/6/6a/Sorting_quicksort_anim.gif)
+
+## 复杂度
+
+| Name           |     Best      |    Average    |     Worst     | Memory | Stable | Comments                                                      |
+| -------------- | :-----------: | :-----------: | :-----------: | :----: | :----: | :------------------------------------------------------------ |
+| **Quick sort** | n&nbsp;log(n) | n&nbsp;log(n) | n<sup>2</sup> | log(n) |   No   | Quicksort is usually done in-place with O(log(n)) stack space |
+
+## 引用
+
+- [Wikipedia](https://en.wikipedia.org/wiki/Quicksort)
+
+- [YouTube](https://www.youtube.com/watch?v=SLauY6PpjW4&index=28&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)

From cc26b93f31717c10c1af017eaffbdb6ca41d8d20 Mon Sep 17 00:00:00 2001
From: kyong4 <60618382+kyong4@users.noreply.github.com>
Date: Tue, 25 Jan 2022 03:36:45 -0500
Subject: [PATCH 132/264] Grammar change and "Block " to "Jump" (#780)
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

* Grammar change and "Block " to "Jump"

ジャンプ is jump in katakana

* Update README.ja-JP.md

* Update README.ja-JP.md
---
 README.ja-JP.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/README.ja-JP.md b/README.ja-JP.md
index 44b6b6c13e..c90fa3e7e2 100644
--- a/README.ja-JP.md
+++ b/README.ja-JP.md
@@ -7,7 +7,7 @@
 
 
 各アルゴリズムとデータ構造には独自のREADMEがあります。
-関連する説明と、さらに読むためのリンク (関連YouTubeのビデオ)も含まれています。
+関連する説明、そして参考資料 (YouTube動画)も含まれています。
 
 _Read this in other languages:_
 [_English_](https://github.com/trekhleb/javascript-algorithms/),
@@ -100,7 +100,7 @@ _Read this in other languages:_
   * `A` [正規表現マッチング](src/algorithms/string/regular-expression-matching)
 * **検索**
   * `B` [リニアサーチ](src/algorithms/search/linear-search)
-  * `B` [ジャンプ検索](src/algorithms/search/jump-search) (or Block Search) - ソートされた配列で検索
+  * `B` [ジャンプ検索](src/algorithms/search/jump-search) (Jump Search) - ソートされた配列で検索
   * `B` [バイナリ検索](src/algorithms/search/binary-search) - ソートされた配列で検索
   * `B` [補間探索](src/algorithms/search/interpolation-search) - 一様分布のソート配列で検索する
 * **並べ替え**

From 40c54d8354508b09a12904ee8a696018a6977d25 Mon Sep 17 00:00:00 2001
From: Suman kumar <80208204+Suman-kumar23@users.noreply.github.com>
Date: Tue, 25 Jan 2022 14:07:30 +0530
Subject: [PATCH 133/264] Updating a typo in " Get bit" section (#777)

typo- ADD-> AND operation

From ae915372d91dd41352984f37b1d743966c95f2ab Mon Sep 17 00:00:00 2001
From: OscarRG <80918302+OscarRG@users.noreply.github.com>
Date: Tue, 25 Jan 2022 09:39:11 +0100
Subject: [PATCH 134/264] fix typos (#773)

---
 src/data-structures/doubly-linked-list/README.es-ES.md | 10 +++++-----
 1 file changed, 5 insertions(+), 5 deletions(-)

diff --git a/src/data-structures/doubly-linked-list/README.es-ES.md b/src/data-structures/doubly-linked-list/README.es-ES.md
index 0736d499ac..15a623550f 100644
--- a/src/data-structures/doubly-linked-list/README.es-ES.md
+++ b/src/data-structures/doubly-linked-list/README.es-ES.md
@@ -7,11 +7,11 @@ _Lea esto en otros idiomas:_
 [_Português_](README.pt-BR.md)
 [_한국어_](README.ko-KR.md)
 
-En informática, una **lista doblemente enlazada** es una estructura de datos enlazados que consta de un conjunto de registros enlazados secuencialmente llamados nodos. Cada nodo contiene dos campos, llamados enlaces, que son referencias al nodo anterior y al siguiente en la secuencia de nodos. Los enlaces anterior y siguiente de los nodos inicial y final, respectivamente, apuntan a algún tipo de terminador, normalmente un nodo centinela o nulo, para facilitar el recorrido de la lista. Si solo hay un ganglio centinela, la lista se enlaza circularmente a través del ganglio centinela. Puede conceptualizarse como dos listas enlazadas individualmente formadas a partir de los mismos elementos de datos, pero en órdenes secuenciales opuestos.
+En informática, una **lista doblemente enlazada** es una estructura de datos relacionados que consta de un conjunto de registros conectados secuencialmente llamados nodos. Cada nodo contiene dos campos, llamados enlaces, que son referencias al nodo anterior y al siguiente en la secuencia de nodos. Los enlaces anterior y siguiente de los nodos inicial y final, apuntan respectivamente a algún tipo de terminador (normalmente un nodo centinela o nulo), facilitando así el recorrido de la lista. Si solo hay un nodo nulo, la lista se enlaza circularmente a través este. Puede conceptualizarse como dos listas enlazadas individualmente formadas a partir de los mismos elementos de datos, pero en órdenes secuenciales opuestos.
 
 ![Lista doblemente enlazada](https://upload.wikimedia.org/wikipedia/commons/5/5e/Doubly-linked-list.svg)
 
-Los dos enlaces de nodo permiten recorrer la lista en cualquier dirección. Si bien agregar o eliminar un nodo en una lista doblemente enlazada requiere cambiar más enlaces que las mismas operaciones en una lista enlazada individualmente, las operaciones son más simples y potencialmente más eficientes (para nodos que no sean los primeros) porque no hay necesidad de realizar un seguimiento de el nodo anterior durante el recorrido o no es necesario recorrer la lista para encontrar el nodo anterior, de modo que se pueda modificar su enlace.
+Los dos enlaces de un nodo permiten recorrer la lista en cualquier dirección. Si bien agregar o eliminar un nodo en una lista doblemente enlazada requiere cambiar más enlaces que las mismas operaciones en una lista enlazada individualmente, las operaciones son más simples y potencialmente más eficientes (para nodos que no sean los primeros) porque no hay necesidad de realizar un seguimiento del nodo anterior durante el recorrido o no es necesario recorrer la lista para encontrar el nodo anterior, de modo que se pueda modificar su enlace.
 
 ## Pseudocódigo para operaciones básicas
 
@@ -88,9 +88,9 @@ end Reverse Traversal
 
 ## Complejidad del Tiempo
 
-| Acceso    | Busqueda    | Inserción | Supresión  |
-| :-------: | :-------: | :-------: | :-------: |
-| O(n)      | O(n)      | O(1)      | O(n)      |
+| Acceso | Búsqueda | Inserción | Eliminación |
+| :----: | :------: | :-------: | :---------: |
+|  O(n)  |   O(n)   |   O(1)    |    O(n)     |
 
 ### Complejidad del Espacio
 

From 5dc17089bcadce02d33c8fdf29fea9474e3933d4 Mon Sep 17 00:00:00 2001
From: Bravo Yeung <yangle20081982@163.com>
Date: Tue, 25 Jan 2022 17:02:35 +0800
Subject: [PATCH 135/264] Correct inaccurate Chinese translation. (#768)

---
 README.zh-CN.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.zh-CN.md b/README.zh-CN.md
index 8bf216d6bd..c8d419bc16 100644
--- a/README.zh-CN.md
+++ b/README.zh-CN.md
@@ -175,7 +175,7 @@ _Read this in other languages:_
   * `B` [快速算次方](src/algorithms/math/fast-powering)
   * `A` [排列](src/algorithms/sets/permutations) (有/无重复)
   * `A` [组合](src/algorithms/sets/combinations) (有/无重复)
-* **动态编程** - 使用以前找到的子解决方案构建解决方案
+* **动态规划(Dynamic programming)** - 使用以前找到的子解决方案构建解决方案
   * `B` [斐波那契数](src/algorithms/math/fibonacci)
   * `B` [跳跃游戏](src/algorithms/uncategorized/jump-game)
   * `B` [独特路径](src/algorithms/uncategorized/unique-paths)

From c29b12ee3b5d6bb8353cbb5207dd1e7ad19bf9a8 Mon Sep 17 00:00:00 2001
From: OscarRG <80918302+OscarRG@users.noreply.github.com>
Date: Tue, 25 Jan 2022 10:03:19 +0100
Subject: [PATCH 136/264] fix typos (#771)

---
 src/data-structures/linked-list/README.es-ES.md | 12 ++++++------
 1 file changed, 6 insertions(+), 6 deletions(-)

diff --git a/src/data-structures/linked-list/README.es-ES.md b/src/data-structures/linked-list/README.es-ES.md
index 3e49e88e91..e117f718c3 100644
--- a/src/data-structures/linked-list/README.es-ES.md
+++ b/src/data-structures/linked-list/README.es-ES.md
@@ -1,6 +1,6 @@
 # Lista Enlazada (Linked List)
 
-_Lee esto en otros idiomas:_
+_Lee este artículo en otros idiomas:_
 [_简体中文_](README.zh-CN.md),
 [_Русский_](README.ru-RU.md),
 [_日本語_](README.ja-JP.md),
@@ -12,17 +12,17 @@ de elementos de datos, en los cuales el orden linear no es dado por
 su posción física en memoria. En cambio, cada
 elemento señala al siguiente. Es una estructura de datos
 que consiste en un grupo de nodos los cuales juntos representan
-una secuencia. Bajo la forma más simple, cada nodo es
+una secuencia. Bajo la forma más simple, cada nodo esta
 compuesto de datos y una referencia (en otras palabras,
 un lazo) al siguiente nodo en la secuencia. Esta estructura
 permite la inserción o remoción de elementos
 desde cualquier posición en la secuencia durante la iteración.
 Variantes más complejas agregan lazos adicionales, permitiendo
 una eficiente inserción o remoción desde referencias arbitrarias
-del elemento. Una desventaja de las listas lazadas es que el tiempo de
+del elemento. Una desventaja de las listas enlazadas es que el tiempo de
 acceso es linear (y difícil de canalizar). Un acceso
-más rápido, como un acceso aleatorio, no es factible. Los arreglos
-tienen una mejor locazion comparados con las listas lazadas.
+más rápido, como el aleatorio, no es factible. Los arreglos
+tienen una mejor locazion comparados con las listas enlazadas.
 
 ![Linked List](https://upload.wikimedia.org/wikipedia/commons/6/6d/Singly-linked-list.svg)
 
@@ -149,7 +149,7 @@ end ReverseTraversal
 
 ### Complejidad del Tiempo
 
-| Access | Search | Insertion | Deletion |
+| Acceso | Búsqueda | Inserción | Eliminación |
 | :----: | :----: | :-------: | :------: |
 |  O(n)  |  O(n)  |   O(1)    |   O(n)   |
 

From 5a83ecc00dc8f9daaac417bf4805ba5509e48ffb Mon Sep 17 00:00:00 2001
From: Anton Kazarinov <askazarinov@gmail.com>
Date: Tue, 25 Jan 2022 12:04:32 +0300
Subject: [PATCH 137/264] fixed spelling error for hash-table (ru) (#775)

---
 src/data-structures/hash-table/README.ru-RU.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/data-structures/hash-table/README.ru-RU.md b/src/data-structures/hash-table/README.ru-RU.md
index d5487cb900..1b829049ab 100644
--- a/src/data-structures/hash-table/README.ru-RU.md
+++ b/src/data-structures/hash-table/README.ru-RU.md
@@ -2,7 +2,7 @@
 
 **Хеш-таблица** - структура данных, реализующая абстрактный тип данных *ассоциативный массив*, т.е. структура, которая
 *связывает ключи со значениями*. Хеш-таблица использует *хеш-функцию* для вычисления индекса в массиве, в котором может
-быть найдено желаемое значение. Ниже представлена хеш-таблица, в которой ключём выступает имя человека, а значениями 
+быть найдено желаемое значение. Ниже представлена хеш-таблица, в которой ключом выступает имя человека, а значениями 
 являются телефонные номера. Хеш-функция преобразует ключ-имя в индекс массива с телефонными номерами.
 
 ![Хеш-таблица](https://upload.wikimedia.org/wikipedia/commons/7/7d/Hash_table_3_1_1_0_1_0_0_SP.svg)

From d11f7fadd68b30785e591569ccaa308a813b18dd Mon Sep 17 00:00:00 2001
From: Sewook Han <hkihki306@gmail.com>
Date: Wed, 26 Jan 2022 01:48:56 +0900
Subject: [PATCH 138/264] Add Korean translation (#767)

Co-authored-by: Oleksii Trekhleb <trehleb@gmail.com>
---
 .../hash-table/README.ko-KR.md                | 21 ++++++++++++++-----
 src/data-structures/hash-table/README.md      |  4 ++--
 2 files changed, 18 insertions(+), 7 deletions(-)

diff --git a/src/data-structures/hash-table/README.ko-KR.md b/src/data-structures/hash-table/README.ko-KR.md
index 1ffc9f5534..0b847df5ca 100644
--- a/src/data-structures/hash-table/README.ko-KR.md
+++ b/src/data-structures/hash-table/README.ko-KR.md
@@ -1,12 +1,23 @@
-# 해시 테이블
+# Hash Table
 
-컴퓨터 과학에서 **해시 테이블** (해시맵)은 키를 값에 매핑할 수 있는 *연관배열(associative array)* 기능을 가진 데이터 구조입니다. 해시 테이블은 해시함수를 사용해 버킷이나 슬롯 배열에 대한 인덱스를 계산하고 원하는 값을 찾을 수 있습니다. (사실상 해시함수에서 배열은 bucket 또는 slot으로 부릅니다.)
-따라서 해시테이블은 특정 키에 값을 매핑 시킨 형태의 자료구조로 키값에 매핑된 값을 검색 할 때 매우 유용합니다. 이때 해시함수는 찾고자 하는 키가 버킷 또는 슬롯의 몇 번째 인덱스에 해당하는지를 확인할 때 사용합니다.
+_Read this in other languages:_
+[_简体中文_](README.zh-CN.md),
+[_Русский_](README.ru-RU.md),
+[_日本語_](README.ja-JP.md),
+[_Français_](README.fr-FR.md),
+[_Português_](README.pt-BR.md)
 
-이상적으로는 해시함수는 각 키를 하나의 버킷에 할당하지만 대부분의 해시 테이블은 불완전한 해시함수를 채택하고 있기 때문에 복수의 키에 대해 같은 인덱스를 생성했을 때 해시의 충돌이 발생합니다. 이러한 충돌은 어떤 방법으로든 대처할 필요가 있습니다.
+컴퓨팅에서, **해시 테이블**(해시 맵)은 키를 값에 매핑할 수 있는 구조인 *연관 배열*을 구현하는 자료 구조입니다. 해시 테이블은 *해시 함수*를 사용해 원하는 값을 담을 수 있는 버킷 또는 슬롯 배열의 인덱스를 계산합니다.
+
+이상적으로, 해시 함수는 각 키들을 고유 버킷에 할당하지만 대부분의 해시 테이블은 불완전한 해시 함수를 사용하기 때문에 해시 함수를 통해 두 개 이상의 키에 대해 동일한 인덱스를 생성하는 해시 충돌이 발생할 수 있습니다. 이러한 해시 충돌은 어떠한 방법으로든 해결되어야 합니다.
 
 ![Hash Table](https://upload.wikimedia.org/wikipedia/commons/7/7d/Hash_table_3_1_1_0_1_0_0_SP.svg)
 
-체이닝에 따른 해시충돌(Hash Collision)의 해결법
+다음은 분리 연결법을 통해 해시 충돌을 해결한 예시입니다.
 
 ![Hash Collision](https://upload.wikimedia.org/wikipedia/commons/d/d0/Hash_table_5_0_1_1_1_1_1_LL.svg)
+
+## 참고
+
+- [Wikipedia](https://en.wikipedia.org/wiki/Hash_table)
+- [YouTube](https://www.youtube.com/watch?v=shs0KM3wKv8&index=4&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
\ No newline at end of file
diff --git a/src/data-structures/hash-table/README.md b/src/data-structures/hash-table/README.md
index 37d20a6199..df199257e7 100644
--- a/src/data-structures/hash-table/README.md
+++ b/src/data-structures/hash-table/README.md
@@ -5,8 +5,8 @@ _Read this in other languages:_
 [_Русский_](README.ru-RU.md),
 [_日本語_](README.ja-JP.md),
 [_Français_](README.fr-FR.md),
-[_Português_](README.pt-BR.md)
- 
+[_Português_](README.pt-BR.md), [_한국어_](README.ko-KR.md)
+
 In computing, a **hash table** (hash map) is a data 
 structure which implements an *associative array* 
 abstract data type, a structure that can *map keys 

From d0c359e990d9f5ed5775a1dcc324c9e9529e1496 Mon Sep 17 00:00:00 2001
From: Sewook Han <hkihki306@gmail.com>
Date: Wed, 26 Jan 2022 01:54:01 +0900
Subject: [PATCH 139/264] Add Korean translation (#752)

* Add Korean translation

* Add link to Korean translation in Queue README.
---
 src/data-structures/queue/README.ko-KR.md | 21 +++++++++++++++++++++
 src/data-structures/queue/README.md       |  2 +-
 2 files changed, 22 insertions(+), 1 deletion(-)
 create mode 100644 src/data-structures/queue/README.ko-KR.md

diff --git a/src/data-structures/queue/README.ko-KR.md b/src/data-structures/queue/README.ko-KR.md
new file mode 100644
index 0000000000..204f6b9b84
--- /dev/null
+++ b/src/data-structures/queue/README.ko-KR.md
@@ -0,0 +1,21 @@
+# Queue
+
+_Read this in other languages:_
+[_简体中文_](README.zh-CN.md),
+[_Русский_](README.ru-RU.md),
+[_日本語_](README.ja-JP.md),
+[_Français_](README.fr-FR.md),
+[_Português_](README.pt-BR.md)
+
+컴퓨터 공학에서 **큐**는 일종의 추상 데이터 타입이자 컬렉션입니다. 큐 내부의 엔터티들은 순서를 유지하며 컬렉션의 가장 뒷 부분에 엔터티를 추가하는 인큐(enqueue), 컬렉션의 가장 앞에 위치한 엔터티를 제거하는 디큐(dequeue) 작업을 수행합니다. 이것은 큐를 선입선출 자료 구조로 만듭니다. 선입선출 자료 구조에서는, 추가된 첫 번째 요소가 가장 먼저 제거되는 요소가 됩니다. 이는 새로운 요소가 추가되면 이전에 추가되었던 모든 요소들을 제거해야 새로운 요소를 제거할 수 있다는것과 같은 의미입니다. 또한 큐의 가장 앞에 위치한 요소를 반환하기 위한 작업이 입력되면 디큐 작업 없이 해당 요소를 반환합니다.
+
+큐는 선형 자료 구조의 예시이며, 더 추상적으로는 순차적인 컬렉션입니다.
+
+선입선출 자료 구조인 큐를 나타내면 다음과 같습니다.
+
+![Queue](https://upload.wikimedia.org/wikipedia/commons/5/52/Data_Queue.svg)
+
+## 참고
+
+- [Wikipedia](https://en.wikipedia.org/wiki/Queue_(abstract_data_type))
+- [YouTube](https://www.youtube.com/watch?v=wjI1WNcIntg&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8&index=3&)
diff --git a/src/data-structures/queue/README.md b/src/data-structures/queue/README.md
index e6c9bc2d23..86046d8fe4 100644
--- a/src/data-structures/queue/README.md
+++ b/src/data-structures/queue/README.md
@@ -5,7 +5,7 @@ _Read this in other languages:_
 [_Русский_](README.ru-RU.md),
 [_日本語_](README.ja-JP.md),
 [_Français_](README.fr-FR.md),
-[_Português_](README.pt-BR.md)
+[_Português_](README.pt-BR.md), [_한국어_](README.ko-KR.md)
 
 In computer science, a **queue** is a particular kind of abstract data 
 type or collection in which the entities in the collection are 

From 5b64117a2c60979bf0e407165848c591f2702bb0 Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Tue, 25 Jan 2022 17:56:34 +0100
Subject: [PATCH 140/264] Fex READMEs.

---
 src/data-structures/hash-table/README.md | 21 ++++++++--------
 src/data-structures/heap/README.md       |  7 +++---
 src/data-structures/queue/README.md      | 31 ++++++++++++------------
 3 files changed, 31 insertions(+), 28 deletions(-)

diff --git a/src/data-structures/hash-table/README.md b/src/data-structures/hash-table/README.md
index df199257e7..3aec51b5c2 100644
--- a/src/data-structures/hash-table/README.md
+++ b/src/data-structures/hash-table/README.md
@@ -5,18 +5,19 @@ _Read this in other languages:_
 [_Русский_](README.ru-RU.md),
 [_日本語_](README.ja-JP.md),
 [_Français_](README.fr-FR.md),
-[_Português_](README.pt-BR.md), [_한국어_](README.ko-KR.md)
-
-In computing, a **hash table** (hash map) is a data 
-structure which implements an *associative array* 
-abstract data type, a structure that can *map keys 
-to values*. A hash table uses a *hash function* to 
-compute an index into an array of buckets or slots, 
+[_Português_](README.pt-BR.md),
+[_한국어_](README.ko-KR.md)
+
+In computing, a **hash table** (hash map) is a data
+structure which implements an *associative array*
+abstract data type, a structure that can *map keys
+to values*. A hash table uses a *hash function* to
+compute an index into an array of buckets or slots,
 from which the desired value can be found
 
-Ideally, the hash function will assign each key to a 
-unique bucket, but most hash table designs employ an 
-imperfect hash function, which might cause hash 
+Ideally, the hash function will assign each key to a
+unique bucket, but most hash table designs employ an
+imperfect hash function, which might cause hash
 collisions where the hash function generates the same
 index for more than one key. Such collisions must be
 accommodated in some way.
diff --git a/src/data-structures/heap/README.md b/src/data-structures/heap/README.md
index cbd7f12ef8..2610a9ff4a 100644
--- a/src/data-structures/heap/README.md
+++ b/src/data-structures/heap/README.md
@@ -6,9 +6,10 @@ _Read this in other languages:_
 [_日本語_](README.ja-JP.md),
 [_Français_](README.fr-FR.md),
 [_Português_](README.pt-BR.md),
-[_Türkçe_](README.tr-TR.md)
+[_Türkçe_](README.tr-TR.md),
+[_한국어_](README.ko-KR.md)
 
-In computer science, a **heap** is a specialized tree-based 
+In computer science, a **heap** is a specialized tree-based
 data structure that satisfies the heap property described
 below.
 
@@ -23,7 +24,7 @@ to the key of `C`
 
 ![Heap](https://upload.wikimedia.org/wikipedia/commons/3/38/Max-Heap.svg)
 
-The node at the "top" of the heap with no parents is 
+The node at the "top" of the heap with no parents is
 called the root node.
 
 ## References
diff --git a/src/data-structures/queue/README.md b/src/data-structures/queue/README.md
index 86046d8fe4..4db98224a1 100644
--- a/src/data-structures/queue/README.md
+++ b/src/data-structures/queue/README.md
@@ -5,22 +5,23 @@ _Read this in other languages:_
 [_Русский_](README.ru-RU.md),
 [_日本語_](README.ja-JP.md),
 [_Français_](README.fr-FR.md),
-[_Português_](README.pt-BR.md), [_한국어_](README.ko-KR.md)
+[_Português_](README.pt-BR.md),
+[_한국어_](README.ko-KR.md)
 
-In computer science, a **queue** is a particular kind of abstract data 
-type or collection in which the entities in the collection are 
-kept in order and the principle (or only) operations on the 
-collection are the addition of entities to the rear terminal 
-position, known as enqueue, and removal of entities from the 
-front terminal position, known as dequeue. This makes the queue 
-a First-In-First-Out (FIFO) data structure. In a FIFO data 
-structure, the first element added to the queue will be the 
-first one to be removed. This is equivalent to the requirement 
-that once a new element is added, all elements that were added 
-before have to be removed before the new element can be removed. 
-Often a peek or front operation is also entered, returning the 
-value of the front element without dequeuing it. A queue is an 
-example of a linear data structure, or more abstractly a 
+In computer science, a **queue** is a particular kind of abstract data
+type or collection in which the entities in the collection are
+kept in order and the principle (or only) operations on the
+collection are the addition of entities to the rear terminal
+position, known as enqueue, and removal of entities from the
+front terminal position, known as dequeue. This makes the queue
+a First-In-First-Out (FIFO) data structure. In a FIFO data
+structure, the first element added to the queue will be the
+first one to be removed. This is equivalent to the requirement
+that once a new element is added, all elements that were added
+before have to be removed before the new element can be removed.
+Often a peek or front operation is also entered, returning the
+value of the front element without dequeuing it. A queue is an
+example of a linear data structure, or more abstractly a
 sequential collection.
 
 Representation of a FIFO (first in, first out) queue

From 7f7e4eae3eacc15c2b7bc2db920c9e26c258cbed Mon Sep 17 00:00:00 2001
From: qiugu <33192247+qiugu@users.noreply.github.com>
Date: Thu, 27 Jan 2022 03:29:51 +0800
Subject: [PATCH 141/264] feat: add linkedList insert method (#774)

Co-authored-by: byj <youjia.bi@weimob.com>
---
 src/data-structures/linked-list/LinkedList.js | 34 +++++++++++++++++++
 .../linked-list/__test__/LinkedList.test.js   | 15 ++++++++
 2 files changed, 49 insertions(+)

diff --git a/src/data-structures/linked-list/LinkedList.js b/src/data-structures/linked-list/LinkedList.js
index 71c2b49755..310af779d3 100644
--- a/src/data-structures/linked-list/LinkedList.js
+++ b/src/data-structures/linked-list/LinkedList.js
@@ -54,6 +54,40 @@ export default class LinkedList {
     return this;
   }
 
+  /**
+   * @param {*} value
+   * @param {*} index
+   * @return {LinkedList}
+   */
+  insert(value, index) {
+    index = index < 0 ? 0 : index;
+    if (index === 0) {
+      this.prepend(value);
+    } else {
+      let count = 1;
+      let currentNode = this.head;
+      const newNode = new LinkedListNode(value);
+      while (currentNode) {
+        if (count === index) break;
+        currentNode = currentNode.next;
+        count++;
+      }
+      if (currentNode) {
+        newNode.next = currentNode.next;
+        currentNode.next = newNode;
+      } else {
+        if (this.tail) {
+          this.tail.next = newNode;
+          this.tail = newNode;
+        } else {
+          this.head = newNode;
+          this.tail = newNode;
+        }
+      }
+    }
+    return this;
+  }
+
   /**
    * @param {*} value
    * @return {LinkedListNode}
diff --git a/src/data-structures/linked-list/__test__/LinkedList.test.js b/src/data-structures/linked-list/__test__/LinkedList.test.js
index f4eb83e2bd..cc9440f162 100644
--- a/src/data-structures/linked-list/__test__/LinkedList.test.js
+++ b/src/data-structures/linked-list/__test__/LinkedList.test.js
@@ -32,6 +32,21 @@ describe('LinkedList', () => {
     expect(linkedList.toString()).toBe('3,2,1');
   });
 
+  it('should insert node to linked list', () => {
+    const linkedList = new LinkedList();
+
+    linkedList.insert(4, 3);
+    expect(linkedList.head.toString()).toBe('4');
+    expect(linkedList.tail.toString()).toBe('4');
+
+    linkedList.insert(3, 2);
+    linkedList.insert(2, 1);
+    linkedList.insert(1, -7);
+    linkedList.insert(10, 9);
+
+    expect(linkedList.toString()).toBe('1,4,2,3,10');
+  })
+
   it('should delete node by value from linked list', () => {
     const linkedList = new LinkedList();
 

From 00887c2d405a1246738be0eef9f529f87362b145 Mon Sep 17 00:00:00 2001
From: "observer.js" <fncolon@pm.me>
Date: Thu, 27 Jan 2022 02:35:01 +0700
Subject: [PATCH 142/264] [ID] Minor Improvements (#742)

* fix: `menghapus` typo

should be `menghapus` instead of `mengahpus`

* fix: translations

Should be `algoritma` instead of `algoritme`.
etc is in EN, replace it with `dan lain-lain` (etc in ID)

* fix: adding space to z-algorithm

since Z is the name of the algorithm.

Co-authored-by: Oleksii Trekhleb <trehleb@gmail.com>
---
 README.id-ID.md | 72 ++++++++++++++++++++++++-------------------------
 1 file changed, 36 insertions(+), 36 deletions(-)

diff --git a/README.id-ID.md b/README.id-ID.md
index 17e940576f..cb42feb196 100644
--- a/README.id-ID.md
+++ b/README.id-ID.md
@@ -5,7 +5,7 @@
 
 Repositori ini berisi contoh-contoh algoritme dan struktur data yang populer menggunakan JavaScript.
 
-Setiap algoritme dan struktur data memiliki README-nya tersendiri dengan penjelasan yang berkaitan dan tautan untuk bacaan lebih lanjut (termasuk tautan menuju video YouTube).
+Setiap algoritma dan struktur data memiliki README-nya tersendiri dengan penjelasan yang berkaitan dan tautan untuk bacaan lebih lanjut (termasuk tautan menuju video YouTube).
 
 _Baca ini dalam bahasa yang lain:_
 [_English_](https://github.com/trekhleb/javascript-algorithms/),
@@ -50,24 +50,24 @@ Struktur data adalah cara tertentu untuk mengatur dan menyimpan data dalam kompu
 - `L` [_Disjoint Set_](src/data-structures/disjoint-set)
 - `L` [_Bloom Filter_](src/data-structures/bloom-filter)
 
-## Algoritme
+## Algoritma
 
-Algoritme adalah sebuah perincian yang jelas tentang cara untuk memecahkan suatu masalah. Ia adalah sekumpulan aturan yang menjelaskan secara tepat urutan-urutan dari sebuah operasi.
+Algoritma adalah sebuah perincian yang jelas tentang cara untuk memecahkan suatu masalah. Ia adalah sekumpulan aturan yang menjelaskan secara tepat urutan-urutan dari sebuah operasi.
 
 `P` - Pemula, `L` - Lanjutan
 
-### Algoritme Berdasarkanan Topik
+### Algoritma Berdasarkanan Topik
 
 - **Matematika**
-  - `P` [Manipulasi Bit](src/algorithms/math/bits) - menetapkan/mendapatkan/memperbarui/menghapus bit, perkalian/pembagian dengan angka 2, membuat bilangan negatif dsb.
+  - `P` [Manipulasi Bit](src/algorithms/math/bits) - menetapkan/mendapatkan/memperbarui/menghapus bit, perkalian/pembagian dengan angka 2, membuat bilangan negatif dan lain-lain.
   - `P` [Faktorial](src/algorithms/math/Faktorial)
   - `P` [Bilangan Fibonacci](src/algorithms/math/fibonacci) - versi klasik dan bentuk tertutup
   - `P` [Faktor Prima](src/algorithms/math/prime-factors) - menemukan faktor prima dan menghitungnya menggunakan teorema Hardy-Ramanujan
   - `P` [Pengujian Bilangan Prima](src/algorithms/math/primality-test) (metode _trial division_)
-  - `P` [Algoritme Euclidean](src/algorithms/math/euclidean-algorithm) - menghitung Faktor Persekutuan Terbesar (FPB)
+  - `P` [Algoritma Euclidean](src/algorithms/math/euclidean-algorithm) - menghitung Faktor Persekutuan Terbesar (FPB)
   - `P` [_Least Common Multiple_](src/algorithms/math/least-common-multiple) (LCM)
   - `P` [_Sieve of Eratosthenes_](src/algorithms/math/sieve-of-eratosthenes) - menemukan semua bilangan prima hingga batas yang ditentukan
-  - `P` [_Is Power of Two_](src/algorithms/math/is-power-of-two) - mengecek apakah sebuah bilangan adalah hasil dari pangkat dua (algoritme _naive_ dan _bitwise_)
+  - `P` [_Is Power of Two_](src/algorithms/math/is-power-of-two) - mengecek apakah sebuah bilangan adalah hasil dari pangkat dua (algoritma _naive_ dan _bitwise_)
   - `P` [Segitiga Pascal](src/algorithms/math/pascal-triangle)
   - `P` [Bilangan Kompleks](src/algorithms/math/complex-number) - bilangan kompleks dengan operasi dasarnya
   - `P` [Radian & Derajat](src/algorithms/math/radian) - konversi radian ke derajat dan sebaliknya
@@ -75,7 +75,7 @@ Algoritme adalah sebuah perincian yang jelas tentang cara untuk memecahkan suatu
   - `P` [Metode Horner](src/algorithms/math/horner-method) - evaluasi polinomial
   - `L` [Partisi Bilangan Bulat](src/algorithms/math/integer-partition)
   - `L` [Akar Pangkat Dua](src/algorithms/math/square-root) - metode Newton
-  - `L` [Algoritme π Liu Hui](src/algorithms/math/liu-hui) - perkiraan perhitungan π berdasarkan segibanyak
+  - `L` [Algoritma π Liu Hui](src/algorithms/math/liu-hui) - perkiraan perhitungan π berdasarkan segibanyak
   - `L` [Transformasi Diskrit Fourier](src/algorithms/math/fourier-transform) - menguraikan fungsi waktu (sinyal) menjadi frekuensi yang menyusunnya
 - **Himpunan**
   - `P` [Produk Kartesian](src/algorithms/sets/cartesian-product) - hasil dari beberapa himpunan
@@ -91,10 +91,10 @@ Algoritme adalah sebuah perincian yang jelas tentang cara untuk memecahkan suatu
   - `L` [_Combination Sum_](src/algorithms/sets/combination-sum) - menemukan semua kombinasi yang membentuk jumlah tertentu
 - **String**
   - `P` [Jarak Hamming](src/algorithms/string/hamming-distance) - jumlah posisi di mana ditemukan simbol-simbol yang berbeda
-  - `L` [Algoritme Jarak Levenshtein](src/algorithms/string/levenshtein-distance) - _edit distance_ minimum antara dua urutan
-  - `L` [Algoritme Knuth–Morris–Pratt](src/algorithms/string/knuth-morris-pratt) (Algoritme KMP) - pencarian substring (pencocokan pola)
-  - `L` [AlgoritmeZ](src/algorithms/string/z-algorithm) - pencarian substring (pencocokan pola)
-  - `L` [Algoritme Rabin Karp](src/algorithms/string/rabin-karp) - pencarian substring
+  - `L` [Algoritma Jarak Levenshtein](src/algorithms/string/levenshtein-distance) - _edit distance_ minimum antara dua urutan
+  - `L` [Algoritma Knuth–Morris–Pratt](src/algorithms/string/knuth-morris-pratt) (Algoritma KMP) - pencarian substring (pencocokan pola)
+  - `L` [Algoritma Z](src/algorithms/string/z-algorithm) - pencarian substring (pencocokan pola)
+  - `L` [Algoritma Rabin Karp](src/algorithms/string/rabin-karp) - pencarian substring
   - `L` [_Longest Common Substring_](src/algorithms/string/longest-common-substring)
   - `L` [Pencocokan Ekspresi Reguler](src/algorithms/string/regular-expression-matching)
 - **Pencarian**
@@ -121,18 +121,18 @@ Algoritme adalah sebuah perincian yang jelas tentang cara untuk memecahkan suatu
 - **Graf**
   - `P` [Pencarian Kedalaman Pertama](src/algorithms/graph/depth-first-search) (DFS)
   - `P` [Pencarian Luas Pertama](src/algorithms/graph/breadth-first-search) (BFS)
-  - `P` [Algoritme Kruskal](src/algorithms/graph/kruskal) - mencari rentang pohon minimum untuk graf tidak berarah berbobot
-  - `L` [Algoritme Dijkstra](src/algorithms/graph/dijkstra) - menemukan jalur terpendek ke semua sudut graf dari sudut tunggal
-  - `L` [Algoritme Bellman-Ford](src/algorithms/graph/bellman-ford) - menemukan jalur terpendek ke semua sudut graf dari sudut tunggal
-  - `L` [Algoritme Floyd-Warshall](src/algorithms/graph/floyd-warshall) - menemukan jalur terpendek antara semua pasangan sudut
+  - `P` [Algoritma Kruskal](src/algorithms/graph/kruskal) - mencari rentang pohon minimum untuk graf tidak berarah berbobot
+  - `L` [Algoritma Dijkstra](src/algorithms/graph/dijkstra) - menemukan jalur terpendek ke semua sudut graf dari sudut tunggal
+  - `L` [Algoritma Bellman-Ford](src/algorithms/graph/bellman-ford) - menemukan jalur terpendek ke semua sudut graf dari sudut tunggal
+  - `L` [Algoritma Floyd-Warshall](src/algorithms/graph/floyd-warshall) - menemukan jalur terpendek antara semua pasangan sudut
   - `L` [Mendeteksi Siklus](src/algorithms/graph/detect-cycle) - untuk graf berarah dan tidak berarah (berdasarkan versi DFS dan _Disjoint Set_)
-  - `L` [ALgoritme Prim](src/algorithms/graph/prim) - mencari rentang pohon minimum untuk graf tidak berarah berbobot
+  - `L` [ALgoritma Prim](src/algorithms/graph/prim) - mencari rentang pohon minimum untuk graf tidak berarah berbobot
   - `L` [Sortir Topologi](src/algorithms/graph/topological-sorting) - metode DFS
-  - `L` [Poin Artikulasi](src/algorithms/graph/articulation-points) - Algoritme Tarjan (berdasarkan DFS)
-  - `L` [Jembatan](src/algorithms/graph/bridges) - Algoritme berdasarkan DFS
-  - `L` [Jalur dan Sirkuit Eulerian](src/algorithms/graph/eulerian-path) - Algoritme Fleury - Mengunjungi setiap tepinya tepat satu kali
+  - `L` [Poin Artikulasi](src/algorithms/graph/articulation-points) - Algoritma Tarjan (berdasarkan DFS)
+  - `L` [Jembatan](src/algorithms/graph/bridges) - Algoritma berdasarkan DFS
+  - `L` [Jalur dan Sirkuit Eulerian](src/algorithms/graph/eulerian-path) - Algoritma Fleury - Mengunjungi setiap tepinya tepat satu kali
   - `L` [Siklus Hamiltonian](src/algorithms/graph/hamiltonian-cycle) - mengunjungi setiap sudutnya tepat satu kali
-  - `L` [Komponen yang Terkoneksi dengan Kuat](src/algorithms/graph/strongly-connected-components) - Algoritme Kosaraju
+  - `L` [Komponen yang Terkoneksi dengan Kuat](src/algorithms/graph/strongly-connected-components) - Algoritma Kosaraju
   - `L` [Permasalahan Penjual Keliling](src/algorithms/graph/travelling-salesman) - kemungkinan rute terpendek untuk mengunjungi setiap kota dan kembali lagi ke kota asal
 - **Kriptografi**
   - `P` [Polinomial Hash](src/algorithms/cryptography/polynomial-hash) - fungsi rolling hash berdasarkan polinomial
@@ -141,7 +141,7 @@ Algoritme adalah sebuah perincian yang jelas tentang cara untuk memecahkan suatu
   - `P` [NanoNeuron](https://github.com/trekhleb/nano-neuron) - 7 fungsi JS sederhana yang mengilustrasikan bagaimana mesin-mesin dapat benar-benar belajar (perambatan maju/mundur)
 - **Tidak Dikategorikan**
   - `P` [Menara Hanoi](src/algorithms/uncategorized/hanoi-tower)
-  - `P` [Perputaran Matriks Persegi](src/algorithms/uncategorized/square-matrix-rotation) - algoritme _in-place_
+  - `P` [Perputaran Matriks Persegi](src/algorithms/uncategorized/square-matrix-rotation) - algoritma _in-place_
   - `P` [Permainan Melompat](src/algorithms/uncategorized/jump-game) - runut-balik, pemrograman dinamis (atas ke bawah + bawah ke atas) and contoh-contoh _greedy_
   - `P` [_Unique Paths_](src/algorithms/uncategorized/unique-paths) - runut-balik, pemrograman dinamis and contoh-contoh beradsarkan Segitiga Pascal
   - `P` [_Rain Terraces_](src/algorithms/uncategorized/rain-terraces) - permasalahan _trapping rain water_ (versi pemrograman dinamis and _brute force_)
@@ -149,9 +149,9 @@ Algoritme adalah sebuah perincian yang jelas tentang cara untuk memecahkan suatu
   - `L` [Permainan N-Queen](src/algorithms/uncategorized/n-queens)
   - `L` [Permainan Knight's Tour](src/algorithms/uncategorized/knight-tour)
 
-### Algoritme Berdasarkan Paradigma
+### Algoritma Berdasarkan Paradigma
 
-Paradigma algoritmik adalah sebuah metode atau pendekatan umum yang mendasari desain sebuah tingkatan algoritme. Paradigma algoritmik merupakan abstraksi yang lebih tinggi dari gagasan sebuah algoritme, seperti halnya sebuah algoritme merupakan abstraksi yang lebih tinggi dari sebuah program komputer.
+Paradigma algoritmik adalah sebuah metode atau pendekatan umum yang mendasari desain sebuah tingkatan algoritma. Paradigma algoritmik merupakan abstraksi yang lebih tinggi dari gagasan sebuah algoritma, seperti halnya sebuah algoritma merupakan abstraksi yang lebih tinggi dari sebuah program komputer.
 
 - **_Brute Force_** - melihat ke semua kemungkinan dan memilih solusi yang terbaik
   - `P` [Pencarian Linier](src/algorithms/search/linear-search)
@@ -163,14 +163,14 @@ Paradigma algoritmik adalah sebuah metode atau pendekatan umum yang mendasari de
 - **_Greedy_** - memilih pilihan terbaik pada saat ini tanpa mempertimbangkan masa yang akan datang
   - `P` [Permainan Melompat](src/algorithms/uncategorized/jump-game)
   - `L` [Permasalahan Knapsack yang Tidak Dibatasi](src/algorithms/sets/knapsack-problem)
-  - `L` [Algoritme Dijkstra](src/algorithms/graph/dijkstra) - menemukan jalur terpendek ke semua sudut graf dari sudut tunggal
-  - `L` [Algoritme Prim](src/algorithms/graph/prim) - mencari rentang pohon minimum untuk graf tidak berarah berbobot
-  - `L` [Algoritme Kruskal](src/algorithms/graph/kruskal) - mencari rentang pohon minimum untuk graf tidak berarah berbobot
+  - `L` [Algoritma Dijkstra](src/algorithms/graph/dijkstra) - menemukan jalur terpendek ke semua sudut graf dari sudut tunggal
+  - `L` [Algoritma Prim](src/algorithms/graph/prim) - mencari rentang pohon minimum untuk graf tidak berarah berbobot
+  - `L` [Algoritma Kruskal](src/algorithms/graph/kruskal) - mencari rentang pohon minimum untuk graf tidak berarah berbobot
 - **Memecah dan Menaklukkan** - membagi masalah menjadi bagian-bagian yang kecil, lalu memcahkan bagian-bagian tersebut
   - `P` [Pencarian Biner](src/algorithms/search/binary-search)
   - `P` [Menara Hanoi](src/algorithms/uncategorized/hanoi-tower)
   - `P` [Segitiga Pascal](src/algorithms/math/pascal-triangle)
-  - `P` [Algoritme Euclidean](src/algorithms/math/euclidean-algorithm) - menghitung Faktor Persekutuan Terbesar (FPB)
+  - `P` [Algoritma Euclidean](src/algorithms/math/euclidean-algorithm) - menghitung Faktor Persekutuan Terbesar (FPB)
   - `P` [Sortir Gabungan](src/algorithms/sorting/merge-sort)
   - `P` [Sortir Cepat](src/algorithms/sorting/quick-sort)
   - `P` [Pencarian Kedalaman Pertama untuk Pohon](src/algorithms/tree/depth-first-search) (DFS)
@@ -185,7 +185,7 @@ Paradigma algoritmik adalah sebuah metode atau pendekatan umum yang mendasari de
   - `P` [_Unique Paths_](src/algorithms/uncategorized/unique-paths)
   - `P` [_Rain Terraces_](src/algorithms/uncategorized/rain-terraces) - permasalahan _trapping rain water_
   - `P` [Tangga Rekursif](src/algorithms/uncategorized/recursive-staircase) - menghitung jumlah cara untuk mencapai ke atas tangga
-  - `L` [Algoritme Jarak Levenshtein](src/algorithms/string/levenshtein-distance) - _edit distance_ minimum antara dua urutan
+  - `L` [Algoritma Jarak Levenshtein](src/algorithms/string/levenshtein-distance) - _edit distance_ minimum antara dua urutan
   - `L` [_Longest Common Subsquence_](src/algorithms/sets/longest-common-subsequence) (LCS)
   - `L` [_Longest Common Substring_](src/algorithms/string/longest-common-substring)
   - `L` [_Longest Increasing Subsequence_](src/algorithms/sets/longest-increasing-subsequence)
@@ -193,10 +193,10 @@ Paradigma algoritmik adalah sebuah metode atau pendekatan umum yang mendasari de
   - `L` [Permasalahan Knapsack 0/1](src/algorithms/sets/knapsack-problem)
   - `L` [Partisi Bilangan Bulat](src/algorithms/math/integer-partition)
   - `L` [Upalarik Maksimum](src/algorithms/sets/maximum-subarray)
-  - `L` [Algoritme Bellman-Ford](src/algorithms/graph/bellman-ford) - menemukan jalur terpendek ke semua sudut graf dari sudut tunggal
-  - `L` [Algoritme Floyd-Warshall](src/algorithms/graph/floyd-warshall) - menemukan jalur terpendek antara semua pasangan sudut
+  - `L` [Algoritma Bellman-Ford](src/algorithms/graph/bellman-ford) - menemukan jalur terpendek ke semua sudut graf dari sudut tunggal
+  - `L` [Algoritma Floyd-Warshall](src/algorithms/graph/floyd-warshall) - menemukan jalur terpendek antara semua pasangan sudut
   - `L` [Pencocokan Ekspresi Reguler](src/algorithms/string/regular-expression-matching)
-- **Runut-balik** - sama halnya dengan _brute force_, algoritme ini mencoba untuk menghasilkan segala kemungkinan solusi, tetapi setiap kali anda menghasilkan solusi selanjutnya, anda akan menguji apakah solusi tersebut memenuhi semua kondisi dan setelah itu baru akan menghasilkan solusi berikutnya. Apabila tidak, maka akan merunut-balik dan mencari solusi di jalur yang berbeda. Biasanya menggunakan lintas DFS dari ruang keadaan.
+- **Runut-balik** - sama halnya dengan _brute force_, algoritma ini mencoba untuk menghasilkan segala kemungkinan solusi, tetapi setiap kali anda menghasilkan solusi selanjutnya, anda akan menguji apakah solusi tersebut memenuhi semua kondisi dan setelah itu baru akan menghasilkan solusi berikutnya. Apabila tidak, maka akan merunut-balik dan mencari solusi di jalur yang berbeda. Biasanya menggunakan lintas DFS dari ruang keadaan.
   - `P` [Permainan Melompat](src/algorithms/uncategorized/jump-game)
   - `P` [_Unique Paths_](src/algorithms/uncategorized/unique-paths)
   - `P` [Himpunan Kuasa](src/algorithms/sets/power-set) - semua himpunan bagian dari sebuah himpunan
@@ -236,7 +236,7 @@ npm test -- 'LinkedList'
 
 **_Playground_**
 
-Anda dapat bermain dengan algoritme dan struktur data di _file_ `./src/playground/playground.js` dan menuliskan tesnya di `./src/playground/__test__/playground.test.js`.
+Anda dapat bermain dengan algoritma dan struktur data di _file_ `./src/playground/playground.js` dan menuliskan tesnya di `./src/playground/__test__/playground.test.js`.
 
 Lalu, hanya tinggal menjalankan perintah berikut untuk mengetes apakah kode _playground_ anda bekerja sesuai dengan keinginan:
 
@@ -248,11 +248,11 @@ npm test -- 'playground'
 
 ### Referensi
 
-[▶ Algoritme dan Struktur Data di YouTube](https://www.youtube.com/playlist?list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
+[▶ Algoritma dan Struktur Data di YouTube](https://www.youtube.com/playlist?list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
 
 ### Notasi _Big O_
 
-Notasi _Big O_ digunakan untuk mengklasifikasikan algoritme berdasarkan durasi atau ruang yang dibutuhkan seiring bertambahnya _input_. Pada grafik dibawah, anda dapat menemukan urutan pertumbuhan yang paling umum dari algoritme yang ditentukan dalam notasi _Big O_.
+Notasi _Big O_ digunakan untuk mengklasifikasikan algoritma berdasarkan durasi atau ruang yang dibutuhkan seiring bertambahnya _input_. Pada grafik dibawah, anda dapat menemukan urutan pertumbuhan yang paling umum dari algoritma yang ditentukan dalam notasi _Big O_.
 
 ![Big O graphs](./assets/big-o-graph.png)
 
@@ -285,7 +285,7 @@ Di bawah ini adalah daftar dari beberapa notasi _Big O_ yang sering digunakan da
 | **AVL Tree**                                 | log(n) |  log(n)   |   log(n)   |   log(n)    |                                                          |
 | **Bloom Filter**                             |   -    |     1     |     1      |      -      | Positif palsu dimungkinkan saat pencarian                |
 
-### Kompleksitas Algoritme Sortir Larik
+### Kompleksitas Algoritma Sortir Larik
 
 | Nama                                   |    Terbaik    |          Rata-rata           |          Terburuk           | Memori | Stabil | Keterangan                                                                        |
 | -------------------------------------- | :-----------: | :--------------------------: | :-------------------------: | :----: | :----: | :-------------------------------------------------------------------------------- |

From c1b2e893ff913ab4162620acf3b0adebe13b55ef Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Muhammed=20Erdin=C3=A7?=
 <33763365+muhammederdinc@users.noreply.github.com>
Date: Wed, 26 Jan 2022 22:35:45 +0300
Subject: [PATCH 143/264] Factorial turkish readme (#740)

* added turkish readme for factorial

* Added redirect link to Turkish document.
---
 src/algorithms/math/factorial/README.md       |  2 +-
 src/algorithms/math/factorial/README.tr-TR.md | 38 +++++++++++++++++++
 2 files changed, 39 insertions(+), 1 deletion(-)
 create mode 100644 src/algorithms/math/factorial/README.tr-TR.md

diff --git a/src/algorithms/math/factorial/README.md b/src/algorithms/math/factorial/README.md
index 107b55a3d3..032121dfdf 100644
--- a/src/algorithms/math/factorial/README.md
+++ b/src/algorithms/math/factorial/README.md
@@ -1,7 +1,7 @@
 # Factorial
 
 _Read this in other languages:_
-[_简体中文_](README.zh-CN.md), [français](README.fr-FR.md).
+[_简体中文_](README.zh-CN.md), [français](README.fr-FR.md), [turkish](README.tr-TR.md).
 
 In mathematics, the factorial of a non-negative integer `n`,
 denoted by `n!`, is the product of all positive integers less
diff --git a/src/algorithms/math/factorial/README.tr-TR.md b/src/algorithms/math/factorial/README.tr-TR.md
new file mode 100644
index 0000000000..68ce21a299
--- /dev/null
+++ b/src/algorithms/math/factorial/README.tr-TR.md
@@ -0,0 +1,38 @@
+# Faktöriyel
+
+_Bunu diğer dillerde okuyun:_
+[_简体中文_](README.zh-CN.md), [français](README.fr-FR.md).
+
+Faktöriyel, matematikte, sağına ünlem işareti konulmuş sayıya
+verilen isim, daha genel olan Gama fonksiyonunun tam sayılarla
+sınırlanmış özel bir durumudur. 1'den başlayarak belirli bir
+sayma sayısına kadar olan sayıların çarpımına o sayının
+faktöriyeli denir. Basit bir şekilde faktöriyel, n tane ayrık
+elemanın kaç farklı şekilde sıralanabileceğidir.
+
+```
+5! = 5 * 4 * 3 * 2 * 1 = 120
+```
+
+| n   |                n! |
+| --- | ----------------: |
+| 0   |                 1 |
+| 1   |                 1 |
+| 2   |                 2 |
+| 3   |                 6 |
+| 4   |                24 |
+| 5   |               120 |
+| 6   |               720 |
+| 7   |             5 040 |
+| 8   |            40 320 |
+| 9   |           362 880 |
+| 10  |         3 628 800 |
+| 11  |        39 916 800 |
+| 12  |       479 001 600 |
+| 13  |     6 227 020 800 |
+| 14  |    87 178 291 200 |
+| 15  | 1 307 674 368 000 |
+
+## Referanslar
+
+[Wikipedia](https://en.wikipedia.org/wiki/Factorial)

From aa0f47ed658cbd84e975bd5aa4f0d8659e3817e2 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Muhammed=20Erdin=C3=A7?=
 <33763365+muhammederdinc@users.noreply.github.com>
Date: Wed, 26 Jan 2022 22:36:54 +0300
Subject: [PATCH 144/264] Linked list turkish readme (#739)

* added README.tr-TR.md for linked-list

* added gap

* linked list description edited.
---
 src/data-structures/linked-list/README.md     |   1 +
 .../linked-list/README.tr-TR.md               | 159 ++++++++++++++++++
 2 files changed, 160 insertions(+)
 create mode 100644 src/data-structures/linked-list/README.tr-TR.md

diff --git a/src/data-structures/linked-list/README.md b/src/data-structures/linked-list/README.md
index f30dbffaf7..d4b9fa53e9 100644
--- a/src/data-structures/linked-list/README.md
+++ b/src/data-structures/linked-list/README.md
@@ -7,6 +7,7 @@ _Read this in other languages:_
 [_Português_](README.pt-BR.md),
 [_한국어_](README.ko-KR.md),
 [_Español_](README.es-ES.md),
+[_Turkish_](README.tr-TR.md),
 
 In computer science, a **linked list** is a linear collection
 of data elements, in which linear order is not given by
diff --git a/src/data-structures/linked-list/README.tr-TR.md b/src/data-structures/linked-list/README.tr-TR.md
new file mode 100644
index 0000000000..e3f73fdf63
--- /dev/null
+++ b/src/data-structures/linked-list/README.tr-TR.md
@@ -0,0 +1,159 @@
+# Bağlantılı Liste
+
+_Bunu diğer dillerde okuyun:_
+[_简体中文_](README.zh-CN.md),
+[_Русский_](README.ru-RU.md),
+[_日本語_](README.ja-JP.md),
+[_Português_](README.pt-BR.md),
+[_한국어_](README.ko-KR.md),
+[_Español_](README.es-ES.md),
+
+Bilgisayar bilimlerinde, **Bağlantılı liste**, her biri hem gerçek verileri
+hem de listedeki bir sonraki düğümün bir bağlantısını içeren dinamik bir
+veri yapısıdır. Bu yapı, yineleme sırasında rastgele bir konumda
+öğeleri verimli bir şekilde eklemenize ve kaldırmanıza olanak tanır.
+Daha karmaşık seçenekler için, isteğe bağlı öğeleri verimli bir şekilde
+eklemek ve kaldırmak için ek bağlantılar içerir.
+
+Bağlantılı listelerin bir dezavantajı, erişim süresinin doğrusal olmasıdır
+(ve ardışık düzene geçirilmesi zordur). Rastgele erişim gibi daha hızlı erişim
+mümkün değildir. Diziler, bağlantılı listelere kıyasla daha iyi önbellek konumuna sahiptir.
+
+![Bağlantılı Liste](https://upload.wikimedia.org/wikipedia/commons/6/6d/Singly-linked-list.svg)
+
+## Temel İşlemler için Sözde Kod
+
+### Ekleme
+
+```text
+Add(value)
+  Pre: value is the value to add to the list
+  Post: value has been placed at the tail of the list
+  n ← node(value)
+  if head = ø
+    head ← n
+    tail ← n
+  else
+    tail.next ← n
+    tail ← n
+  end if
+end Add
+```
+
+```text
+Prepend(value)
+ Pre: value is the value to add to the list
+ Post: value has been placed at the head of the list
+ n ← node(value)
+ n.next ← head
+ head ← n
+ if tail = ø
+   tail ← n
+ end
+end Prepend
+```
+
+### Arama
+
+```text
+Contains(head, value)
+  Pre: head is the head node in the list
+       value is the value to search for
+  Post: the item is either in the linked list, true; otherwise false
+  n ← head
+  while n != ø and n.value != value
+    n ← n.next
+  end while
+  if n = ø
+    return false
+  end if
+  return true
+end Contains
+```
+
+### Silme
+
+```text
+Remove(head, value)
+  Pre: head is the head node in the list
+       value is the value to remove from the list
+  Post: value is removed from the list, true, otherwise false
+  if head = ø
+    return false
+  end if
+  n ← head
+  if n.value = value
+    if head = tail
+      head ← ø
+      tail ← ø
+    else
+      head ← head.next
+    end if
+    return true
+  end if
+  while n.next != ø and n.next.value != value
+    n ← n.next
+  end while
+  if n.next != ø
+    if n.next = tail
+      tail ← n
+      tail.next = null
+    end if
+    n.next ← n.next.next
+    return true
+  end if
+  return false
+end Remove
+```
+
+### Geçiş
+
+```text
+Traverse(head)
+  Pre: head is the head node in the list
+  Post: the items in the list have been traversed
+  n ← head
+  while n != ø
+    yield n.value
+    n ← n.next
+  end while
+end Traverse
+```
+
+### Ters Geçiş
+
+```text
+ReverseTraversal(head, tail)
+  Pre: head and tail belong to the same list
+  Post: the items in the list have been traversed in reverse order
+  if tail != ø
+    curr ← tail
+    while curr != head
+      prev ← head
+      while prev.next != curr
+        prev ← prev.next
+      end while
+      yield curr.value
+      curr ← prev
+    end while
+   yield curr.value
+  end if
+end ReverseTraversal
+```
+
+## Karmaşıklıklar
+
+### Zaman Karmaşıklığı
+
+| Erişim    | Arama     | Ekleme    | Silme     |
+| :-------: | :-------: | :-------: | :-------: |
+| O(n)      | O(n)      | O(1)      | O(n)      |
+
+### Uzay Karmaşıklığı
+
+O(n)
+
+## Referanslar
+
+- [Wikipedia](https://en.wikipedia.org/wiki/Linked_list)
+- [YouTube](https://www.youtube.com/watch?v=njTh_OwMljA&index=2&t=1s&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)

From 2a49b7045a5718c7623cbc4591a8f8c45b5e4721 Mon Sep 17 00:00:00 2001
From: rmagillxyz <r@magill.xyz>
Date: Wed, 26 Jan 2022 14:38:56 -0500
Subject: [PATCH 145/264] Add type name to Big O table (#717)

---
 README.md | 18 +++++++++---------
 1 file changed, 9 insertions(+), 9 deletions(-)

diff --git a/README.md b/README.md
index 6bc124c357..914b233240 100644
--- a/README.md
+++ b/README.md
@@ -305,15 +305,15 @@ Source: [Big O Cheat Sheet](http://bigocheatsheet.com/).
 
 Below is the list of some of the most used Big O notations and their performance comparisons against different sizes of the input data.
 
-| Big O Notation | Computations for 10 elements | Computations for 100 elements | Computations for 1000 elements  |
-| -------------- | ---------------------------- | ----------------------------- | ------------------------------- |
-| **O(1)**       | 1                            | 1                             | 1                               |
-| **O(log N)**   | 3                            | 6                             | 9                               |
-| **O(N)**       | 10                           | 100                           | 1000                            |
-| **O(N log N)** | 30                           | 600                           | 9000                            |
-| **O(N^2)**     | 100                          | 10000                         | 1000000                         |
-| **O(2^N)**     | 1024                         | 1.26e+29                      | 1.07e+301                       |
-| **O(N!)**      | 3628800                      | 9.3e+157                      | 4.02e+2567                      |
+| Type        | Big O Notation | Computations for 10 elements | Computations for 100 elements | Computations for 1000 elements  |
+| ----------- | -------------- | ---------------------------- | ----------------------------- | ------------------------------- |
+| Constant    | **O(1)**       | 1                            | 1                             | 1                               |
+| Logarithmic | **O(log N)**   | 3                            | 6                             | 9                               |
+| Linear      | **O(N)**       | 10                           | 100                           | 1000                            |
+| n log(n)    | **O(N log N)** | 30                           | 600                           | 9000                            |
+| Quadratic   | **O(N^2)**     | 100                          | 10000                         | 1000000                         |
+| Exponential | **O(2^N)**     | 1024                         | 1.26e+29                      | 1.07e+301                       |
+| Factorial   | **O(N!)**      | 3628800                      | 9.3e+157                      | 4.02e+2567                      |
 
 ### Data Structure Operations Complexity
 

From 9ca459ff657318de2d5a86f2c56b8442db8b297f Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Wed, 26 Jan 2022 20:50:39 +0100
Subject: [PATCH 146/264] Fix lint issue.

---
 src/data-structures/linked-list/LinkedList.js             | 8 ++++----
 .../linked-list/__test__/LinkedList.test.js               | 2 +-
 2 files changed, 5 insertions(+), 5 deletions(-)

diff --git a/src/data-structures/linked-list/LinkedList.js b/src/data-structures/linked-list/LinkedList.js
index 310af779d3..ba7d0e3ee1 100644
--- a/src/data-structures/linked-list/LinkedList.js
+++ b/src/data-structures/linked-list/LinkedList.js
@@ -56,11 +56,11 @@ export default class LinkedList {
 
   /**
    * @param {*} value
-   * @param {*} index
+   * @param {number} index
    * @return {LinkedList}
    */
-  insert(value, index) {
-    index = index < 0 ? 0 : index;
+  insert(value, rawIndex) {
+    const index = rawIndex < 0 ? 0 : rawIndex;
     if (index === 0) {
       this.prepend(value);
     } else {
@@ -70,7 +70,7 @@ export default class LinkedList {
       while (currentNode) {
         if (count === index) break;
         currentNode = currentNode.next;
-        count++;
+        count += 1;
       }
       if (currentNode) {
         newNode.next = currentNode.next;
diff --git a/src/data-structures/linked-list/__test__/LinkedList.test.js b/src/data-structures/linked-list/__test__/LinkedList.test.js
index cc9440f162..fc534c262e 100644
--- a/src/data-structures/linked-list/__test__/LinkedList.test.js
+++ b/src/data-structures/linked-list/__test__/LinkedList.test.js
@@ -45,7 +45,7 @@ describe('LinkedList', () => {
     linkedList.insert(10, 9);
 
     expect(linkedList.toString()).toBe('1,4,2,3,10');
-  })
+  });
 
   it('should delete node by value from linked list', () => {
     const linkedList = new LinkedList();

From 1216d00937ce43ce525254264a2557406fafbc8c Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Wed, 26 Jan 2022 20:53:22 +0100
Subject: [PATCH 147/264] Restructure the Big O Notation table.

---
 README.md | 18 +++++++++---------
 1 file changed, 9 insertions(+), 9 deletions(-)

diff --git a/README.md b/README.md
index 914b233240..4f6cb03803 100644
--- a/README.md
+++ b/README.md
@@ -305,15 +305,15 @@ Source: [Big O Cheat Sheet](http://bigocheatsheet.com/).
 
 Below is the list of some of the most used Big O notations and their performance comparisons against different sizes of the input data.
 
-| Type        | Big O Notation | Computations for 10 elements | Computations for 100 elements | Computations for 1000 elements  |
-| ----------- | -------------- | ---------------------------- | ----------------------------- | ------------------------------- |
-| Constant    | **O(1)**       | 1                            | 1                             | 1                               |
-| Logarithmic | **O(log N)**   | 3                            | 6                             | 9                               |
-| Linear      | **O(N)**       | 10                           | 100                           | 1000                            |
-| n log(n)    | **O(N log N)** | 30                           | 600                           | 9000                            |
-| Quadratic   | **O(N^2)**     | 100                          | 10000                         | 1000000                         |
-| Exponential | **O(2^N)**     | 1024                         | 1.26e+29                      | 1.07e+301                       |
-| Factorial   | **O(N!)**      | 3628800                      | 9.3e+157                      | 4.02e+2567                      |
+| Big O Notation | Type        | Computations for 10 elements | Computations for 100 elements | Computations for 1000 elements  |
+| -------------- | ----------- | ---------------------------- | ----------------------------- | ------------------------------- |
+| **O(1)**       | Constant    | 1                            | 1                             | 1                               |
+| **O(log N)**   | Logarithmic | 3                            | 6                             | 9                               |
+| **O(N)**       | Linear      | 10                           | 100                           | 1000                            |
+| **O(N log N)** | n log(n)    | 30                           | 600                           | 9000                            |
+| **O(N^2)**     | Quadratic   | 100                          | 10000                         | 1000000                         |
+| **O(2^N)**     | Exponential | 1024                         | 1.26e+29                      | 1.07e+301                       |
+| **O(N!)**      | Factorial   | 3628800                      | 9.3e+157                      | 4.02e+2567                      |
 
 ### Data Structure Operations Complexity
 

From 7ef78c48aa9303c0e7776d8825db24ae10a50a49 Mon Sep 17 00:00:00 2001
From: tusba <11007086+tusba@users.noreply.github.com>
Date: Thu, 27 Jan 2022 01:57:01 +0600
Subject: [PATCH 148/264] Typos in a doubly linked list's "ru" readme (#724)

---
 src/data-structures/doubly-linked-list/README.ru-RU.md | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/src/data-structures/doubly-linked-list/README.ru-RU.md b/src/data-structures/doubly-linked-list/README.ru-RU.md
index 66637691fa..ddad0312b0 100644
--- a/src/data-structures/doubly-linked-list/README.ru-RU.md
+++ b/src/data-structures/doubly-linked-list/README.ru-RU.md
@@ -3,11 +3,11 @@
 **Двусвязный список** — связная структура данных в информатике, состоящая из набора
 последовательно связанных записей, называемых узлами. Каждый узел содержит два поля,
 называемых ссылками, которые указывают на предыдущий и последующий элементы в
-последовательности узлов. Ссылка на предыдущий элемент корневого узла ссылка на
-последующий элемент последнего узла, указывают на некого рода прерыватель, обычно
+последовательности узлов. Ссылка на предыдущий элемент корневого узла и ссылка на
+последующий элемент последнего узла указывают на некого рода прерыватель, обычно
 сторожевой узел или null, для облегчения обхода списка. Если в списке только один
-сторожевой узел, тогда список циклически связана через него.
-Двусвязный список можно представить, как два связных списка, которые образованны из
+сторожевой узел, тогда список циклически связан через него.
+Двусвязный список можно представить, как два связных списка, которые образованы из
 одних и тех же данных, но расположенных в противоположном порядке.
 
 ![Двусвязный список](https://upload.wikimedia.org/wikipedia/commons/5/5e/Doubly-linked-list.svg)

From 80649156ea9ccb8d3e92c4d4e86a72b41b4022b3 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Rafael=20Ara=C3=BAjo?= <rafaelbpa@gmail.com>
Date: Thu, 27 Jan 2022 05:49:11 -0300
Subject: [PATCH 149/264] Created Quicksort documentation in pt-BR (#735)

Co-authored-by: Oleksii Trekhleb <trehleb@gmail.com>
---
 src/algorithms/sorting/quick-sort/README.md   |  2 +-
 .../sorting/quick-sort/README.pt-BR.md        | 35 +++++++++++++++++++
 2 files changed, 36 insertions(+), 1 deletion(-)
 create mode 100644 src/algorithms/sorting/quick-sort/README.pt-BR.md

diff --git a/src/algorithms/sorting/quick-sort/README.md b/src/algorithms/sorting/quick-sort/README.md
index 21c6391989..2daedb46cf 100644
--- a/src/algorithms/sorting/quick-sort/README.md
+++ b/src/algorithms/sorting/quick-sort/README.md
@@ -1,9 +1,9 @@
 # Quicksort
 
 _Read this in other languages:_
+[_Português_](README.pt-BR.md),
 [_简体中文_](README.zh-CN.md)
 
-
 Quicksort is a divide and conquer algorithm.
 Quicksort first divides a large array into two smaller 
 sub-arrays: the low elements and the high elements.
diff --git a/src/algorithms/sorting/quick-sort/README.pt-BR.md b/src/algorithms/sorting/quick-sort/README.pt-BR.md
new file mode 100644
index 0000000000..a52f3725de
--- /dev/null
+++ b/src/algorithms/sorting/quick-sort/README.pt-BR.md
@@ -0,0 +1,35 @@
+# Quicksort
+
+Quicksort é um algoritmo de dividir para conquistar é um algoritmo de divisão e conquista.
+Quicksort primeiro divide uma grande matriz em duas menores
+submatrizes: os elementos baixos e os elementos altos.
+O Quicksort pode então classificar recursivamente as submatrizes
+
+As etapas são:
+
+1. Escolha um elemento, denominado pivô, na matriz.
+2. Particionamento: reordene a matriz para que todos os elementos com
+valores menores que o pivô vêm antes do pivô, enquanto todos
+elementos com valores maiores do que o pivô vêm depois dele
+(valores iguais podem ser usados em qualquer direção). Após este particionamento,
+o pivô está em sua posição final. Isso é chamado de
+operação de partição.
+3. Aplique recursivamente as etapas acima à submatriz de
+elementos com valores menores e separadamente para o
+submatriz de elementos com valores maiores.
+
+Visualização animada do algoritmo quicksort.
+As linhas horizontais são valores dinâmicos. 
+
+![Quicksort](https://upload.wikimedia.org/wikipedia/commons/6/6a/Sorting_quicksort_anim.gif)
+
+## Complexidade
+
+| Nome                  | Melhor            | Média             | Pior               | Memória    | Estável    | Comentários  |
+| --------------------- | :-------------: | :-----------------: | :-----------------: | :-------: | :-------: | :-------- |
+| **Quick sort**        | n&nbsp;log(n)   | n&nbsp;log(n)       | n<sup>2</sup>       | log(n)    | No        |  Quicksort geralmente é feito no local com espaço de pilha O(log(n)) |
+
+## Referências
+
+- [Wikipedia](https://pt.wikipedia.org/wiki/Quicksort)
+- [YouTube](https://www.youtube.com/watch?v=SLauY6PpjW4&index=28&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)

From c2e5b3d5f1cc1092b2d00386c716980e516484a8 Mon Sep 17 00:00:00 2001
From: tusba <11007086+tusba@users.noreply.github.com>
Date: Thu, 27 Jan 2022 14:50:47 +0600
Subject: [PATCH 150/264] Fix error in Queue definition from README.ru-RU.md
 (#726)

---
 src/data-structures/queue/README.ru-RU.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/src/data-structures/queue/README.ru-RU.md b/src/data-structures/queue/README.ru-RU.md
index 539272475d..419edadecd 100644
--- a/src/data-structures/queue/README.ru-RU.md
+++ b/src/data-structures/queue/README.ru-RU.md
@@ -2,8 +2,8 @@
 
 Очередь (англ. queue) - структура данных в информатике, в которой элементы
 хранятся в порядке их добавления. Добавление новых элементов(enqueue)
-осуществляется в начало списка. А удаление элементов (dequeue)
-осуществляется с конца. Таким образом очередь реализует принцип
+осуществляется в конец списка. А удаление элементов (dequeue)
+осуществляется с начала. Таким образом очередь реализует принцип
 "первым вошёл - первым вышел" (FIFO). Часто реализуется операция чтения
 головного элемента (peek), которая возвращает первый в очереди элемент,
 при этом не удаляя его. Очередь является примером линейной структуры

From d581548b4c804bf24d48921795f4fe7179a1eb78 Mon Sep 17 00:00:00 2001
From: tusba <11007086+tusba@users.noreply.github.com>
Date: Thu, 27 Jan 2022 14:51:29 +0600
Subject: [PATCH 151/264] Fix a typo in linked list's "ru" readme (#723)

Deletion time complexity from O(1) to O(n)
---
 src/data-structures/linked-list/README.ru-RU.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/data-structures/linked-list/README.ru-RU.md b/src/data-structures/linked-list/README.ru-RU.md
index fa8e277e0d..d76bcd82f9 100644
--- a/src/data-structures/linked-list/README.ru-RU.md
+++ b/src/data-structures/linked-list/README.ru-RU.md
@@ -133,7 +133,7 @@ end ReverseTraversal
 
 | Чтение    | Поиск     | Вставка   | Удаление  |
 | :--------: | :-------: | :--------: | :-------: |
-| O(n)       | O(n)      | O(1)       | O(1)      |
+| O(n)       | O(n)      | O(1)       | O(n)      |
 
 ### Пространственная сложность
 

From 1c4e02879af62743ceb3114676bd166e88f04988 Mon Sep 17 00:00:00 2001
From: Kim Chan <Nomyfan@live.com>
Date: Fri, 28 Jan 2022 03:31:19 +0800
Subject: [PATCH 152/264] fix: LinkedList test (#712)

---
 src/data-structures/linked-list/__test__/LinkedList.test.js | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/data-structures/linked-list/__test__/LinkedList.test.js b/src/data-structures/linked-list/__test__/LinkedList.test.js
index fc534c262e..6ac41ddf05 100644
--- a/src/data-structures/linked-list/__test__/LinkedList.test.js
+++ b/src/data-structures/linked-list/__test__/LinkedList.test.js
@@ -230,7 +230,7 @@ describe('LinkedList', () => {
     expect(node).toBeDefined();
     expect(node.value.value).toBe(2);
     expect(node.value.customValue).toBe('test2');
-    expect(linkedList.find({ value: 2, customValue: 'test5' })).toBeNull();
+    expect(linkedList.find({ value: { value: 2, customValue: 'test5' } })).toBeNull();
   });
 
   it('should find preferring callback over compare function', () => {

From d227646201ec734590d71e157dac239a8727dd3c Mon Sep 17 00:00:00 2001
From: Aldo Salas <salas_rdz@outlook.es>
Date: Thu, 27 Jan 2022 13:33:47 -0600
Subject: [PATCH 153/264] Fixing typos in Linked List README.es-ES.md (#710)

Co-authored-by: Oleksii Trekhleb <trehleb@gmail.com>
---
 .../linked-list/README.es-ES.md               | 34 +++++++++----------
 1 file changed, 17 insertions(+), 17 deletions(-)

diff --git a/src/data-structures/linked-list/README.es-ES.md b/src/data-structures/linked-list/README.es-ES.md
index e117f718c3..0a9ec6b3a2 100644
--- a/src/data-structures/linked-list/README.es-ES.md
+++ b/src/data-structures/linked-list/README.es-ES.md
@@ -7,26 +7,26 @@ _Lee este artículo en otros idiomas:_
 [_Português_](README.pt-BR.md)
 [_English_](README.md)
 
-En ciencias de la computación una **lista enlazada** es una colección linear
-de elementos de datos, en los cuales el orden linear no es dado por
-su posción física en memoria. En cambio, cada
-elemento señala al siguiente. Es una estructura de datos
+En ciencias de la computación una **lista enlazada** es una colección lineal
+de elementos de datos, en los cuales el orden lineal no es dado por
+su posición física en memoria. En cambio, cada
+elemento apunta al siguiente. Es una estructura de datos
 que consiste en un grupo de nodos los cuales juntos representan
-una secuencia. Bajo la forma más simple, cada nodo esta
+una secuencia. En su forma más sencilla, cada nodo está
 compuesto de datos y una referencia (en otras palabras,
-un lazo) al siguiente nodo en la secuencia. Esta estructura
-permite la inserción o remoción de elementos
+un enlace) al siguiente nodo en la secuencia. Esta estructura
+permite la inserción o eliminación de elementos
 desde cualquier posición en la secuencia durante la iteración.
-Variantes más complejas agregan lazos adicionales, permitiendo
-una eficiente inserción o remoción desde referencias arbitrarias
-del elemento. Una desventaja de las listas enlazadas es que el tiempo de
-acceso es linear (y difícil de canalizar). Un acceso
-más rápido, como el aleatorio, no es factible. Los arreglos
-tienen una mejor locazion comparados con las listas enlazadas.
+Las variantes más complejas agregan enlaces adicionales, permitiendo
+una eficiente inserción o eliminación desde referencias arbitrarias
+del elemento. Una desventaja de las listas lazadas es que el tiempo de
+acceso es lineal (y difícil de canalizar). Un acceso
+más rápido, como un acceso aleatorio, no es factible. Los arreglos
+tienen una mejor locazion en caché comparados con las listas lazadas.
 
 ![Linked List](https://upload.wikimedia.org/wikipedia/commons/6/6d/Singly-linked-list.svg)
 
-## Pseudocódigo para operacones básicas
+## Pseudocódigo para operaciones básicas
 
 ### Insertar
 
@@ -147,11 +147,11 @@ end ReverseTraversal
 
 ## Complejidades
 
-### Complejidad del Tiempo
+### Complejidad de Tiempo
 
 | Acceso | Búsqueda | Inserción | Eliminación |
-| :----: | :----: | :-------: | :------: |
-|  O(n)  |  O(n)  |   O(1)    |   O(n)   |
+| :----: | :------: | :-------: | :---------: |
+|  O(n)  |   O(n)   |   O(1)    |    O(n)     |
 
 ### Complejidad Espacial
 

From 8e8f28ffcf475ff869ec47d05f8753d8fac7117a Mon Sep 17 00:00:00 2001
From: H2rmone <3357458@qq.com>
Date: Fri, 28 Jan 2022 03:36:39 +0800
Subject: [PATCH 154/264] Use exist method to be consistent with Stack (#708)

---
 src/data-structures/queue/Queue.js | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/data-structures/queue/Queue.js b/src/data-structures/queue/Queue.js
index f6ec6d2dad..64e646fc00 100644
--- a/src/data-structures/queue/Queue.js
+++ b/src/data-structures/queue/Queue.js
@@ -21,7 +21,7 @@ export default class Queue {
    * @return {*}
    */
   peek() {
-    if (!this.linkedList.head) {
+    if (this.isEmpty()) {
       return null;
     }
 

From f0ec1395c10cc8a319adb6887883ae3991767afd Mon Sep 17 00:00:00 2001
From: szhou <qianchengyimeng@qq.com>
Date: Fri, 28 Jan 2022 03:40:50 +0800
Subject: [PATCH 155/264] Update README.zh-CN.md (#685)

---
 src/data-structures/hash-table/README.zh-CN.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/data-structures/hash-table/README.zh-CN.md b/src/data-structures/hash-table/README.zh-CN.md
index 5de3cc5ea2..f9219df8df 100644
--- a/src/data-structures/hash-table/README.zh-CN.md
+++ b/src/data-structures/hash-table/README.zh-CN.md
@@ -1,7 +1,7 @@
 # 哈希表
 
 在计算中, 一个  **哈希表(hash table 或hash map)**  是一种实现 *关联数组(associative array)* 
-的抽象数据；类型, 该结构可以将 *键映射到值*。
+的抽象数据类型, 该结构可以将 *键映射到值*。
 
 哈希表使用 *哈希函数/散列函数* 来计算一个值在数组或桶(buckets)中或槽(slots)中对应的索引,可使用该索引找到所需的值。
 

From 9083fe12f64593de7ce1914e281a7fd5ebc4deac Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Dar=C3=ADo=20Here=C3=B1=C3=BA?= <magallania@gmail.com>
Date: Thu, 27 Jan 2022 16:44:03 -0300
Subject: [PATCH 156/264] Typos fixed (lines 81, 130, 166, 248) (#668)

---
 README.es-ES.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/README.es-ES.md b/README.es-ES.md
index df7b61fb1a..35bc08b884 100644
--- a/README.es-ES.md
+++ b/README.es-ES.md
@@ -164,7 +164,7 @@ Es una abstracción superior a la noción de algoritmo, del mismo modo que un al
   * `P` [Juego de los saltos](src/algorithms/uncategorized/jump-game)
   * `A` [Problema de la mochila sin límite](src/algorithms/sets/knapsack-problem)
   * `A` [Algoritmo de Dijkstra](src/algorithms/graph/dijkstra) - encontrar los caminos más cortos a todos los vértices del grafo desde un solo vértice
-  * `A` [Algortimo de Prim](src/algorithms/graph/prim) - encontrar el árbol de cubrimiento mínimo (MST) para un grafo no dirigido ponderado
+  * `A` [Algoritmo de Prim](src/algorithms/graph/prim) - encontrar el árbol de cubrimiento mínimo (MST) para un grafo no dirigido ponderado
   * `A` [Algoritmo de Kruskal](src/algorithms/graph/kruskal) - encontrar el árbol de cubrimiento mínimo (MST) para un grafo no dirigido ponderado
 * **Divide y Vencerás** - divide el problema en partes más pequeñas y luego resuelve esas partes
   * `P` [Búsqueda binaria](src/algorithms/search/binary-search)
@@ -246,7 +246,7 @@ npm test -- 'playground'
 
 ## Información útil
 
-### Refrencias
+### Referencias
 
 [▶ Estructuras de datos y algoritmos en YouTube](https://www.youtube.com/playlist?list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
 

From b816825232d9704913221270f579b4a337a6b9e3 Mon Sep 17 00:00:00 2001
From: Marcio Flavio <mflaviof1995@gmail.com>
Date: Thu, 27 Jan 2022 16:46:06 -0300
Subject: [PATCH 157/264] Adding single quotes type to editorconfig (#670)

---
 .editorconfig | 1 +
 1 file changed, 1 insertion(+)

diff --git a/.editorconfig b/.editorconfig
index 11c2bd2445..c658e4879e 100644
--- a/.editorconfig
+++ b/.editorconfig
@@ -8,3 +8,4 @@ charset = utf-8
 indent_style = space
 indent_size = 2
 trim_trailing_whitespace = true
+quote_type = single
\ No newline at end of file

From 945e7c384e9d9a1683d51521b7d0dcf1d5a16bd9 Mon Sep 17 00:00:00 2001
From: Trang Nguyen <trangnguyen.281198@gmail.com>
Date: Thu, 27 Jan 2022 22:52:47 +0300
Subject: [PATCH 158/264] Add Vietnamese translation (#667)

Co-authored-by: Oleksii Trekhleb <trehleb@gmail.com>
---
 README.ar-AR.md |   1 +
 README.es-ES.md |   1 +
 README.fr-FR.md |   1 +
 README.id-ID.md |   1 +
 README.it-IT.md |   1 +
 README.ja-JP.md |   1 +
 README.ko-KR.md |   1 +
 README.md       |   1 +
 README.pl-PL.md |   1 +
 README.pt-BR.md |   1 +
 README.ru-RU.md |   1 +
 README.tr-TR.md |   1 +
 README.uk-UA.md |   1 +
 README.vi-VN.md | 328 ++++++++++++++++++++++++++++++++++++++++++++++++
 README.zh-CN.md |   1 +
 README.zh-TW.md |   1 +
 16 files changed, 343 insertions(+)
 create mode 100644 README.vi-VN.md

diff --git a/README.ar-AR.md b/README.ar-AR.md
index 07522e78a6..cbcfd02409 100644
--- a/README.ar-AR.md
+++ b/README.ar-AR.md
@@ -22,6 +22,7 @@ _اقرأ هذا في لغات أخرى:_
 [_Русский_](README.ru-RU.md),
 [_Türk_](README.tr-TR.md),
 [_Italiana_](README.it-IT.md),
+[_Tiếng Việt_](README.vi-VN.md),
 [_Deutsch_](README.de-DE.md)
 
  ☝ ملاحضة هذا المشروع مخصص للاستخدام لأغراض التعلم والبحث
diff --git a/README.es-ES.md b/README.es-ES.md
index 35bc08b884..d79baf6022 100644
--- a/README.es-ES.md
+++ b/README.es-ES.md
@@ -24,6 +24,7 @@ _Léelo en otros idiomas:_
 [_Bahasa Indonesia_](README.id-ID.md),
 [_Українська_](README.uk-UA.md),
 [_Arabic_](README.ar-AR.md),
+[_Tiếng Việt_](README.vi-VN.md),
 [_Deutsch_](README.de-DE.md)
 
 *☝ Nótese que este proyecto está pensado con fines de aprendizaje e investigación,
diff --git a/README.fr-FR.md b/README.fr-FR.md
index 59087825ff..469a4f52d9 100644
--- a/README.fr-FR.md
+++ b/README.fr-FR.md
@@ -25,6 +25,7 @@ _Lisez ceci dans d'autres langues:_
 [_Bahasa Indonesia_](README.id-ID.md),
 [_Українська_](README.uk-UA.md),
 [_Arabic_](README.ar-AR.md),
+[_Tiếng Việt_](README.vi-VN.md),
 [_Deutsch_](README.de-DE.md)
 
 ## Data Structures
diff --git a/README.id-ID.md b/README.id-ID.md
index cb42feb196..b204f2a8f8 100644
--- a/README.id-ID.md
+++ b/README.id-ID.md
@@ -22,6 +22,7 @@ _Baca ini dalam bahasa yang lain:_
 [_Italiana_](README.it-IT.md),
 [_Українська_](README.uk-UA.md),
 [_Arabic_](README.ar-AR.md),
+[_Tiếng Việt_](README.vi-VN.md),
 [_Deutsch_](README.de-DE.md)
 
 _☝ Perhatikan bahwa proyek ini hanya dimaksudkan untuk tujuan pembelajaran dan riset, dan **tidak** dimaksudkan untuk digunakan sebagai produksi._
diff --git a/README.it-IT.md b/README.it-IT.md
index b459ac87d1..6ac47fa5bc 100644
--- a/README.it-IT.md
+++ b/README.it-IT.md
@@ -21,6 +21,7 @@ _Leggilo in altre lingue:_
 [_Bahasa Indonesia_](README.id-ID.md),
 [_Українська_](README.uk-UA.md),
 [_Arabic_](README.ar-AR.md),
+[_Tiếng Việt_](README.vi-VN.md),
 [_Deutsch_](README.de-DE.md)
 
 *☝ Si noti che questo progetto è destinato ad essere utilizzato solo per l'apprendimento e la ricerca e non è destinato ad essere utilizzato per il commercio.*
diff --git a/README.ja-JP.md b/README.ja-JP.md
index c90fa3e7e2..1a03f74ce8 100644
--- a/README.ja-JP.md
+++ b/README.ja-JP.md
@@ -24,6 +24,7 @@ _Read this in other languages:_
 [_Bahasa Indonesia_](README.id-ID.md),
 [_Українська_](README.uk-UA.md),
 [_Arabic_](README.ar-AR.md),
+[_Tiếng Việt_](README.vi-VN.md),
 [_Deutsch_](README.de-DE.md)
 
 ## データ構造
diff --git a/README.ko-KR.md b/README.ko-KR.md
index 040ac8a57d..75a4621aba 100644
--- a/README.ko-KR.md
+++ b/README.ko-KR.md
@@ -23,6 +23,7 @@ _Read this in other languages:_
 [_Bahasa Indonesia_](README.id-ID.md),
 [_Українська_](README.uk-UA.md),
 [_Arabic_](README.ar-AR.md),
+[_Tiếng Việt_](README.vi-VN.md),
 [_Deutsch_](README.de-DE.md)
 
 ## 자료 구조
diff --git a/README.md b/README.md
index 4f6cb03803..d949642e1c 100644
--- a/README.md
+++ b/README.md
@@ -25,6 +25,7 @@ _Read this in other languages:_
 [_Bahasa Indonesia_](README.id-ID.md),
 [_Українська_](README.uk-UA.md),
 [_Arabic_](README.ar-AR.md),
+[_Tiếng Việt_](README.vi-VN.md),
 [_Deutsch_](README.de-DE.md)
 
 *☝ Note that this project is meant to be used for learning and researching purposes
diff --git a/README.pl-PL.md b/README.pl-PL.md
index 38f0bcea27..52ba75a5e4 100644
--- a/README.pl-PL.md
+++ b/README.pl-PL.md
@@ -25,6 +25,7 @@ _Read this in other languages:_
 [_Bahasa Indonesia_](README.id-ID.md),
 [_Українська_](README.uk-UA.md),
 [_Arabic_](README.ar-AR.md),
+[_Tiếng Việt_](README.vi-VN.md),
 [_Deutsch_](README.de-DE.md)
 
 ## Struktury Danych
diff --git a/README.pt-BR.md b/README.pt-BR.md
index de9e316bc6..3218869a07 100644
--- a/README.pt-BR.md
+++ b/README.pt-BR.md
@@ -25,6 +25,7 @@ _Leia isto em outros idiomas:_
 [_Bahasa Indonesia_](README.id-ID.md),
 [_Українська_](README.uk-UA.md),
 [_Arabic_](README.ar-AR.md),
+[_Tiếng Việt_](README.vi-VN.md),
 [_Deutsch_](README.de-DE.md)
 
 ## Estrutura de Dados
diff --git a/README.ru-RU.md b/README.ru-RU.md
index b6acf63a16..1b74695b79 100644
--- a/README.ru-RU.md
+++ b/README.ru-RU.md
@@ -22,6 +22,7 @@ _Читать на других языках:_
 [_Bahasa Indonesia_](README.id-ID.md),
 [_Українська_](README.uk-UA.md),
 [_Arabic_](README.ar-AR.md),
+[_Tiếng Việt_](README.vi-VN.md),
 [_Deutsch_](README.de-DE.md)
 
 *☝ Замечание: этот репозиторий предназначен для учебно-исследовательских целей (**не** для использования в продакшн-системах).*
diff --git a/README.tr-TR.md b/README.tr-TR.md
index edbc0ebdaa..805bf7b431 100644
--- a/README.tr-TR.md
+++ b/README.tr-TR.md
@@ -22,6 +22,7 @@ _Read this in other languages:_
 [_Bahasa Indonesia_](README.id-ID.md),
 [_Українська_](README.uk-UA.md),
 [_Arabic_](README.ar-AR.md),
+[_Tiếng Việt_](README.vi-VN.md),
 [_Deutsch_](README.de-DE.md)
 
 *☝ Not, bu proje araştırma ve öğrenme amacı ile yapılmış
diff --git a/README.uk-UA.md b/README.uk-UA.md
index b43da83ca6..dd129b2c3c 100644
--- a/README.uk-UA.md
+++ b/README.uk-UA.md
@@ -22,6 +22,7 @@ _Вивчення матеріалу на інших мовах:_
 [_Italiana_](README.it-IT.md),
 [_Bahasa Indonesia_](README.id-ID.md),
 [_Arabic_](README.ar-AR.md),
+[_Tiếng Việt_](README.vi-VN.md),
 [_Deutsch_](README.de-DE.md)
 
 *☝ Зверніть увагу! Даний проект призначений лише для навчальних та дослідницьких цілей, і він **не** призначений для виробництва (продакшн).*
diff --git a/README.vi-VN.md b/README.vi-VN.md
new file mode 100644
index 0000000000..a5cbb72e07
--- /dev/null
+++ b/README.vi-VN.md
@@ -0,0 +1,328 @@
+# JavaScript Thuật Toán và Cấu Trúc Dữ Liệu
+
+[![CI](https://github.com/trekhleb/javascript-algorithms/workflows/CI/badge.svg)](https://github.com/trekhleb/javascript-algorithms/actions?query=workflow%3ACI+branch%3Amaster)
+[![codecov](https://codecov.io/gh/trekhleb/javascript-algorithms/branch/master/graph/badge.svg)](https://codecov.io/gh/trekhleb/javascript-algorithms)
+
+Repository này bao gồm nhiều ví dụ thuật toán và cấu trúc dữ liệu phổ biến
+dựa trên Javascript.
+
+Mối thuật toán và cấu trúc dữ liệu có README riêng với những lý giải và links
+liên quan để đọc thêm (bao gồm cả những videos trên Youtube).
+
+_Đọc bằng ngôn ngữ khác:_
+[_English_](README.md),
+[_简体中文_](README.zh-CN.md),
+[_繁體中文_](README.zh-TW.md),
+[_한국어_](README.ko-KR.md),
+[_日本語_](README.ja-JP.md),
+[_Polski_](README.pl-PL.md),
+[_Français_](README.fr-FR.md),
+[_Español_](README.es-ES.md),
+[_Português_](README.pt-BR.md),
+[_Русский_](README.ru-RU.md),
+[_Türk_](README.tr-TR.md),
+[_Italiana_](README.it-IT.md),
+[_Bahasa Indonesia_](README.id-ID.md),
+[_Українська_](README.uk-UA.md),
+[_Arabic_](README.ar-AR.md)
+
+*☝ Dự án này chỉ được sử dụng cho mục đích học tập và nghiên cứu, **không** được dùng
+cho mục đích thương mại.*
+
+## Cấu Trúc Dữ Liệu
+
+Cấu trúc dữ liệu là một cách cụ thể để tổ chức và lưu trữ dữ liệu trong máy tính để nó có thể
+được truy cập và sửa đổi một cách hiệu quả. Chính xác hơn, cấu trúc dữ liệu là một tập hợp
+các giá trị dữ liệu, các mối quan hệ giữa chúng và các hàm hoặc phép toán có thể được áp dụng
+cho dữ liệu.
+
+`B` - Cơ bản, `A` - Nâng cao
+
+* `B` [Danh sách liên kết](src/data-structures/linked-list)
+* `B` [Danh sách liên kết đôi](src/data-structures/doubly-linked-list)
+* `B` [Hàng đợi](src/data-structures/queue)
+* `B` [Ngăn xếp](src/data-structures/stack)
+* `B` [Bảng băm](src/data-structures/hash-table)
+* `B` [Đống](src/data-structures/heap) - max và min heap
+* `B` [Hàng đợi ưu tiên](src/data-structures/priority-queue)
+* `A` [Cây tiền tố](src/data-structures/trie)
+* `A` [Cây](src/data-structures/tree)
+  * `A` [Cây tìm kiếm nhị phân](src/data-structures/tree/binary-search-tree)
+  * `A` [Cây AVL](src/data-structures/tree/avl-tree)
+  * `A` [Cây đỏ đen](src/data-structures/tree/red-black-tree)
+  * `A` [Cây phân đoạn](src/data-structures/tree/segment-tree) - với các ví dụ truy vấn phạm vi nhỏ nhất/lớn nhất/tổng
+  * `A` [CÂy Fenwick](src/data-structures/tree/fenwick-tree) (Cây chỉ mục nhị phân)
+* `A` [Đồ thị](src/data-structures/graph) (có hướng và vô hướng)
+* `A` [Tập hợp không giao nhau](src/data-structures/disjoint-set)
+* `A` [Bộ lọc Bloom](src/data-structures/bloom-filter)
+
+## Thuật Toán
+
+Thuật toán là một đặc tả rõ ràng về cách giải quyết một lớp vấn đề. Nó là một tập hợp các
+quy tắc xác định chính xác một chuỗi phép toán.
+
+`B` - Cơ bản, `A` - Nâng cao
+
+### Thuật toán theo chủ đề
+
+* **Toán**
+  * `B` [Thao tác bit](src/algorithms/math/bits) - đặt/lấy/cập nhật/xóa bit, nhân/chia 2, đổi dấu âm,...
+  * `B` [Giai thừa](src/algorithms/math/factorial)
+  * `B` [Số Fibonacci](src/algorithms/math/fibonacci) - cổ điển và dạng đóng
+  * `B` [Thừa số nguyên tố](src/algorithms/math/prime-factors) - tìm và đếm thừa số nguyên tố sử dụng định luật Hardy-Ramanujan's
+  * `B` [Kiểm tra tính nguyên tố](src/algorithms/math/primality-test) (phân chia thử nghiệm)
+  * `B` [Thuật toán Euclid](src/algorithms/math/euclidean-algorithm) - tính ước số chung lớn nhất (GCD)
+  * `B` [Bội số chung nhỏ nhất](src/algorithms/math/least-common-multiple) (LCM)
+  * `B` [Sàng số nguyên tố](src/algorithms/math/sieve-of-eratosthenes) - tìm tất cả các số nguyên tố trong bất kỳ phạm vi nhất định nào
+  * `B` [Xác định lũy thừa của 2](src/algorithms/math/is-power-of-two) - kiểm tra xem số có phải là lũy thừa của 2 hay không (thuật toán nguyên bản và theo bit)
+  * `B` [Tam giác Pascal](src/algorithms/math/pascal-triangle)
+  * `B` [Số phức](src/algorithms/math/complex-number) - số phức và các phép toán cơ bản với số phức
+  * `B` [Radian & độ](src/algorithms/math/radian) - chuyển đổi giữa đơn vị radian và độ
+  * `B` [Tính nhanh lũy thừa](src/algorithms/math/fast-powering)
+  * `B` [Phương pháp Horner's](src/algorithms/math/horner-method) - tính giá trị đa thức
+  * `B` [Ma trận](src/algorithms/math/matrix) - ma trận và các phép toán cơ bản (phép nhân, phép chuyển vị,...)
+  * `B` [Khoảng cách Euclid](src/algorithms/math/euclidean-distance) - khoảng cách giữa hai điểm/véc-tơ/ma trận
+  * `A` [Phân hoạch](src/algorithms/math/integer-partition)
+  * `A` [Căn bậc hai](src/algorithms/math/square-root) - phương pháp Newton
+  * `A` [Thuật cắt đường tròn - Lưu Huy](src/algorithms/math/liu-hui) - phép tính gần đúng số π dựa vào đa giác
+  * `A` [Biến đổi Fourier rời rạc](src/algorithms/math/fourier-transform) - phân giải tín hiệu thời gian thành các tần số tạo nên tín hiệu đó
+* **Tập hợp**
+  * `B` [Tích Đề-các](src/algorithms/sets/cartesian-product) - tích của nhiều tập hợp
+  * `B` [Thuật toán xáo trộn](src/algorithms/sets/fisher-yates) - dãy hữu hạn hoán vị ngẫu nhiên
+  * `A` [Tập lũy thừa](src/algorithms/sets/power-set) - tập hợp chứa tất cả các tập con (theo bit và quay lui)
+  * `A` [Hoán vị](src/algorithms/sets/permutations) (lặp và không lặp)
+  * `A` [Tổ hợp](src/algorithms/sets/combinations) (lặp và không lặp)
+  * `A` [Dãy con chung dài nhất](src/algorithms/sets/longest-common-subsequence) (LCS)
+  * `A` [Dãy con chung tăng dần dài nhất](src/algorithms/sets/longest-increasing-subsequence)
+  * `A` [Dãy con chung ngắn nhất](src/algorithms/sets/shortest-common-supersequence) (SCS)
+  * `A` [Bài toán xếp ba lô](src/algorithms/sets/knapsack-problem) - dạng 0-1 và không bị chặn
+  * `A` [Mảng con lớn nhất](src/algorithms/sets/maximum-subarray) - phiên bản vét cạn và quy hoạch động (Kadane)
+  * `A` [Tổ hợp của tổng](src/algorithms/sets/combination-sum) - tìm tất cả các tổ hợp tạo thành tổng cụ thể 
+* **Chuỗi**
+  * `B` [Khoảng cách Hamming](src/algorithms/string/hamming-distance) - số các vị trí các ký hiệu khác nhau 
+  * `A` [Khoảng cách Levenshtein](src/algorithms/string/levenshtein-distance) - khoảng cách thay đổi nhỏ nhất giữa hai chuỗi ký tự
+  * `A` [Thuật toán Knuth–Morris–Pratt](src/algorithms/string/knuth-morris-pratt) (thuật toán KMP) - tìm chuỗi con (đối sánh mẫu) 
+  * `A` [Thuật toán Z](src/algorithms/string/z-algorithm) - tìm chuỗi con (đối sánh mẫu)
+  * `A` [Thuật toán Rabin Karp](src/algorithms/string/rabin-karp) - tìm chuỗi con
+  * `A` [Xâu con chung dài nhất](src/algorithms/string/longest-common-substring)
+  * `A` [Phối biểu thức chính quy](src/algorithms/string/regular-expression-matching)
+* **Tìm kiếm**
+  * `B` [Tìm kiếm tuyến tính](src/algorithms/search/linear-search)
+  * `B` [Tìm kiếm nhảy](src/algorithms/search/jump-search) (tìm khối) - tìm kiếm trong mảng đã sắp xếp 
+  * `B` [Tìm kiếm nhị phân](src/algorithms/search/binary-search) - tìm kiếm trong mảng đã sắp xếp 
+  * `B` [Tìm kiếm nội suy ](src/algorithms/search/interpolation-search) - Tìm kiếm strong mảng có thứ tự được phân phối đồng nhất
+* **Sắp xếp**
+  * `B` [Sắp xếp nổi bọt](src/algorithms/sorting/bubble-sort)
+  * `B` [Sắp xếp chọn](src/algorithms/sorting/selection-sort)
+  * `B` [Sắp xếp chèn](src/algorithms/sorting/insertion-sort)
+  * `B` [Sắp xếp vun đống](src/algorithms/sorting/heap-sort)
+  * `B` [Sắp xếp trộn](src/algorithms/sorting/merge-sort)
+  * `B` [Sắp xếp nhanh](src/algorithms/sorting/quick-sort) - Tại chỗ và không tại chỗ
+  * `B` [Shellsort](src/algorithms/sorting/shell-sort)
+  * `B` [Sắp xếp đếm](src/algorithms/sorting/counting-sort)
+  * `B` [Sắp xếp theo cơ số](src/algorithms/sorting/radix-sort)
+* **Danh sách liên kết**
+  * `B` [Di chuyển chính hướng](src/algorithms/linked-list/traversal)
+  * `B` [Di chuyển ngược hướng](src/algorithms/linked-list/reverse-traversal)
+* **Cây**
+  * `B` [Depth-First Search](src/algorithms/tree/depth-first-search) (DFS)
+  * `B` [Breadth-First Search](src/algorithms/tree/breadth-first-search) (BFS)
+* **Đồ thị**
+  * `B` [Tìm kiếm theo chiều sâu](src/algorithms/graph/depth-first-search) (DFS)
+  * `B` [Tìm kiếm theo chiều rộng](src/algorithms/graph/breadth-first-search) (BFS)
+  * `B` [Thuật toán Kruskal](src/algorithms/graph/kruskal) - tìm cây bao trùm nhỏ nhất (MST) cho đồ thị vô hướng có trọng số
+  * `A` [Thuật toán Dijkstra Algorithm](src/algorithms/graph/dijkstra) - tìm những đường ngắn nhất từ một định tới tất cả các đỉnh
+  * `A` [Thuật toán Bellman-Ford](src/algorithms/graph/bellman-ford) - tìm những đường ngắn nhất từ một đỉnh tới tất cả các đỉnh của đồ thị
+  * `A` [Thuật toán Floyd-Warshall](src/algorithms/graph/floyd-warshall) - tìm những đường ngắn nhất giữa tất cả các cặp đỉnh
+  * `A` [Phát hiện vòng](src/algorithms/graph/detect-cycle) - cho cả đồ thị có hướng và vô hướng (dựa trên DFS và tập không giao)
+  * `A` [Thuật toán Prim](src/algorithms/graph/prim) - tìm cây bao trùm nhỏ nhất (MST) cho đồ thị vô hướng có trọng số
+  * `A` [Sắp xếp tô pô](src/algorithms/graph/topological-sorting) - phương pháp DFS
+  * `A` [Điểm khớp](src/algorithms/graph/articulation-points) - Thuật toán Tarjan (dựa trên DFS)
+  * `A` [Cầu nối](src/algorithms/graph/bridges) - dựa trên DFS
+  * `A` [Đường đi Euler và Chu trình Euler](src/algorithms/graph/eulerian-path) - thuật toán Fleury - đi qua các cạnh chỉ một lần duy nhất
+  * `A` [Chu trình Hamilton](src/algorithms/graph/hamiltonian-cycle) - đi qua các đỉnh chỉ một lần duy nhất
+  * `A` [Các thành phần kết nối chặt](src/algorithms/graph/strongly-connected-components) - Thuật toán Kosaraju
+  * `A` [Bài toán người bán hàng](src/algorithms/graph/travelling-salesman) - tuyến đường ngắn nhất có thể đến thăm từng thành phố và trở về thành phố gốc
+* **Mật mã học**
+  * `B` [Băm đa thức](src/algorithms/cryptography/polynomial-hash) - lăn hàm băm dựa trên đa thức 
+  * `B` [Mật mã hàng rào đường sắt](src/algorithms/cryptography/rail-fence-cipher) - một thuật toán mật mã chuyển vị để mã hóa thông điệp 
+  * `B` [Mật mã Caesar](src/algorithms/cryptography/caesar-cipher) - mật mã chuyển vị đơn giản
+  * `B` [Mật mã Hill](src/algorithms/cryptography/hill-cipher) - mật mã chuyển vị đơn giản dựa trên đại số tuyến tính
+* **Học máy**
+  * `B` [NanoNeuron](https://github.com/trekhleb/nano-neuron) - 7 hàm JS đơn giản minh họa cách máy tính thực sự có thể học (truyền thuận / truyền ngược) 
+  * `B` [k-NN](src/algorithms/ml/knn) - thuật toán phân loại k láng giềng gần nhất
+  * `B` [k-Means](src/algorithms/ml/k-means) - thuật toán phân cụm k-Means
+* **Khác**
+  * `B` [Tháp Hà Nội](src/algorithms/uncategorized/hanoi-tower)
+  * `B` [Xoay ma trận vuông](src/algorithms/uncategorized/square-matrix-rotation) - thuật toán tại chỗ
+  * `B` [Trò chơi nhảy](src/algorithms/uncategorized/jump-game) - ví dụ quay lui, quy hoạch động (từ trên xuống + từ dưới lên), dynamic programming (top-down + bottom-up) và tham lam
+  * `B` [Các đường đi đặc trưng duy nhất](src/algorithms/uncategorized/unique-paths) - ví dụ quay lui, quy hoạch động và tam giác Pascal
+  * `B` [Thu thập nước mưa](src/algorithms/uncategorized/rain-terraces) - bài toán bẫy nước mưa (phiên bản quy hoạch động và vét cạn)
+  * `B` [Cầu thang đệ quy](src/algorithms/uncategorized/recursive-staircase) - đếm số cách lên đến đỉnh (4 lời giải)
+  * `B` [Thời điểm tốt nhất để mua bán cổ phiếu ](src/algorithms/uncategorized/best-time-to-buy-sell-stocks) - ví dụ chia để trị và một đường chuyền
+  * `A` [Bài toán n quân hậu](src/algorithms/uncategorized/n-queens)
+  * `A` [Mã đi tuần](src/algorithms/uncategorized/knight-tour)
+
+### Thuật toán theo mẫu hình
+
+Mẫu hình thuật toán là một phương pháp hoặc cách tiếp cận chung làm cơ sở cho việc thiết kế một
+lớp thuật toán. Nó là một sự trừu tượng cao hơn khái niệm về một thuật toán, cũng giống như
+một thuật toán là một sự trừu tượng cao hơn một chương trình máy tính. 
+
+* **Vét cạn** - xem xét tất cả các khả năng và chọn giải pháp tốt nhất 
+  * `B` [Tìm kiếm tuyến tính](src/algorithms/search/linear-search)
+  * `B` [Thu thập nước mưa](src/algorithms/uncategorized/rain-terraces) - bài toán bẫy nước mưa
+  * `B` [Cầu thang đệ quy](src/algorithms/uncategorized/recursive-staircase) - đếm số cách lên đến đỉnh
+  * `A` [Mảng con lớn nhất](src/algorithms/sets/maximum-subarray)
+  * `A` [Bài toán người bán hàng](src/algorithms/graph/travelling-salesman) - tuyến đường ngắn nhất có thể đến thăm từng thành phố và trở về thành phố gốc
+  * `A` [Biến đổi Fourier rời rạc](src/algorithms/math/fourier-transform) - phân giải tín hiệu thời gian thành các tần số tạo nên tín hiệu đó
+* **Tham lam** - chọn phương án tốt nhất vào thời điểm hiện tại mà không cần cân nhắc đến tương lai 
+  * `B` [Trò chơi nhảy](src/algorithms/uncategorized/jump-game)
+  * `A` [Bài xếp ba lô không bị chặn](src/algorithms/sets/knapsack-problem)
+  * `A` [Thuật toán Dijkstra](src/algorithms/graph/dijkstra) - tìm những đường ngắn nhất từ một định tới tất cả các đỉnh
+  * `A` [Thuật toán Prim](src/algorithms/graph/prim) - tìm cây bao trùm nhỏ nhất (MST) cho đồ thị vô hướng có trọng số
+  * `A` [Thuật toán Kruskal](src/algorithms/graph/kruskal) - tìm cây bao trùm nhỏ nhất (MST) cho đồ thị vô hướng có trọng số
+* **Chia để trị** - chia vấn đề thành các phần nhỏ hơn rồi giải quyết các phần đó 
+  * `B` [Tìm kiếm nhị phân](src/algorithms/search/binary-search)
+  * `B` [Tháp Hà Nội](src/algorithms/uncategorized/hanoi-tower)
+  * `B` [Tam giác Pascal](src/algorithms/math/pascal-triangle)
+  * `B` [Thuật toán Euclid](src/algorithms/math/euclidean-algorithm) - tính ước số chung lớn nhất
+  * `B` [Sắp xếp trộn](src/algorithms/sorting/merge-sort)
+  * `B` [Sắp xếp nhanh](src/algorithms/sorting/quick-sort)
+  * `B` [Cây tìm kiếm theo chiều sâu](src/algorithms/tree/depth-first-search) (DFS)
+  * `B` [Đồ thị tìm kiếm theo chiều sâu](src/algorithms/graph/depth-first-search) (DFS)
+  * `B` [Ma trận](src/algorithms/math/matrix) - tạo và duyệt các ma trận có kích thước khác nhau 
+  * `B` [Trò chơi nhảy](src/algorithms/uncategorized/jump-game)
+  * `B` [Tính nhanh lũy thừa](src/algorithms/math/fast-powering)
+  * `B` [Thời điểm tốt nhất để mua bán cổ phiếu](src/algorithms/uncategorized/best-time-to-buy-sell-stocks) - ví dụ chia để trị và một đường chuyền
+  * `A` [Hoán vị](src/algorithms/sets/permutations) (lặp và không lặp)
+  * `A` [Tổ hợp](src/algorithms/sets/combinations) (lặp và không lặp)
+* **Quy hoạch động** - xây dựng một giải pháp bằng cách sử dụng các giải pháp phụ đã tìm thấy trước đây
+  * `B` [Số Fibonacci](src/algorithms/math/fibonacci)
+  * `B` [Trò chơi nhảy](src/algorithms/uncategorized/jump-game)
+  * `B` [Đường đi độc nhất](src/algorithms/uncategorized/unique-paths)
+  * `B` [Thu thập nước mưa](src/algorithms/uncategorized/rain-terraces) - bài toán bẫy nước mưa
+  * `B` [Cầu thang đệ quy](src/algorithms/uncategorized/recursive-staircase) - đếm số cách lên đến đỉnh
+  * `A` [Khoảng cách Levenshtein](src/algorithms/string/levenshtein-distance) - khoảng cách thay đổi nhỏ nhất giữa hai chuỗi ký tự
+  * `A` [Dãy con chung dài nhất](src/algorithms/sets/longest-common-subsequence) (LCS)
+  * `A` [Xâu con chung dài nhất](src/algorithms/string/longest-common-substring)
+  * `A` [Dãy con chung tăng dần dài nhất](src/algorithms/sets/longest-increasing-subsequence)
+  * `A` [Dãy con chung ngắn nhất](src/algorithms/sets/shortest-common-supersequence)
+  * `A` [Bài xếp ba lô dạng 0-1](src/algorithms/sets/knapsack-problem)
+  * `A` [Integer Partition](src/algorithms/math/integer-partition)
+  * `A` [Mảng con lớn nhất](src/algorithms/sets/maximum-subarray)
+  * `A` [Thuật toán Bellman-Ford](src/algorithms/graph/bellman-ford) - tìm những đường ngắn nhất từ một đỉnh tới tất cả các đỉnh của đồ thị
+  * `A` [Thuật toán Floyd-Warshall](src/algorithms/graph/floyd-warshall) - tìm những đường ngắn nhất giữa tất cả các cặp đỉnh
+  * `A` [Phối biểu thức chính quy](src/algorithms/string/regular-expression-matching)
+* **Quay lui** - tương tự như vét cạn, cố tạo ra tất cả các giải pháp có thể, nhưng mỗi lần bạn tạo ra giải pháp tiếp theo,
+bạn sẽ kiểm tra xem nó có thỏa mãn tất cả các điều kiện hay không và chỉ khi thỏa mãn mới tiếp tục tạo ra các giải pháp tiếp theo.
+Nếu không, hãy quay lại và đi trên một con đường khác để tìm ra giải pháp. Thông thường, truyền DFS của không gian trạng thái được sử dụng. 
+  * `B` [Trò chơi nhảy](src/algorithms/uncategorized/jump-game)
+  * `B` [Đường đi độc nhất](src/algorithms/uncategorized/unique-paths)
+  * `B` [Tập lũy thừa](src/algorithms/sets/power-set) - tập hợp chứa tất cả các tập con
+  * `A` [Chu trình Hamilton](src/algorithms/graph/hamiltonian-cycle) - đi qua các đỉnh một lần duy nhất
+  * `A` [Bài toán n quân hậu](src/algorithms/uncategorized/n-queens)
+  * `A` [Mã đi tuần](src/algorithms/uncategorized/knight-tour)
+  * `A` [Tổ hợp của tổng](src/algorithms/sets/combination-sum) - tìm tất cả các tổ hợp tạo thành tổng cụ thể 
+* **Branch & Bound** - ghi nhớ giải pháp chi với phí thấp nhất được tìm thấy ở mỗi giai đoạn của quá trình tìm kiếm quay lui,
+sử dụng chi phí của giải pháp có chi phí thấp nhất được tìm thấy cho đến nay như một giới hạn dưới về chi phí của
+một giải pháp ít chi phí nhân cho bài toán, để loại bỏ các giải pháp từng phần với chi phí lớn hơn giải pháp chi phí thấp nhất được tìm thấy cho đến nay. 
+Thông thường BFS duyệt kết hợp với duyệt DFS của cây không gian trạng thái đang được sử dụng. 
+
+## Hướng dẫn sử dụng repository
+
+**Cài đặt tất cả các phụ thuộc**
+```
+npm install
+```
+
+**Chạy ESLint**
+
+Bạn có thể muốn chạy nó để kiểm tra chất lượng code. 
+
+```
+npm run lint
+```
+
+**Chạy tất cả các kiểm thử**
+```
+npm test
+```
+
+**Chạy kiểm thử theo tên**
+```
+npm test -- 'LinkedList'
+```
+
+**Sân chơi**
+
+Bạn có thể chơi với các cấu trúc dữ liệu và thuật toán trong tệp `./src/playground/playground.js`
+và viết các bài kiểm thử cho nó ở `./src/playground/__test__/playground.test.js`.
+
+Sau đó, chỉ cần chạy lệnh sau để kiểm tra xem sân chơi của bạn có hoạt động như mong đợi hay không: 
+
+```
+npm test -- 'playground'
+```
+
+## Thông tin hữu ích
+
+### Tham khảo
+
+[▶ Data Structures and Algorithms on YouTube](https://www.youtube.com/playlist?list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
+
+### Kí hiệu O lớn
+
+*Kí hiệu O lớn* được dùng để phân loại thuật toán theo thời gian chạy hoặc yêu cầu không gian gia tăng khi kích thước đầu vào gia tăng.
+Trên biểu đồ bên dưới, bạn có thể tìm thấy hầu hết các thứ tự tăng trưởng phổ biến của các thuật toán được chỉ định trong ký hiệu O lớn. 
+
+![Đồ thị O lớn](./assets/big-o-graph.png)
+
+Nguồn: [Big O Cheat Sheet](http://bigocheatsheet.com/).
+
+Dưới đây là danh sách một số ký hiệu O lớn thông dụng và so sánh với các kích thước khác nhau của dữ liệu đầu vào.
+
+| Kí hiệu O lớn | Tính toán cho 10 phần tử | Tính toán cho 100 phần tử  | Tính toán cho 1000 phần tử   |
+| -------------- | ---------------------------- | ----------------------------- | ------------------------------- |
+| **O(1)**       | 1                            | 1                             | 1                               |
+| **O(log N)**   | 3                            | 6                             | 9                               |
+| **O(N)**       | 10                           | 100                           | 1000                            |
+| **O(N log N)** | 30                           | 600                           | 9000                            |
+| **O(N^2)**     | 100                          | 10000                         | 1000000                         |
+| **O(2^N)**     | 1024                         | 1.26e+29                      | 1.07e+301                       |
+| **O(N!)**      | 3628800                      | 9.3e+157                      | 4.02e+2567                      |
+
+### Độ phức tạp của các phép toán cấu trúc dữ liệu
+
+| Cấu trúc dữ liệu        | Truy cập   | Tìm kiếm    | Chèn | Xóa  | Bình luận  |
+| ----------------------- | :-------: | :-------: | :-------: | :-------: | :-------- |
+| **Mảng**               | 1         | n         | n         | n         |           |
+| **Ngăn xếp**               | n         | n         | 1         | 1         |           |
+| **Hàng đợi**               | n         | n         | 1         | 1         |           |
+| **Danh sách liên kết**         | n         | n         | 1         | n         |           |
+| **Bảng băm**          | -         | n         | n         | n         | Trong trường hợp hàm băm hoàn hảo, chi phí sẽ là O(1) |
+| **Cây tìm kiếm nhị phân**  | n         | n         | n         | n         | Trong trường hợp cây cân bằng, chi phí sẽ là  O(log(n)) |
+| **Cây B**              | log(n)    | log(n)    | log(n)    | log(n)    |           |
+| **Cây đỏ đen**      | log(n)    | log(n)    | log(n)    | log(n)    |           |
+| **Cây AVL**            | log(n)    | log(n)    | log(n)    | log(n)    |           |
+| **Bộ lọc Bloom**        | -         | 1         | 1         | -         | Có thể có kết quả dương tính giả trong khi tìm kiếm  |
+
+### Độ phức tạp của các thuật toán sắp xếp mảng
+
+| Tên                  | Tốt nhất            | Trung bình             | Tệ nhất              | Bộ nhớ    | Ổn định    | Bình luận  |
+| --------------------- | :-------------: | :-----------------: | :-----------------: | :-------: | :-------: | :-------- |
+| **Sắp xếp nổi bọt**       | n               | n<sup>2</sup>       | n<sup>2</sup>       | 1         | Có       |           |
+| **Sắp xếp chèn**    | n               | n<sup>2</sup>       | n<sup>2</sup>       | 1         | Có       |           |
+| **Sắp xếp chọn**    | n<sup>2</sup>   | n<sup>2</sup>       | n<sup>2</sup>       | 1         | Không        |           |
+| **Sắp xếp vun đống**         | n&nbsp;log(n)   | n&nbsp;log(n)       | n&nbsp;log(n)       | 1         | Không        |           |
+| **Sắp xếp trộn**        | n&nbsp;log(n)   | n&nbsp;log(n)       | n&nbsp;log(n)       | n         | Có       |           |
+| **Sắp xếp nhanh**        | n&nbsp;log(n)   | n&nbsp;log(n)       | n<sup>2</sup>       | log(n)    | Không        | Sắp xếp nhanh thường được thực hiện tại chỗ với không gian ngăn xếp O (log (n))  |
+| **Shell sort**        | n&nbsp;log(n)   | phụ thuộc vào khoảng cách dãy   | n&nbsp;(log(n))<sup>2</sup>  | 1         | Không         |           |
+| **Sắp xếp đếm**     | n + r           | n + r               | n + r               | n + r     | Có       | r - số lớn nhất trong mảng |
+| **Sắp xếp theo cơ số**        | n * k           | n * k               | n * k               | n + k     | Có       | k - độ dài của khóa dài nhất |
+
+## Project Backers
+
+> Bạn có thể hỗ trợ dự án này qua ❤️️ [GitHub](https://github.com/sponsors/trekhleb) hoặc ❤️️ [Patreon](https://www.patreon.com/trekhleb).
+
+[Những người đang ủng hộ dự án này](https://github.com/trekhleb/javascript-algorithms/blob/master/BACKERS.md) `∑ = 0`
diff --git a/README.zh-CN.md b/README.zh-CN.md
index c8d419bc16..cdef9cabea 100644
--- a/README.zh-CN.md
+++ b/README.zh-CN.md
@@ -22,6 +22,7 @@ _Read this in other languages:_
 [_Bahasa Indonesia_](README.id-ID.md),
 [_Українська_](README.uk-UA.md),
 [_Arabic_](README.ar-AR.md),
+[_Tiếng Việt_](README.vi-VN.md),
 [_Deutsch_](README.de-DE.md)
 
 *注意：这个项目仅用于学习和研究，**不是**用于生产环境。*
diff --git a/README.zh-TW.md b/README.zh-TW.md
index e42aba445d..20d4381a2a 100644
--- a/README.zh-TW.md
+++ b/README.zh-TW.md
@@ -21,6 +21,7 @@ _Read this in other languages:_
 [_Bahasa Indonesia_](README.id-ID.md),
 [_Українська_](README.uk-UA.md),
 [_Arabic_](README.ar-AR.md),
+[_Tiếng Việt_](README.vi-VN.md),
 [_Deutsch_](README.de-DE.md)
 
 ## 資料結構

From 61f2d192f6ff49ef8cff1049e8f5f51ea916d4fc Mon Sep 17 00:00:00 2001
From: Perry <perry2008084@gmail.com>
Date: Fri, 28 Jan 2022 03:53:42 +0800
Subject: [PATCH 159/264] Update breadthFirstSearch.js (#666)

fix comment
---
 .../tree/breadth-first-search/breadthFirstSearch.js         | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/src/algorithms/tree/breadth-first-search/breadthFirstSearch.js b/src/algorithms/tree/breadth-first-search/breadthFirstSearch.js
index 503ec34f96..e1c7b70e14 100644
--- a/src/algorithms/tree/breadth-first-search/breadthFirstSearch.js
+++ b/src/algorithms/tree/breadth-first-search/breadthFirstSearch.js
@@ -3,9 +3,9 @@ import Queue from '../../../data-structures/queue/Queue';
 /**
  * @typedef {Object} Callbacks
  * @property {function(node: BinaryTreeNode, child: BinaryTreeNode): boolean} allowTraversal -
- *   Determines whether DFS should traverse from the node to its child.
- * @property {function(node: BinaryTreeNode)} enterNode - Called when DFS enters the node.
- * @property {function(node: BinaryTreeNode)} leaveNode - Called when DFS leaves the node.
+ *   Determines whether BFS should traverse from the node to its child.
+ * @property {function(node: BinaryTreeNode)} enterNode - Called when BFS enters the node.
+ * @property {function(node: BinaryTreeNode)} leaveNode - Called when BFS leaves the node.
  */
 
 /**

From ef50238ebad761e5c6aab09cea343181cc4ef4e7 Mon Sep 17 00:00:00 2001
From: Felipe Veronezi Peters
 <80159972+fveronezipeters@users.noreply.github.com>
Date: Thu, 27 Jan 2022 16:54:40 -0300
Subject: [PATCH 160/264] Add pt-BR translation to sorting/selection-sort
 (#665)

---
 .../sorting/selection-sort/README.md          |  3 +++
 .../sorting/selection-sort/README.pt-BR.md    | 20 +++++++++++++++++++
 2 files changed, 23 insertions(+)
 create mode 100644 src/algorithms/sorting/selection-sort/README.pt-BR.md

diff --git a/src/algorithms/sorting/selection-sort/README.md b/src/algorithms/sorting/selection-sort/README.md
index 6a708d2579..b584777a59 100644
--- a/src/algorithms/sorting/selection-sort/README.md
+++ b/src/algorithms/sorting/selection-sort/README.md
@@ -1,5 +1,8 @@
 # Selection Sort
 
+_Read this in other languages:_
+[Português brasileiro](README.pt-BR.md).
+
 Selection sort is a sorting algorithm, specifically an 
 in-place comparison sort. It has O(n2) time complexity, 
 making it inefficient on large lists, and generally 
diff --git a/src/algorithms/sorting/selection-sort/README.pt-BR.md b/src/algorithms/sorting/selection-sort/README.pt-BR.md
new file mode 100644
index 0000000000..c9c1afd6a1
--- /dev/null
+++ b/src/algorithms/sorting/selection-sort/README.pt-BR.md
@@ -0,0 +1,20 @@
+# Selection Sort
+
+_Leia isso em outras línguas:_
+[english](README.md).
+
+Selection Sort é um algoritmo de ordenação, mais especificamente um algoritmo de ordenação por comparação in-place (requer uma quantidade constante de espaço de memória adicional). Tem complexidade O(n²), tornando-o ineficiente em listas grandes e, geralmente, tem desempenho inferior ao similar Insertion Sort. O Selection Sort é conhecido por sua simplicidade e tem vantagens de desempenho sobre algoritmos mais complexos em certas situações, particularmente quando a memória auxiliar é limitada.
+
+![Visualização do algoritmo](https://upload.wikimedia.org/wikipedia/commons/b/b0/Selection_sort_animation.gif)
+
+![Visualização do algoritmo](https://upload.wikimedia.org/wikipedia/commons/9/94/Selection-Sort-Animation.gif)
+
+## Complexidade
+
+| Nome                  | Melhor          | Médio               | Pior                | Memória   | Estável    | Comentários  |
+| --------------------- | :-------------: | :-----------------: | :-----------------: | :-------: | :-------:  | :----------: |
+| **Selection sort**    | n<sup>2</sup>   | n<sup>2</sup>       | n<sup>2</sup>       | 1         | Não        |              |
+
+## Referências
+
+[Wikipedia](https://en.wikipedia.org/wiki/Selection_sort)

From 8bd329d5e5a03b379ad0869128e10746ad2ab62d Mon Sep 17 00:00:00 2001
From: Felipe Veronezi Peters
 <80159972+fveronezipeters@users.noreply.github.com>
Date: Thu, 27 Jan 2022 16:55:13 -0300
Subject: [PATCH 161/264] Add pt-BR translation to search/binary-search (#664)

---
 src/algorithms/search/binary-search/README.md |  3 +++
 .../search/binary-search/README.pt-BR.md      | 22 +++++++++++++++++++
 2 files changed, 25 insertions(+)
 create mode 100644 src/algorithms/search/binary-search/README.pt-BR.md

diff --git a/src/algorithms/search/binary-search/README.md b/src/algorithms/search/binary-search/README.md
index 2259b94406..ebf3e123e0 100644
--- a/src/algorithms/search/binary-search/README.md
+++ b/src/algorithms/search/binary-search/README.md
@@ -1,5 +1,8 @@
 # Binary Search
 
+_Read this in other languages:_
+[Português brasileiro](README.pt-BR.md).
+
 In computer science, binary search, also known as half-interval 
 search, logarithmic search, or binary chop, is a search algorithm 
 that finds the position of a target value within a sorted 
diff --git a/src/algorithms/search/binary-search/README.pt-BR.md b/src/algorithms/search/binary-search/README.pt-BR.md
new file mode 100644
index 0000000000..14445a048e
--- /dev/null
+++ b/src/algorithms/search/binary-search/README.pt-BR.md
@@ -0,0 +1,22 @@
+# Busca Binária
+
+_Leia isso em outras línguas:_
+[english](README.md).
+
+Em ciência da computação, busca binária, também conhecida como busca de meio-intervalo, busca logarítmica ou corte binário, é um algoritmo de pesquisa
+que encontra a posição de um elemento alvo dentro de um
+vetor ordenado. O algoritmo compara o elemento alvo com o elemento central do vetor; se eles são diferentes, a metade em que
+o elemento alvo não pode estar é eliminada e a busca continua
+na metade remanescente até que o elemento alvo seja encontrado. Se a busca
+terminar com a metade remanescente vazia, o elemento alvo não está presente no vetor.
+
+![Busca Binária](https://upload.wikimedia.org/wikipedia/commons/8/83/Binary_Search_Depiction.svg)
+
+## Complexidade
+
+**Complexidade de Tempo**: `O(log(n))` - pois a área de busca é dividida por dois a cada iteração.
+
+## Referências
+
+- [Wikipedia](https://en.wikipedia.org/wiki/Binary_search_algorithm)
+- [YouTube](https://www.youtube.com/watch?v=P3YID7liBug&index=29&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)

From 47d5c8f744e44d4967bc9e0d295eb94495b73dbd Mon Sep 17 00:00:00 2001
From: Felipe Veronezi Peters
 <80159972+fveronezipeters@users.noreply.github.com>
Date: Thu, 27 Jan 2022 16:56:02 -0300
Subject: [PATCH 162/264] Add pt-BR translation to search/linear-search (#663)

---
 src/algorithms/search/linear-search/README.md |  4 ++++
 .../search/linear-search/README.pt-BR.md      | 19 +++++++++++++++++++
 2 files changed, 23 insertions(+)
 create mode 100644 src/algorithms/search/linear-search/README.pt-BR.md

diff --git a/src/algorithms/search/linear-search/README.md b/src/algorithms/search/linear-search/README.md
index 942058785f..8feb422eb2 100644
--- a/src/algorithms/search/linear-search/README.md
+++ b/src/algorithms/search/linear-search/README.md
@@ -1,4 +1,8 @@
 # Linear Search
+
+_Read this in other languages:_
+[Português brasileiro](README.pt-BR.md).
+
 In computer science, linear search or sequential search is a 
 method for finding a target value within a list. It sequentially 
 checks each element of the list for the target value until a 
diff --git a/src/algorithms/search/linear-search/README.pt-BR.md b/src/algorithms/search/linear-search/README.pt-BR.md
new file mode 100644
index 0000000000..e0af42f4ea
--- /dev/null
+++ b/src/algorithms/search/linear-search/README.pt-BR.md
@@ -0,0 +1,19 @@
+# Busca Linear
+
+_Leia isso em outras línguas:_
+[english](README.md).
+
+Na Ciência da Computação, busca linear ou busca sequencial é um método para encontrar um elemento alvo em uma lista. 
+O algoritmo verifica sequencialmente cada elemento da lista procurando o elemento alvo até ele ser encontrado ou até ter verificado todos os elementos.
+A Busca linear realiza no máximo `n` comparações, onde `n` é o tamanho da lista.
+
+![Busca Linear](https://www.tutorialspoint.com/data_structures_algorithms/images/linear_search.gif)
+
+## Complexidade
+
+**Complexidade de Tempo**: `O(n)` - pois no pior caso devemos verificar cada elemento exatamente uma vez.
+
+## Referências
+- [Wikipedia](https://en.wikipedia.org/wiki/Linear_search)
+- [TutorialsPoint](https://www.tutorialspoint.com/data_structures_algorithms/linear_search_algorithm.htm)
+- [Youtube](https://www.youtube.com/watch?v=SGU9duLE30w)

From 82680c03eeeb135c681897c0bfd824eb6e4a391a Mon Sep 17 00:00:00 2001
From: m11o <43847020+masahito1997@users.noreply.github.com>
Date: Fri, 28 Jan 2022 04:56:33 +0900
Subject: [PATCH 163/264] fix small modification in README.ja-JP.md (#651)

---
 README.ja-JP.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.ja-JP.md b/README.ja-JP.md
index 1a03f74ce8..e10bb94083 100644
--- a/README.ja-JP.md
+++ b/README.ja-JP.md
@@ -151,7 +151,7 @@ _Read this in other languages:_
 ### Paradigmによるアルゴリズム
 
 アルゴリズムパラダイムは、あるクラスのアルゴリズムの設計の基礎をなす一般的な方法またはアプローチである。それは、アルゴリズムがコンピュータプログラムよりも高い抽象であるのと同様に、アルゴリズムの概念よりも高い抽象である。
-* **ブルートフォース** - べての可能性を見て最適なソリューションを選択する
+* **ブルートフォース** - すべての可能性を見て最適なソリューションを選択する
   * `B` [線形探索](src/algorithms/search/linear-search)
   * `B` [レインテラス](src/algorithms/uncategorized/rain-terraces) - 雨水問題
   * `B` [Recursive Staircase](src/algorithms/uncategorized/recursive-staircase) - 先頭に到達する方法の数を数えます

From 677862540e12b2189f535ff237633c7e25f1afe0 Mon Sep 17 00:00:00 2001
From: MrBrain295 <66077254+MrBrain295@users.noreply.github.com>
Date: Thu, 27 Jan 2022 13:57:33 -0600
Subject: [PATCH 164/264] Change Copy Write to 2021 (#652)

Change Copy Write to 2021 from 2018.
---
 LICENSE | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/LICENSE b/LICENSE
index e7885bd74b..0bad68016a 100644
--- a/LICENSE
+++ b/LICENSE
@@ -1,6 +1,6 @@
 The MIT License (MIT)
 
-Copyright (c) 2018 Oleksii Trekhleb
+Copyright (c) 2021 Oleksii Trekhleb
 
 Permission is hereby granted, free of charge, to any person obtaining a copy
 of this software and associated documentation files (the "Software"), to deal

From 3fa19670f2c0dca1e2bf474c266712d9759e6fd9 Mon Sep 17 00:00:00 2001
From: DS Park <cckn1985@gmail.com>
Date: Fri, 28 Jan 2022 05:00:45 +0900
Subject: [PATCH 165/264] Add Korean translation.  (#644)

* Translate the Heap README to Korean.

* Translate Priority Queue's README to Korean

* Translate Kruskal Algorithm's README into Korean.

* fix typo

* Translate the Dijkstra README to Korean.

Co-authored-by: cckn <pds@enitt.co.kr>
Co-authored-by: Oleksii Trekhleb <trehleb@gmail.com>
---
 src/algorithms/graph/dijkstra/README.ko-KR.md | 16 ++++++++++
 src/algorithms/graph/dijkstra/README.md       |  3 ++
 src/algorithms/graph/kruskal/README.ko-KR.md  | 29 +++++++++++++++++++
 src/algorithms/graph/kruskal/README.md        |  3 ++
 src/data-structures/heap/README.ko-KR.md      | 14 ++++++---
 .../priority-queue/README.ko-KR.md            | 12 ++++++++
 src/data-structures/priority-queue/README.md  |  3 +-
 7 files changed, 75 insertions(+), 5 deletions(-)
 create mode 100644 src/algorithms/graph/dijkstra/README.ko-KR.md
 create mode 100644 src/algorithms/graph/kruskal/README.ko-KR.md
 create mode 100644 src/data-structures/priority-queue/README.ko-KR.md

diff --git a/src/algorithms/graph/dijkstra/README.ko-KR.md b/src/algorithms/graph/dijkstra/README.ko-KR.md
new file mode 100644
index 0000000000..e2595bbe23
--- /dev/null
+++ b/src/algorithms/graph/dijkstra/README.ko-KR.md
@@ -0,0 +1,16 @@
+# 다익스트라 알고리즘(Dijkstra's algorithm)
+
+다익스트라 알고리즘은 도로 네트워크 등을 나타낼 수 있는 그래프에서 노드 간의 최단 경로를 찾는 알고리즘입니다.
+
+이 알고리즘은 다양한 형태로 존재합니다. 다익스트라의 원래 형태는 두 노드 간의 최단 경로를 찾았지만, 더 일반적인 형태는 단일 노드를 "소스"노드로 수정하고 그래프의 소스에서 다른 모든 노드까지의 최단 경로를 찾아 최단 경로 트리(shortest-path tree)를 생성합니다.
+
+![Dijkstra](https://upload.wikimedia.org/wikipedia/commons/5/57/Dijkstra_Animation.gif)
+
+`a`와 `b` 사이의 최단 경로를 찾는 다익스트라 알고리즘입니다.
+가장 낮은 거리를 가지며 방문하지 않은 정점(vertex)를 선택하고, 이를 통해 방문하지 않은 각 이웃까지의 거리를 계산하며, 더 작은 경우 이웃의 거리를 업데이트합니다. 이웃에 대한 작업을 마치면 방문한 것으로 표시(빨간색으로 변경)합니다.
+
+## 참조
+
+- [Wikipedia](https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm)
+- [On YouTube by Nathaniel Fan](https://www.youtube.com/watch?v=gdmfOwyQlcI&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
+- [On YouTube by Tushar Roy](https://www.youtube.com/watch?v=lAXZGERcDf4&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
diff --git a/src/algorithms/graph/dijkstra/README.md b/src/algorithms/graph/dijkstra/README.md
index e1c5002f18..d94e2a3cdf 100644
--- a/src/algorithms/graph/dijkstra/README.md
+++ b/src/algorithms/graph/dijkstra/README.md
@@ -1,5 +1,8 @@
 # Dijkstra's Algorithm
 
+_Read this in other languages:_
+[_한국어_](README.ko-KR.md)
+
 Dijkstra's algorithm is an algorithm for finding the shortest 
 paths between nodes in a graph, which may represent, for example, 
 road networks. 
diff --git a/src/algorithms/graph/kruskal/README.ko-KR.md b/src/algorithms/graph/kruskal/README.ko-KR.md
new file mode 100644
index 0000000000..eefb6a6756
--- /dev/null
+++ b/src/algorithms/graph/kruskal/README.ko-KR.md
@@ -0,0 +1,29 @@
+# 크루스칼 알고리즘
+
+크루스칼 알고리즘은 두 트리를 연결하는 최소 간선 가중치를 찾는 최소 신장 트리 알고리즘입니다.
+각 단계에서 비용을 더하는 연결된 가중 그래프에 대한 최소 신장 트리를 찾기 때문에 그래프 이론에서의 그리디 알고리즘입니다. 즉, 트리의 모든 간선의 총 가중치가 최소화되는 모든 정점을 포함하는 트리를 형성하는 간선의 하위 집합을 찾습니다. 그래프가 연결되어 있지 않으면 최소 신장 포레스트(연결된 각 구성 요소의 최소 신장 트리)를 찾습니다.
+
+![Kruskal Algorithm](https://upload.wikimedia.org/wikipedia/commons/5/5c/MST_kruskal_en.gif)
+
+![Kruskal Demo](https://upload.wikimedia.org/wikipedia/commons/b/bb/KruskalDemo.gif)
+
+유클리드 거리를 기반으로 한 크루스칼 알고리즘의 데모입니다.
+
+## 최소 신장 트리
+
+**최소 신장 트리(MST)** 또는 최소 가중치 신장 트리는 연결된 간선 가중치 무 방향 그래프의 간선의 하위 집합으로, 사이클 없이 가능한 최소 총 간선 가중치로 모든 정점을 연결합니다. 즉, 간선 가중치의 합이 가능한 작은 신장 트리입니다. 보다 일반적으로, 간선-가중치 비방향 그래프(꼭 연결되지는 않음)에는 연결된 구성 요소에 대한 최소 신장 트리의 결합인 최소 신장 포레스트(minimum spanning forest)가 있습니다.
+
+![Minimum Spanning Tree](https://upload.wikimedia.org/wikipedia/commons/d/d2/Minimum_spanning_tree.svg)
+
+평면 그래프와 해당 최소 신장 트리입니다. 각 간선은 가중치로 레이블이 지정되며, 이 값은 길이에 거의 비례합니다.
+
+![Minimum Spanning Tree](https://upload.wikimedia.org/wikipedia/commons/c/c9/Multiple_minimum_spanning_trees.svg)
+
+이 그림은 그래프에 최소 신장 트리가 두 개 이상 있을 수 있음을 보여 줍니다. 그림에서 그래프 아래의 두 트리는 주어진 그래프에서 최소 신장 트리가 될 수 있는 두 가지 경우입니다.
+
+## 참조
+
+- [Minimum Spanning Tree on Wikipedia](https://en.wikipedia.org/wiki/Minimum_spanning_tree)
+- [Kruskal's Algorithm on Wikipedia](https://en.wikipedia.org/wiki/Kruskal%27s_algorithm)
+- [Kruskal's Algorithm on YouTube by Tushar Roy](https://www.youtube.com/watch?v=fAuF0EuZVCk&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
+- [Kruskal's Algorithm on YouTube by Michael Sambol](https://www.youtube.com/watch?v=71UQH7Pr9kU&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
diff --git a/src/algorithms/graph/kruskal/README.md b/src/algorithms/graph/kruskal/README.md
index eb8a0ebf42..1a71390e2f 100644
--- a/src/algorithms/graph/kruskal/README.md
+++ b/src/algorithms/graph/kruskal/README.md
@@ -1,5 +1,8 @@
 # Kruskal's Algorithm
 
+_Read this in other languages:_
+[_한국어_](README.ko-KR.md)
+
 Kruskal's algorithm is a minimum-spanning-tree algorithm which 
 finds an edge of the least possible weight that connects any two 
 trees in the forest. It is a greedy algorithm in graph theory 
diff --git a/src/data-structures/heap/README.ko-KR.md b/src/data-structures/heap/README.ko-KR.md
index 1f8c4932e4..ace702da9e 100644
--- a/src/data-structures/heap/README.ko-KR.md
+++ b/src/data-structures/heap/README.ko-KR.md
@@ -1,13 +1,19 @@
 # 힙 (자료구조)
 
-컴퓨터 사이언스에서 힙은 특수한 트리구조의 데이터 구조로 다음과 같은 특성을 갖고 있습니다.
+컴퓨터 과학에서의 **힙**은 아래에 설명된 힙 속성을 만족하는 전문화된 트리 기반 데이터구조입니다.
 
- *최소 힙* 에서는 만약 `P`가 `C`의 부모노드일 경우, `P` 키(값)는 `C` 키보다 작거나 동일합니다.
+*최소 힙*에서 `P`가 `C`의 상위 노드라면 `P`의 키(값)는 `C`의 키보다 작거나 같습니다.
 
 ![MinHeap](https://upload.wikimedia.org/wikipedia/commons/6/69/Min-heap.png)
 
- - *최대 힙* 에서 `P` 키는 `C` 키보다 크거나 동일합니다.
+*최대 힙*에서 `P`의 키는 `C`의 키보다 크거나 같습니다.
 
 ![Heap](https://upload.wikimedia.org/wikipedia/commons/3/38/Max-Heap.svg)
 
- - 힙의 "최상단" 노드에는 부모노드가 존재하지 않으며, 루트노드라고 부릅니다.
+상위 노드가 없는 힙의 "상단"에 있는 노드를 루트 노드라고 합니다.
+
+## 참조
+
+- [Wikipedia](<https://en.wikipedia.org/wiki/Heap_(data_structure)>)
+- [YouTube](https://www.youtube.com/watch?v=t0Cq6tVNRBA&index=5&t=0s&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
+
diff --git a/src/data-structures/priority-queue/README.ko-KR.md b/src/data-structures/priority-queue/README.ko-KR.md
new file mode 100644
index 0000000000..50a064d05a
--- /dev/null
+++ b/src/data-structures/priority-queue/README.ko-KR.md
@@ -0,0 +1,12 @@
+# 우선 순위 큐 
+
+컴퓨터 과학에서 **우선 순위 큐**는 일반 큐 또는 스택 데이터 구조와 같은 추상 데이터 유형이지만, 여기서 각 요소에는 "우선 순위"가 연결됩니다. 
+우선 순위 큐에서는 우선 순위가 높은 요소가 낮은 요소 앞에 제공됩니다. 두 요소가 동일한 우선 순위를 가질 경우 큐의 순서에 따라 제공됩니다.
+
+우선 순위 큐는 종종 힙을 사용하여 구현되지만 개념적으로는 힙과 구별됩니다. 우선 순위 대기열은 "리스트(list)" 또는 "맵(map)"과 같은 추상적인 개념입니다; 
+리스트가 링크드 리스트나 배열로 구현될 수 있는 것처럼 우선 순위 큐는 힙이나 정렬되지 않은 배열과 같은 다양한 다른 방법으로 구현될 수 있습니다.
+
+## 참조
+
+- [Wikipedia](https://en.wikipedia.org/wiki/Priority_queue)
+- [YouTube](https://www.youtube.com/watch?v=wptevk0bshY&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8&index=6)
diff --git a/src/data-structures/priority-queue/README.md b/src/data-structures/priority-queue/README.md
index a487678ad8..eb5ec72985 100644
--- a/src/data-structures/priority-queue/README.md
+++ b/src/data-structures/priority-queue/README.md
@@ -5,7 +5,8 @@ _Read this in other languages:_
 [_Русский_](README.ru-RU.md),
 [_日本語_](README.ja-JP.md),
 [_Français_](README.fr-FR.md),
-[_Português_](README.pt-BR.md)
+[_Português_](README.pt-BR.md),
+[_한국어_](README.ko-KR.md)
 
 In computer science, a **priority queue** is an abstract data type 
 which is like a regular queue or stack data structure, but where 

From cadee1405310b779e965738ff900d2864f40cc17 Mon Sep 17 00:00:00 2001
From: TheJang <33803975+jangwonyoon@users.noreply.github.com>
Date: Fri, 28 Jan 2022 05:01:42 +0900
Subject: [PATCH 166/264] Fix: spacing word (#639)

---
 README.ko-KR.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.ko-KR.md b/README.ko-KR.md
index 75a4621aba..b48c43aa56 100644
--- a/README.ko-KR.md
+++ b/README.ko-KR.md
@@ -5,7 +5,7 @@
 
 이 저장소에는 많이 알려진 알고리즘 및 자료 구조의 Javascript 기반 예제를 담고 있습니다.
 
-각 알고리즘과 자료 구조에 대해 연관되어있는 설명이 README에 작성되어 있으며,
+각 알고리즘과 자료 구조에 대해 연관되어 있는 설명이 README에 작성되어 있으며,
 링크를 통해 더 자세한 설명을 만날 수 있습니다. (관련된 YouTube 영상도 포함).
 
 _Read this in other languages:_

From 3038c77a8c59269d300a15b5925c22b7ec47a6f3 Mon Sep 17 00:00:00 2001
From: 0xFF <45086516+bqio@users.noreply.github.com>
Date: Thu, 27 Jan 2022 23:02:10 +0300
Subject: [PATCH 167/264] fix error (#637)

---
 README.ru-RU.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.ru-RU.md b/README.ru-RU.md
index 1b74695b79..541e1d2703 100644
--- a/README.ru-RU.md
+++ b/README.ru-RU.md
@@ -37,7 +37,7 @@ _Читать на других языках:_
 * `B` [Двунаправленный связный список](src/data-structures/doubly-linked-list)
 * `B` [Очередь](src/data-structures/queue)
 * `B` [Стек](src/data-structures/stack)
-* `B` [Хеш-табица](src/data-structures/hash-table)
+* `B` [Хеш-таблица](src/data-structures/hash-table)
 * `B` [Куча](src/data-structures/heap) — максимальная и минимальная версии
 * `B` [Очередь с приоритетом](src/data-structures/priority-queue)
 * `A` [Префиксное дерево](src/data-structures/trie)

From 8d0f300aa5d54c3dbd9da30097a14646acb2fffb Mon Sep 17 00:00:00 2001
From: Antonio Gonzalez Capel <47994122+DoxtorDoz@users.noreply.github.com>
Date: Thu, 27 Jan 2022 21:03:12 +0100
Subject: [PATCH 168/264] Update README.es-ES.md (#628)

Co-authored-by: Oleksii Trekhleb <trehleb@gmail.com>
---
 src/data-structures/linked-list/README.es-ES.md | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/src/data-structures/linked-list/README.es-ES.md b/src/data-structures/linked-list/README.es-ES.md
index 0a9ec6b3a2..62cda8d14a 100644
--- a/src/data-structures/linked-list/README.es-ES.md
+++ b/src/data-structures/linked-list/README.es-ES.md
@@ -7,10 +7,10 @@ _Lee este artículo en otros idiomas:_
 [_Português_](README.pt-BR.md)
 [_English_](README.md)
 
-En ciencias de la computación una **lista enlazada** es una colección lineal
-de elementos de datos, en los cuales el orden lineal no es dado por
-su posición física en memoria. En cambio, cada
-elemento apunta al siguiente. Es una estructura de datos
+En ciencias de la computaciòn una **lista enlazada** es una  coleccion linear 
+de elementos de datos, en los cuales el orden linear no es dado por
+su posciòn fisica en memoria. En cambio, cada 
+elemento señala al siguiente. Es una estructura de datos
 que consiste en un grupo de nodos los cuales juntos representan
 una secuencia. En su forma más sencilla, cada nodo está
 compuesto de datos y una referencia (en otras palabras,

From 0006350cc76f6dc8b1245f625bc268cea8feb447 Mon Sep 17 00:00:00 2001
From: Lucas De Angelis <deangelis.lucas@outlook.com>
Date: Thu, 27 Jan 2022 21:03:48 +0100
Subject: [PATCH 169/264] French translation for module "Graph" (#634)

The first part of the translation is a direct translation of the
english part. The second is too, although it wasn't done by me
but by wikipedia contributors (the second paragraph of the
English wikipedia introduction is exactly the same as the first
paragraph of the French wikipedia "Description")

Add french version redirection on the README.md. The french
version is placed before the portuguese version to have a
cleaner diff (no trailing commas to edit)
---
 src/data-structures/graph/README.fr-FR.md | 23 +++++++++++++++++++++++
 src/data-structures/graph/README.md       |  1 +
 2 files changed, 24 insertions(+)
 create mode 100644 src/data-structures/graph/README.fr-FR.md

diff --git a/src/data-structures/graph/README.fr-FR.md b/src/data-structures/graph/README.fr-FR.md
new file mode 100644
index 0000000000..48d3ccd766
--- /dev/null
+++ b/src/data-structures/graph/README.fr-FR.md
@@ -0,0 +1,23 @@
+# Graph
+
+En informatique, un **graphe** est une structure de
+données abstraite qui implémente les concepts de 
+graphe orienté et de graphe non-orienté venant
+des mathématiques, plus précisément du domaine de
+la théorie des graphes.
+
+La structure de données abstraite de graphe consiste 
+en un ensemble fini, éventuellement mutable de sommets 
+ou nœuds ou points, avec un ensemble de paires ordonnées 
+ou non de tels éléments. Ces paires sont des arêtes, arcs 
+non orientés, ou lignes pour un graphe non orienté, et
+flèches, arêtes orientées , arcs, ou lignes orientées 
+dans le cas orienté. Les sommets peuvent faire partie 
+de la structure, ou être des entités extérieures, 
+représentées par des entiers ou des références.
+
+![Graph](https://www.tutorialspoint.com/data_structures_algorithms/images/graph.jpg)
+
+## References
+
+- [Wikipedia](https://fr.wikipedia.org/wiki/Graphe_(type_abstrait))
\ No newline at end of file
diff --git a/src/data-structures/graph/README.md b/src/data-structures/graph/README.md
index 98acf43616..2c8602d94a 100644
--- a/src/data-structures/graph/README.md
+++ b/src/data-structures/graph/README.md
@@ -3,6 +3,7 @@
 _Read this in other languages:_
 [_简体中文_](README.zh-CN.md),
 [_Русский_](README.ru-RU.md),
+[_Français_](README.fr-FR.md),
 [_Português_](README.pt-BR.md)
 
 In computer science, a **graph** is an abstract data type 

From 294eb3c53f3f8d13b7ce4cbd1ebcd90c9688d6f0 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=EC=84=9C=EB=8B=A4=EC=86=94?=
 <30617570+dasol-seo@users.noreply.github.com>
Date: Fri, 28 Jan 2022 05:04:41 +0900
Subject: [PATCH 170/264] Add merge sort document in Korean (#632)

* Add merge sort doc in Korean

* Update README.md
---
 .../sorting/merge-sort/README.ko-KR.md        | 22 +++++++++++++++
 src/algorithms/sorting/merge-sort/README.md   | 27 ++++++++++---------
 2 files changed, 37 insertions(+), 12 deletions(-)
 create mode 100644 src/algorithms/sorting/merge-sort/README.ko-KR.md

diff --git a/src/algorithms/sorting/merge-sort/README.ko-KR.md b/src/algorithms/sorting/merge-sort/README.ko-KR.md
new file mode 100644
index 0000000000..5447fd217e
--- /dev/null
+++ b/src/algorithms/sorting/merge-sort/README.ko-KR.md
@@ -0,0 +1,22 @@
+# 병합 정렬
+
+컴퓨터과학에서, 병합 정렬(일반적으로 mergesort라고 쓰는)은 효율적이고, 범용적인, 비교 기반의 정렬 알고리즘입니다. 대부분의 구현들은 안정적인 정렬을 만들어내며, 이는 정렬된 산출물에서 동일한 요소들의 입력 순서가 유지된다는 것을 의미합니다. 병합 정렬은 1945년에 John von Neumann이 만든 분할 정복 알고리즘입니다.
+
+병합 정렬의 예시입니다. 우선 리스트를 가장 작은 단위로 나누고(한 개의 요소), 두 개의 인접한 리스트를 정렬하고 병합하기 위해 각 요소와 인접한 리스트를 비교합니다. 마지막으로 모든 요소들은 정렬되고 병합됩니다.
+
+![Merge Sort](https://upload.wikimedia.org/wikipedia/commons/c/cc/Merge-sort-example-300px.gif)
+
+재귀적인 병합 정렬 알고리즘은 7개의 정수값을 가진 배열을 정렬하는데 사용됩니다. 다음은 합병 정렬을 모방하기 위해 사람이 취하는 단계입니다.(하향식)
+
+![Merge Sort](https://upload.wikimedia.org/wikipedia/commons/e/e6/Merge_sort_algorithm_diagram.svg)
+
+## 복잡도
+
+| Name                  | Best            | Average             | Worst               | Memory    | Stable    | Comments  |
+| --------------------- | :-------------: | :-----------------: | :-----------------: | :-------: | :-------: | :-------- |
+| **Merge sort**        | n&nbsp;log(n)   | n&nbsp;log(n)       | n&nbsp;log(n)       | n         | Yes       |           |
+
+## 참조
+
+- [Wikipedia](https://en.wikipedia.org/wiki/Merge_sort)
+- [YouTube](https://www.youtube.com/watch?v=KF2j-9iSf4Q&index=27&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
diff --git a/src/algorithms/sorting/merge-sort/README.md b/src/algorithms/sorting/merge-sort/README.md
index f4ed837a22..b4d76b90a6 100644
--- a/src/algorithms/sorting/merge-sort/README.md
+++ b/src/algorithms/sorting/merge-sort/README.md
@@ -1,23 +1,26 @@
 # Merge Sort
 
-In computer science, merge sort (also commonly spelled 
-mergesort) is an efficient, general-purpose, 
-comparison-based sorting algorithm. Most implementations 
-produce a stable sort, which means that the implementation 
-preserves the input order of equal elements in the sorted 
-output. Mergesort is a divide and conquer algorithm that 
+_Read this in other languages:_
+[_한국어_](README.ko-KR.md)
+
+In computer science, merge sort (also commonly spelled
+mergesort) is an efficient, general-purpose,
+comparison-based sorting algorithm. Most implementations
+produce a stable sort, which means that the implementation
+preserves the input order of equal elements in the sorted
+output. Mergesort is a divide and conquer algorithm that
 was invented by John von Neumann in 1945.
 
-An example of merge sort. First divide the list into 
-the smallest unit (1 element), then compare each 
-element with the adjacent list to sort and merge the 
-two adjacent lists. Finally all the elements are sorted 
+An example of merge sort. First divide the list into
+the smallest unit (1 element), then compare each
+element with the adjacent list to sort and merge the
+two adjacent lists. Finally all the elements are sorted
 and merged.
 
 ![Merge Sort](https://upload.wikimedia.org/wikipedia/commons/c/cc/Merge-sort-example-300px.gif)
 
-A recursive merge sort algorithm used to sort an array of 7 
-integer values. These are the steps a human would take to 
+A recursive merge sort algorithm used to sort an array of 7
+integer values. These are the steps a human would take to
 emulate merge sort (top-down).
 
 ![Merge Sort](https://upload.wikimedia.org/wikipedia/commons/e/e6/Merge_sort_algorithm_diagram.svg)

From 819f38f7926866a141198f0feff61f3ee4fc6e9d Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Thu, 27 Jan 2022 21:05:22 +0100
Subject: [PATCH 171/264] Some text fixes.

---
 .editorconfig | 2 +-
 LICENSE       | 2 +-
 2 files changed, 2 insertions(+), 2 deletions(-)

diff --git a/.editorconfig b/.editorconfig
index c658e4879e..086af2d930 100644
--- a/.editorconfig
+++ b/.editorconfig
@@ -8,4 +8,4 @@ charset = utf-8
 indent_style = space
 indent_size = 2
 trim_trailing_whitespace = true
-quote_type = single
\ No newline at end of file
+quote_type = single
diff --git a/LICENSE b/LICENSE
index 0bad68016a..e7885bd74b 100644
--- a/LICENSE
+++ b/LICENSE
@@ -1,6 +1,6 @@
 The MIT License (MIT)
 
-Copyright (c) 2021 Oleksii Trekhleb
+Copyright (c) 2018 Oleksii Trekhleb
 
 Permission is hereby granted, free of charge, to any person obtaining a copy
 of this software and associated documentation files (the "Software"), to deal

From 82f0b5edf04fba49d5fcff898e50142cac9d67a9 Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Fri, 4 Feb 2022 08:56:15 +0100
Subject: [PATCH 172/264] Add a Divide and Conquer version of the MaxSubArray
 problem.

---
 .npmrc                                        |  2 +-
 .nvmrc                                        |  1 +
 README.md                                     |  3 ++
 .../sets/maximum-subarray/README.md           | 16 ++++++---
 .../__test__/bfMaximumSubarray.test.js        |  2 +-
 .../__test__/dcMaximumSubarraySum.test.js     | 16 +++++++++
 .../__test__/dpMaximumSubarray.test.js        |  2 +-
 .../maximum-subarray/dcMaximumSubarraySum.js  | 33 +++++++++++++++++++
 8 files changed, 67 insertions(+), 8 deletions(-)
 create mode 100644 .nvmrc
 create mode 100644 src/algorithms/sets/maximum-subarray/__test__/dcMaximumSubarraySum.test.js
 create mode 100644 src/algorithms/sets/maximum-subarray/dcMaximumSubarraySum.js

diff --git a/.npmrc b/.npmrc
index c0c80ba447..b6f27f1359 100644
--- a/.npmrc
+++ b/.npmrc
@@ -1 +1 @@
-engine-strict=false
+engine-strict=true
diff --git a/.nvmrc b/.nvmrc
new file mode 100644
index 0000000000..958b5a36e1
--- /dev/null
+++ b/.nvmrc
@@ -0,0 +1 @@
+v14
diff --git a/README.md b/README.md
index d949642e1c..6adff75da3 100644
--- a/README.md
+++ b/README.md
@@ -207,6 +207,7 @@ algorithm is an abstraction higher than a computer program.
   * `B` [Best Time To Buy Sell Stocks](src/algorithms/uncategorized/best-time-to-buy-sell-stocks) - divide and conquer and one-pass examples
   * `A` [Permutations](src/algorithms/sets/permutations) (with and without repetitions)
   * `A` [Combinations](src/algorithms/sets/combinations) (with and without repetitions)
+  * `A` [Maximum Subarray](src/algorithms/sets/maximum-subarray)
 * **Dynamic Programming** - build up a solution using previously found sub-solutions
   * `B` [Fibonacci Number](src/algorithms/math/fibonacci)
   * `B` [Jump Game](src/algorithms/uncategorized/jump-game)
@@ -278,6 +279,8 @@ rm -rf ./node_modules
 npm i
 ```
 
+Also make sure that you're using a correct Node version (`>=14.16.0`). If you're using [nvm](https://github.com/nvm-sh/nvm) for Node version management you may run `nvm use` from the root folder of the project and the correct version will be picked up.
+
 **Playground**
 
 You may play with data-structures and algorithms in `./src/playground/playground.js` file and write
diff --git a/src/algorithms/sets/maximum-subarray/README.md b/src/algorithms/sets/maximum-subarray/README.md
index c152f54edc..c65c502640 100644
--- a/src/algorithms/sets/maximum-subarray/README.md
+++ b/src/algorithms/sets/maximum-subarray/README.md
@@ -1,7 +1,7 @@
 # Maximum subarray problem
 
-The maximum subarray problem is the task of finding the contiguous 
-subarray within a one-dimensional array, `a[1...n]`, of numbers 
+The maximum subarray problem is the task of finding the contiguous
+subarray within a one-dimensional array, `a[1...n]`, of numbers
 which has the largest sum, where,
 
 ![Maximum subarray](https://wikimedia.org/api/rest_v1/media/math/render/svg/e8960f093107b71b21827e726e2bad8b023779b2)
@@ -10,11 +10,17 @@ which has the largest sum, where,
 
 ## Example
 
-The list usually contains both positive and negative numbers along 
-with `0`. For example, for the array of 
-values `−2, 1, −3, 4, −1, 2, 1, −5, 4` the contiguous subarray 
+The list usually contains both positive and negative numbers along
+with `0`. For example, for the array of
+values `−2, 1, −3, 4, −1, 2, 1, −5, 4` the contiguous subarray
 with the largest sum is `4, −1, 2, 1`, with sum `6`.
 
+## Solutions
+
+- Brute Force solution `O(n^2)`: [bfMaximumSubarray.js](./bfMaximumSubarray.js)
+- Divide and Conquer solution `O(n^2)`: [dcMaximumSubarraySum.js](./dcMaximumSubarraySum.js)
+- Dynamic Programming solution `O(n)`: [dpMaximumSubarray.js](./dpMaximumSubarray.js)
+
 ## References
 
 - [Wikipedia](https://en.wikipedia.org/wiki/Maximum_subarray_problem)
diff --git a/src/algorithms/sets/maximum-subarray/__test__/bfMaximumSubarray.test.js b/src/algorithms/sets/maximum-subarray/__test__/bfMaximumSubarray.test.js
index e0faf0cbfe..6bff427110 100644
--- a/src/algorithms/sets/maximum-subarray/__test__/bfMaximumSubarray.test.js
+++ b/src/algorithms/sets/maximum-subarray/__test__/bfMaximumSubarray.test.js
@@ -1,7 +1,7 @@
 import bfMaximumSubarray from '../bfMaximumSubarray';
 
 describe('bfMaximumSubarray', () => {
-  it('should find maximum subarray using brute force algorithm', () => {
+  it('should find maximum subarray using the brute force algorithm', () => {
     expect(bfMaximumSubarray([])).toEqual([]);
     expect(bfMaximumSubarray([0, 0])).toEqual([0]);
     expect(bfMaximumSubarray([0, 0, 1])).toEqual([0, 0, 1]);
diff --git a/src/algorithms/sets/maximum-subarray/__test__/dcMaximumSubarraySum.test.js b/src/algorithms/sets/maximum-subarray/__test__/dcMaximumSubarraySum.test.js
new file mode 100644
index 0000000000..3b3ace08d3
--- /dev/null
+++ b/src/algorithms/sets/maximum-subarray/__test__/dcMaximumSubarraySum.test.js
@@ -0,0 +1,16 @@
+import dcMaximumSubarray from '../dcMaximumSubarraySum';
+
+describe('dcMaximumSubarraySum', () => {
+  it('should find maximum subarray sum using the divide and conquer algorithm', () => {
+    expect(dcMaximumSubarray([])).toEqual(-Infinity);
+    expect(dcMaximumSubarray([0, 0])).toEqual(0);
+    expect(dcMaximumSubarray([0, 0, 1])).toEqual(1);
+    expect(dcMaximumSubarray([0, 0, 1, 2])).toEqual(3);
+    expect(dcMaximumSubarray([0, 0, -1, 2])).toEqual(2);
+    expect(dcMaximumSubarray([-1, -2, -3, -4, -5])).toEqual(-1);
+    expect(dcMaximumSubarray([1, 2, 3, 2, 3, 4, 5])).toEqual(20);
+    expect(dcMaximumSubarray([-2, 1, -3, 4, -1, 2, 1, -5, 4])).toEqual(6);
+    expect(dcMaximumSubarray([-2, -3, 4, -1, -2, 1, 5, -3])).toEqual(7);
+    expect(dcMaximumSubarray([1, -3, 2, -5, 7, 6, -1, 4, 11, -23])).toEqual(27);
+  });
+});
diff --git a/src/algorithms/sets/maximum-subarray/__test__/dpMaximumSubarray.test.js b/src/algorithms/sets/maximum-subarray/__test__/dpMaximumSubarray.test.js
index d8cf39d8e6..c00727cc66 100644
--- a/src/algorithms/sets/maximum-subarray/__test__/dpMaximumSubarray.test.js
+++ b/src/algorithms/sets/maximum-subarray/__test__/dpMaximumSubarray.test.js
@@ -1,7 +1,7 @@
 import dpMaximumSubarray from '../dpMaximumSubarray';
 
 describe('dpMaximumSubarray', () => {
-  it('should find maximum subarray using dynamic programming algorithm', () => {
+  it('should find maximum subarray using the dynamic programming algorithm', () => {
     expect(dpMaximumSubarray([])).toEqual([]);
     expect(dpMaximumSubarray([0, 0])).toEqual([0]);
     expect(dpMaximumSubarray([0, 0, 1])).toEqual([0, 0, 1]);
diff --git a/src/algorithms/sets/maximum-subarray/dcMaximumSubarraySum.js b/src/algorithms/sets/maximum-subarray/dcMaximumSubarraySum.js
new file mode 100644
index 0000000000..3ed9ab3ee7
--- /dev/null
+++ b/src/algorithms/sets/maximum-subarray/dcMaximumSubarraySum.js
@@ -0,0 +1,33 @@
+/**
+ * Divide and Conquer solution.
+ * Complexity: O(n^2) in case if no memoization applied
+ *
+ * @param {Number[]} inputArray
+ * @return {Number[]}
+ */
+export default function dcMaximumSubarraySum(inputArray) {
+  /**
+   * We are going through the inputArray array and for each element we have two options:
+   * - to pick
+   * - not to pick
+   *
+   * Also keep in mind, that the maximum sub-array must be contiguous. It means if we picked
+   * the element, we need to continue picking the next elements or stop counting the max sum.
+   *
+   * @param {number} elementIndex - the index of the element we're deciding to pick or not
+   * @param {boolean} mustPick - to pick or not to pick the element
+   * @returns {number} - maximum subarray sum that we'll get
+   */
+  function solveRecursively(elementIndex, mustPick) {
+    if (elementIndex >= inputArray.length) {
+      return mustPick ? 0 : -Infinity;
+    }
+    return Math.max(
+      // Option #1: Pick the current element, and continue picking next one.
+      inputArray[elementIndex] + solveRecursively(elementIndex + 1, true),
+      // Option #2: Don't pick the current element.
+      mustPick ? 0 : solveRecursively(elementIndex + 1, false),
+    );
+  }
+  return solveRecursively(0, false);
+}

From 7a37a6b86e76ee22bf93ffd9d01d7acfd79d0714 Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Fri, 4 Feb 2022 08:57:25 +0100
Subject: [PATCH 173/264] Add more followup links for Max Subarray problem.

---
 src/algorithms/sets/maximum-subarray/README.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/src/algorithms/sets/maximum-subarray/README.md b/src/algorithms/sets/maximum-subarray/README.md
index c65c502640..f06300f500 100644
--- a/src/algorithms/sets/maximum-subarray/README.md
+++ b/src/algorithms/sets/maximum-subarray/README.md
@@ -26,3 +26,4 @@ with the largest sum is `4, −1, 2, 1`, with sum `6`.
 - [Wikipedia](https://en.wikipedia.org/wiki/Maximum_subarray_problem)
 - [YouTube](https://www.youtube.com/watch?v=ohHWQf1HDfU&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
 - [GeeksForGeeks](https://www.geeksforgeeks.org/largest-sum-contiguous-subarray/)
+- [LeetCode](https://leetcode.com/explore/interview/card/top-interview-questions-easy/97/dynamic-programming/566/discuss/1595195/C++Python-7-Simple-Solutions-w-Explanation-or-Brute-Force-+-DP-+-Kadane-+-Divide-and-Conquer)

From c89388445e11b4776c40c92e0907f1ed1792d03c Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Tue, 1 Mar 2022 18:26:25 +0100
Subject: [PATCH 174/264] Help Ukraine

---
 README.md | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/README.md b/README.md
index 6adff75da3..1420e65e5b 100644
--- a/README.md
+++ b/README.md
@@ -1,5 +1,9 @@
 # JavaScript Algorithms and Data Structures
 
+> 🇺🇦 UKRAINE IS BEING ATTACKED BY RUSSIAN ARMY. CIVILIANS ARE GETTING KILLED. RESIDENTIAL AREAS ARE GETTING BOMBED.
+> - Help Ukraine via [National Bank of Ukraine](https://bank.gov.ua/en/news/all/natsionalniy-bank-vidkriv-spetsrahunok-dlya-zboru-koshtiv-na-potrebi-armiyi)
+> - Help Ukraine via [SaveLife](https://savelife.in.ua/en/donate/) fund
+
 [![CI](https://github.com/trekhleb/javascript-algorithms/workflows/CI/badge.svg)](https://github.com/trekhleb/javascript-algorithms/actions?query=workflow%3ACI+branch%3Amaster)
 [![codecov](https://codecov.io/gh/trekhleb/javascript-algorithms/branch/master/graph/badge.svg)](https://codecov.io/gh/trekhleb/javascript-algorithms)
 

From b2427d0e18b97f83ecc30311b83d699f03b7d79a Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Tue, 1 Mar 2022 18:31:32 +0100
Subject: [PATCH 175/264] Help Ukraine

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 1420e65e5b..16e517b514 100644
--- a/README.md
+++ b/README.md
@@ -1,6 +1,6 @@
 # JavaScript Algorithms and Data Structures
 
-> 🇺🇦 UKRAINE IS BEING ATTACKED BY RUSSIAN ARMY. CIVILIANS ARE GETTING KILLED. RESIDENTIAL AREAS ARE GETTING BOMBED.
+> 🇺🇦 UKRAINE [IS BEING ATTACKED](https://twitter.com/MFA_Ukraine) BY RUSSIAN ARMY. CIVILIANS ARE GETTING KILLED. RESIDENTIAL AREAS ARE GETTING BOMBED.
 > - Help Ukraine via [National Bank of Ukraine](https://bank.gov.ua/en/news/all/natsionalniy-bank-vidkriv-spetsrahunok-dlya-zboru-koshtiv-na-potrebi-armiyi)
 > - Help Ukraine via [SaveLife](https://savelife.in.ua/en/donate/) fund
 

From cd34b52e22b35358395bd1aa41e90f3cc451cbba Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Sat, 12 Mar 2022 17:45:45 +0100
Subject: [PATCH 176/264] Update README.md

---
 README.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/README.md b/README.md
index 16e517b514..8315cfa8f6 100644
--- a/README.md
+++ b/README.md
@@ -3,6 +3,7 @@
 > 🇺🇦 UKRAINE [IS BEING ATTACKED](https://twitter.com/MFA_Ukraine) BY RUSSIAN ARMY. CIVILIANS ARE GETTING KILLED. RESIDENTIAL AREAS ARE GETTING BOMBED.
 > - Help Ukraine via [National Bank of Ukraine](https://bank.gov.ua/en/news/all/natsionalniy-bank-vidkriv-spetsrahunok-dlya-zboru-koshtiv-na-potrebi-armiyi)
 > - Help Ukraine via [SaveLife](https://savelife.in.ua/en/donate/) fund
+> - [More info](https://war.ukraine.ua/)
 
 [![CI](https://github.com/trekhleb/javascript-algorithms/workflows/CI/badge.svg)](https://github.com/trekhleb/javascript-algorithms/actions?query=workflow%3ACI+branch%3Amaster)
 [![codecov](https://codecov.io/gh/trekhleb/javascript-algorithms/branch/master/graph/badge.svg)](https://codecov.io/gh/trekhleb/javascript-algorithms)

From cb7afe18ef003995d8e23cc0b179ee7e37e8a19e Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Sat, 12 Mar 2022 17:46:09 +0100
Subject: [PATCH 177/264] Update README.md

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 8315cfa8f6..ca85cb40c2 100644
--- a/README.md
+++ b/README.md
@@ -3,7 +3,7 @@
 > 🇺🇦 UKRAINE [IS BEING ATTACKED](https://twitter.com/MFA_Ukraine) BY RUSSIAN ARMY. CIVILIANS ARE GETTING KILLED. RESIDENTIAL AREAS ARE GETTING BOMBED.
 > - Help Ukraine via [National Bank of Ukraine](https://bank.gov.ua/en/news/all/natsionalniy-bank-vidkriv-spetsrahunok-dlya-zboru-koshtiv-na-potrebi-armiyi)
 > - Help Ukraine via [SaveLife](https://savelife.in.ua/en/donate/) fund
-> - [More info](https://war.ukraine.ua/)
+> - More info on [war.ukraine.ua](https://war.ukraine.ua/)
 
 [![CI](https://github.com/trekhleb/javascript-algorithms/workflows/CI/badge.svg)](https://github.com/trekhleb/javascript-algorithms/actions?query=workflow%3ACI+branch%3Amaster)
 [![codecov](https://codecov.io/gh/trekhleb/javascript-algorithms/branch/master/graph/badge.svg)](https://codecov.io/gh/trekhleb/javascript-algorithms)

From 28b43226a4dec973fc9d440b30f1cde50d25c4cb Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Sat, 2 Jul 2022 17:50:13 +0200
Subject: [PATCH 178/264] Update README.md

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index ca85cb40c2..4a870ccfed 100644
--- a/README.md
+++ b/README.md
@@ -2,7 +2,7 @@
 
 > 🇺🇦 UKRAINE [IS BEING ATTACKED](https://twitter.com/MFA_Ukraine) BY RUSSIAN ARMY. CIVILIANS ARE GETTING KILLED. RESIDENTIAL AREAS ARE GETTING BOMBED.
 > - Help Ukraine via [National Bank of Ukraine](https://bank.gov.ua/en/news/all/natsionalniy-bank-vidkriv-spetsrahunok-dlya-zboru-koshtiv-na-potrebi-armiyi)
-> - Help Ukraine via [SaveLife](https://savelife.in.ua/en/donate/) fund
+> - Help Ukraine via [SaveLife](https://savelife.in.ua/en/donate-en/) fund
 > - More info on [war.ukraine.ua](https://war.ukraine.ua/)
 
 [![CI](https://github.com/trekhleb/javascript-algorithms/workflows/CI/badge.svg)](https://github.com/trekhleb/javascript-algorithms/actions?query=workflow%3ACI+branch%3Amaster)

From 5a28fef1a7393c8b991352e2dd011d099c7cd5fb Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Sun, 24 Jul 2022 17:49:21 +0200
Subject: [PATCH 179/264] Update Queue images.

---
 src/data-structures/queue/README.fr-FR.md   |   4 +++-
 src/data-structures/queue/README.ja-JP.md   |   4 +++-
 src/data-structures/queue/README.ko-KR.md   |   4 +++-
 src/data-structures/queue/README.md         |   4 +++-
 src/data-structures/queue/README.pt-BR.md   |   4 +++-
 src/data-structures/queue/README.ru-RU.md   |   4 +++-
 src/data-structures/queue/README.zh-CN.md   |   4 +++-
 src/data-structures/queue/images/queue.jpeg | Bin 0 -> 62391 bytes
 8 files changed, 21 insertions(+), 7 deletions(-)
 create mode 100644 src/data-structures/queue/images/queue.jpeg

diff --git a/src/data-structures/queue/README.fr-FR.md b/src/data-structures/queue/README.fr-FR.md
index 452e875bcf..8bad714e0f 100644
--- a/src/data-structures/queue/README.fr-FR.md
+++ b/src/data-structures/queue/README.fr-FR.md
@@ -20,7 +20,9 @@ structure de données linéaire, ou, plus abstraitement, une collection séquent
 
 Représentation d'une file PEPS (premier entré, premier sorti)
 
-![Queue](https://upload.wikimedia.org/wikipedia/commons/5/52/Data_Queue.svg)
+![Queue](./images/queue.jpeg)
+
+<small><i>Made with <a href="https://okso.app/">okso.app</a></i></small>
 
 ## Références
 
diff --git a/src/data-structures/queue/README.ja-JP.md b/src/data-structures/queue/README.ja-JP.md
index 7b033b0938..d879064b73 100644
--- a/src/data-structures/queue/README.ja-JP.md
+++ b/src/data-structures/queue/README.ja-JP.md
@@ -4,7 +4,9 @@
 
 FIFO(先入れ先出し)のキュー
 
-![Queue](https://upload.wikimedia.org/wikipedia/commons/5/52/Data_Queue.svg)
+![Queue](./images/queue.jpeg)
+
+<small><i>Made with <a href="https://okso.app/">okso.app</a></i></small>
 
 ## 参考
 
diff --git a/src/data-structures/queue/README.ko-KR.md b/src/data-structures/queue/README.ko-KR.md
index 204f6b9b84..527ea5030b 100644
--- a/src/data-structures/queue/README.ko-KR.md
+++ b/src/data-structures/queue/README.ko-KR.md
@@ -13,7 +13,9 @@ _Read this in other languages:_
 
 선입선출 자료 구조인 큐를 나타내면 다음과 같습니다.
 
-![Queue](https://upload.wikimedia.org/wikipedia/commons/5/52/Data_Queue.svg)
+![Queue](./images/queue.jpeg)
+
+<small><i>Made with <a href="https://okso.app/">okso.app</a></i></small>
 
 ## 참고
 
diff --git a/src/data-structures/queue/README.md b/src/data-structures/queue/README.md
index 4db98224a1..e9ad6f54a3 100644
--- a/src/data-structures/queue/README.md
+++ b/src/data-structures/queue/README.md
@@ -26,7 +26,9 @@ sequential collection.
 
 Representation of a FIFO (first in, first out) queue
 
-![Queue](https://upload.wikimedia.org/wikipedia/commons/5/52/Data_Queue.svg)
+![Queue](./images/queue.jpeg)
+
+<small><i>Made with <a href="https://okso.app/">okso.app</a></i></small>
 
 ## References
 
diff --git a/src/data-structures/queue/README.pt-BR.md b/src/data-structures/queue/README.pt-BR.md
index b86c9713c9..ad24d23188 100644
--- a/src/data-structures/queue/README.pt-BR.md
+++ b/src/data-structures/queue/README.pt-BR.md
@@ -20,7 +20,9 @@ coleção seqüencial.
 
 Representação de uma file FIFO (first in, first out)
 
-![Queue](https://upload.wikimedia.org/wikipedia/commons/5/52/Data_Queue.svg)
+![Queue](./images/queue.jpeg)
+
+<small><i>Made with <a href="https://okso.app/">okso.app</a></i></small>
 
 ## References
 
diff --git a/src/data-structures/queue/README.ru-RU.md b/src/data-structures/queue/README.ru-RU.md
index 419edadecd..c1ebe46a88 100644
--- a/src/data-structures/queue/README.ru-RU.md
+++ b/src/data-structures/queue/README.ru-RU.md
@@ -11,7 +11,9 @@
 
 Иллюстрация работы с очередью.
 
-![Очередь](https://upload.wikimedia.org/wikipedia/commons/5/52/Data_Queue.svg)
+![Очередь](./images/queue.jpeg)
+
+<small><i>Made with <a href="https://okso.app/">okso.app</a></i></small>
 
 ## References
 
diff --git a/src/data-structures/queue/README.zh-CN.md b/src/data-structures/queue/README.zh-CN.md
index d61a2c7dac..d4aa76cffe 100644
--- a/src/data-structures/queue/README.zh-CN.md
+++ b/src/data-structures/queue/README.zh-CN.md
@@ -7,7 +7,9 @@
 
 队列中元素先进先出 FIFO (first in, first out)的示意
 
-![Queue](https://upload.wikimedia.org/wikipedia/commons/5/52/Data_Queue.svg)
+![Queue](./images/queue.jpeg)
+
+<small><i>Made with <a href="https://okso.app/">okso.app</a></i></small>
 
 ## 参考
 
diff --git a/src/data-structures/queue/images/queue.jpeg b/src/data-structures/queue/images/queue.jpeg
new file mode 100644
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HcmV?d00001


From 58491c74c9b226205f22faf983c8782ebba167b9 Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Sun, 24 Jul 2022 17:53:46 +0200
Subject: [PATCH 180/264] Update Queue images.

---
 src/data-structures/queue/README.fr-FR.md | 2 +-
 src/data-structures/queue/README.ja-JP.md | 2 +-
 src/data-structures/queue/README.ko-KR.md | 2 +-
 src/data-structures/queue/README.md       | 2 +-
 src/data-structures/queue/README.pt-BR.md | 2 +-
 src/data-structures/queue/README.ru-RU.md | 2 +-
 src/data-structures/queue/README.zh-CN.md | 2 +-
 7 files changed, 7 insertions(+), 7 deletions(-)

diff --git a/src/data-structures/queue/README.fr-FR.md b/src/data-structures/queue/README.fr-FR.md
index 8bad714e0f..33d327744f 100644
--- a/src/data-structures/queue/README.fr-FR.md
+++ b/src/data-structures/queue/README.fr-FR.md
@@ -22,7 +22,7 @@ Représentation d'une file PEPS (premier entré, premier sorti)
 
 ![Queue](./images/queue.jpeg)
 
-<small><i>Made with <a href="https://okso.app/">okso.app</a></i></small>
+*Made with [okso.app](https://okso.app)*
 
 ## Références
 
diff --git a/src/data-structures/queue/README.ja-JP.md b/src/data-structures/queue/README.ja-JP.md
index d879064b73..1ffa9c1a68 100644
--- a/src/data-structures/queue/README.ja-JP.md
+++ b/src/data-structures/queue/README.ja-JP.md
@@ -6,7 +6,7 @@ FIFO(先入れ先出し)のキュー
 
 ![Queue](./images/queue.jpeg)
 
-<small><i>Made with <a href="https://okso.app/">okso.app</a></i></small>
+*Made with [okso.app](https://okso.app)*
 
 ## 参考
 
diff --git a/src/data-structures/queue/README.ko-KR.md b/src/data-structures/queue/README.ko-KR.md
index 527ea5030b..606c8ff35e 100644
--- a/src/data-structures/queue/README.ko-KR.md
+++ b/src/data-structures/queue/README.ko-KR.md
@@ -15,7 +15,7 @@ _Read this in other languages:_
 
 ![Queue](./images/queue.jpeg)
 
-<small><i>Made with <a href="https://okso.app/">okso.app</a></i></small>
+*Made with [okso.app](https://okso.app)*
 
 ## 참고
 
diff --git a/src/data-structures/queue/README.md b/src/data-structures/queue/README.md
index e9ad6f54a3..c1e40d735c 100644
--- a/src/data-structures/queue/README.md
+++ b/src/data-structures/queue/README.md
@@ -28,7 +28,7 @@ Representation of a FIFO (first in, first out) queue
 
 ![Queue](./images/queue.jpeg)
 
-<small><i>Made with <a href="https://okso.app/">okso.app</a></i></small>
+*Made with [okso.app](https://okso.app)*
 
 ## References
 
diff --git a/src/data-structures/queue/README.pt-BR.md b/src/data-structures/queue/README.pt-BR.md
index ad24d23188..9464864120 100644
--- a/src/data-structures/queue/README.pt-BR.md
+++ b/src/data-structures/queue/README.pt-BR.md
@@ -22,7 +22,7 @@ Representação de uma file FIFO (first in, first out)
 
 ![Queue](./images/queue.jpeg)
 
-<small><i>Made with <a href="https://okso.app/">okso.app</a></i></small>
+*Made with [okso.app](https://okso.app)*
 
 ## References
 
diff --git a/src/data-structures/queue/README.ru-RU.md b/src/data-structures/queue/README.ru-RU.md
index c1ebe46a88..1f9e5ff6f1 100644
--- a/src/data-structures/queue/README.ru-RU.md
+++ b/src/data-structures/queue/README.ru-RU.md
@@ -13,7 +13,7 @@
 
 ![Очередь](./images/queue.jpeg)
 
-<small><i>Made with <a href="https://okso.app/">okso.app</a></i></small>
+*Made with [okso.app](https://okso.app)*
 
 ## References
 
diff --git a/src/data-structures/queue/README.zh-CN.md b/src/data-structures/queue/README.zh-CN.md
index d4aa76cffe..af608107d3 100644
--- a/src/data-structures/queue/README.zh-CN.md
+++ b/src/data-structures/queue/README.zh-CN.md
@@ -9,7 +9,7 @@
 
 ![Queue](./images/queue.jpeg)
 
-<small><i>Made with <a href="https://okso.app/">okso.app</a></i></small>
+*Made with [okso.app](https://okso.app)*
 
 ## 参考
 

From 10b79ee1d74887d8757ad166565629a6346f7b41 Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Sun, 24 Jul 2022 18:18:53 +0200
Subject: [PATCH 181/264] Update Stack images.

---
 src/data-structures/stack/README.fr-FR.md   |   4 +++-
 src/data-structures/stack/README.ja-JP.md   |   4 +++-
 src/data-structures/stack/README.ko-KR.md   |   4 +++-
 src/data-structures/stack/README.md         |  20 +++++++++++---------
 src/data-structures/stack/README.pt-BR.md   |   4 +++-
 src/data-structures/stack/README.ru-RU.md   |   6 ++++--
 src/data-structures/stack/README.zh-CN.md   |   4 +++-
 src/data-structures/stack/images/stack.jpeg | Bin 0 -> 130156 bytes
 8 files changed, 30 insertions(+), 16 deletions(-)
 create mode 100644 src/data-structures/stack/images/stack.jpeg

diff --git a/src/data-structures/stack/README.fr-FR.md b/src/data-structures/stack/README.fr-FR.md
index 5e9a95c81c..0d6c388640 100644
--- a/src/data-structures/stack/README.fr-FR.md
+++ b/src/data-structures/stack/README.fr-FR.md
@@ -20,7 +20,9 @@ autres articles en premier.
 
 Représentation simple de l'éxecution d'une pile avec des opérations empiler (push) et dépiler (pop).
 
-![Stack](https://upload.wikimedia.org/wikipedia/commons/b/b4/Lifo_stack.png)
+![Stack](./images/stack.jpeg)
+
+*Made with [okso.app](https://okso.app)*
 
 ## Références
 
diff --git a/src/data-structures/stack/README.ja-JP.md b/src/data-structures/stack/README.ja-JP.md
index 7f77828425..55ca25206c 100644
--- a/src/data-structures/stack/README.ja-JP.md
+++ b/src/data-structures/stack/README.ja-JP.md
@@ -9,7 +9,9 @@
 
 プッシュとポップの例
 
-![Stack](https://upload.wikimedia.org/wikipedia/commons/b/b4/Lifo_stack.png)
+![Stack](./images/stack.jpeg)
+
+*Made with [okso.app](https://okso.app)*
 
 ## 参考
 
diff --git a/src/data-structures/stack/README.ko-KR.md b/src/data-structures/stack/README.ko-KR.md
index 916aef1d04..c36a472e66 100644
--- a/src/data-structures/stack/README.ko-KR.md
+++ b/src/data-structures/stack/README.ko-KR.md
@@ -16,7 +16,9 @@ _Read this in other languages:_
 
 다음은 push와 pop 연산을 실행하는 간단한 스택의 실행입니다.
 
-![Stack](https://upload.wikimedia.org/wikipedia/commons/b/b4/Lifo_stack.png)
+![Stack](./images/stack.jpeg)
+
+*Made with [okso.app](https://okso.app)*
 
 ## 참조
 
diff --git a/src/data-structures/stack/README.md b/src/data-structures/stack/README.md
index f2335da1d6..645e66c117 100644
--- a/src/data-structures/stack/README.md
+++ b/src/data-structures/stack/README.md
@@ -8,24 +8,26 @@ _Read this in other languages:_
 [_Português_](README.pt-BR.md),
 [_한국어_](README.ko-KR.md)
 
-In computer science, a **stack** is an abstract data type that serves 
+In computer science, a **stack** is an abstract data type that serves
 as a collection of elements, with two principal operations:
 
 * **push**, which adds an element to the collection, and
 * **pop**, which removes the most recently added element that was not yet removed.
 
-The order in which elements come off a stack gives rise to its 
-alternative name, LIFO (last in, first out). Additionally, a 
-peek operation may give access to the top without modifying 
-the stack. The name "stack" for this type of structure comes 
-from the analogy to a set of physical items stacked on top of 
-each other, which makes it easy to take an item off the top 
-of the stack, while getting to an item deeper in the stack 
+The order in which elements come off a stack gives rise to its
+alternative name, LIFO (last in, first out). Additionally, a
+peek operation may give access to the top without modifying
+the stack. The name "stack" for this type of structure comes
+from the analogy to a set of physical items stacked on top of
+each other, which makes it easy to take an item off the top
+of the stack, while getting to an item deeper in the stack
 may require taking off multiple other items first.
 
 Simple representation of a stack runtime with push and pop operations.
 
-![Stack](https://upload.wikimedia.org/wikipedia/commons/b/b4/Lifo_stack.png)
+![Stack](./images/stack.jpeg)
+
+*Made with [okso.app](https://okso.app)*
 
 ## References
 
diff --git a/src/data-structures/stack/README.pt-BR.md b/src/data-structures/stack/README.pt-BR.md
index 9390ea5155..d1269d2437 100644
--- a/src/data-structures/stack/README.pt-BR.md
+++ b/src/data-structures/stack/README.pt-BR.md
@@ -18,7 +18,9 @@ vários outros itens primeiro.
 Representação simples de um tempo de execução de pilha com operações
 _push_ e _pop_.
 
-![Stack](https://upload.wikimedia.org/wikipedia/commons/b/b4/Lifo_stack.png)
+![Stack](./images/stack.jpeg)
+
+*Made with [okso.app](https://okso.app)*
 
 ## Referências
 
diff --git a/src/data-structures/stack/README.ru-RU.md b/src/data-structures/stack/README.ru-RU.md
index 136cd6f4d2..3e33c87119 100644
--- a/src/data-structures/stack/README.ru-RU.md
+++ b/src/data-structures/stack/README.ru-RU.md
@@ -8,14 +8,16 @@
 * **удаление (pop)**, последнего добавленного элемента.
 
 Дополнительная операция чтения головного элемента (peek) даёт доступ
-к последнему элементу стека без изменения самого стека. 
+к последнему элементу стека без изменения самого стека.
 
 Чаще всего принцип работы стека сравнивают со стопкой тарелок: чтобы взять вторую
 сверху, нужно снять верхнюю.
 
 Иллюстрация работы со стеком.
 
-![Стек](https://upload.wikimedia.org/wikipedia/commons/b/b4/Lifo_stack.png)
+![Stack](./images/stack.jpeg)
+
+*Made with [okso.app](https://okso.app)*
 
 ## Ссылки
 
diff --git a/src/data-structures/stack/README.zh-CN.md b/src/data-structures/stack/README.zh-CN.md
index bd9bce4b2a..f00e3eab00 100644
--- a/src/data-structures/stack/README.zh-CN.md
+++ b/src/data-structures/stack/README.zh-CN.md
@@ -13,7 +13,9 @@
 
 栈的 push 和 pop 操作的示意
 
-![Stack](https://upload.wikimedia.org/wikipedia/commons/b/b4/Lifo_stack.png)
+![Stack](./images/stack.jpeg)
+
+*Made with [okso.app](https://okso.app)*
 
 ## 参考
 
diff --git a/src/data-structures/stack/images/stack.jpeg b/src/data-structures/stack/images/stack.jpeg
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From c5c795a7f0b5476409192a64992bef5b6ade46f5 Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Sun, 24 Jul 2022 18:27:23 +0200
Subject: [PATCH 182/264] Update Stack images.

---
 src/data-structures/stack/images/stack.jpeg | Bin 130156 -> 153040 bytes
 1 file changed, 0 insertions(+), 0 deletions(-)

diff --git a/src/data-structures/stack/images/stack.jpeg b/src/data-structures/stack/images/stack.jpeg
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From fc47fff0894b27414bb5419caf5dd601ec3adb59 Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Tue, 26 Jul 2022 07:26:21 +0200
Subject: [PATCH 183/264] Update Queue images.

---
 src/data-structures/queue/images/queue.jpeg | Bin 62391 -> 122739 bytes
 1 file changed, 0 insertions(+), 0 deletions(-)

diff --git a/src/data-structures/queue/images/queue.jpeg b/src/data-structures/queue/images/queue.jpeg
index d7947bc361e021e198f4189a75ea77b93fcaae61..f1df0643585780b568592ab3a321157d365d66e8 100644
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From dc65485196ac5307f90994dc8fa0ce58764c536b Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Tue, 26 Jul 2022 20:54:39 +0200
Subject: [PATCH 184/264] Update images for Linked List, Doubly Linked List,
 Queue, and Stack. (#915)

* Update linked list image.

* Update Queue image.

* Update Stack image.

* Update Doubly Linked List image.
---
 .../doubly-linked-list/README.es-ES.md        |   4 +++-
 .../doubly-linked-list/README.ja-JP.md        |  10 ++++++----
 .../doubly-linked-list/README.ko-KR.md        |  10 ++++++----
 .../doubly-linked-list/README.md              |   4 +++-
 .../doubly-linked-list/README.pt-BR.md        |  10 ++++++----
 .../doubly-linked-list/README.ru-RU.md        |  12 +++++++-----
 .../doubly-linked-list/README.zh-CN.md        |  10 ++++++----
 .../images/doubly-linked-list.jpeg            | Bin 0 -> 115163 bytes
 .../linked-list/README.es-ES.md               |   8 +++++---
 .../linked-list/README.ja-JP.md               |   6 ++++--
 .../linked-list/README.ko-KR.md               |   6 ++++--
 src/data-structures/linked-list/README.md     |   4 +++-
 .../linked-list/README.pt-BR.md               |   4 +++-
 .../linked-list/README.ru-RU.md               |   6 ++++--
 .../linked-list/README.tr-TR.md               |   4 +++-
 .../linked-list/README.zh-CN.md               |   8 +++++---
 .../linked-list/images/linked-list.jpeg       | Bin 0 -> 64733 bytes
 src/data-structures/queue/images/queue.jpeg   | Bin 122739 -> 122630 bytes
 src/data-structures/stack/images/stack.jpeg   | Bin 153040 -> 153582 bytes
 19 files changed, 68 insertions(+), 38 deletions(-)
 create mode 100644 src/data-structures/doubly-linked-list/images/doubly-linked-list.jpeg
 create mode 100644 src/data-structures/linked-list/images/linked-list.jpeg

diff --git a/src/data-structures/doubly-linked-list/README.es-ES.md b/src/data-structures/doubly-linked-list/README.es-ES.md
index 15a623550f..490466d74b 100644
--- a/src/data-structures/doubly-linked-list/README.es-ES.md
+++ b/src/data-structures/doubly-linked-list/README.es-ES.md
@@ -9,7 +9,9 @@ _Lea esto en otros idiomas:_
 
 En informática, una **lista doblemente enlazada** es una estructura de datos relacionados que consta de un conjunto de registros conectados secuencialmente llamados nodos. Cada nodo contiene dos campos, llamados enlaces, que son referencias al nodo anterior y al siguiente en la secuencia de nodos. Los enlaces anterior y siguiente de los nodos inicial y final, apuntan respectivamente a algún tipo de terminador (normalmente un nodo centinela o nulo), facilitando así el recorrido de la lista. Si solo hay un nodo nulo, la lista se enlaza circularmente a través este. Puede conceptualizarse como dos listas enlazadas individualmente formadas a partir de los mismos elementos de datos, pero en órdenes secuenciales opuestos.
 
-![Lista doblemente enlazada](https://upload.wikimedia.org/wikipedia/commons/5/5e/Doubly-linked-list.svg)
+![Lista doblemente enlazada](./images/doubly-linked-list.jpeg)
+
+*Made with [okso.app](https://okso.app)*
 
 Los dos enlaces de un nodo permiten recorrer la lista en cualquier dirección. Si bien agregar o eliminar un nodo en una lista doblemente enlazada requiere cambiar más enlaces que las mismas operaciones en una lista enlazada individualmente, las operaciones son más simples y potencialmente más eficientes (para nodos que no sean los primeros) porque no hay necesidad de realizar un seguimiento del nodo anterior durante el recorrido o no es necesario recorrer la lista para encontrar el nodo anterior, de modo que se pueda modificar su enlace.
 
diff --git a/src/data-structures/doubly-linked-list/README.ja-JP.md b/src/data-structures/doubly-linked-list/README.ja-JP.md
index ede22817ba..0ff96628c9 100644
--- a/src/data-structures/doubly-linked-list/README.ja-JP.md
+++ b/src/data-structures/doubly-linked-list/README.ja-JP.md
@@ -2,7 +2,9 @@
 
 コンピュータサイエンスにおいて、**双方向リスト**はノードと呼ばれる一連のリンクレコードからなる連結データ構造です。各ノードはリンクと呼ばれる2つのフィールドを持っていて、これらは一連のノード内における前のノードと次のノードを参照しています。最初のノードの前のリンクと最後のノードの次のリンクはある種の終端を示していて、一般的にはダミーノードやnullが格納され、リストのトラバースを容易に行えるようにしています。もしダミーノードが1つしかない場合、リストはその1つのノードを介して循環的にリンクされます。これは、それぞれ逆の順番の単方向のリンクリストが2つあるものとして考えることができます。
 
-![Doubly Linked List](https://upload.wikimedia.org/wikipedia/commons/5/5e/Doubly-linked-list.svg)
+![Doubly Linked List](./images/doubly-linked-list.jpeg)
+
+*Made with [okso.app](https://okso.app)*
 
 2つのリンクにより、リストをどちらの方向にもトラバースすることができます。双方向リストはノードの追加や削除の際に、片方向リンクリストと比べてより多くのリンクを変更する必要があります。しかし、その操作は簡単で、より効率的な(最初のノード以外の場合)可能性があります。前のノードのリンクを更新する際に前のノードを保持したり、前のノードを見つけるためにリストをトラバースする必要がありません。
 
@@ -25,7 +27,7 @@ Add(value)
   end if
 end Add
 ```
-    
+
 ### 削除
 
 ```text
@@ -62,7 +64,7 @@ Remove(head, value)
   return false
 end Remove
 ```
-    
+
 ### 逆トラバース
 
 ```text
@@ -76,7 +78,7 @@ ReverseTraversal(tail)
   end while
 end Reverse Traversal
 ```
-    
+
 ## 計算量
 
 ## 時間計算量
diff --git a/src/data-structures/doubly-linked-list/README.ko-KR.md b/src/data-structures/doubly-linked-list/README.ko-KR.md
index 192b189817..9f60e54f32 100644
--- a/src/data-structures/doubly-linked-list/README.ko-KR.md
+++ b/src/data-structures/doubly-linked-list/README.ko-KR.md
@@ -12,7 +12,9 @@ _Read this in other languages:_
 센티넬 노드가 하나만 있으면, 목록이 센티넬 노드를 통해서 원형으로 연결됩니다.
 동일한 데이터 항목으로 구성되어 있지만, 반대 순서로 두 개의 단일 연결 리스트로 개념화 할 수 있습니다.
 
-![이중 연결 리스트](https://upload.wikimedia.org/wikipedia/commons/5/5e/Doubly-linked-list.svg)
+![이중 연결 리스트](./images/doubly-linked-list.jpeg)
+
+*Made with [okso.app](https://okso.app)*
 
 두 개의 노드 링크를 사용하면 어느 방향으로든 리스트를 순회할 수 있습니다.
 이중 연결 리스트에서 노드를 추가하거나 제거하려면, 단일 연결 리스트에서 동일한 작업보다 더 많은 링크를 변경해야 하지만, 첫 번째 노드 이외의 노드인 경우 작업을 추적할 필요가 없으므로 작업이 더 단순해져 잠재적으로 더 효율적입니다.
@@ -37,7 +39,7 @@ Add(value)
   end if
 end Add
 ```
-    
+
 ### 삭제
 
 ```text
@@ -74,7 +76,7 @@ Remove(head, value)
   return false
 end Remove
 ```
-    
+
 ### 역순회
 
 ```text
@@ -88,7 +90,7 @@ ReverseTraversal(tail)
   end while
 end Reverse Traversal
 ```
-    
+
 ## 복잡도
 
 ## 시간 복잡도
diff --git a/src/data-structures/doubly-linked-list/README.md b/src/data-structures/doubly-linked-list/README.md
index 703520aaf4..81c0797f73 100644
--- a/src/data-structures/doubly-linked-list/README.md
+++ b/src/data-structures/doubly-linked-list/README.md
@@ -18,7 +18,9 @@ sentinel node, then the list is circularly linked via the sentinel node. It can
 be conceptualized as two singly linked lists formed from the same data items,
 but in opposite sequential orders.
 
-![Doubly Linked List](https://upload.wikimedia.org/wikipedia/commons/5/5e/Doubly-linked-list.svg)
+![Doubly Linked List](./images/doubly-linked-list.jpeg)
+
+*Made with [okso.app](https://okso.app)*
 
 The two node links allow traversal of the list in either direction. While adding
 or removing a node in a doubly linked list requires changing more links than the
diff --git a/src/data-structures/doubly-linked-list/README.pt-BR.md b/src/data-structures/doubly-linked-list/README.pt-BR.md
index 73c86f5386..9ba3954d0b 100644
--- a/src/data-structures/doubly-linked-list/README.pt-BR.md
+++ b/src/data-structures/doubly-linked-list/README.pt-BR.md
@@ -11,7 +11,9 @@ somente um nó sentinela, então a lista é ligada circularmente através do nó
 sentinela. Ela pode ser conceitualizada como duas listas individualmente ligadas
 e formadas a partir dos mesmos itens, mas em ordem sequencial opostas.
 
-![Doubly Linked List](https://upload.wikimedia.org/wikipedia/commons/5/5e/Doubly-linked-list.svg)
+![Doubly Linked List](./images/doubly-linked-list.jpeg)
+
+*Made with [okso.app](https://okso.app)*
 
 Os dois nós ligados permitem a travessia da lista em qualquer direção.
 Enquanto adicionar ou remover um nó de uma lista duplamente vinculada requer
@@ -41,7 +43,7 @@ Add(value)
   end if
 end Add
 ```
-    
+
 ### Deletar
 
 ```text
@@ -78,7 +80,7 @@ Remove(head, value)
   return false
 end Remove
 ```
-    
+
 ### Travessia reversa
 
 ```text
@@ -92,7 +94,7 @@ ReverseTraversal(tail)
   end while
 end Reverse Traversal
 ```
-    
+
 ## Complexidades
 
 ## Complexidade de Tempo
diff --git a/src/data-structures/doubly-linked-list/README.ru-RU.md b/src/data-structures/doubly-linked-list/README.ru-RU.md
index ddad0312b0..b69d0da393 100644
--- a/src/data-structures/doubly-linked-list/README.ru-RU.md
+++ b/src/data-structures/doubly-linked-list/README.ru-RU.md
@@ -10,14 +10,16 @@
 Двусвязный список можно представить, как два связных списка, которые образованы из
 одних и тех же данных, но расположенных в противоположном порядке.
 
-![Двусвязный список](https://upload.wikimedia.org/wikipedia/commons/5/5e/Doubly-linked-list.svg)
+![Двусвязный список](./images/doubly-linked-list.jpeg)
+
+*Made with [okso.app](https://okso.app)*
 
 Две ссылки позволяют обходить список в обоих направлениях. Добавление и
 удаление узла в двусвязном списке требует изменения большего количества ссылок,
 чем аналогичные операции в связном списке. Однако данные операции проще и потенциально
 более эффективны (для некорневых узлов) - при обходе не нужно следить за предыдущим
 узлом или повторно обходить список в поиске предыдущего узла, плюс его ссылка
-может быть изменена. 
+может быть изменена.
 
 ## Псевдокод основных операций
 
@@ -38,7 +40,7 @@ Add(value)
   end if
 end Add
 ```
-    
+
 ### Удаление
 
 ```text
@@ -75,7 +77,7 @@ Remove(head, value)
   return false
 end Remove
 ```
-    
+
 ### Обратный обход
 
 ```text
@@ -89,7 +91,7 @@ ReverseTraversal(tail)
   end while
 end Reverse Traversal
 ```
-    
+
 ## Сложность
 
 ## Временная сложность
diff --git a/src/data-structures/doubly-linked-list/README.zh-CN.md b/src/data-structures/doubly-linked-list/README.zh-CN.md
index 097ec0c90c..3e669f4c45 100644
--- a/src/data-structures/doubly-linked-list/README.zh-CN.md
+++ b/src/data-structures/doubly-linked-list/README.zh-CN.md
@@ -2,7 +2,9 @@
 
 在计算机科学中, 一个 **双向链表(doubly linked list)** 是由一组称为节点的顺序链接记录组成的链接数据结构。每个节点包含两个字段，称为链接，它们是对节点序列中上一个节点和下一个节点的引用。开始节点和结束节点的上一个链接和下一个链接分别指向某种终止节点，通常是前哨节点或null，以方便遍历列表。如果只有一个前哨节点，则列表通过前哨节点循环链接。它可以被概念化为两个由相同数据项组成的单链表，但顺序相反。
 
-![Doubly Linked List](https://upload.wikimedia.org/wikipedia/commons/5/5e/Doubly-linked-list.svg)
+![Doubly Linked List](./images/doubly-linked-list.jpeg)
+
+*Made with [okso.app](https://okso.app)*
 
 两个节点链接允许在任一方向上遍历列表。
 
@@ -29,7 +31,7 @@ Add(value)
   end if
 end Add
 ```
-    
+
 ### 删除
 
 ```text
@@ -66,7 +68,7 @@ Remove(head, value)
   return false
 end Remove
 ```
-    
+
 ### 反向遍历
 
 ```text
@@ -80,7 +82,7 @@ ReverseTraversal(tail)
   end while
 end Reverse Traversal
 ```
-    
+
 ## 复杂度
 
 ## 时间复杂度
diff --git a/src/data-structures/doubly-linked-list/images/doubly-linked-list.jpeg b/src/data-structures/doubly-linked-list/images/doubly-linked-list.jpeg
new file mode 100644
index 0000000000000000000000000000000000000000..99234ce1e582d28648e7802341bab8f7bd33d489
GIT binary patch
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diff --git a/src/data-structures/linked-list/README.es-ES.md b/src/data-structures/linked-list/README.es-ES.md
index 62cda8d14a..c21c48cded 100644
--- a/src/data-structures/linked-list/README.es-ES.md
+++ b/src/data-structures/linked-list/README.es-ES.md
@@ -7,9 +7,9 @@ _Lee este artículo en otros idiomas:_
 [_Português_](README.pt-BR.md)
 [_English_](README.md)
 
-En ciencias de la computaciòn una **lista enlazada** es una  coleccion linear 
+En ciencias de la computaciòn una **lista enlazada** es una  coleccion linear
 de elementos de datos, en los cuales el orden linear no es dado por
-su posciòn fisica en memoria. En cambio, cada 
+su posciòn fisica en memoria. En cambio, cada
 elemento señala al siguiente. Es una estructura de datos
 que consiste en un grupo de nodos los cuales juntos representan
 una secuencia. En su forma más sencilla, cada nodo está
@@ -24,7 +24,9 @@ acceso es lineal (y difícil de canalizar). Un acceso
 más rápido, como un acceso aleatorio, no es factible. Los arreglos
 tienen una mejor locazion en caché comparados con las listas lazadas.
 
-![Linked List](https://upload.wikimedia.org/wikipedia/commons/6/6d/Singly-linked-list.svg)
+![Linked List](./images/linked-list.jpeg)
+
+*Made with [okso.app](https://okso.app)*
 
 ## Pseudocódigo para operaciones básicas
 
diff --git a/src/data-structures/linked-list/README.ja-JP.md b/src/data-structures/linked-list/README.ja-JP.md
index e68b64fa6a..c78997042b 100644
--- a/src/data-structures/linked-list/README.ja-JP.md
+++ b/src/data-structures/linked-list/README.ja-JP.md
@@ -2,7 +2,9 @@
 
 コンピュータサイエンスにおいて、**リンクリスト**はデータ要素の線形コレクションです。要素の順番はメモリ内の物理的な配置によっては決まりません。代わりに、各要素が次の要素を指しています。リンクリストはノードのグループからなるデータ構造です。最も単純な形式では、各ノードはデータとシーケンス内における次のノードへの参照(つまり、リンク)で構成されています。この構造はイテレーションにおいて任意の位置へ要素を効率的に挿入、削除することを可能にしています。より複雑なリンクリストではリンクをさらに追加することで、任意の要素の参照から要素を効率的に挿入、削除することを可能にしています。リンクリストの欠点はアクセスタイムが線形である(そして、パイプライン処理が難しい)ことです。ランダムアクセスのような高速なアクセスは実現不可能です。配列の方がリンクリストと比較して参照の局所性が優れています。
 
-![Linked List](https://upload.wikimedia.org/wikipedia/commons/6/6d/Singly-linked-list.svg)
+![Linked List](./images/linked-list.jpeg)
+
+*Made with [okso.app](https://okso.app)*
 
 ## 基本操作の擬似コード
 
@@ -53,7 +55,7 @@ Contains(head, value)
   return true
 end Contains
 ```
-    
+
 ### 削除
 
 ```text
diff --git a/src/data-structures/linked-list/README.ko-KR.md b/src/data-structures/linked-list/README.ko-KR.md
index a6d0fd4669..f68d8a464d 100644
--- a/src/data-structures/linked-list/README.ko-KR.md
+++ b/src/data-structures/linked-list/README.ko-KR.md
@@ -8,7 +8,9 @@ _Read this in other languages:_
 
 컴퓨터과학에서, **링크드 리스트**는 데이터 요소의 선형 집합이며, 이 집합에서 논리적 저장 순서는 메모리의 물리적 저장 순서와 일치하지 않습니다. 그 대신, 각각의 원소들은 자기 자신 다음의 원소를 가리킵니다. **링크드 리스트**는 순서를 표현하는 노드들의 집합으로 이루어져 있습니다. 간단하게, 각각의 노드들은 데이터와 다음 순서의 노드를 가리키는 레퍼런스로 이루어져 있습니다. (링크라고 부릅니다.) 이 자료구조는 순회하는 동안 순서에 상관없이 효율적인 삽입이나 삭제가 가능합니다. 더 복잡한 변형은 추가적인 링크를 더해, 임의의 원소 참조로부터 효율적인 삽입과 삭제를 가능하게 합니다. 링크드 리스트의 단점은 접근 시간이 선형이라는 것이고, 병렬처리도 하지 못합니다. 임의 접근처럼 빠른 접근은 불가능합니다. 링크드 리스트에 비해 배열이 더 나은 캐시 지역성을 가지고 있습니다.
 
-![링크드 리스트](https://upload.wikimedia.org/wikipedia/commons/6/6d/Singly-linked-list.svg)
+![Linked List](./images/linked-list.jpeg)
+
+*Made with [okso.app](https://okso.app)*
 
 ## 기본 연산에 대한 수도코드
 
@@ -60,7 +62,7 @@ Contains(head, value)
   return true
 end Contains
 ```
-    
+
 ### 삭제
 
 ```text
diff --git a/src/data-structures/linked-list/README.md b/src/data-structures/linked-list/README.md
index d4b9fa53e9..8819a390d3 100644
--- a/src/data-structures/linked-list/README.md
+++ b/src/data-structures/linked-list/README.md
@@ -26,7 +26,9 @@ time is linear (and difficult to pipeline). Faster
 access, such as random access, is not feasible. Arrays
 have better cache locality as compared to linked lists.
 
-![Linked List](https://upload.wikimedia.org/wikipedia/commons/6/6d/Singly-linked-list.svg)
+![Linked List](./images/linked-list.jpeg)
+
+*Made with [okso.app](https://okso.app)*
 
 ## Pseudocode for Basic Operations
 
diff --git a/src/data-structures/linked-list/README.pt-BR.md b/src/data-structures/linked-list/README.pt-BR.md
index 95a244d06f..579a4fce8c 100644
--- a/src/data-structures/linked-list/README.pt-BR.md
+++ b/src/data-structures/linked-list/README.pt-BR.md
@@ -18,7 +18,9 @@ pipeline). Acesso mais rápido, como acesso aleatório, não é viável.
 Arrays possuem uma melhor localização de cache em comparação
 com listas encadeadas (linked lists).
 
-![Linked List](https://upload.wikimedia.org/wikipedia/commons/6/6d/Singly-linked-list.svg)
+![Linked List](./images/linked-list.jpeg)
+
+*Made with [okso.app](https://okso.app)*
 
 ## Pseudo código para Operações Básicas
 
diff --git a/src/data-structures/linked-list/README.ru-RU.md b/src/data-structures/linked-list/README.ru-RU.md
index d76bcd82f9..98ad6c4727 100644
--- a/src/data-structures/linked-list/README.ru-RU.md
+++ b/src/data-structures/linked-list/README.ru-RU.md
@@ -6,7 +6,9 @@
 
 Недостатком связных списков является то, что время доступа линейно (и затруднительно для реализации конвейеров). Быстрый доступ(случайный) невозможен.
 
-![Связный список](https://upload.wikimedia.org/wikipedia/commons/6/6d/Singly-linked-list.svg)
+![Linked List](./images/linked-list.jpeg)
+
+*Made with [okso.app](https://okso.app)*
 
 ## Псевдокод основных операций
 
@@ -57,7 +59,7 @@ Contains(head, value)
   return true
 end Contains
 ```
-    
+
 ### Удаление
 
 ```text
diff --git a/src/data-structures/linked-list/README.tr-TR.md b/src/data-structures/linked-list/README.tr-TR.md
index e3f73fdf63..e5ed05623d 100644
--- a/src/data-structures/linked-list/README.tr-TR.md
+++ b/src/data-structures/linked-list/README.tr-TR.md
@@ -19,7 +19,9 @@ Bağlantılı listelerin bir dezavantajı, erişim süresinin doğrusal olmasıd
 (ve ardışık düzene geçirilmesi zordur). Rastgele erişim gibi daha hızlı erişim
 mümkün değildir. Diziler, bağlantılı listelere kıyasla daha iyi önbellek konumuna sahiptir.
 
-![Bağlantılı Liste](https://upload.wikimedia.org/wikipedia/commons/6/6d/Singly-linked-list.svg)
+![Linked List](./images/linked-list.jpeg)
+
+*Made with [okso.app](https://okso.app)*
 
 ## Temel İşlemler için Sözde Kod
 
diff --git a/src/data-structures/linked-list/README.zh-CN.md b/src/data-structures/linked-list/README.zh-CN.md
index 81f036ab08..f0b75121e7 100644
--- a/src/data-structures/linked-list/README.zh-CN.md
+++ b/src/data-structures/linked-list/README.zh-CN.md
@@ -8,7 +8,9 @@
 
 更快的访问，如随机访问，是不可行的。与链表相比，数组具有更好的缓存位置。
 
-![Linked List](https://upload.wikimedia.org/wikipedia/commons/6/6d/Singly-linked-list.svg)
+![Linked List](./images/linked-list.jpeg)
+
+*Made with [okso.app](https://okso.app)*
 
 ## 基本操作的伪代码
 
@@ -59,7 +61,7 @@ Contains(head, value)
   return true
 end Contains
 ```
-    
+
 ### 删除
 
 ```text
@@ -107,7 +109,7 @@ Traverse(head)
   end while
 end Traverse
 ```
-    
+
 ### 反向遍历
 
 ```text
diff --git a/src/data-structures/linked-list/images/linked-list.jpeg b/src/data-structures/linked-list/images/linked-list.jpeg
new file mode 100644
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From ceb6c858c7442035f65b82578bd7ac1c67d2eba0 Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Tue, 26 Jul 2022 20:59:47 +0200
Subject: [PATCH 185/264] Update image for the Doubly Linked List.

---
 .../images/doubly-linked-list.jpeg            | Bin 115163 -> 109315 bytes
 1 file changed, 0 insertions(+), 0 deletions(-)

diff --git a/src/data-structures/doubly-linked-list/images/doubly-linked-list.jpeg b/src/data-structures/doubly-linked-list/images/doubly-linked-list.jpeg
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From b7017ede9880c29578debc3389a514cbeb188159 Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Wed, 27 Jul 2022 18:25:52 +0200
Subject: [PATCH 186/264] Update Tree image.

---
 src/data-structures/tree/README.md        |  22 ++++++++++++----------
 src/data-structures/tree/README.pt-BR.md  |   4 +++-
 src/data-structures/tree/README.zh-CN.md  |   6 ++++--
 src/data-structures/tree/images/tree.jpeg | Bin 0 -> 60051 bytes
 4 files changed, 19 insertions(+), 13 deletions(-)
 create mode 100644 src/data-structures/tree/images/tree.jpeg

diff --git a/src/data-structures/tree/README.md b/src/data-structures/tree/README.md
index d2d338f434..7eb7ec1db1 100644
--- a/src/data-structures/tree/README.md
+++ b/src/data-structures/tree/README.md
@@ -10,24 +10,26 @@ _Read this in other languages:_
 * [Segment Tree](segment-tree) - with min/max/sum range queries examples
 * [Fenwick Tree](fenwick-tree) (Binary Indexed Tree)
 
-In computer science, a **tree** is a widely used abstract data 
-type (ADT) — or data structure implementing this ADT—that 
-simulates a hierarchical tree structure, with a root value 
-and subtrees of children with a parent node, represented as 
+In computer science, a **tree** is a widely used abstract data
+type (ADT) — or data structure implementing this ADT—that
+simulates a hierarchical tree structure, with a root value
+and subtrees of children with a parent node, represented as
 a set of linked nodes.
 
-A tree data structure can be defined recursively (locally) 
-as a collection of nodes (starting at a root node), where 
-each node is a data structure consisting of a value, 
-together with a list of references to nodes (the "children"), 
-with the constraints that no reference is duplicated, and none 
+A tree data structure can be defined recursively (locally)
+as a collection of nodes (starting at a root node), where
+each node is a data structure consisting of a value,
+together with a list of references to nodes (the "children"),
+with the constraints that no reference is duplicated, and none
 points to the root.
 
 A simple unordered tree; in this diagram, the node labeled 7 has
 two children, labeled 2 and 6, and one parent, labeled 2. The
 root node, at the top, has no parent.
 
-![Tree](https://upload.wikimedia.org/wikipedia/commons/f/f7/Binary_tree.svg)
+![Tree](./images/tree.jpeg)
+
+*Made with [okso.app](https://okso.app)*
 
 ## References
 
diff --git a/src/data-structures/tree/README.pt-BR.md b/src/data-structures/tree/README.pt-BR.md
index 905c419c19..173e096c48 100644
--- a/src/data-structures/tree/README.pt-BR.md
+++ b/src/data-structures/tree/README.pt-BR.md
@@ -22,7 +22,9 @@ Uma árvore não ordenada simples; neste diagrama, o nó rotulado como `7`
 possui dois filhos, rotulados como `2` e `6`, e um pai, rotulado como `2`.
 O nó raíz, no topo, não possui nenhum pai.
 
-![Tree](https://upload.wikimedia.org/wikipedia/commons/f/f7/Binary_tree.svg)
+![Tree](./images/tree.jpeg)
+
+*Made with [okso.app](https://okso.app)*
 
 ## Referências
 
diff --git a/src/data-structures/tree/README.zh-CN.md b/src/data-structures/tree/README.zh-CN.md
index 3188c2b0e2..2f4df983d4 100644
--- a/src/data-structures/tree/README.zh-CN.md
+++ b/src/data-structures/tree/README.zh-CN.md
@@ -13,10 +13,12 @@
 
 一棵简单的无序树; 在下图中:
 
-标记为7的节点具有两个子节点, 标记为2和6; 
+标记为7的节点具有两个子节点, 标记为2和6;
 一个父节点,标记为2,作为根节点, 在顶部,没有父节点。
 
-![Tree](https://upload.wikimedia.org/wikipedia/commons/f/f7/Binary_tree.svg)
+![Tree](./images/tree.jpeg)
+
+*Made with [okso.app](https://okso.app)*
 
 ## 参考
 
diff --git a/src/data-structures/tree/images/tree.jpeg b/src/data-structures/tree/images/tree.jpeg
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From 3d2cfb99b78dde8da9342a47affa8b09b2210b38 Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Fri, 29 Jul 2022 21:47:38 +0200
Subject: [PATCH 187/264] Do

---
 src/data-structures/heap/README.fr-FR.md      |   8 +++-
 src/data-structures/heap/README.ja-JP.md      |   8 +++-
 src/data-structures/heap/README.ko-KR.md      |   8 +++-
 src/data-structures/heap/README.md            |   8 +++-
 src/data-structures/heap/README.pt-BR.md      |   8 +++-
 src/data-structures/heap/README.ru-RU.md      |   8 +++-
 src/data-structures/heap/README.tr-TR.md      |  12 +++--
 src/data-structures/heap/README.zh-CN.md      |  42 ++++++++++--------
 .../heap/images/array-representation.jpeg     | Bin 0 -> 111908 bytes
 src/data-structures/heap/images/max-heap.jpeg | Bin 0 -> 80393 bytes
 src/data-structures/heap/images/min-heap.jpeg | Bin 0 -> 82405 bytes
 11 files changed, 67 insertions(+), 35 deletions(-)
 create mode 100644 src/data-structures/heap/images/array-representation.jpeg
 create mode 100644 src/data-structures/heap/images/max-heap.jpeg
 create mode 100644 src/data-structures/heap/images/min-heap.jpeg

diff --git a/src/data-structures/heap/README.fr-FR.md b/src/data-structures/heap/README.fr-FR.md
index 49ad73cc9f..56f184b593 100644
--- a/src/data-structures/heap/README.fr-FR.md
+++ b/src/data-structures/heap/README.fr-FR.md
@@ -4,11 +4,15 @@ En informatique, un **tas** est une structure de données arborescente spéciali
 
 Dans un *tas minimal* (en anglais *min heap*), si `P` est un nœud parent de `C`, alors la clé (la valeur) de `P` est inférieure ou égale à la clé de `C`.
 
-![MinHeap](https://upload.wikimedia.org/wikipedia/commons/6/69/Min-heap.png)
+![MinHeap](./images/min-heap.jpeg)
+
+*Made with [okso.app](https://okso.app)*
 
 Dans un *tas maximal* (en anglais *max heap*), la clé de `P` est supérieure ou égale à la clé de `C`.
 
-![Heap](https://upload.wikimedia.org/wikipedia/commons/3/38/Max-Heap.svg)
+![MaxHeap](./images/max-heap.jpeg)
+
+![Array Representation](./images/array-representation.jpeg)
 
 Le nœud au «sommet» du tas sans parents est appelé le nœud racine.
 
diff --git a/src/data-structures/heap/README.ja-JP.md b/src/data-structures/heap/README.ja-JP.md
index 465e11a049..13d3e36338 100644
--- a/src/data-structures/heap/README.ja-JP.md
+++ b/src/data-structures/heap/README.ja-JP.md
@@ -4,11 +4,15 @@
 
 *最小ヒープ*では、もし`P`が`C`の親ノードの場合、`P`のキー(値)は`C`のキーより小さい、または等しくなります。
 
-![MinHeap](https://upload.wikimedia.org/wikipedia/commons/6/69/Min-heap.png)
+![MinHeap](./images/min-heap.jpeg)
+
+*Made with [okso.app](https://okso.app)*
 
 *最大ヒープ*では、`P`のキーは`C`のキーより大きい、もしくは等しくなります。
 
-![Heap](https://upload.wikimedia.org/wikipedia/commons/3/38/Max-Heap.svg)
+![MaxHeap](./images/max-heap.jpeg)
+
+![Array Representation](./images/array-representation.jpeg)
 
 ヒープの「トップ」のノードには親ノードが存在せず、ルートノードと呼ばれます。
 
diff --git a/src/data-structures/heap/README.ko-KR.md b/src/data-structures/heap/README.ko-KR.md
index ace702da9e..136a87b420 100644
--- a/src/data-structures/heap/README.ko-KR.md
+++ b/src/data-structures/heap/README.ko-KR.md
@@ -4,11 +4,15 @@
 
 *최소 힙*에서 `P`가 `C`의 상위 노드라면 `P`의 키(값)는 `C`의 키보다 작거나 같습니다.
 
-![MinHeap](https://upload.wikimedia.org/wikipedia/commons/6/69/Min-heap.png)
+![MinHeap](./images/min-heap.jpeg)
+
+*Made with [okso.app](https://okso.app)*
 
 *최대 힙*에서 `P`의 키는 `C`의 키보다 크거나 같습니다.
 
-![Heap](https://upload.wikimedia.org/wikipedia/commons/3/38/Max-Heap.svg)
+![MaxHeap](./images/max-heap.jpeg)
+
+![Array Representation](./images/array-representation.jpeg)
 
 상위 노드가 없는 힙의 "상단"에 있는 노드를 루트 노드라고 합니다.
 
diff --git a/src/data-structures/heap/README.md b/src/data-structures/heap/README.md
index 2610a9ff4a..ef1d2e8b9a 100644
--- a/src/data-structures/heap/README.md
+++ b/src/data-structures/heap/README.md
@@ -17,12 +17,16 @@ In a *min heap*, if `P` is a parent node of `C`, then the
 key (the value) of `P` is less than or equal to the
 key of `C`.
 
-![MinHeap](https://upload.wikimedia.org/wikipedia/commons/6/69/Min-heap.png)
+![MinHeap](./images/min-heap.jpeg)
+
+*Made with [okso.app](https://okso.app)*
 
 In a *max heap*, the key of `P` is greater than or equal
 to the key of `C`
 
-![Heap](https://upload.wikimedia.org/wikipedia/commons/3/38/Max-Heap.svg)
+![MaxHeap](./images/max-heap.jpeg)
+
+![Array Representation](./images/array-representation.jpeg)
 
 The node at the "top" of the heap with no parents is
 called the root node.
diff --git a/src/data-structures/heap/README.pt-BR.md b/src/data-structures/heap/README.pt-BR.md
index e78f6c199a..f229048d3a 100644
--- a/src/data-structures/heap/README.pt-BR.md
+++ b/src/data-structures/heap/README.pt-BR.md
@@ -6,12 +6,16 @@ baseada em uma árvore especializada que satisfaz a propriedade _heap_ descrita
 Em um *heap mínimo* (min heap), caso `P` é um nó pai de `C`, então a chave
 (o valor) de `P` é menor ou igual a chave de `C`.
 
-![MinHeap](https://upload.wikimedia.org/wikipedia/commons/6/69/Min-heap.png)
+![MinHeap](./images/min-heap.jpeg)
+
+*Made with [okso.app](https://okso.app)*
 
 Em uma *heap máximo* (max heap), a chave de `P` é maior ou igual
 a chave de `C`.
 
-![Heap](https://upload.wikimedia.org/wikipedia/commons/3/38/Max-Heap.svg)
+![MaxHeap](./images/max-heap.jpeg)
+
+![Array Representation](./images/array-representation.jpeg)
 
 O nó no "topo" do _heap_, cujo não possui pais, é chamado de nó raiz.
 
diff --git a/src/data-structures/heap/README.ru-RU.md b/src/data-structures/heap/README.ru-RU.md
index 760fc479ab..4c074d1f7c 100644
--- a/src/data-structures/heap/README.ru-RU.md
+++ b/src/data-structures/heap/README.ru-RU.md
@@ -4,11 +4,15 @@
 если B является узлом-потомком узла A, то ключ(A) ≥ ключ(B). Из этого следует, что элемент с наибольшим ключом всегда
 является корневым узлом кучи, поэтому иногда такие кучи называют max-кучами.
 
-![Max-куча](https://upload.wikimedia.org/wikipedia/commons/3/38/Max-Heap.svg)
+![MaxHeap](./images/max-heap.jpeg)
+
+![Array Representation](./images/array-representation.jpeg)
 
 Если сравнение перевернуть, то наименьший элемент будет всегда корневым узлом, такие кучи называют min-кучами.
 
-![Min-куча](https://upload.wikimedia.org/wikipedia/commons/6/69/Min-heap.png)
+![MinHeap](./images/min-heap.jpeg)
+
+*Made with [okso.app](https://okso.app)*
 
 Не существует никаких ограничений относительно того, сколько узлов-потомков имеет каждый узел кучи. На практике их
 число обычно не более двух. Куча является максимально эффективной реализацией абстрактного типа данных, который
diff --git a/src/data-structures/heap/README.tr-TR.md b/src/data-structures/heap/README.tr-TR.md
index b741ef305c..05906391e8 100644
--- a/src/data-structures/heap/README.tr-TR.md
+++ b/src/data-structures/heap/README.tr-TR.md
@@ -4,15 +4,19 @@ Bilgisayar biliminde, **yığın (heap)** aşağıda açıklanan özellikleri ka
 
 *min heap*, Eğer `P`, `C`'nin üst düğümü ise, `P`'nin anahtarı (değeri)  `C`'nin anahtarından (değerinden) küçük veya ona eşittir.
 
-![MinHeap](https://upload.wikimedia.org/wikipedia/commons/6/69/Min-heap.png)
+![MinHeap](./images/min-heap.jpeg)
 
-*max heap*, `P`'nin anahtarı `C`'nin anahtarından büyük veya eşittir. 
+*Made with [okso.app](https://okso.app)*
 
-![Heap](https://upload.wikimedia.org/wikipedia/commons/3/38/Max-Heap.svg)
+*max heap*, `P`'nin anahtarı `C`'nin anahtarından büyük veya eşittir.
+
+![MaxHeap](./images/max-heap.jpeg)
+
+![Array Representation](./images/array-representation.jpeg)
 
 Yığının (Heap) "en üstündeki" ebeveyni olmayan düğüme kök düğüm (root node) denir.
 
 ## Referanslar
 
 - [Wikipedia](https://en.wikipedia.org/wiki/Heap_(data_structure))
-- [YouTube](https://www.youtube.com/watch?v=t0Cq6tVNRBA&index=5&t=0s&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
\ No newline at end of file
+- [YouTube](https://www.youtube.com/watch?v=t0Cq6tVNRBA&index=5&t=0s&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
diff --git a/src/data-structures/heap/README.zh-CN.md b/src/data-structures/heap/README.zh-CN.md
index 4c1ecaf068..8ba42dfb05 100644
--- a/src/data-structures/heap/README.zh-CN.md
+++ b/src/data-structures/heap/README.zh-CN.md
@@ -1,19 +1,23 @@
-# 堆 (数据结构)
-
-在计算机科学中, 一个 **堆(heap)** 是一种特殊的基于树的数据结构，它满足下面描述的堆属性。
-
-在一个 *最小堆(min heap)* 中, 如果 `P` 是 `C` 的一个父级节点, 那么 `P`  的key(或value)应小于或等于 `C` 的对应值.
-
-![最小堆](https://upload.wikimedia.org/wikipedia/commons/6/69/Min-heap.png)
-
-在一个  *最大堆(max heap)* 中,  `P` 的key(或value)大于 `C` 的对应值。
-
-![堆](https://upload.wikimedia.org/wikipedia/commons/3/38/Max-Heap.svg)
-
-
-在堆“顶部”的没有父级节点的节点,被称之为根节点。
-
-## 参考
-
-- [Wikipedia](https://en.wikipedia.org/wiki/Heap_(data_structure))
-- [YouTube](https://www.youtube.com/watch?v=t0Cq6tVNRBA&index=5&t=0s&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
+# 堆 (数据结构)
+
+在计算机科学中, 一个 **堆(heap)** 是一种特殊的基于树的数据结构，它满足下面描述的堆属性。
+
+在一个 *最小堆(min heap)* 中, 如果 `P` 是 `C` 的一个父级节点, 那么 `P`  的key(或value)应小于或等于 `C` 的对应值.
+
+![M最小堆](./images/min-heap.jpeg)
+
+*Made with [okso.app](https://okso.app)*
+
+在一个  *最大堆(max heap)* 中,  `P` 的key(或value)大于 `C` 的对应值。
+
+![堆](./images/max-heap.jpeg)
+
+![Array Representation](./images/array-representation.jpeg)
+
+
+在堆“顶部”的没有父级节点的节点,被称之为根节点。
+
+## 参考
+
+- [Wikipedia](https://en.wikipedia.org/wiki/Heap_(data_structure))
+- [YouTube](https://www.youtube.com/watch?v=t0Cq6tVNRBA&index=5&t=0s&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
diff --git a/src/data-structures/heap/images/array-representation.jpeg b/src/data-structures/heap/images/array-representation.jpeg
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HcmV?d00001


From ac31c913b2c62582430e6de41826300062338eb6 Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Thu, 11 Aug 2022 16:34:05 +0200
Subject: [PATCH 188/264] Update Graph image.

---
 src/data-structures/graph/README.fr-FR.md   |  22 +++++++++--------
 src/data-structures/graph/README.md         |  26 +++++++++++---------
 src/data-structures/graph/README.pt-BR.md   |   4 ++-
 src/data-structures/graph/README.ru-RU.md   |   6 +++--
 src/data-structures/graph/README.zh-CN.md   |   4 +--
 src/data-structures/graph/images/graph.jpeg | Bin 0 -> 135330 bytes
 6 files changed, 35 insertions(+), 27 deletions(-)
 create mode 100644 src/data-structures/graph/images/graph.jpeg

diff --git a/src/data-structures/graph/README.fr-FR.md b/src/data-structures/graph/README.fr-FR.md
index 48d3ccd766..c6a6c90892 100644
--- a/src/data-structures/graph/README.fr-FR.md
+++ b/src/data-structures/graph/README.fr-FR.md
@@ -1,23 +1,25 @@
 # Graph
 
 En informatique, un **graphe** est une structure de
-données abstraite qui implémente les concepts de 
+données abstraite qui implémente les concepts de
 graphe orienté et de graphe non-orienté venant
 des mathématiques, plus précisément du domaine de
 la théorie des graphes.
 
-La structure de données abstraite de graphe consiste 
-en un ensemble fini, éventuellement mutable de sommets 
-ou nœuds ou points, avec un ensemble de paires ordonnées 
-ou non de tels éléments. Ces paires sont des arêtes, arcs 
+La structure de données abstraite de graphe consiste
+en un ensemble fini, éventuellement mutable de sommets
+ou nœuds ou points, avec un ensemble de paires ordonnées
+ou non de tels éléments. Ces paires sont des arêtes, arcs
 non orientés, ou lignes pour un graphe non orienté, et
-flèches, arêtes orientées , arcs, ou lignes orientées 
-dans le cas orienté. Les sommets peuvent faire partie 
-de la structure, ou être des entités extérieures, 
+flèches, arêtes orientées , arcs, ou lignes orientées
+dans le cas orienté. Les sommets peuvent faire partie
+de la structure, ou être des entités extérieures,
 représentées par des entiers ou des références.
 
-![Graph](https://www.tutorialspoint.com/data_structures_algorithms/images/graph.jpg)
+![Graph](./images/graph.jpeg)
+
+*Made with [okso.app](https://okso.app)*
 
 ## References
 
-- [Wikipedia](https://fr.wikipedia.org/wiki/Graphe_(type_abstrait))
\ No newline at end of file
+- [Wikipedia](https://fr.wikipedia.org/wiki/Graphe_(type_abstrait))
diff --git a/src/data-structures/graph/README.md b/src/data-structures/graph/README.md
index 2c8602d94a..9930053772 100644
--- a/src/data-structures/graph/README.md
+++ b/src/data-structures/graph/README.md
@@ -6,23 +6,25 @@ _Read this in other languages:_
 [_Français_](README.fr-FR.md),
 [_Português_](README.pt-BR.md)
 
-In computer science, a **graph** is an abstract data type 
-that is meant to implement the undirected graph and 
+In computer science, a **graph** is an abstract data type
+that is meant to implement the undirected graph and
 directed graph concepts from mathematics, specifically
 the field of graph theory
 
-A graph data structure consists of a finite (and possibly 
-mutable) set of vertices or nodes or points, together 
-with a set of unordered pairs of these vertices for an 
-undirected graph or a set of ordered pairs for a 
-directed graph. These pairs are known as edges, arcs, 
-or lines for an undirected graph and as arrows, 
-directed edges, directed arcs, or directed lines 
-for a directed graph. The vertices may be part of 
-the graph structure, or may be external entities 
+A graph data structure consists of a finite (and possibly
+mutable) set of vertices or nodes or points, together
+with a set of unordered pairs of these vertices for an
+undirected graph or a set of ordered pairs for a
+directed graph. These pairs are known as edges, arcs,
+or lines for an undirected graph and as arrows,
+directed edges, directed arcs, or directed lines
+for a directed graph. The vertices may be part of
+the graph structure, or may be external entities
 represented by integer indices or references.
 
-![Graph](https://www.tutorialspoint.com/data_structures_algorithms/images/graph.jpg)
+![Graph](./images/graph.jpeg)
+
+*Made with [okso.app](https://okso.app)*
 
 ## References
 
diff --git a/src/data-structures/graph/README.pt-BR.md b/src/data-structures/graph/README.pt-BR.md
index 194a4eb04c..de7947cba8 100644
--- a/src/data-structures/graph/README.pt-BR.md
+++ b/src/data-structures/graph/README.pt-BR.md
@@ -17,7 +17,9 @@ para um grafo direcionado.
 Os vértices podem fazer parte a estrutura do grafo, ou podem
 ser entidades externas representadas por índices inteiros ou referências.
 
-![Graph](https://www.tutorialspoint.com/data_structures_algorithms/images/graph.jpg)
+![Graph](./images/graph.jpeg)
+
+*Made with [okso.app](https://okso.app)*
 
 ## Referências
 
diff --git a/src/data-structures/graph/README.ru-RU.md b/src/data-structures/graph/README.ru-RU.md
index 2f656730c2..950198451b 100644
--- a/src/data-structures/graph/README.ru-RU.md
+++ b/src/data-structures/graph/README.ru-RU.md
@@ -3,7 +3,7 @@
 **Граф** в информатике - абстрактный тип данных, который должен реализовывать концепции направленного и ненаправленного
 графа в математике, особенно в области теории графов.
 
-Структура данных графа состоит из конечного (и возможно изменяющегося) набора вершин или узлов, или точек, совместно с 
+Структура данных графа состоит из конечного (и возможно изменяющегося) набора вершин или узлов, или точек, совместно с
 набором ненаправленных пар этих вершин для ненаправленного графа или с набором направленных пар для направленного графа.
 Эти пары известны как рёбра, арки или линии для ненаправленного графа и как стрелки, направленные рёбра, направленные
 арки или направленные линии для направленного графа. Эти вершины могут быть частью структуры графа, или внешними
@@ -14,7 +14,9 @@
 информатике, могут быть представлены графами. Например, строение Википедии можно смоделировать при помощи
 ориентированного графа, в котором вершины — это статьи, а дуги (ориентированные рёбра) — гиперссылки.
 
-![Граф](https://www.tutorialspoint.com/data_structures_algorithms/images/graph.jpg)
+![Граф](./images/graph.jpeg)
+
+*Made with [okso.app](https://okso.app)*
 
 ## Ссылки
 
diff --git a/src/data-structures/graph/README.zh-CN.md b/src/data-structures/graph/README.zh-CN.md
index 49c977157e..1f885a43b9 100644
--- a/src/data-structures/graph/README.zh-CN.md
+++ b/src/data-structures/graph/README.zh-CN.md
@@ -11,9 +11,9 @@
 
 如果顶点对之间的边是有权重的,该图可称为加权图。
 
+![Graph](./images/graph.jpeg)
 
-
-![Graph](https://www.tutorialspoint.com/data_structures_algorithms/images/graph.jpg)
+*Made with [okso.app](https://okso.app)*
 
 ## 参考
 
diff --git a/src/data-structures/graph/images/graph.jpeg b/src/data-structures/graph/images/graph.jpeg
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From 18fcead0dcceeb9b91edfe0ae84e559a085a04cb Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Thu, 11 Aug 2022 17:26:11 +0200
Subject: [PATCH 189/264] Update Hash Table image.

---
 src/data-structures/hash-table/README.fr-FR.md |   4 +++-
 src/data-structures/hash-table/README.ja-JP.md |   6 ++++--
 src/data-structures/hash-table/README.ko-KR.md |   6 ++++--
 src/data-structures/hash-table/README.md       |   4 +++-
 src/data-structures/hash-table/README.pt-BR.md |   4 +++-
 src/data-structures/hash-table/README.ru-RU.md |   8 ++++++--
 src/data-structures/hash-table/README.zh-CN.md |   6 ++++--
 .../hash-table/images/hash-table.jpeg          | Bin 0 -> 168634 bytes
 8 files changed, 27 insertions(+), 11 deletions(-)
 create mode 100644 src/data-structures/hash-table/images/hash-table.jpeg

diff --git a/src/data-structures/hash-table/README.fr-FR.md b/src/data-structures/hash-table/README.fr-FR.md
index f32d8e5624..3dd176305b 100644
--- a/src/data-structures/hash-table/README.fr-FR.md
+++ b/src/data-structures/hash-table/README.fr-FR.md
@@ -17,7 +17,9 @@ hachage où la fonction de hachage génère le même index
 pour plusieurs clés. De telles collisions doivent être
 accommodées d'une manière ou d'une autre.
 
-![Hash Table](https://upload.wikimedia.org/wikipedia/commons/7/7d/Hash_table_3_1_1_0_1_0_0_SP.svg)
+![Hash Table](./images/hash-table.jpeg)
+
+*Made with [okso.app](https://okso.app)*
 
 Collision de hachage résolue par chaînage séparé.
 
diff --git a/src/data-structures/hash-table/README.ja-JP.md b/src/data-structures/hash-table/README.ja-JP.md
index 85bf71d19c..e73ed01207 100644
--- a/src/data-structures/hash-table/README.ja-JP.md
+++ b/src/data-structures/hash-table/README.ja-JP.md
@@ -1,10 +1,12 @@
 # ハッシュテーブル
- 
+
 コンピュータサイエンスにおいて、**ハッシュテーブル**（ハッシュマップ)は*キーを値にマッピング*できる*連想配列*の機能を持ったデータ構造です。ハッシュテーブルは*ハッシュ関数*を使ってバケットやスロットの配列へのインデックスを計算し、そこから目的の値を見つけることができます。
 
 理想的には、ハッシュ関数は各キーを一意のバケットに割り当てますが、ほとんどのハッシュテーブルは不完全なハッシュ関数を採用しているため、複数のキーに対して同じインデックスを生成した時にハッシュの衝突が起こります。このような衝突は何らかの方法で対処する必要があります。
 
-![Hash Table](https://upload.wikimedia.org/wikipedia/commons/7/7d/Hash_table_3_1_1_0_1_0_0_SP.svg)
+![Hash Table](./images/hash-table.jpeg)
+
+*Made with [okso.app](https://okso.app)*
 
 チェイン法によるハッシュの衝突の解決例
 
diff --git a/src/data-structures/hash-table/README.ko-KR.md b/src/data-structures/hash-table/README.ko-KR.md
index 0b847df5ca..b7d13d6c28 100644
--- a/src/data-structures/hash-table/README.ko-KR.md
+++ b/src/data-structures/hash-table/README.ko-KR.md
@@ -11,7 +11,9 @@ _Read this in other languages:_
 
 이상적으로, 해시 함수는 각 키들을 고유 버킷에 할당하지만 대부분의 해시 테이블은 불완전한 해시 함수를 사용하기 때문에 해시 함수를 통해 두 개 이상의 키에 대해 동일한 인덱스를 생성하는 해시 충돌이 발생할 수 있습니다. 이러한 해시 충돌은 어떠한 방법으로든 해결되어야 합니다.
 
-![Hash Table](https://upload.wikimedia.org/wikipedia/commons/7/7d/Hash_table_3_1_1_0_1_0_0_SP.svg)
+![Hash Table](./images/hash-table.jpeg)
+
+*Made with [okso.app](https://okso.app)*
 
 다음은 분리 연결법을 통해 해시 충돌을 해결한 예시입니다.
 
@@ -20,4 +22,4 @@ _Read this in other languages:_
 ## 참고
 
 - [Wikipedia](https://en.wikipedia.org/wiki/Hash_table)
-- [YouTube](https://www.youtube.com/watch?v=shs0KM3wKv8&index=4&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
\ No newline at end of file
+- [YouTube](https://www.youtube.com/watch?v=shs0KM3wKv8&index=4&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
diff --git a/src/data-structures/hash-table/README.md b/src/data-structures/hash-table/README.md
index 3aec51b5c2..42c4a8dd3c 100644
--- a/src/data-structures/hash-table/README.md
+++ b/src/data-structures/hash-table/README.md
@@ -22,7 +22,9 @@ collisions where the hash function generates the same
 index for more than one key. Such collisions must be
 accommodated in some way.
 
-![Hash Table](https://upload.wikimedia.org/wikipedia/commons/7/7d/Hash_table_3_1_1_0_1_0_0_SP.svg)
+![Hash Table](./images/hash-table.jpeg)
+
+*Made with [okso.app](https://okso.app)*
 
 Hash collision resolved by separate chaining.
 
diff --git a/src/data-structures/hash-table/README.pt-BR.md b/src/data-structures/hash-table/README.pt-BR.md
index 0adf9ca96b..6a9b660c21 100644
--- a/src/data-structures/hash-table/README.pt-BR.md
+++ b/src/data-structures/hash-table/README.pt-BR.md
@@ -13,7 +13,9 @@ imperfeita, pela qual poderá causar colisões de hashes onde a função de hash
 gera o mesmo índice para mais de uma chave.Tais colisões devem ser
 acomodados de alguma forma.
 
-![Hash Table](https://upload.wikimedia.org/wikipedia/commons/7/7d/Hash_table_3_1_1_0_1_0_0_SP.svg)
+![Hash Table](./images/hash-table.jpeg)
+
+*Made with [okso.app](https://okso.app)*
 
 Colisão de hash resolvida por encadeamento separado.
 
diff --git a/src/data-structures/hash-table/README.ru-RU.md b/src/data-structures/hash-table/README.ru-RU.md
index 1b829049ab..513f403824 100644
--- a/src/data-structures/hash-table/README.ru-RU.md
+++ b/src/data-structures/hash-table/README.ru-RU.md
@@ -2,10 +2,12 @@
 
 **Хеш-таблица** - структура данных, реализующая абстрактный тип данных *ассоциативный массив*, т.е. структура, которая
 *связывает ключи со значениями*. Хеш-таблица использует *хеш-функцию* для вычисления индекса в массиве, в котором может
-быть найдено желаемое значение. Ниже представлена хеш-таблица, в которой ключом выступает имя человека, а значениями 
+быть найдено желаемое значение. Ниже представлена хеш-таблица, в которой ключом выступает имя человека, а значениями
 являются телефонные номера. Хеш-функция преобразует ключ-имя в индекс массива с телефонными номерами.
 
-![Хеш-таблица](https://upload.wikimedia.org/wikipedia/commons/7/7d/Hash_table_3_1_1_0_1_0_0_SP.svg)
+![Hash Table](./images/hash-table.jpeg)
+
+*Made with [okso.app](https://okso.app)*
 
 В идеале хеш-функция будет присваивать элементу массива уникальный ключ. Однако большинство реальных хеш-таблиц
 используют несовершенные хеш-функции. Это может привести к ситуациям, когда хеш-функция генерирует одинаковый индекс для
@@ -14,9 +16,11 @@
 Существует два варианта решения коллизий - хеш-таблица с цепочками и с открытой адресацией.
 
 Метод цепочек подразумевает хранение значений, соответствующих одному и тому же индексу в виде связного списка(цепочки).
+
 ![Хеш цепочки](https://upload.wikimedia.org/wikipedia/commons/d/d0/Hash_table_5_0_1_1_1_1_1_LL.svg)
 
 Метод открытой адресации помещает значение, для которого получен дублирующий индекс, в первую свободную ячейку.
+
 ![Хеш открытая адресация](https://upload.wikimedia.org/wikipedia/commons/thumb/b/bf/Hash_table_5_0_1_1_1_1_0_SP.svg/380px-Hash_table_5_0_1_1_1_1_0_SP.svg.png)
 
 ## Ссылки
diff --git a/src/data-structures/hash-table/README.zh-CN.md b/src/data-structures/hash-table/README.zh-CN.md
index f9219df8df..3170283d59 100644
--- a/src/data-structures/hash-table/README.zh-CN.md
+++ b/src/data-structures/hash-table/README.zh-CN.md
@@ -1,6 +1,6 @@
 # 哈希表
 
-在计算中, 一个  **哈希表(hash table 或hash map)**  是一种实现 *关联数组(associative array)* 
+在计算中, 一个  **哈希表(hash table 或hash map)**  是一种实现 *关联数组(associative array)*
 的抽象数据类型, 该结构可以将 *键映射到值*。
 
 哈希表使用 *哈希函数/散列函数* 来计算一个值在数组或桶(buckets)中或槽(slots)中对应的索引,可使用该索引找到所需的值。
@@ -9,7 +9,9 @@
 以某种方式进行处理。
 
 
-![Hash Table](https://upload.wikimedia.org/wikipedia/commons/7/7d/Hash_table_3_1_1_0_1_0_0_SP.svg)
+![Hash Table](./images/hash-table.jpeg)
+
+*Made with [okso.app](https://okso.app)*
 
 通过单独的链接解决哈希冲突
 
diff --git a/src/data-structures/hash-table/images/hash-table.jpeg b/src/data-structures/hash-table/images/hash-table.jpeg
new file mode 100644
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HcmV?d00001


From 21b72902f0914269a60288e7f204d4ac32784297 Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Fri, 12 Aug 2022 20:45:10 +0200
Subject: [PATCH 190/264] Update Hash Table image.

---
 src/data-structures/hash-table/README.fr-FR.md |   6 +++---
 src/data-structures/hash-table/README.ja-JP.md |   6 +++---
 src/data-structures/hash-table/README.ko-KR.md |   4 +++-
 src/data-structures/hash-table/README.md       |   6 +++---
 src/data-structures/hash-table/README.pt-BR.md |   6 +++---
 src/data-structures/hash-table/README.ru-RU.md |   6 +++---
 src/data-structures/hash-table/README.zh-CN.md |   4 +++-
 .../images/collision-resolution.jpeg           | Bin 0 -> 288967 bytes
 8 files changed, 21 insertions(+), 17 deletions(-)
 create mode 100644 src/data-structures/hash-table/images/collision-resolution.jpeg

diff --git a/src/data-structures/hash-table/README.fr-FR.md b/src/data-structures/hash-table/README.fr-FR.md
index 3dd176305b..2fd41c8838 100644
--- a/src/data-structures/hash-table/README.fr-FR.md
+++ b/src/data-structures/hash-table/README.fr-FR.md
@@ -19,11 +19,11 @@ accommodées d'une manière ou d'une autre.
 
 ![Hash Table](./images/hash-table.jpeg)
 
-*Made with [okso.app](https://okso.app)*
-
 Collision de hachage résolue par chaînage séparé.
 
-![Hash Collision](https://upload.wikimedia.org/wikipedia/commons/d/d0/Hash_table_5_0_1_1_1_1_1_LL.svg)
+![Hash Collision](./images/collision-resolution.jpeg)
+
+*Made with [okso.app](https://okso.app)*
 
 ## Références
 
diff --git a/src/data-structures/hash-table/README.ja-JP.md b/src/data-structures/hash-table/README.ja-JP.md
index e73ed01207..d71cb273b9 100644
--- a/src/data-structures/hash-table/README.ja-JP.md
+++ b/src/data-structures/hash-table/README.ja-JP.md
@@ -6,11 +6,11 @@
 
 ![Hash Table](./images/hash-table.jpeg)
 
-*Made with [okso.app](https://okso.app)*
-
 チェイン法によるハッシュの衝突の解決例
 
-![Hash Collision](https://upload.wikimedia.org/wikipedia/commons/d/d0/Hash_table_5_0_1_1_1_1_1_LL.svg)
+![Hash Collision](./images/collision-resolution.jpeg)
+
+*Made with [okso.app](https://okso.app)*
 
 ## 参考
 
diff --git a/src/data-structures/hash-table/README.ko-KR.md b/src/data-structures/hash-table/README.ko-KR.md
index b7d13d6c28..b3a8c94066 100644
--- a/src/data-structures/hash-table/README.ko-KR.md
+++ b/src/data-structures/hash-table/README.ko-KR.md
@@ -17,7 +17,9 @@ _Read this in other languages:_
 
 다음은 분리 연결법을 통해 해시 충돌을 해결한 예시입니다.
 
-![Hash Collision](https://upload.wikimedia.org/wikipedia/commons/d/d0/Hash_table_5_0_1_1_1_1_1_LL.svg)
+![Hash Collision](./images/collision-resolution.jpeg)
+
+*Made with [okso.app](https://okso.app)*
 
 ## 참고
 
diff --git a/src/data-structures/hash-table/README.md b/src/data-structures/hash-table/README.md
index 42c4a8dd3c..8711bd9b49 100644
--- a/src/data-structures/hash-table/README.md
+++ b/src/data-structures/hash-table/README.md
@@ -24,11 +24,11 @@ accommodated in some way.
 
 ![Hash Table](./images/hash-table.jpeg)
 
-*Made with [okso.app](https://okso.app)*
-
 Hash collision resolved by separate chaining.
 
-![Hash Collision](https://upload.wikimedia.org/wikipedia/commons/d/d0/Hash_table_5_0_1_1_1_1_1_LL.svg)
+![Hash Collision](./images/collision-resolution.jpeg)
+
+*Made with [okso.app](https://okso.app)*
 
 ## References
 
diff --git a/src/data-structures/hash-table/README.pt-BR.md b/src/data-structures/hash-table/README.pt-BR.md
index 6a9b660c21..9abbb48890 100644
--- a/src/data-structures/hash-table/README.pt-BR.md
+++ b/src/data-structures/hash-table/README.pt-BR.md
@@ -15,11 +15,11 @@ acomodados de alguma forma.
 
 ![Hash Table](./images/hash-table.jpeg)
 
-*Made with [okso.app](https://okso.app)*
-
 Colisão de hash resolvida por encadeamento separado.
 
-![Hash Collision](https://upload.wikimedia.org/wikipedia/commons/d/d0/Hash_table_5_0_1_1_1_1_1_LL.svg)
+![Hash Collision](./images/collision-resolution.jpeg)
+
+*Made with [okso.app](https://okso.app)*
 
 ## Referências
 
diff --git a/src/data-structures/hash-table/README.ru-RU.md b/src/data-structures/hash-table/README.ru-RU.md
index 513f403824..4f17d93f52 100644
--- a/src/data-structures/hash-table/README.ru-RU.md
+++ b/src/data-structures/hash-table/README.ru-RU.md
@@ -7,8 +7,6 @@
 
 ![Hash Table](./images/hash-table.jpeg)
 
-*Made with [okso.app](https://okso.app)*
-
 В идеале хеш-функция будет присваивать элементу массива уникальный ключ. Однако большинство реальных хеш-таблиц
 используют несовершенные хеш-функции. Это может привести к ситуациям, когда хеш-функция генерирует одинаковый индекс для
 нескольких ключей. Данные ситуации называются коллизиями и должны быть как-то разрешены.
@@ -21,7 +19,9 @@
 
 Метод открытой адресации помещает значение, для которого получен дублирующий индекс, в первую свободную ячейку.
 
-![Хеш открытая адресация](https://upload.wikimedia.org/wikipedia/commons/thumb/b/bf/Hash_table_5_0_1_1_1_1_0_SP.svg/380px-Hash_table_5_0_1_1_1_1_0_SP.svg.png)
+![Hash Collision](./images/collision-resolution.jpeg)
+
+*Made with [okso.app](https://okso.app)*
 
 ## Ссылки
 
diff --git a/src/data-structures/hash-table/README.zh-CN.md b/src/data-structures/hash-table/README.zh-CN.md
index 3170283d59..c53214aa88 100644
--- a/src/data-structures/hash-table/README.zh-CN.md
+++ b/src/data-structures/hash-table/README.zh-CN.md
@@ -15,7 +15,9 @@
 
 通过单独的链接解决哈希冲突
 
-![Hash Collision](https://upload.wikimedia.org/wikipedia/commons/d/d0/Hash_table_5_0_1_1_1_1_1_LL.svg)
+![Hash Collision](./images/collision-resolution.jpeg)
+
+*Made with [okso.app](https://okso.app)*
 
 ## 参考
 
diff --git a/src/data-structures/hash-table/images/collision-resolution.jpeg b/src/data-structures/hash-table/images/collision-resolution.jpeg
new file mode 100644
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HcmV?d00001


From ad2f49af381e8ae9c8403b7d8d0244b260f09cc1 Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Fri, 12 Aug 2022 20:58:53 +0200
Subject: [PATCH 191/264] Update Hash Table image.

---
 .../hash-table/README.ru-RU.md                |   8 ++++----
 .../images/collision-resolution.jpeg          | Bin 288967 -> 281785 bytes
 2 files changed, 4 insertions(+), 4 deletions(-)

diff --git a/src/data-structures/hash-table/README.ru-RU.md b/src/data-structures/hash-table/README.ru-RU.md
index 4f17d93f52..e1e21129da 100644
--- a/src/data-structures/hash-table/README.ru-RU.md
+++ b/src/data-structures/hash-table/README.ru-RU.md
@@ -15,14 +15,14 @@
 
 Метод цепочек подразумевает хранение значений, соответствующих одному и тому же индексу в виде связного списка(цепочки).
 
-![Хеш цепочки](https://upload.wikimedia.org/wikipedia/commons/d/d0/Hash_table_5_0_1_1_1_1_1_LL.svg)
-
-Метод открытой адресации помещает значение, для которого получен дублирующий индекс, в первую свободную ячейку.
-
 ![Hash Collision](./images/collision-resolution.jpeg)
 
 *Made with [okso.app](https://okso.app)*
 
+Метод открытой адресации помещает значение, для которого получен дублирующий индекс, в первую свободную ячейку.
+
+![Хеш открытая адресация](https://upload.wikimedia.org/wikipedia/commons/thumb/b/bf/Hash_table_5_0_1_1_1_1_0_SP.svg/380px-Hash_table_5_0_1_1_1_1_0_SP.svg.png)
+
 ## Ссылки
 
 - [Wikipedia](https://ru.wikipedia.org/wiki/%D0%A5%D0%B5%D1%88-%D1%82%D0%B0%D0%B1%D0%BB%D0%B8%D1%86%D0%B0)
diff --git a/src/data-structures/hash-table/images/collision-resolution.jpeg b/src/data-structures/hash-table/images/collision-resolution.jpeg
index 5bc2bed752529cb92feaa8e951333ae8d7be4a28..c693a52d786168a0b2a01013d3dbc51bdefffb2b 100644
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From 28109b4f416dabda7da5b34a6046e6c1a7a6dbd1 Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Fri, 19 Aug 2022 19:07:38 +0200
Subject: [PATCH 192/264] Update Trie image.

---
 src/data-structures/trie/README.md       |  26 ++++++++++++-----------
 src/data-structures/trie/README.pt-BR.md |   6 ++++--
 src/data-structures/trie/README.ru-RU.md |   4 +++-
 src/data-structures/trie/README.zh-CN.md |   6 ++++--
 src/data-structures/trie/images/trie.jpg | Bin 0 -> 134559 bytes
 5 files changed, 25 insertions(+), 17 deletions(-)
 create mode 100644 src/data-structures/trie/images/trie.jpg

diff --git a/src/data-structures/trie/README.md b/src/data-structures/trie/README.md
index d07c69feb1..f6f38ece09 100644
--- a/src/data-structures/trie/README.md
+++ b/src/data-structures/trie/README.md
@@ -5,22 +5,24 @@ _Read this in other languages:_
 [_Русский_](README.ru-RU.md),
 [_Português_](README.pt-BR.md)
 
-In computer science, a **trie**, also called digital tree and sometimes 
-radix tree or prefix tree (as they can be searched by prefixes), 
-is a kind of search tree—an ordered tree data structure that is 
-used to store a dynamic set or associative array where the keys 
-are usually strings. Unlike a binary search tree, no node in the 
-tree stores the key associated with that node; instead, its 
+In computer science, a **trie**, also called digital tree and sometimes
+radix tree or prefix tree (as they can be searched by prefixes),
+is a kind of search tree—an ordered tree data structure that is
+used to store a dynamic set or associative array where the keys
+are usually strings. Unlike a binary search tree, no node in the
+tree stores the key associated with that node; instead, its
 position in the tree defines the key with which it is associated.
 All the descendants of a node have a common prefix of the string
-associated with that node, and the root is associated with the 
-empty string. Values are not necessarily associated with every 
-node. Rather, values tend only to be associated with leaves, 
-and with some inner nodes that correspond to keys of interest. 
-For the space-optimized presentation of prefix tree, see compact 
+associated with that node, and the root is associated with the
+empty string. Values are not necessarily associated with every
+node. Rather, values tend only to be associated with leaves,
+and with some inner nodes that correspond to keys of interest.
+For the space-optimized presentation of prefix tree, see compact
 prefix tree.
 
-![Trie](https://upload.wikimedia.org/wikipedia/commons/b/be/Trie_example.svg)
+![Trie](./images/trie.jpg)
+
+*Made with [okso.app](https://okso.app)*
 
 ## References
 
diff --git a/src/data-structures/trie/README.pt-BR.md b/src/data-structures/trie/README.pt-BR.md
index 7a1415814d..b0d49de1e1 100644
--- a/src/data-structures/trie/README.pt-BR.md
+++ b/src/data-structures/trie/README.pt-BR.md
@@ -3,7 +3,7 @@
 Na ciência da computação, uma **trie**, também chamada de árvore digital (digital tree)
 e algumas vezes de _radix tree_ ou _prefix tree_ (tendo em vista que eles
 podem ser pesquisados por prefixos), é um tipo de árvore de pesquisa, uma
-uma estrutura de dados de árvore ordenada que é usado para armazenar um 
+uma estrutura de dados de árvore ordenada que é usado para armazenar um
 conjunto dinâmico ou matriz associativa onde as chaves são geralmente _strings_.
 Ao contrário de uma árvore de pesquisa binária (binary search tree),
 nenhum nó na árvore armazena a chave associada a esse nó; em vez disso,
@@ -17,7 +17,9 @@ internos que correspondem a chaves de interesse.
 Para a apresentação otimizada do espaço da árvore de prefixo (_prefix tree_),
 veja árvore de prefixo compacto.
 
-![Trie](https://upload.wikimedia.org/wikipedia/commons/b/be/Trie_example.svg)
+![Trie](./images/trie.jpg)
+
+*Made with [okso.app](https://okso.app)*
 
 ## Referências
 
diff --git a/src/data-structures/trie/README.ru-RU.md b/src/data-structures/trie/README.ru-RU.md
index f447f8eb0e..30a4536383 100644
--- a/src/data-structures/trie/README.ru-RU.md
+++ b/src/data-structures/trie/README.ru-RU.md
@@ -16,7 +16,9 @@
 дополнительную информацию, связанную с ключом, и обычно выделенными являются только листья и, возможно, некоторые
 внутренние узлы.
 
-![Префиксное дерево](https://upload.wikimedia.org/wikipedia/commons/b/be/Trie_example.svg)
+![Префиксное дерево](./images/trie.jpg)
+
+*Made with [okso.app](https://okso.app)*
 
 На рисунке представлено префиксное дерево, содержащее ключи «A», «to», «tea», «ted», «ten», «i», «in», «inn».
 
diff --git a/src/data-structures/trie/README.zh-CN.md b/src/data-structures/trie/README.zh-CN.md
index bad277d4bd..e812f57523 100644
--- a/src/data-structures/trie/README.zh-CN.md
+++ b/src/data-structures/trie/README.zh-CN.md
@@ -2,13 +2,15 @@
 
 在计算机科学中, **字典树(trie,中文又被称为”单词查找树“或 ”键树“)**, 也称为数字树,有时候也被称为基数树或前缀树（因为它们可以通过前缀搜索）,它是一种搜索树--一种已排序的数据结构,通常用于存储动态集或键为字符串的关联数组。
 
-与二叉搜索树不同, 树上没有节点存储与该节点关联的键; 相反,节点在树上的位置定义了与之关联的键。一个节点的全部后代节点都有一个与该节点关联的通用的字符串前缀, 与根节点关联的是空字符串。 
+与二叉搜索树不同, 树上没有节点存储与该节点关联的键; 相反,节点在树上的位置定义了与之关联的键。一个节点的全部后代节点都有一个与该节点关联的通用的字符串前缀, 与根节点关联的是空字符串。
 
 值对于字典树中关联的节点来说,不是必需的,相反,值往往和相关的叶子相关,以及与一些键相关的内部节点相关。
 
 有关字典树的空间优化示意,请参阅紧凑前缀树
 
-![Trie](https://upload.wikimedia.org/wikipedia/commons/b/be/Trie_example.svg)
+![Trie](./images/trie.jpg)
+
+*Made with [okso.app](https://okso.app)*
 
 ## 参考
 
diff --git a/src/data-structures/trie/images/trie.jpg b/src/data-structures/trie/images/trie.jpg
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From 7236dacb349e2125a5758873466d10bfc3b21c84 Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Fri, 19 Aug 2022 19:08:53 +0200
Subject: [PATCH 193/264] Update Trie image.

---
 src/data-structures/trie/images/trie.jpg | Bin 134559 -> 146598 bytes
 1 file changed, 0 insertions(+), 0 deletions(-)

diff --git a/src/data-structures/trie/images/trie.jpg b/src/data-structures/trie/images/trie.jpg
index 9284e71de7f7b23c66a934cc725b540fd55a1ab1..5a4221da075b74ad98b629f7c9dae7ed4f4c821c 100644
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From b55e79aed2fa35fc0c6b47cc24f4747bb712c95e Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Fri, 19 Aug 2022 19:20:48 +0200
Subject: [PATCH 194/264] Update BST image.

---
 .../tree/binary-search-tree/README.md         |  56 +++++++++---------
 .../tree/binary-search-tree/README.pt-BR.md   |  19 +++---
 .../images/binary-search-tree.jpg             | Bin 0 -> 149145 bytes
 3 files changed, 39 insertions(+), 36 deletions(-)
 create mode 100644 src/data-structures/tree/binary-search-tree/images/binary-search-tree.jpg

diff --git a/src/data-structures/tree/binary-search-tree/README.md b/src/data-structures/tree/binary-search-tree/README.md
index f3e448a995..d05a891545 100644
--- a/src/data-structures/tree/binary-search-tree/README.md
+++ b/src/data-structures/tree/binary-search-tree/README.md
@@ -3,32 +3,34 @@
 _Read this in other languages:_
 [_Português_](README.pt-BR.md)
 
-In computer science, **binary search trees** (BST), sometimes called 
-ordered or sorted binary trees, are a particular type of container: 
-data structures that store "items" (such as numbers, names etc.) 
-in memory. They allow fast lookup, addition and removal of 
-items, and can be used to implement either dynamic sets of 
-items, or lookup tables that allow finding an item by its key 
+In computer science, **binary search trees** (BST), sometimes called
+ordered or sorted binary trees, are a particular type of container:
+data structures that store "items" (such as numbers, names etc.)
+in memory. They allow fast lookup, addition and removal of
+items, and can be used to implement either dynamic sets of
+items, or lookup tables that allow finding an item by its key
 (e.g., finding the phone number of a person by name).
 
-Binary search trees keep their keys in sorted order, so that lookup 
-and other operations can use the principle of binary search: 
-when looking for a key in a tree (or a place to insert a new key), 
-they traverse the tree from root to leaf, making comparisons to 
-keys stored in the nodes of the tree and deciding, on the basis 
-of the comparison, to continue searching in the left or right 
-subtrees. On average, this means that each comparison allows 
-the operations to skip about half of the tree, so that each 
-lookup, insertion or deletion takes time proportional to the 
-logarithm of the number of items stored in the tree. This is 
-much better than the linear time required to find items by key 
-in an (unsorted) array, but slower than the corresponding 
+Binary search trees keep their keys in sorted order, so that lookup
+and other operations can use the principle of binary search:
+when looking for a key in a tree (or a place to insert a new key),
+they traverse the tree from root to leaf, making comparisons to
+keys stored in the nodes of the tree and deciding, on the basis
+of the comparison, to continue searching in the left or right
+subtrees. On average, this means that each comparison allows
+the operations to skip about half of the tree, so that each
+lookup, insertion or deletion takes time proportional to the
+logarithm of the number of items stored in the tree. This is
+much better than the linear time required to find items by key
+in an (unsorted) array, but slower than the corresponding
 operations on hash tables.
 
 A binary search tree of size 9 and depth 3, with 8 at the root.
 The leaves are not drawn.
 
-![Binary Search Tree](https://upload.wikimedia.org/wikipedia/commons/d/da/Binary_search_tree.svg)
+![Trie](./images/binary-search-tree.jpg)
+
+*Made with [okso.app](https://okso.app)*
 
 ## Pseudocode for Basic Operations
 
@@ -45,7 +47,7 @@ insert(value)
   end if
 end insert
 ```
-    
+
 ```text
 insertNode(current, value)
   Pre: current is the node to start from
@@ -84,8 +86,8 @@ contains(root, value)
   end if
 end contains
 ```
-    
-     
+
+
 ### Deletion
 
 ```text
@@ -186,7 +188,7 @@ findNode(root, value)
   end if
 end findNode
 ```
-    
+
 ### Find Minimum
 
 ```text
@@ -200,7 +202,7 @@ findMin(root)
   findMin(root.left)
 end findMin
 ```
-    
+
 ### Find Maximum
 
 ```text
@@ -214,7 +216,7 @@ findMax(root)
   findMax(root.right)
 end findMax
 ```
-    
+
 ### Traversal
 
 #### InOrder Traversal
@@ -244,7 +246,7 @@ preorder(root)
   end if
 end preorder
 ```
-   
+
 #### PostOrder Traversal
 
 ```text
@@ -258,7 +260,7 @@ postorder(root)
   end if
 end postorder
 ```
-     
+
 ## Complexities
 
 ### Time Complexity
diff --git a/src/data-structures/tree/binary-search-tree/README.pt-BR.md b/src/data-structures/tree/binary-search-tree/README.pt-BR.md
index 4565538a7b..1e71714104 100644
--- a/src/data-structures/tree/binary-search-tree/README.pt-BR.md
+++ b/src/data-structures/tree/binary-search-tree/README.pt-BR.md
@@ -26,8 +26,9 @@ Uma pesquisa de árvore binária de tamanho 9 e profundidade 3, com valor 8
 na raíz.
 As folhas não foram desenhadas.
 
+![Trie](./images/binary-search-tree.jpg)
 
-![Binary Search Tree](https://upload.wikimedia.org/wikipedia/commons/d/da/Binary_search_tree.svg)
+*Made with [okso.app](https://okso.app)*
 
 ## Pseudocódigo para Operações Básicas
 
@@ -44,7 +45,7 @@ insert(value)
   end if
 end insert
 ```
-    
+
 ```text
 insertNode(current, value)
   Pre: current is the node to start from
@@ -83,8 +84,8 @@ contains(root, value)
   end if
 end contains
 ```
-    
-     
+
+
 ### Remoção
 
 ```text
@@ -185,7 +186,7 @@ findNode(root, value)
   end if
 end findNode
 ```
-    
+
 ### Encontrar Mínimo
 
 ```text
@@ -199,7 +200,7 @@ findMin(root)
   findMin(root.left)
 end findMin
 ```
-    
+
 ### Encontrar Máximo
 
 ```text
@@ -213,7 +214,7 @@ findMax(root)
   findMax(root.right)
 end findMax
 ```
-    
+
 ### Traversal
 
 #### Na Ordem Traversal (InOrder Traversal)
@@ -243,7 +244,7 @@ preorder(root)
   end if
 end preorder
 ```
-   
+
 #### Pós Ordem Traversal (PostOrder Traversal)
 
 ```text
@@ -257,7 +258,7 @@ postorder(root)
   end if
 end postorder
 ```
-     
+
 ## Complexidades
 
 ### Complexidade de Tempo
diff --git a/src/data-structures/tree/binary-search-tree/images/binary-search-tree.jpg b/src/data-structures/tree/binary-search-tree/images/binary-search-tree.jpg
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From 036a67b9b4852c52f7cdf6eaa0a89fcbf2313e8d Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Sun, 21 Aug 2022 17:08:30 +0200
Subject: [PATCH 195/264] Update DS images.

---
 .../images/doubly-linked-list.jpeg            | Bin 109315 -> 108334 bytes
 src/data-structures/graph/images/graph.jpeg   | Bin 135330 -> 134354 bytes
 .../images/collision-resolution.jpeg          | Bin 281785 -> 267727 bytes
 .../hash-table/images/hash-table.jpeg         | Bin 168634 -> 164355 bytes
 .../heap/images/array-representation.jpeg     | Bin 111908 -> 113837 bytes
 src/data-structures/heap/images/max-heap.jpeg | Bin 80393 -> 79702 bytes
 src/data-structures/heap/images/min-heap.jpeg | Bin 82405 -> 82268 bytes
 .../linked-list/images/linked-list.jpeg       | Bin 64733 -> 64648 bytes
 .../images/binary-search-tree.jpg             | Bin 149145 -> 149808 bytes
 src/data-structures/trie/images/trie.jpg      | Bin 146598 -> 148834 bytes
 10 files changed, 0 insertions(+), 0 deletions(-)

diff --git a/src/data-structures/doubly-linked-list/images/doubly-linked-list.jpeg b/src/data-structures/doubly-linked-list/images/doubly-linked-list.jpeg
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From 8fd8e752eaec9d6f986b344af3f548a64f283e1f Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Fri, 26 Aug 2022 07:14:32 +0200
Subject: [PATCH 196/264] Update data-structure images.

---
 .../linked-list/images/linked-list.jpeg       | Bin 64648 -> 185069 bytes
 1 file changed, 0 insertions(+), 0 deletions(-)

diff --git a/src/data-structures/linked-list/images/linked-list.jpeg b/src/data-structures/linked-list/images/linked-list.jpeg
index 518f19c7c7eef6261f211e7ca36989096e6e0c8d..61a07120663853eb2a1022acfe8944507fb3817e 100644
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From 928bac1f54d2bef3fa2171c58212f3ee71b04bd0 Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Fri, 26 Aug 2022 20:13:14 +0200
Subject: [PATCH 197/264] Update data-structure images.

---
 .../images/doubly-linked-list.jpeg            | Bin 108334 -> 217712 bytes
 1 file changed, 0 insertions(+), 0 deletions(-)

diff --git a/src/data-structures/doubly-linked-list/images/doubly-linked-list.jpeg b/src/data-structures/doubly-linked-list/images/doubly-linked-list.jpeg
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From 41038d329728e8136f0604113d0afb64eabf2e97 Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Sat, 27 Aug 2022 14:35:09 +0200
Subject: [PATCH 198/264] Update data-structure images.

---
 src/data-structures/queue/images/queue.jpeg | Bin 122630 -> 163552 bytes
 src/data-structures/stack/images/stack.jpg  | Bin 0 -> 203274 bytes
 2 files changed, 0 insertions(+), 0 deletions(-)
 create mode 100644 src/data-structures/stack/images/stack.jpg

diff --git a/src/data-structures/queue/images/queue.jpeg b/src/data-structures/queue/images/queue.jpeg
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From 8c7950a389f948439fc162b74a88f5a9d38a5178 Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Sat, 27 Aug 2022 17:33:39 +0200
Subject: [PATCH 199/264] Update data-structure images.

---
 src/data-structures/tree/images/tree.jpeg | Bin 60051 -> 234561 bytes
 1 file changed, 0 insertions(+), 0 deletions(-)

diff --git a/src/data-structures/tree/images/tree.jpeg b/src/data-structures/tree/images/tree.jpeg
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From a81c0bdb2c5a9302fb73b67948cd6ff6b754bf3c Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Sat, 27 Aug 2022 17:39:41 +0200
Subject: [PATCH 200/264] Update data-structure images.

---
 .../images/binary-search-tree.jpg             | Bin 149808 -> 196992 bytes
 1 file changed, 0 insertions(+), 0 deletions(-)

diff --git a/src/data-structures/tree/binary-search-tree/images/binary-search-tree.jpg b/src/data-structures/tree/binary-search-tree/images/binary-search-tree.jpg
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From 6914c654a389a60101cdcce0f3bbaa203b3ef06e Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Sat, 27 Aug 2022 17:58:14 +0200
Subject: [PATCH 201/264] Update data-structure images.

---
 src/data-structures/heap/images/max-heap.jpeg | Bin 79702 -> 163685 bytes
 src/data-structures/heap/images/min-heap.jpeg | Bin 82268 -> 160107 bytes
 2 files changed, 0 insertions(+), 0 deletions(-)

diff --git a/src/data-structures/heap/images/max-heap.jpeg b/src/data-structures/heap/images/max-heap.jpeg
index c818c07f0624acf4f8d1b36d9bb7779691f9e4e8..c1585d0302421f56fcbe3f2ae1becdda1e9e8554 100644
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From f9b558b802f8c1fb1b670c7313202457069c1cfb Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Sat, 27 Aug 2022 18:18:07 +0200
Subject: [PATCH 202/264] Update data-structure images.

---
 .../heap/images/array-representation.jpeg     | Bin 113837 -> 131761 bytes
 1 file changed, 0 insertions(+), 0 deletions(-)

diff --git a/src/data-structures/heap/images/array-representation.jpeg b/src/data-structures/heap/images/array-representation.jpeg
index 0a757d7ac0e373cfbeb96355213023183f4662a5..8914e7102e2c2d3bc5833e7c915b16df426e9456 100644
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From 1d02cd6596df17c74bf33059ee6521321a5627d3 Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Mon, 29 Aug 2022 18:39:05 +0200
Subject: [PATCH 203/264] Update data-structure images.

---
 src/data-structures/trie/images/trie.jpg | Bin 148834 -> 309646 bytes
 1 file changed, 0 insertions(+), 0 deletions(-)

diff --git a/src/data-structures/trie/images/trie.jpg b/src/data-structures/trie/images/trie.jpg
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From 4d2d7189c631218b9c713c8ac070ac4a1d98f6ff Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Tue, 30 Aug 2022 09:26:36 +0200
Subject: [PATCH 204/264] Add a link to minimalistic data structure sketches.
 (#933)

---
 README.md | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 4a870ccfed..f0e90fc8d3 100644
--- a/README.md
+++ b/README.md
@@ -301,7 +301,8 @@ npm test -- 'playground'
 
 ### References
 
-[▶ Data Structures and Algorithms on YouTube](https://www.youtube.com/playlist?list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
+- [▶ Data Structures and Algorithms on YouTube](https://www.youtube.com/playlist?list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
+- [✍🏻 Data Structure Sketches](https://okso.app/showcase/data-structures)
 
 ### Big O Notation
 

From ebfe961f0f61b641a1f4d340ddffe323891ab0b0 Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Wed, 21 Sep 2022 09:10:09 +0200
Subject: [PATCH 205/264] Update README.md

---
 README.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/README.md b/README.md
index f0e90fc8d3..dd4ef9b531 100644
--- a/README.md
+++ b/README.md
@@ -1,9 +1,9 @@
 # JavaScript Algorithms and Data Structures
 
-> 🇺🇦 UKRAINE [IS BEING ATTACKED](https://twitter.com/MFA_Ukraine) BY RUSSIAN ARMY. CIVILIANS ARE GETTING KILLED. RESIDENTIAL AREAS ARE GETTING BOMBED.
+> 🇺🇦 UKRAINE [IS BEING ATTACKED](https://war.ukraine.ua/) BY RUSSIAN ARMY. CIVILIANS ARE GETTING KILLED. RESIDENTIAL AREAS ARE GETTING BOMBED.
 > - Help Ukraine via [National Bank of Ukraine](https://bank.gov.ua/en/news/all/natsionalniy-bank-vidkriv-spetsrahunok-dlya-zboru-koshtiv-na-potrebi-armiyi)
 > - Help Ukraine via [SaveLife](https://savelife.in.ua/en/donate-en/) fund
-> - More info on [war.ukraine.ua](https://war.ukraine.ua/)
+> - More info on [war.ukraine.ua](https://war.ukraine.ua/) and [MFA of Ukraine](https://twitter.com/MFA_Ukraine)
 
 [![CI](https://github.com/trekhleb/javascript-algorithms/workflows/CI/badge.svg)](https://github.com/trekhleb/javascript-algorithms/actions?query=workflow%3ACI+branch%3Amaster)
 [![codecov](https://codecov.io/gh/trekhleb/javascript-algorithms/branch/master/graph/badge.svg)](https://codecov.io/gh/trekhleb/javascript-algorithms)

From d3c0ee6f7af3fce4a3a2bdc1c5be36d7c2d9793a Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Wed, 21 Sep 2022 09:12:46 +0200
Subject: [PATCH 206/264] Update README.md

---
 README.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/README.md b/README.md
index dd4ef9b531..d2d0bc75a4 100644
--- a/README.md
+++ b/README.md
@@ -5,6 +5,8 @@
 > - Help Ukraine via [SaveLife](https://savelife.in.ua/en/donate-en/) fund
 > - More info on [war.ukraine.ua](https://war.ukraine.ua/) and [MFA of Ukraine](https://twitter.com/MFA_Ukraine)
 
+<hr/>
+
 [![CI](https://github.com/trekhleb/javascript-algorithms/workflows/CI/badge.svg)](https://github.com/trekhleb/javascript-algorithms/actions?query=workflow%3ACI+branch%3Amaster)
 [![codecov](https://codecov.io/gh/trekhleb/javascript-algorithms/branch/master/graph/badge.svg)](https://codecov.io/gh/trekhleb/javascript-algorithms)
 

From 26a27f360a86548039af5dd0e1d593569a37c3b4 Mon Sep 17 00:00:00 2001
From: "David (Dato) Kadaria" <94402615+davidkadaria@users.noreply.github.com>
Date: Mon, 10 Oct 2022 17:02:41 +0400
Subject: [PATCH 207/264] Add Georgian translation for 'algorithms: Factorial'
 (#947)

* Translated Factorial

* Renamed file and added link to it from the original file

* Replaced Wikipedia link with Georgian version
---
 src/algorithms/math/factorial/README.ka-GE.md | 32 +++++++++++++++++++
 src/algorithms/math/factorial/README.md       |  2 +-
 2 files changed, 33 insertions(+), 1 deletion(-)
 create mode 100644 src/algorithms/math/factorial/README.ka-GE.md

diff --git a/src/algorithms/math/factorial/README.ka-GE.md b/src/algorithms/math/factorial/README.ka-GE.md
new file mode 100644
index 0000000000..1d02b9f7d3
--- /dev/null
+++ b/src/algorithms/math/factorial/README.ka-GE.md
@@ -0,0 +1,32 @@
+# ფაქტორიალი
+
+მათემატიკაში `n` ნატურალური რიცხვის ფაქტორიალი
+(აღინიშნება `n!` სიმბოლოთი)
+არის ყველა ნატურალური რიცხვის ნამრავლი 1-იდან `n`-ის ჩათვლით. მაგალითად:
+
+```
+5! = 5 * 4 * 3 * 2 * 1 = 120
+```
+
+| n   |                n! |
+| --- | ----------------: |
+| 0   |                 1 |
+| 1   |                 1 |
+| 2   |                 2 |
+| 3   |                 6 |
+| 4   |                24 |
+| 5   |               120 |
+| 6   |               720 |
+| 7   |             5 040 |
+| 8   |            40 320 |
+| 9   |           362 880 |
+| 10  |         3 628 800 |
+| 11  |        39 916 800 |
+| 12  |       479 001 600 |
+| 13  |     6 227 020 800 |
+| 14  |    87 178 291 200 |
+| 15  | 1 307 674 368 000 |
+
+## სქოლიო
+
+[Wikipedia](https://ka.wikipedia.org/wiki/%E1%83%9B%E1%83%90%E1%83%97%E1%83%94%E1%83%9B%E1%83%90%E1%83%A2%E1%83%98%E1%83%99%E1%83%A3%E1%83%A0%E1%83%98_%E1%83%A4%E1%83%90%E1%83%A5%E1%83%A2%E1%83%9D%E1%83%A0%E1%83%98%E1%83%90%E1%83%9A%E1%83%98)
diff --git a/src/algorithms/math/factorial/README.md b/src/algorithms/math/factorial/README.md
index 032121dfdf..5f7f0e1129 100644
--- a/src/algorithms/math/factorial/README.md
+++ b/src/algorithms/math/factorial/README.md
@@ -1,7 +1,7 @@
 # Factorial
 
 _Read this in other languages:_
-[_简体中文_](README.zh-CN.md), [français](README.fr-FR.md), [turkish](README.tr-TR.md).
+[_简体中文_](README.zh-CN.md), [français](README.fr-FR.md), [turkish](README.tr-TR.md), [ქართული](README.ka-GE.md).
 
 In mathematics, the factorial of a non-negative integer `n`,
 denoted by `n!`, is the product of all positive integers less

From 9ef6650207338c41eccb0e303b865ac8c3ff3e2b Mon Sep 17 00:00:00 2001
From: "Oleksandr (Sasha) Khivrych" <alexander.khivrych@gmail.com>
Date: Mon, 10 Oct 2022 15:05:58 +0200
Subject: [PATCH 208/264] feat: added ukrainian translations for hash table
 (#948)

Co-authored-by: Oleksii Trekhleb <trehleb@gmail.com>
---
 src/data-structures/hash-table/README.md      | 11 +++----
 .../hash-table/README.uk-UA.md                | 29 +++++++++++++++++++
 2 files changed, 35 insertions(+), 5 deletions(-)
 create mode 100644 src/data-structures/hash-table/README.uk-UA.md

diff --git a/src/data-structures/hash-table/README.md b/src/data-structures/hash-table/README.md
index 8711bd9b49..f0d0c9932d 100644
--- a/src/data-structures/hash-table/README.md
+++ b/src/data-structures/hash-table/README.md
@@ -6,12 +6,13 @@ _Read this in other languages:_
 [_日本語_](README.ja-JP.md),
 [_Français_](README.fr-FR.md),
 [_Português_](README.pt-BR.md),
-[_한국어_](README.ko-KR.md)
+[_한국어_](README.ko-KR.md),
+[_Українська_](README.uk-UA.md)
 
 In computing, a **hash table** (hash map) is a data
-structure which implements an *associative array*
-abstract data type, a structure that can *map keys
-to values*. A hash table uses a *hash function* to
+structure which implements an _associative array_
+abstract data type, a structure that can _map keys
+to values_. A hash table uses a _hash function_ to
 compute an index into an array of buckets or slots,
 from which the desired value can be found
 
@@ -28,7 +29,7 @@ Hash collision resolved by separate chaining.
 
 ![Hash Collision](./images/collision-resolution.jpeg)
 
-*Made with [okso.app](https://okso.app)*
+_Made with [okso.app](https://okso.app)_
 
 ## References
 
diff --git a/src/data-structures/hash-table/README.uk-UA.md b/src/data-structures/hash-table/README.uk-UA.md
new file mode 100644
index 0000000000..2ab3183599
--- /dev/null
+++ b/src/data-structures/hash-table/README.uk-UA.md
@@ -0,0 +1,29 @@
+# Геш таблиця
+
+**Геш таблиця** - структура даних, що реалізує абстрактний тип даних асоціативний масив, тобто. структура, яка
+_зв'язує ключі зі значеннями_. Геш-таблиця використовує _геш-функцію_ для обчислення індексу в масиві, в якому може
+бути знайдено бажане значення. Нижче представлена геш-таблиця, у якій ключем виступає ім'я людини, а значеннями
+телефонні номери. Геш-функція перетворює ключ-ім'я на індекс масиву з телефонними номерами.
+
+![Hash Table](./images/hash-table.jpeg)
+
+В ідеалі геш-функція присвоюватиме елементу масиву унікальний ключ. Проте більшість реальних геш-таблиць
+використовують недосконалі геш-функції. Це може призвести до ситуацій, коли геш-функція генерує однаковий індекс для
+кількох ключів. Ці ситуації називаються колізіями і мають бути якось вирішені.
+
+Існує два варіанти вирішення колізій - геш-таблиця з ланцюжками та з відкритою адресацією.
+
+Метод ланцюжків передбачає зберігання значень, відповідних одному й тому індексу як зв'язкового списку(ланцюжка).
+
+![Hash Collision](./images/collision-resolution.jpeg)
+
+_Made with [okso.app](https://okso.app)_
+
+Метод відкритої адресації поміщає значення, для якого отримано дублюючий індекс, в першу вільну комірку.
+
+![Геш відкрита адресація](https://upload.wikimedia.org/wikipedia/commons/thumb/b/bf/Hash_table_5_0_1_1_1_1_0_SP.svg/380px-Hash_table_5_0_1_1_1_1_0_SP.svg.png)
+
+## Посилання
+
+- [Wikipedia](https://uk.wikipedia.org/wiki/%D0%93%D0%B5%D1%88-%D1%82%D0%B0%D0%B1%D0%BB%D0%B8%D1%86%D1%8F)
+- [YouTube](https://www.youtube.com/watch?v=WTYaboK-NMk)

From da6ae08851b4bb6f35cb3e7a36263cd68689168a Mon Sep 17 00:00:00 2001
From: Mateus Pfeffer <92607757+StPfeffer@users.noreply.github.com>
Date: Mon, 10 Oct 2022 10:23:32 -0300
Subject: [PATCH 209/264] Brazilian Portuguese translation and typos fixes
 (#943)

* Update README.pt-BR.md

* TRIE README.pt-BR typo

* TREE README.pt-BR typo

* Stack README.pt-BR typo

* Priority Queue README.pt-BR typo

* hash-table README.pt-BR typo

* doubly-linked-list README.pt-BR typo

* disjoint-set README.pt-BR typo

* bloom-filter README.pt-BR typo

* merge-sort pt-BR translation

* merge-sort README added pt-BR option

* insertion sort pt-BR translation

* insertion sort README added pt-br option

* heap-sort pt-BR translation

* heap-sort READMED added pt-BR option

* bubble sort pt-BR typo

* pt-BR translation for sorting algorithms

Fixed typos and translated all the missing algorithms

* Update README.pt-BR.md

* linked list pt-BR translation

* ml pt-BR translation

* fix typo in README

Co-authored-by: Oleksii Trekhleb <trehleb@gmail.com>
---
 README.pt-BR.md                               | 217 +++++++++---------
 .../linked-list/reverse-traversal/README.md   |   3 +-
 .../reverse-traversal/README.pt-BR.md         |  23 ++
 .../linked-list/traversal/README.md           |   3 +-
 .../linked-list/traversal/README.pt-BR.md     |  24 ++
 src/algorithms/ml/k-means/README.md           |   3 +
 src/algorithms/ml/k-means/README.pt-BR.md     |  35 +++
 src/algorithms/ml/knn/README.md               |   3 +
 src/algorithms/ml/knn/README.pt-BR.md         |  44 ++++
 .../sorting/bubble-sort/README.pt-BR.md       |  11 +-
 .../sorting/counting-sort/README.md           |   3 +
 .../sorting/counting-sort/README.pt-br.md     |  70 ++++++
 src/algorithms/sorting/heap-sort/README.md    |   3 +
 .../sorting/heap-sort/README.pt-BR.md         |  20 ++
 .../sorting/insertion-sort/README.md          |   3 +
 .../sorting/insertion-sort/README.pt-BR.md    |  22 ++
 src/algorithms/sorting/merge-sort/README.md   |   3 +-
 .../sorting/merge-sort/README.pt-BR.md        |  38 +++
 src/algorithms/sorting/quick-sort/README.md   |   4 +-
 .../sorting/quick-sort/README.pt-BR.md        |  12 +-
 src/algorithms/sorting/radix-sort/README.md   |   3 +
 .../sorting/radix-sort/README.pt-BR.md        |  48 ++++
 .../sorting/selection-sort/README.md          |   2 +-
 .../sorting/selection-sort/README.pt-BR.md    |   4 +-
 src/algorithms/sorting/shell-sort/README.md   |   3 +
 .../sorting/shell-sort/README.pt-BR.md        |  60 +++++
 .../bloom-filter/README.pt-BR.md              |   4 +-
 .../disjoint-set/README.pt-BR.md              |  10 +-
 .../doubly-linked-list/README.pt-BR.md        |   6 +-
 .../hash-table/README.pt-BR.md                |   4 +-
 .../priority-queue/README.pt-BR.md            |   8 +-
 src/data-structures/stack/README.pt-BR.md     |   8 +-
 src/data-structures/tree/README.pt-BR.md      |   2 +-
 src/data-structures/trie/README.pt-BR.md      |   6 +-
 34 files changed, 567 insertions(+), 145 deletions(-)
 create mode 100644 src/algorithms/linked-list/reverse-traversal/README.pt-BR.md
 create mode 100644 src/algorithms/linked-list/traversal/README.pt-BR.md
 create mode 100644 src/algorithms/ml/k-means/README.pt-BR.md
 create mode 100644 src/algorithms/ml/knn/README.pt-BR.md
 create mode 100644 src/algorithms/sorting/counting-sort/README.pt-br.md
 create mode 100644 src/algorithms/sorting/heap-sort/README.pt-BR.md
 create mode 100644 src/algorithms/sorting/insertion-sort/README.pt-BR.md
 create mode 100644 src/algorithms/sorting/merge-sort/README.pt-BR.md
 create mode 100644 src/algorithms/sorting/radix-sort/README.pt-BR.md
 create mode 100644 src/algorithms/sorting/shell-sort/README.pt-BR.md

diff --git a/README.pt-BR.md b/README.pt-BR.md
index 3218869a07..a937e8c0bf 100644
--- a/README.pt-BR.md
+++ b/README.pt-BR.md
@@ -31,9 +31,7 @@ _Leia isto em outros idiomas:_
 ## Estrutura de Dados
 
 Uma estrutura de dados é uma maneira particular de organizar e armazenar dados em um computador para que ele possa
-ser acessado e modificado de forma eficiente. Mais precisamente, uma estrutura de dados é uma coleção de dados
-valores, as relações entre eles e as funções ou operações que podem ser aplicadas a
-os dados.
+ser acessado e modificado de forma eficiente. Mais precisamente, uma estrutura de dados é uma coleção de valores de dados, as relações entre eles e as funções ou operações que podem ser aplicadas aos dados.
 
 `B` - Iniciante, `A` - Avançado
 
@@ -42,17 +40,17 @@ os dados.
 * `B` [Fila (Queue)](src/data-structures/queue/README.pt-BR.md)
 * `B` [Pilha (Stack)](src/data-structures/stack/README.pt-BR.md)
 * `B` [Tabela de Hash (Hash Table)](src/data-structures/hash-table/README.pt-BR.md)
-* `B` [Heap](src/data-structures/heap/README.pt-BR.md)
+* `B` [Heap](src/data-structures/heap/README.pt-BR.md) - versões de heap máximo e mínimo
 * `B` [Fila de Prioridade (Priority Queue)](src/data-structures/priority-queue/README.pt-BR.md)
-* `A` [Árvore de prefixos (Trie)](src/data-structures/trie/README.pt-BR.md)
+* `A` [Árvore de Prefixos (Trie)](src/data-structures/trie/README.pt-BR.md)
 * `A` [Árvore (Tree)](src/data-structures/tree/README.pt-BR.md)
   * `A` [Árvore de Pesquisa Binária (Binary Search Tree)](src/data-structures/tree/binary-search-tree/README.pt-BR.md)
   * `A` [Árvore AVL (AVL Tree)](src/data-structures/tree/avl-tree/README.pt-BR.md)
-  * `A` [Árvore Vermelha-Preta (Red-Black Tree)](src/data-structures/tree/red-black-tree/README.pt-BR.md)
-  * `A` [Árvore de Segmento (Segment Tree)](src/data-structures/tree/segment-tree/README.pt-BR.md) - Com exemplos de consultas min / max / sum range
+  * `A` [Árvore Rubro-Negra (Red-Black Tree)](src/data-structures/tree/red-black-tree/README.pt-BR.md)
+  * `A` [Árvore de Segmento (Segment Tree)](src/data-structures/tree/segment-tree/README.pt-BR.md) - com exemplos de consultas min / max / sum range
   * `A` [Árvore Fenwick (Fenwick Tree)](src/data-structures/tree/fenwick-tree/README.pt-BR.md) (Árvore indexada binária)
 * `A` [Grafo (Graph)](src/data-structures/graph/README.pt-BR.md) (ambos dirigidos e não direcionados)
-* `A` [Conjunto Disjuntor (Disjoint Set)](src/data-structures/disjoint-set/README.pt-BR.md)
+* `A` [Conjunto Disjunto (Disjoint Set)](src/data-structures/disjoint-set/README.pt-BR.md)
 * `A` [Filtro Bloom (Bloom Filter)](src/data-structures/bloom-filter/README.pt-BR.md)
 
 ## Algoritmos
@@ -72,36 +70,37 @@ um conjunto de regras que define precisamente uma sequência de operações.
   * `B` [Algoritmo Euclidiano](src/algorithms/math/euclidean-algorithm) - Calcular o Máximo Divisor Comum (MDC)
   * `B` [Mínimo Múltiplo Comum](src/algorithms/math/least-common-multiple) Calcular o Mínimo Múltiplo Comum (MMC)
   * `B` [Peneira de Eratóstenes](src/algorithms/math/sieve-of-eratosthenes) - Encontrar todos os números primos até um determinado limite
-  * `B` [Potência de dois](src/algorithms/math/is-power-of-two) - Verifique se o número é a potência de dois (algoritmos ingênuos e bit a bit)
+  * `B` [Potência de Dois](src/algorithms/math/is-power-of-two) - Verifique se o número é a potência de dois (algoritmos ingênuos e bit a bit)
   * `B` [Triângulo de Pascal](src/algorithms/math/pascal-triangle)
-  * `B` [Número complexo](src/algorithms/math/complex-number) - Números complexos e operações básicas com eles
-  * `A` [Partição inteira](src/algorithms/math/integer-partition)
+  * `B` [Número Complexo](src/algorithms/math/complex-number) - Números complexos e operações básicas com eles
+  * `A` [Partição Inteira](src/algorithms/math/integer-partition)
   * `A` [Algoritmo Liu Hui π](src/algorithms/math/liu-hui) - Cálculos aproximados de π baseados em N-gons
 * **Conjuntos**
-  * `B` [Produto cartesiano](src/algorithms/sets/cartesian-product) - Produto de vários conjuntos
+  * `B` [Produto Cartesiano](src/algorithms/sets/cartesian-product) - Produto de vários conjuntos
   * `B` [Permutações de Fisher–Yates](src/algorithms/sets/fisher-yates) - Permutação aleatória de uma sequência finita
   * `A` [Potência e Conjunto](src/algorithms/sets/power-set) - Todos os subconjuntos de um conjunto
   * `A` [Permutações](src/algorithms/sets/permutations) (com e sem repetições)
   * `A` [Combinações](src/algorithms/sets/combinations) (com e sem repetições)
-  * `A` [Mais longa subsequência comum](src/algorithms/sets/longest-common-subsequence) (LCS)
-  * `A` [Maior subsequência crescente](src/algorithms/sets/longest-increasing-subsequence)
-  * `A` [Supersequência Comum mais curta](src/algorithms/sets/shortest-common-supersequence) (SCS)
-  * `A` [Problema da mochila](src/algorithms/sets/knapsack-problem) - "0/1" e "Não consolidado"
-  * `A` [Máximo Subarray](src/algorithms/sets/maximum-subarray) - "Força bruta" e " Programação Dinâmica" versões (Kadane's)
+  * `A` [Mais Longa Subsequência Comum](src/algorithms/sets/longest-common-subsequence) (LCS)
+  * `A` [Maior Subsequência Crescente](src/algorithms/sets/longest-increasing-subsequence)
+  * `A` [Supersequência Comum Mais Curta](src/algorithms/sets/shortest-common-supersequence) (SCS)
+  * `A` [Problema da Mochila](src/algorithms/sets/knapsack-problem) - "0/1" e "Não consolidado"
+  * `A` [Subarray Máximo](src/algorithms/sets/maximum-subarray) - "Força bruta" e "Programação Dinâmica", versões de Kadane
   * `A` [Soma de Combinação](src/algorithms/sets/combination-sum) - Encontre todas as combinações que formam uma soma específica
 * **Cadeia de Caracteres**
-  * `B` [Hamming Distance](src/algorithms/string/hamming-distance) - Número de posições em que os símbolos são diferentes
-  * `A` [Levenshtein Distance](src/algorithms/string/levenshtein-distance) - Distância mínima de edição entre duas sequências
-  * `A` [Knuth–Morris–Pratt Algorithm](src/algorithms/string/knuth-morris-pratt) (Algoritmo KMP) - Pesquisa de substring (correspondência de padrão)
+  * `B` [Distância de Hamming](src/algorithms/string/hamming-distance) - Número de posições em que os símbolos são diferentes
+  * `B` [Palíndromos](src/algorithms/string/palindrome) - Verifique se a cadeia de caracteres (string) é a mesma ao contrário
+  * `A` [Distância Levenshtein](src/algorithms/string/levenshtein-distance) - Distância mínima de edição entre duas sequências
+  * `A` [Algoritmo Knuth–Morris–Pratt](src/algorithms/string/knuth-morris-pratt) (Algoritmo KMP) - Pesquisa de substring (correspondência de padrão)
   * `A` [Z Algorithm](src/algorithms/string/z-algorithm) - Pesquisa de substring (correspondência de padrão)
-  * `A` [Rabin Karp Algorithm](src/algorithms/string/rabin-karp) - Pesquisa de substring
-  * `A` [Longest Common Substring](src/algorithms/string/longest-common-substring)
-  * `A` [Regular Expression Matching](src/algorithms/string/regular-expression-matching)
+  * `A` [Algoritmo de Rabin Karp](src/algorithms/string/rabin-karp) - Pesquisa de substring
+  * `A` [Substring Comum Mais Longa](src/algorithms/string/longest-common-substring)
+  * `A` [Expressões Regulares Correspondentes](src/algorithms/string/regular-expression-matching)
 * **Buscas**
-  * `B` [Linear Search](src/algorithms/search/linear-search)
-  * `B` [Jump Search](src/algorithms/search/jump-search) (ou Bloquear pesquisa) - Pesquisar na matriz ordenada
-  * `B` [Binary Search](src/algorithms/search/binary-search) - Pesquisar na matriz ordenada
-  * `B` [Interpolation Search](src/algorithms/search/interpolation-search) - Pesquisar em matriz classificada uniformemente distribuída
+  * `B` [Busca Linear (Linear Search)](src/algorithms/search/linear-search)
+  * `B` [Busca por Saltos (Jump Search)](src/algorithms/search/jump-search) - Pesquisa em matriz ordenada
+  * `B` [Busca Binária (Binary Search)](src/algorithms/search/binary-search) - Pesquisa em matriz ordenada
+  * `B` [Busca por Interpolação (Interpolation Search)](src/algorithms/search/interpolation-search) - Pesquisa em matriz classificada uniformemente distribuída
 * **Classificação**
   * `B` [Bubble Sort](src/algorithms/sorting/bubble-sort)
   * `B` [Selection Sort](src/algorithms/sorting/selection-sort)
@@ -112,35 +111,35 @@ um conjunto de regras que define precisamente uma sequência de operações.
   * `B` [Shellsort](src/algorithms/sorting/shell-sort)
   * `B` [Counting Sort](src/algorithms/sorting/counting-sort)
   * `B` [Radix Sort](src/algorithms/sorting/radix-sort)
-* **Arvóres**
-  * `B` [Depth-First Search](src/algorithms/tree/depth-first-search) (DFS)
-  * `B` [Breadth-First Search](src/algorithms/tree/breadth-first-search) (BFS)
+* **Árvores**
+  * `B` [Busca em Profundidade (Depth-First Search)](src/algorithms/tree/depth-first-search) (DFS)
+  * `B` [Busca em Largura (Breadth-First Search)](src/algorithms/tree/breadth-first-search) (BFS)
 * **Grafos**
-  * `B` [Depth-First Search](src/algorithms/graph/depth-first-search) (DFS)
-  * `B` [Breadth-First Search](src/algorithms/graph/breadth-first-search) (BFS)
-  * `B` [Kruskal’s Algorithm](src/algorithms/graph/kruskal) - Encontrar Árvore Mínima de Abrangência (MST) para grafo não direcionado ponderado
-  * `A` [Dijkstra Algorithm](src/algorithms/graph/dijkstra) - Encontrar caminhos mais curtos para todos os vértices do grafo a partir de um único vértice
-  * `A` [Bellman-Ford Algorithm](src/algorithms/graph/bellman-ford) - Encontrar caminhos mais curtos para todos os vértices do grafo a partir de um único vértice
-  * `A` [Floyd-Warshall Algorithm](src/algorithms/graph/floyd-warshall) - Encontrar caminhos mais curtos entre todos os pares de vértices
-  * `A` [Detect Cycle](src/algorithms/graph/detect-cycle) - Para gráficos direcionados e não direcionados (versões baseadas em DFS e Conjunto Disjuntivo)
-  * `A` [Prim’s Algorithm](src/algorithms/graph/prim) - Encontrando Árvore Mínima de Abrangência (MST) para grafo não direcionado ponderado
-  * `A` [Topological Sorting](src/algorithms/graph/topological-sorting) - Métodos DFS
-  * `A` [Articulation Points](src/algorithms/graph/articulation-points) -O algoritmo de Tarjan (baseado em DFS)
-  * `A` [Bridges](src/algorithms/graph/bridges) - Algoritmo baseado em DFS
-  * `A` [Eulerian Path and Eulerian Circuit](src/algorithms/graph/eulerian-path) - Algoritmo de Fleury - Visite todas as bordas exatamente uma vez
-  * `A` [Hamiltonian Cycle](src/algorithms/graph/hamiltonian-cycle) - Visite todas as bordas exatamente uma vez
-  * `A` [Strongly Connected Components](src/algorithms/graph/strongly-connected-components) - Algoritmo de Kosaraju's
-  * `A` [Travelling Salesman Problem](src/algorithms/graph/travelling-salesman) - Rota mais curta possível que visita cada cidade e retorna à cidade de origem
+  * `B` [Busca em Profundidade (Depth-First Search)](src/algorithms/graph/depth-first-search) (DFS)
+  * `B` [Busca em Largura (Breadth-First Search)](src/algorithms/graph/breadth-first-search) (BFS)
+  * `B` [Algoritmo de Kruskal](src/algorithms/graph/kruskal) - Encontrando Árvore Mínima de Abrangência (MST) para grafo conexo com pesos
+  * `A` [Algoritmo de Dijkstra](src/algorithms/graph/dijkstra) - Encontrar caminhos mais curtos para todos os vértices do grafo a partir de um único vértice
+  * `A` [Algoritmo de Bellman-Ford](src/algorithms/graph/bellman-ford) - Encontrar caminhos mais curtos para todos os vértices do grafo a partir de um único vértice
+  * `A` [Algoritmo de Floyd-Warshall](src/algorithms/graph/floyd-warshall) - Encontrar caminhos mais curtos entre todos os pares de vértices
+  * `A` [Detectar Ciclo](src/algorithms/graph/detect-cycle) - Para grafos direcionados e não direcionados (versões baseadas em DFS e Conjunto Disjuntivo)
+  * `A` [Algoritmo de Prim](src/algorithms/graph/prim) - Encontrando Árvore Mínima de Abrangência (MST) para grafo não direcionado ponderado
+  * `A` [Ordenação Topológica](src/algorithms/graph/topological-sorting) - Métodos DFS
+  * `A` [Pontos de Articulação](src/algorithms/graph/articulation-points) - O algoritmo de Tarjan (baseado em DFS)
+  * `A` [Pontes](src/algorithms/graph/bridges) - Algoritmo baseado em DFS
+  * `A` [Caminho e Circuito Euleriano](src/algorithms/graph/eulerian-path) - Algoritmo de Fleury - Visite todas as bordas exatamente uma vez
+  * `A` [Ciclo Hamiltoniano](src/algorithms/graph/hamiltonian-cycle) - Visite todas as bordas exatamente uma vez
+  * `A` [Componentes Fortemente Conectados](src/algorithms/graph/strongly-connected-components) - Algoritmo de Kosaraju
+  * `A` [Problema do Caixeiro Viajante](src/algorithms/graph/travelling-salesman) - Rota mais curta possível que visita cada cidade e retorna à cidade de origem
 * **Criptografia**
-  * `B` [Polynomial Hash](src/algorithms/cryptography/polynomial-hash) - Função de hash de rolagem baseada em polinômio
+  * `B` [Hash Polinomial](src/algorithms/cryptography/polynomial-hash) - Função de hash de rolagem baseada em polinômio
 * **Sem categoria**
-  * `B` [Tower of Hanoi](src/algorithms/uncategorized/hanoi-tower)
-  * `B` [Square Matrix Rotation](src/algorithms/uncategorized/square-matrix-rotation) - Algoritmo no local
-  * `B` [Jump Game](src/algorithms/uncategorized/jump-game) - Backtracking, programação dinâmica (top-down + bottom-up) e exemplos gananciosos
-  * `B` [Unique Paths](src/algorithms/uncategorized/unique-paths) - Backtracking, programação dinâmica e exemplos baseados no triângulo de Pascal
-  * `B` [Rain Terraces](src/algorithms/uncategorized/rain-terraces) - Trapping problema da água da chuva (programação dinâmica e versões de força bruta)
-  * `A` [N-Queens Problem](src/algorithms/uncategorized/n-queens)
-  * `A` [Knight's Tour](src/algorithms/uncategorized/knight-tour)
+  * `B` [Torre de Hanoi](src/algorithms/uncategorized/hanoi-tower)
+  * `B` [Rotação de Matriz Quadrada](src/algorithms/uncategorized/square-matrix-rotation) - Algoritmo no local
+  * `B` [Jogo do Salto](src/algorithms/uncategorized/jump-game) - Backtracking, programação dinâmica (top-down + bottom-up) e exemplos gananciosos
+  * `B` [Caminhos Únicos](src/algorithms/uncategorized/unique-paths) - Backtracking, programação dinâmica e exemplos baseados no triângulo de Pascal
+  * `B` [Terraços de Chuva](src/algorithms/uncategorized/rain-terraces) - Problema de retenção da água da chuva (programação dinâmica e versões de força bruta)
+  * `A` [Problema das N-Rainhas](src/algorithms/uncategorized/n-queens)
+  * `A` [Passeio do Cavaleiro](src/algorithms/uncategorized/knight-tour)
 
 ### Algoritmos por Paradigma
 
@@ -149,54 +148,52 @@ de algoritmos. É uma abstração maior do que a noção de um algoritmo, assim
 algoritmo é uma abstração maior que um programa de computador.
 
 * **Força bruta** - Pense em todas as possibilidades e escolha a melhor solução
-  * `B` [Linear Search](src/algorithms/search/linear-search)
-  * `B` [Rain Terraces](src/algorithms/uncategorized/rain-terraces) - Trapping problema da água da chuva
-  * `A` [Maximum Subarray](src/algorithms/sets/maximum-subarray)
-  * `A` [Travelling Salesman Problem](src/algorithms/graph/travelling-salesman) - Rota mais curta possível que visita cada cidade e retorna à cidade de origem
+  * `B` [Busca Linear (Linear Search)](src/algorithms/search/linear-search)
+  * `B` [Terraços de Chuva](src/algorithms/uncategorized/rain-terraces) - Problema de retenção de água da chuva (programação dinâmica e versões de força bruta)
+  * `A` [Subarray Máximo](src/algorithms/sets/maximum-subarray)
+  * `A` [Problema do Caixeiro Viajante](src/algorithms/graph/travelling-salesman) - Rota mais curta possível que visita cada cidade e retorna à cidade de origem
 * **Ganância** - Escolha a melhor opção no momento, sem qualquer consideração pelo futuro
-  * `B` [Jump Game](src/algorithms/uncategorized/jump-game)
-  * `A` [Unbound Knapsack Problem](src/algorithms/sets/knapsack-problem)
-  * `A` [Dijkstra Algorithm](src/algorithms/graph/dijkstra) - Encontrar o caminho mais curto para todos os vértices do gráfico
-  * `A` [Prim’s Algorithm](src/algorithms/graph/prim) - Encontrando Árvore Mínima de Abrangência (MST) para grafo não direcionado ponderado
-  * `A` [Kruskal’s Algorithm](src/algorithms/graph/kruskal) - Encontrando Árvore Mínima de Abrangência (MST) para grafo não direcionado ponderado
+  * `B` [Jogo do Salto](src/algorithms/uncategorized/jump-game)
+  * `A` [Problema da Mochila](src/algorithms/sets/knapsack-problem)
+  * `A` [Algoritmo de Dijkstra](src/algorithms/graph/dijkstra) - Encontrar caminhos mais curtos para todos os vértices do grafo a partir de um único vértice
+  * `A` [Algoritmo de Prim](src/algorithms/graph/prim) - Encontrando Árvore Mínima de Abrangência (MST) para grafo não direcionado ponderado
+  * `A` [Algoritmo de Kruskal](src/algorithms/graph/kruskal) - Encontrando Árvore Mínima de Abrangência (MST) para grafo conexo com pesos
 * **Dividir e Conquistar** - Dividir o problema em partes menores e então resolver essas partes
-  * `B` [Busca binária (Binary Search)](src/algorithms/search/binary-search)
-  * `B` [Tower of Hanoi](src/algorithms/uncategorized/hanoi-tower)
-  * `B` [Pascal's Triangle](src/algorithms/math/pascal-triangle)
-  * `B` [Euclidean Algorithm](src/algorithms/math/euclidean-algorithm) - Calcular o Máximo Divisor Comum (MDC)
+  * `B` [Busca Binária (Binary Search)](src/algorithms/search/binary-search)
+  * `B` [Torre de Hanoi](src/algorithms/uncategorized/hanoi-tower)
+  * `B` [Triângulo de Pascal](src/algorithms/math/pascal-triangle)
+  * `B` [Algoritmo Euclidiano](src/algorithms/math/euclidean-algorithm) - Calcular o Máximo Divisor Comum (MDC)
   * `B` [Merge Sort](src/algorithms/sorting/merge-sort)
   * `B` [Quicksort](src/algorithms/sorting/quick-sort)
-  * `B` [Tree Depth-First Search](src/algorithms/tree/depth-first-search) (DFS)
-  * `B` [Graph Depth-First Search](src/algorithms/graph/depth-first-search) (DFS)
-  * `B` [Jump Game](src/algorithms/uncategorized/jump-game)
-  * `A` [Permutations](src/algorithms/sets/permutations) (com e sem repetições)
-  * `A` [Combinations](src/algorithms/sets/combinations) (com e sem repetições)
+  * `B` [Busca em Profundidade (Depth-First Search)](src/algorithms/tree/depth-first-search) (DFS)
+  * `B` [Busca em Largura (Breadth-First Search)](src/algorithms/graph/breadth-first-search) (BFS)
+  * `B` [Jogo do Salto](src/algorithms/uncategorized/jump-game)
+  * `A` [Permutações](src/algorithms/sets/permutations) (com e sem repetições)
+  * `A` [Combinações](src/algorithms/sets/combinations) (com e sem repetições)
 * **Programação Dinâmica** - Criar uma solução usando sub-soluções encontradas anteriormente
-  * `B` [Fibonacci Number](src/algorithms/math/fibonacci)
-  * `B` [Jump Game](src/algorithms/uncategorized/jump-game)
-  * `B` [Unique Paths](src/algorithms/uncategorized/unique-paths)
-  * `B` [Rain Terraces](src/algorithms/uncategorized/rain-terraces) - Trapping problema da água da chuva
-  * `A` [Levenshtein Distance](src/algorithms/string/levenshtein-distance) - Distância mínima de edição entre duas sequências
-  * `A` [Longest Common Subsequence](src/algorithms/sets/longest-common-subsequence) (LCS)
-  * `A` [Longest Common Substring](src/algorithms/string/longest-common-substring)
-  * `A` [Longest Increasing Subsequence](src/algorithms/sets/longest-increasing-subsequence)
-  * `A` [Shortest Common Supersequence](src/algorithms/sets/shortest-common-supersequence)
-  * `A` [0/1 Knapsack Problem](src/algorithms/sets/knapsack-problem)
-  * `A` [Integer Partition](src/algorithms/math/integer-partition)
-  * `A` [Maximum Subarray](src/algorithms/sets/maximum-subarray)
-  * `A` [Bellman-Ford Algorithm](src/algorithms/graph/bellman-ford) - Encontrar o caminho mais curto para todos os vértices do gráfico
-  * `A` [Floyd-Warshall Algorithm](src/algorithms/graph/floyd-warshall) - Encontrar caminhos mais curtos entre todos os pares de vértices
-  * `A` [Regular Expression Matching](src/algorithms/string/regular-expression-matching)
-* **Backtracking** - Da mesma forma que a força bruta, tente gerar todas as soluções possíveis, mas cada vez que você gerar a próxima solução, você testará
-se satisfizer todas as condições, e só então continuar gerando soluções subseqüentes. Caso contrário, volte atrás e siga um caminho diferente para encontrar uma solução. Normalmente, a passagem DFS do espaço de estados está sendo usada.
-  * `B` [Jump Game](src/algorithms/uncategorized/jump-game)
-  * `B` [Unique Paths](src/algorithms/uncategorized/unique-paths)
-  * `A` [Hamiltonian Cycle](src/algorithms/graph/hamiltonian-cycle) - Visite todos os vértices exatamente uma vez
-  * `A` [N-Queens Problem](src/algorithms/uncategorized/n-queens)
-  * `A` [Knight's Tour](src/algorithms/uncategorized/knight-tour)
-  * `A` [Combination Sum](src/algorithms/sets/combination-sum) - Encontre todas as combinações que formam uma soma específica
-* **Branch & Bound** - Lembre-se da solução de menor custo encontrada em cada etapa do retrocesso
-pesquisar e usar o custo da solução de menor custo encontrada até o limite inferior do custo de
+  * `B` [Número de Fibonacci](src/algorithms/math/fibonacci)
+  * `B` [Jogo do Salto](src/algorithms/uncategorized/jump-game)
+  * `B` [Caminhos Únicos](src/algorithms/uncategorized/unique-paths)
+  * `B` [Terraços de Chuva](src/algorithms/uncategorized/rain-terraces) - Trapping problema da água da chuva
+  * `A` [Distância Levenshtein](src/algorithms/string/levenshtein-distance) - Distância mínima de edição entre duas sequências
+  * `A` [Mais Longa Subsequência Comum](src/algorithms/sets/longest-common-subsequence) (LCS)
+  * `A` [Substring Comum Mais Longa](src/algorithms/string/longest-common-substring)
+  * `A` [Maior Subsequência Crescente](src/algorithms/sets/longest-increasing-subsequence)
+  * `A` [Supersequência Comum Mais Curta](src/algorithms/sets/shortest-common-supersequence)
+  * `A` [Problema da Mochila](src/algorithms/sets/knapsack-problem)
+  * `A` [Partição Inteira](src/algorithms/math/integer-partition)
+  * `A` [Subarray Máximo](src/algorithms/sets/maximum-subarray)
+  * `A` [Algoritmo de Bellman-Ford](src/algorithms/graph/bellman-ford) - Encontrar caminhos mais curtos para todos os vértices do grafo a partir de um único vértice
+  * `A` [Algoritmo de Floyd-Warshall](src/algorithms/graph/floyd-warshall) - Encontrar caminhos mais curtos entre todos os pares de vértices
+  * `A` [Expressões Regulares Correspondentes](src/algorithms/string/regular-expression-matching)
+* **Backtracking** - Da mesma forma que a força bruta, tente gerar todas as soluções possíveis, mas, cada vez que você gerar a próxima solução será necessário testar se a mesma satisfaz todas as condições, e só então continuará a gerar as soluções subsequentes. Caso contrário, volte atrás e siga um caminho diferente para encontrar uma solução. Normalmente, a passagem DFS do espaço de estados está sendo usada.
+  * `B` [Jogo do Salto](src/algorithms/uncategorized/jump-game)
+  * `B` [Caminhos Únicos](src/algorithms/uncategorized/unique-paths)
+  * `A` [Ciclo Hamiltoniano](src/algorithms/graph/hamiltonian-cycle) - Visite todos os vértices exatamente uma vez
+  * `A` [Problema das N-Rainhas](src/algorithms/uncategorized/n-queens)
+  * `A` [Passeio do Cavaleiro](src/algorithms/uncategorized/knight-tour)
+  * `A` [Soma de Combinação](src/algorithms/sets/combination-sum) - Encontre todas as combinações que formam uma soma específica
+* **Branch & Bound** - Lembre-se da solução de menor custo encontrada em cada etapa do retrocesso, pesquisar e usar o custo da solução de menor custo encontrada até o limite inferior do custo de
 solução de menor custo para o problema, a fim de descartar soluções parciais com custos maiores que o
 solução de menor custo encontrada até o momento. Normalmente, a travessia BFS em combinação com a passagem DFS do espaço de estados
 árvore está sendo usada
@@ -225,10 +222,19 @@ npm test
 ```
 npm test -- 'LinkedList'
 ```
+**Solução de problemas**
+
+Caso o linting ou o teste estejam falhando, tente excluir a pasta node_modules e reinstalar os pacotes npm:
+```
+rm -rf ./node_modules
+npm i
+```
+
+Verifique também se você está usando uma versão correta do Node (>=14.16.0). Se você estiver usando [nvm](https://github.com/nvm-sh/nvm) para gerenciamento de versão do Node, você pode executar `nvm use` a partir da pasta raiz do projeto e a versão correta será escolhida.
 
-**Parque infantil**
+**Playground**
 
-Você pode brincar com estruturas de dados e algoritmos em `./src/playground/playground.js` arquivar e escrever
+Você pode brincar com estruturas de dados e algoritmos no arquivo `./src/playground/playground.js` e escrever
 testes para isso em `./src/playground/__test__/playground.test.js`.
 
 Em seguida, basta executar o seguinte comando para testar se o código do seu playground funciona conforme o esperado:
@@ -241,15 +247,16 @@ npm test -- 'playground'
 
 ### Referências
 
-[▶ Estruturas de dados e algoritmos no YouTube](https://www.youtube.com/playlist?list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
+- [▶ Estruturas de Dados e Algoritmos no YouTube](https://www.youtube.com/playlist?list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
+- [✍🏻 Esboços de Estruturas de Dados](https://okso.app/showcase/data-structures)
 
 ### Notação Big O
 
-Ordem de crescimento dos algoritmos especificados em notação Big O.
+A notação Big O é usada para classificar algoritmos de acordo com a forma como seu tempo de execução ou requisitos de espaço crescem à medida que o tamanho da entrada aumenta. No gráfico abaixo você pode encontrar as ordens mais comuns de crescimento de algoritmos especificados na notação Big O.
 
 ![Notação Big-O](./assets/big-o-graph.png)
 
-Fonte: [Notação Big-O dicas](http://bigocheatsheet.com/).
+Fonte: [Notação Big-O Dicas](http://bigocheatsheet.com/).
 
 Abaixo está a lista de algumas das notações Big O mais usadas e suas comparações de desempenho em relação aos diferentes tamanhos dos dados de entrada.
 
@@ -271,14 +278,14 @@ Abaixo está a lista de algumas das notações Big O mais usadas e suas compara
 | **Stack**               | n         | n         | 1         | 1          |             |
 | **Queue**               | n         | n         | 1         | 1          |             |
 | **Linked List**         | n         | n         | 1         | 1          |             |
-| **Hash Table**          | -         | n         | n         | n          | Em caso de uma função hash perfeita, os custos seriam O (1) |
-| **Binary Search Tree**  | n         | n         | n         | n          | No caso de custos de árvore equilibrados seria O (log (n))
+| **Hash Table**          | -         | n         | n         | n          | Em caso de uma função hash perfeita, os custos seriam O(1) |
+| **Binary Search Tree**  | n         | n         | n         | n          | No caso de custos de árvore equilibrados seria O(log(n))
 | **B-Tree**              | log(n)    | log(n)    | log(n)    | log(n)     |             |
 | **Red-Black Tree**      | log(n)    | log(n)    | log(n)    | log(n)     |             |
 | **AVL Tree**            | log(n)    | log(n)    | log(n)    | log(n)     |             |
 | **Bloom Filter**        | -         | 1         | 1         | -          | Falsos positivos são possíveis durante a pesquisa |
 
-### Array Sorting Algorithms Complexity
+### Complexidade dos Algoritmos de Ordenação de Matrizes
 
 | Nome                  | Melhor          | Média               | Pior                | Mémoria   | Estável   | Comentários |
 | --------------------- | :-------------: | :-----------------: | :-----------------: | :-------: | :-------: | :--------   |
@@ -287,7 +294,7 @@ Abaixo está a lista de algumas das notações Big O mais usadas e suas compara
 | **Selection sort**    | n<sup>2</sup>   | n<sup>2</sup>       | n<sup>2</sup>       | 1         | Não       |             |
 | **Heap sort**         | n&nbsp;log(n)   | n&nbsp;log(n)       | n&nbsp;log(n)       | 1         | Não       |             |
 | **Merge sort**        | n&nbsp;log(n)   | n&nbsp;log(n)       | n&nbsp;log(n)       | n         | Sim       |             |
-| **Quick sort**        | n&nbsp;log(n)   | n&nbsp;log(n)       | n<sup>2</sup>       | log(n)    | Não       | O Quicksort geralmente é feito no local com o espaço de pilha O  O(log(n)) stack space |
+| **Quick sort**        | n&nbsp;log(n)   | n&nbsp;log(n)       | n<sup>2</sup>       | log(n)    | Não       | O Quicksort geralmente é feito no local com espaço de pilha O(log(n)) |
 | **Shell sort**        | n&nbsp;log(n)   | depende da sequência de lacunas | n&nbsp;(log(n))<sup>2</sup>     | 1      | Não    |                   |
 | **Counting sort**     | n + r           | n + r               | n + r               | n + r     | Sim       | r - maior número na matriz          |
 | **Radix sort**        | n * k           | n * k               | n * k               | n + k     | Sim       | k - comprimento da chave mais longa |
diff --git a/src/algorithms/linked-list/reverse-traversal/README.md b/src/algorithms/linked-list/reverse-traversal/README.md
index 8a7e3d9e66..7e3f3cd6bb 100644
--- a/src/algorithms/linked-list/reverse-traversal/README.md
+++ b/src/algorithms/linked-list/reverse-traversal/README.md
@@ -1,7 +1,8 @@
 # Reversed Linked List Traversal
 
 _Read this in other languages:_
-[中文](README.zh-CN.md)
+[_中文_](README.zh-CN.md),
+[_Português_](README.pt-BR.md)
 
 The task is to traverse the given linked list in reversed order.
 
diff --git a/src/algorithms/linked-list/reverse-traversal/README.pt-BR.md b/src/algorithms/linked-list/reverse-traversal/README.pt-BR.md
new file mode 100644
index 0000000000..b2761ad720
--- /dev/null
+++ b/src/algorithms/linked-list/reverse-traversal/README.pt-BR.md
@@ -0,0 +1,23 @@
+# Travessia de Lista Encadeada Reversa
+
+_Leia isso em outros idiomas:_
+[_中文_](README.zh-CN.md),
+[_English_](README.md)
+
+A tarefa é percorrer a lista encadeada fornecida em ordem inversa.
+
+Por exemplo, para a seguinte lista vinculada:
+
+![](https://upload.wikimedia.org/wikipedia/commons/6/6d/Singly-linked-list.svg)
+
+A ordem de travessia deve ser:
+
+```texto
+37 → 99 → 12
+```
+
+A complexidade de tempo é `O(n)` porque visitamos cada nó apenas uma vez.
+
+## Referência
+
+- [Wikipedia](https://en.wikipedia.org/wiki/Linked_list)
diff --git a/src/algorithms/linked-list/traversal/README.md b/src/algorithms/linked-list/traversal/README.md
index 9acbe98dd9..09b177494c 100644
--- a/src/algorithms/linked-list/traversal/README.md
+++ b/src/algorithms/linked-list/traversal/README.md
@@ -2,7 +2,8 @@
 
 _Read this in other languages:_
 [_Русский_](README.ru-RU.md),
-[中文](README.zh-CN.md)
+[_中文_](README.zh-CN.md),
+[_Português_](README.pt-BR.md)
 
 The task is to traverse the given linked list in straight order.
 
diff --git a/src/algorithms/linked-list/traversal/README.pt-BR.md b/src/algorithms/linked-list/traversal/README.pt-BR.md
new file mode 100644
index 0000000000..0fae9ed01a
--- /dev/null
+++ b/src/algorithms/linked-list/traversal/README.pt-BR.md
@@ -0,0 +1,24 @@
+# Travessia de Lista Encadeada
+
+_Leia isso em outros idiomas:_
+[_Русский_](README.ru-RU.md),
+[_中文_](README.zh-CN.md),
+[_English_](README.md)
+
+A tarefa é percorrer a lista encadeada fornecida em ordem direta.
+
+Por exemplo, para a seguinte lista vinculada:
+
+![Singly linked list](https://upload.wikimedia.org/wikipedia/commons/6/6d/Singly-linked-list.svg)
+
+A ordem de travessia deve ser:
+
+```texto
+12 → 99 → 37
+```
+
+A complexidade de tempo é `O(n)` porque visitamos cada nó apenas uma vez.
+
+## Referência
+
+- [Wikipedia](https://en.wikipedia.org/wiki/Linked_list)
diff --git a/src/algorithms/ml/k-means/README.md b/src/algorithms/ml/k-means/README.md
index aebd60e100..4221880054 100644
--- a/src/algorithms/ml/k-means/README.md
+++ b/src/algorithms/ml/k-means/README.md
@@ -1,5 +1,8 @@
 # k-Means Algorithm
 
+_Read this in other languages:_
+[_Português_](README.pt-BR.md)
+
 The **k-Means algorithm** is an unsupervised Machine Learning algorithm. It's a clustering algorithm, which groups the sample data on the basis of similarity between dimensions of vectors.
 
 In k-Means classification, the output is a set of classes assigned to each vector. Each cluster location is continuously optimized in order to get the accurate locations of each cluster such that they represent each group clearly.
diff --git a/src/algorithms/ml/k-means/README.pt-BR.md b/src/algorithms/ml/k-means/README.pt-BR.md
new file mode 100644
index 0000000000..d814ac19bc
--- /dev/null
+++ b/src/algorithms/ml/k-means/README.pt-BR.md
@@ -0,0 +1,35 @@
+# Algoritmo k-Means
+
+_Leia isso em outros idiomas:_
+[_English_](README.md)
+
+O **algoritmo k-Means** é um algoritmo de aprendizado de máquina não supervisionado. É um algoritmo de agrupamento, que agrupa os dados da amostra com base na semelhança entre as dimensões dos vetores.
+
+Na classificação k-Means, a saída é um conjunto de classes atribuídas a cada vetor. Cada localização de cluster é continuamente otimizada para obter as localizações precisas de cada cluster de forma que representem cada grupo claramente.
+
+A ideia é calcular a similaridade entre a localização do cluster e os vetores de dados e reatribuir os clusters com base nela. [Distância Euclidiana](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/euclidean-distance) é usado principalmente para esta tarefa.
+
+![Distância Euclidiana entre dois pontos](https://upload.wikimedia.org/wikipedia/commons/5/55/Euclidean_distance_2d.svg)
+
+_Fonte: [Wikipedia](https://en.wikipedia.org/wiki/Euclidean_distance)_
+
+O algoritmo é o seguinte:
+
+1. Verifique se há erros como dados inválidos/inconsistentes
+2. Inicialize os locais do cluster `k` com pontos `k` iniciais/aleatórios
+3. Calcule a distância de cada ponto de dados de cada cluster
+4. Atribua o rótulo do cluster de cada ponto de dados igual ao do cluster em sua distância mínima
+5. Calcule o centroide de cada cluster com base nos pontos de dados que ele contém
+6. Repita cada uma das etapas acima até que as localizações do centroide estejam variando
+
+Aqui está uma visualização do agrupamento k-Means para melhor compreensão:
+
+![KNN Visualization 1](https://upload.wikimedia.org/wikipedia/commons/e/ea/K-means_convergence.gif)
+
+_Fonte: [Wikipedia](https://en.wikipedia.org/wiki/K-means_clustering)_
+
+Os centroides estão se movendo continuamente para criar uma melhor distinção entre os diferentes conjuntos de pontos de dados. Como podemos ver, após algumas iterações, a diferença de centroides é bastante baixa entre as iterações. Por exemplo, entre as iterações `13` e `14` a diferença é bem pequena porque o otimizador está ajustando os casos limite.
+
+## Referências
+
+- [k-Means neighbors algorithm on Wikipedia](https://en.wikipedia.org/wiki/K-means_clustering)
diff --git a/src/algorithms/ml/knn/README.md b/src/algorithms/ml/knn/README.md
index 0d61c14fb7..1fc168eaf2 100644
--- a/src/algorithms/ml/knn/README.md
+++ b/src/algorithms/ml/knn/README.md
@@ -1,5 +1,8 @@
 # k-Nearest Neighbors Algorithm
 
+_Read this in other languages:_
+[_Português_](README.pt-BR.md)
+
 The **k-nearest neighbors algorithm (k-NN)** is a supervised Machine Learning algorithm. It's a classification algorithm, determining the class of a sample vector using a sample data.
 
 In k-NN classification, the output is a class membership. An object is classified by a plurality vote of its neighbors, with the object being assigned to the class most common among its `k` nearest neighbors (`k` is a positive integer, typically small). If `k = 1`, then the object is simply assigned to the class of that single nearest neighbor.
diff --git a/src/algorithms/ml/knn/README.pt-BR.md b/src/algorithms/ml/knn/README.pt-BR.md
new file mode 100644
index 0000000000..b2abdd784f
--- /dev/null
+++ b/src/algorithms/ml/knn/README.pt-BR.md
@@ -0,0 +1,44 @@
+# Algoritmo de k-vizinhos mais próximos
+
+_Leia isso em outros idiomas:_
+[_English_](README.md)
+
+O **algoritmo de k-vizinhos mais próximos (k-NN)** é um algoritmo de aprendizado de máquina supervisionado. É um algoritmo de classificação, determinando a classe de um vetor de amostra usando dados de amostra.
+
+Na classificação k-NN, a saída é uma associação de classe. Um objeto é classificado por uma pluralidade de votos de seus vizinhos, com o objeto sendo atribuído à classe mais comum entre seus `k` vizinhos mais próximos (`k` é um inteiro positivo, tipicamente pequeno). Se `k = 1`, então o objeto é simplesmente atribuído à classe daquele único vizinho mais próximo.
+
+The idea is to calculate the similarity between two data points on the basis of a distance metric. [Distância Euclidiana](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/euclidean-distance) é usado principalmente para esta tarefa.
+
+![Distância Euclidiana entre dois pontos](https://upload.wikimedia.org/wikipedia/commons/5/55/Euclidean_distance_2d.svg)
+
+_Fonte: [Wikipedia](https://en.wikipedia.org/wiki/Euclidean_distance)_
+
+O algoritmo é o seguinte:
+
+1. Verifique se há erros como dados/rótulos inválidos.
+2. Calcule a distância euclidiana de todos os pontos de dados nos dados de treinamento com o ponto de classificação
+3. Classifique as distâncias dos pontos junto com suas classes em ordem crescente
+4. Pegue as classes iniciais `K` e encontre o modo para obter a classe mais semelhante
+5. Informe a classe mais semelhante
+
+Aqui está uma visualização da classificação k-NN para melhor compreensão:
+
+![KNN Visualization 1](https://upload.wikimedia.org/wikipedia/commons/e/e7/KnnClassification.svg)
+
+_Fonte: [Wikipedia](https://en.wikipedia.org/wiki/K-nearest_neighbors_algorithm)_
+
+A amostra de teste (ponto verde) deve ser classificada em quadrados azuis ou em triângulos vermelhos. Se `k = 3` (círculo de linha sólida) é atribuído aos triângulos vermelhos porque existem `2` triângulos e apenas `1` quadrado dentro do círculo interno. Se `k = 5` (círculo de linha tracejada) é atribuído aos quadrados azuis (`3` quadrados vs. `2` triângulos dentro do círculo externo).
+
+Outro exemplo de classificação k-NN:
+
+![KNN Visualization 2](https://media.geeksforgeeks.org/wp-content/uploads/graph2-2.png)
+
+_Fonte: [GeeksForGeeks](https://media.geeksforgeeks.org/wp-content/uploads/graph2-2.png)_
+
+Aqui, como podemos ver, a classificação dos pontos desconhecidos será julgada pela proximidade com outros pontos.
+
+É importante notar que `K` é preferível ter valores ímpares para desempate. Normalmente `K` é tomado como `3` ou `5`.
+
+## Referências
+
+- [k-nearest neighbors algorithm on Wikipedia](https://en.wikipedia.org/wiki/K-nearest_neighbors_algorithm)
diff --git a/src/algorithms/sorting/bubble-sort/README.pt-BR.md b/src/algorithms/sorting/bubble-sort/README.pt-BR.md
index c7862bb957..e650523d71 100644
--- a/src/algorithms/sorting/bubble-sort/README.pt-BR.md
+++ b/src/algorithms/sorting/bubble-sort/README.pt-BR.md
@@ -1,16 +1,19 @@
 # Bubble Sort
 
+_Leia isso em outros idiomas:_
+[_English_](README.md)
+
 O bubble sort, ou ordenação por flutuação (literalmente "por bolha"), é um algoritmo de ordenação dos mais simples. A ideia é percorrer o vetor diversas vezes, e a cada passagem fazer flutuar para o topo o maior elemento da sequência. Essa movimentação lembra a forma como as bolhas em um tanque de água procuram seu próprio nível, e disso vem o nome do algoritmo.
 
 ![Algorithm Visualization](https://upload.wikimedia.org/wikipedia/commons/c/c8/Bubble-sort-example-300px.gif)
 
-## Complexity
+## Complexidade
 
-| Name                  | Best            | Average             | Worst               | Memory    | Stable    | Comments  |
+| Nome                  | Melhor            | Média             | Pior               | Memória    | Estável    | Comentários  |
 | --------------------- | :-------------: | :-----------------: | :-----------------: | :-------: | :-------: | :-------- |
-| **Bubble sort**       | n               | n<sup>2</sup>       | n<sup>2</sup>       | 1         | Yes       |           |
+| **Bubble sort**       | n               | n<sup>2</sup>       | n<sup>2</sup>       | 1         | Sim       |           |
 
-## References
+## Referências
 
 - [Wikipedia](https://pt.wikipedia.org/wiki/Bubble_sort)
 - [YouTube](https://www.youtube.com/watch?v=6Gv8vg0kcHc&index=27&t=0s&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
diff --git a/src/algorithms/sorting/counting-sort/README.md b/src/algorithms/sorting/counting-sort/README.md
index 098961a0e0..40a9539a22 100644
--- a/src/algorithms/sorting/counting-sort/README.md
+++ b/src/algorithms/sorting/counting-sort/README.md
@@ -1,5 +1,8 @@
 # Counting Sort
 
+_Read this in other languages:_
+[_Português_](README.pt-BR.md)
+
 In computer science, **counting sort** is an algorithm for sorting 
 a collection of objects according to keys that are small integers; 
 that is, it is an integer sorting algorithm. It operates by 
diff --git a/src/algorithms/sorting/counting-sort/README.pt-br.md b/src/algorithms/sorting/counting-sort/README.pt-br.md
new file mode 100644
index 0000000000..af2c75f6af
--- /dev/null
+++ b/src/algorithms/sorting/counting-sort/README.pt-br.md
@@ -0,0 +1,70 @@
+# Counting Sort
+
+_Leia isso em outros idiomas:_
+[_English_](README.md)
+
+Em ciência da computação, **counting sort** é um algoritmo para ordenar
+uma coleção de objetos de acordo com chaves que são pequenos inteiros;
+ou seja, é um algoritmo de ordenação de inteiros. Ele opera por
+contando o número de objetos que têm cada valor de chave distinto,
+e usando aritmética nessas contagens para determinar as posições
+de cada valor de chave na sequência de saída. Seu tempo de execução é
+linear no número de itens e a diferença entre o
+valores de chave máximo e mínimo, portanto, é adequado apenas para
+uso em situações em que a variação de tonalidades não é significativamente
+maior que o número de itens. No entanto, muitas vezes é usado como
+sub-rotina em outro algoritmo de ordenação, radix sort, que pode
+lidar com chaves maiores de forma mais eficiente.
+
+Como a classificação por contagem usa valores-chave como índices em um vetor,
+não é uma ordenação por comparação, e o limite inferior `Ω(n log n)` para
+a ordenação por comparação não se aplica a ele. A classificação por bucket pode ser usada
+para muitas das mesmas tarefas que a ordenação por contagem, com um tempo semelhante
+análise; no entanto, em comparação com a classificação por contagem, a classificação por bucket requer
+listas vinculadas, arrays dinâmicos ou uma grande quantidade de pré-alocados
+memória para armazenar os conjuntos de itens dentro de cada bucket, enquanto
+A classificação por contagem armazena um único número (a contagem de itens)
+por balde.
+
+A classificação por contagem funciona melhor quando o intervalo de números para cada
+elemento do vetor é muito pequeno.
+
+## Algoritmo
+
+**Passo I**
+
+Na primeira etapa, calculamos a contagem de todos os elementos do
+vetor de entrada 'A'. Em seguida, armazene o resultado no vetor de contagem `C`.
+A maneira como contamos é descrita abaixo.
+
+![Counting Sort](https://3.bp.blogspot.com/-jJchly1BkTc/WLGqCFDdvCI/AAAAAAAAAHA/luljAlz2ptMndIZNH0KLTTuQMNsfzDeFQCLcB/s1600/CSortUpdatedStepI.gif)
+
+**Passo II**
+
+Na segunda etapa, calculamos quantos elementos existem na entrada
+do vetor `A` que são menores ou iguais para o índice fornecido.
+`Ci` = números de elementos menores ou iguais a `i` no vetor de entrada.
+
+![Counting Sort](https://1.bp.blogspot.com/-1vFu-VIRa9Y/WLHGuZkdF3I/AAAAAAAAAHs/8jKu2dbQee4ap9xlVcNsILrclqw0UxAVACLcB/s1600/Step-II.png)
+
+**Passo III**
+
+Nesta etapa, colocamos o elemento `A` do vetor de entrada em classificado
+posição usando a ajuda do vetor de contagem construída `C`, ou seja, o que
+construímos no passo dois. Usamos o vetor de resultados `B` para armazenar
+os elementos ordenados. Aqui nós lidamos com o índice de `B` começando de
+zero.
+ 
+![Counting Sort](https://1.bp.blogspot.com/-xPqylngqASY/WLGq3p9n9vI/AAAAAAAAAHM/JHdtXAkJY8wYzDMBXxqarjmhpPhM0u8MACLcB/s1600/ResultArrayCS.gif)
+
+## Complexidade
+
+| Nome                  | Melhor            | Média             | Pior               | Memória    | Estável    | Comentários  |
+| --------------------- | :-------------: | :-----------------: | :-----------------: | :-------: | :-------: | :-------- |
+| **Counting sort**     | n + r           | n + r               | n + r               | n + r     | Sim       | r - Maior número no vetor |
+
+## Referências
+
+- [Wikipedia](https://en.wikipedia.org/wiki/Counting_sort)
+- [YouTube](https://www.youtube.com/watch?v=OKd534EWcdk&index=61&t=0s&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
+- [EfficientAlgorithms](https://efficientalgorithms.blogspot.com/2016/09/lenear-sorting-counting-sort.html)
diff --git a/src/algorithms/sorting/heap-sort/README.md b/src/algorithms/sorting/heap-sort/README.md
index 6ccc50b3b0..2370776f1b 100644
--- a/src/algorithms/sorting/heap-sort/README.md
+++ b/src/algorithms/sorting/heap-sort/README.md
@@ -1,5 +1,8 @@
 # Heap Sort
 
+_Read this in other languages:_
+[_Português_](README.pt-BR.md)
+
 Heapsort is a comparison-based sorting algorithm.
 Heapsort can be thought of as an improved selection
 sort: like that algorithm, it divides its input into
diff --git a/src/algorithms/sorting/heap-sort/README.pt-BR.md b/src/algorithms/sorting/heap-sort/README.pt-BR.md
new file mode 100644
index 0000000000..6d5a2d4849
--- /dev/null
+++ b/src/algorithms/sorting/heap-sort/README.pt-BR.md
@@ -0,0 +1,20 @@
+# Heap Sort
+
+_Leia isso em outros idiomas:_
+[_English_](README.md)
+
+Heapsort é um algoritmo de ordenação baseado em comparação. O Heapsort pode ser pensado como uma seleção aprimorada sort: como esse algoritmo, ele divide sua entrada em uma região classificada e uma região não classificada, e iterativamente encolhe a região não classificada extraindo o maior elemento e movendo-o para a região classificada. A melhoria consiste no uso de uma estrutura de dados heap em vez de uma busca em tempo linear para encontrar o máximo.
+
+![Visualização do Algoritmo](https://upload.wikimedia.org/wikipedia/commons/1/1b/Sorting_heapsort_anim.gif)
+
+![Visualização do Algoritmo](https://upload.wikimedia.org/wikipedia/commons/4/4d/Heapsort-example.gif)
+
+## Complexidade
+
+| Nome                  | Melhor            | Média             | Pior               | Memória    | Estável    | Comentários  |
+| --------------------- | :-------------: | :-----------------: | :-----------------: | :-------: | :-------: | :-------- |
+| **Heap sort**         | n&nbsp;log(n)   | n&nbsp;log(n)       | n&nbsp;log(n)       | 1         | Não        |           |
+
+## Referências
+
+[Wikipedia](https://en.wikipedia.org/wiki/Heapsort)
diff --git a/src/algorithms/sorting/insertion-sort/README.md b/src/algorithms/sorting/insertion-sort/README.md
index cd3a74ef34..8bc922683f 100644
--- a/src/algorithms/sorting/insertion-sort/README.md
+++ b/src/algorithms/sorting/insertion-sort/README.md
@@ -1,5 +1,8 @@
 # Insertion Sort
 
+_Read this in other languages:_
+[_Português_](README.pt-BR.md)
+
 Insertion sort is a simple sorting algorithm that builds 
 the final sorted array (or list) one item at a time. 
 It is much less efficient on large lists than more 
diff --git a/src/algorithms/sorting/insertion-sort/README.pt-BR.md b/src/algorithms/sorting/insertion-sort/README.pt-BR.md
new file mode 100644
index 0000000000..a36d2742be
--- /dev/null
+++ b/src/algorithms/sorting/insertion-sort/README.pt-BR.md
@@ -0,0 +1,22 @@
+# Insertion Sort
+
+_Leia isso em outros idiomas:_
+[_English_](README.md)
+
+A ordenação por inserção é um algoritmo de ordenação simples que criaa matriz classificada final (ou lista) um item de cada vez.
+É muito menos eficiente em grandes listas do que mais algoritmos avançados, como quicksort, heapsort ou merge
+ordenar.
+
+![Visualização do Algoritmo](https://upload.wikimedia.org/wikipedia/commons/4/42/Insertion_sort.gif)
+
+![Visualização do Algoritmo](https://upload.wikimedia.org/wikipedia/commons/0/0f/Insertion-sort-example-300px.gif)
+
+## Complexidade
+
+| Nome                  | Melhor            | Média             | Pior               | Memória    | Estável    | Comentários  |
+| --------------------- | :-------------: | :-----------------: | :-----------------: | :-------: | :-------: | :-------- |
+| **Insertion sort**    | n               | n<sup>2</sup>       | n<sup>2</sup>       | 1         | Sim       |           |
+
+## Referências
+
+[Wikipedia](https://en.wikipedia.org/wiki/Insertion_sort)
diff --git a/src/algorithms/sorting/merge-sort/README.md b/src/algorithms/sorting/merge-sort/README.md
index b4d76b90a6..2931329482 100644
--- a/src/algorithms/sorting/merge-sort/README.md
+++ b/src/algorithms/sorting/merge-sort/README.md
@@ -1,7 +1,8 @@
 # Merge Sort
 
 _Read this in other languages:_
-[_한국어_](README.ko-KR.md)
+[_한국어_](README.ko-KR.md),
+[_Português_](README.pt-BR.md)
 
 In computer science, merge sort (also commonly spelled
 mergesort) is an efficient, general-purpose,
diff --git a/src/algorithms/sorting/merge-sort/README.pt-BR.md b/src/algorithms/sorting/merge-sort/README.pt-BR.md
new file mode 100644
index 0000000000..f7be449f04
--- /dev/null
+++ b/src/algorithms/sorting/merge-sort/README.pt-BR.md
@@ -0,0 +1,38 @@
+# Merge Sort
+
+_Leia isso em outros idiomas:_
+[_한국어_](README.ko-KR.md),
+[_English_](README.md)
+
+Em ciência da computação, merge sort (também comumente escrito
+mergesort) é uma ferramenta eficiente, de propósito geral,
+algoritmo de ordenação baseado em comparação. A maioria das implementações
+produzir uma classificação estável, o que significa que a implementação
+preserva a ordem de entrada de elementos iguais na ordenação
+resultado. Mergesort é um algoritmo de divisão e conquista que
+foi inventado por John von Neumann em 1945.
+
+Um exemplo de classificação de mesclagem. Primeiro divida a lista em
+a menor unidade (1 elemento), então compare cada
+elemento com a lista adjacente para classificar e mesclar o
+duas listas adjacentes. Finalmente todos os elementos são ordenados
+e mesclado.
+
+![Merge Sort](https://upload.wikimedia.org/wikipedia/commons/c/cc/Merge-sort-example-300px.gif)
+
+Um algoritmo de classificação de mesclagem recursivo usado para classificar uma matriz de 7
+valores inteiros. Estes são os passos que um ser humano daria para
+emular merge sort (top-down).
+
+![Merge Sort](https://upload.wikimedia.org/wikipedia/commons/e/e6/Merge_sort_algorithm_diagram.svg)
+
+## Complexidade
+
+| Nome                  | Melhor            | Média             | Pior               | Memória    | Estável    | Comentários  |
+| --------------------- | :-------------: | :-----------------: | :-----------------: | :-------: | :-------: | :-------- |
+| **Merge sort**        | n&nbsp;log(n)   | n&nbsp;log(n)       | n&nbsp;log(n)       | n         | Sim       |           |
+
+## Referências
+
+- [Wikipedia](https://en.wikipedia.org/wiki/Merge_sort)
+- [YouTube](https://www.youtube.com/watch?v=KF2j-9iSf4Q&index=27&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
diff --git a/src/algorithms/sorting/quick-sort/README.md b/src/algorithms/sorting/quick-sort/README.md
index 2daedb46cf..9dcec0f12f 100644
--- a/src/algorithms/sorting/quick-sort/README.md
+++ b/src/algorithms/sorting/quick-sort/README.md
@@ -1,8 +1,8 @@
 # Quicksort
 
 _Read this in other languages:_
-[_Português_](README.pt-BR.md),
-[_简体中文_](README.zh-CN.md)
+[_简体中文_](README.zh-CN.md),
+[_Português_](README.pt-BR.md)
 
 Quicksort is a divide and conquer algorithm.
 Quicksort first divides a large array into two smaller 
diff --git a/src/algorithms/sorting/quick-sort/README.pt-BR.md b/src/algorithms/sorting/quick-sort/README.pt-BR.md
index a52f3725de..ca3a45699f 100644
--- a/src/algorithms/sorting/quick-sort/README.pt-BR.md
+++ b/src/algorithms/sorting/quick-sort/README.pt-BR.md
@@ -1,15 +1,19 @@
 # Quicksort
 
-Quicksort é um algoritmo de dividir para conquistar é um algoritmo de divisão e conquista.
+_Leia isso em outros idiomas:_
+[_简体中文_](README.zh-CN.md),
+[_English_](README.md)
+
+Quicksort é um algoritmo de dividir para conquistar.
 Quicksort primeiro divide uma grande matriz em duas menores
 submatrizes: os elementos baixos e os elementos altos.
-O Quicksort pode então classificar recursivamente as submatrizes
+O Quicksort pode então classificar recursivamente as submatrizes.
 
 As etapas são:
 
 1. Escolha um elemento, denominado pivô, na matriz.
 2. Particionamento: reordene a matriz para que todos os elementos com
-valores menores que o pivô vêm antes do pivô, enquanto todos
+valores menores que o pivô estejam antes do pivô, enquanto todos
 elementos com valores maiores do que o pivô vêm depois dele
 (valores iguais podem ser usados em qualquer direção). Após este particionamento,
 o pivô está em sua posição final. Isso é chamado de
@@ -27,7 +31,7 @@ As linhas horizontais são valores dinâmicos.
 
 | Nome                  | Melhor            | Média             | Pior               | Memória    | Estável    | Comentários  |
 | --------------------- | :-------------: | :-----------------: | :-----------------: | :-------: | :-------: | :-------- |
-| **Quick sort**        | n&nbsp;log(n)   | n&nbsp;log(n)       | n<sup>2</sup>       | log(n)    | No        |  Quicksort geralmente é feito no local com espaço de pilha O(log(n)) |
+| **Quick sort**        | n&nbsp;log(n)   | n&nbsp;log(n)       | n<sup>2</sup>       | log(n)    | Não        |  Quicksort geralmente é feito no local com espaço de pilha O(log(n)) |
 
 ## Referências
 
diff --git a/src/algorithms/sorting/radix-sort/README.md b/src/algorithms/sorting/radix-sort/README.md
index 2da1f5504b..80129278d1 100644
--- a/src/algorithms/sorting/radix-sort/README.md
+++ b/src/algorithms/sorting/radix-sort/README.md
@@ -1,5 +1,8 @@
 # Radix Sort
 
+_Read this in other languages:_
+[_Português_](README.pt-BR.md),
+
 In computer science, **radix sort** is a non-comparative integer sorting 
 algorithm that sorts data with integer keys by grouping keys by the individual 
 digits which share the same significant position and value. A positional notation
diff --git a/src/algorithms/sorting/radix-sort/README.pt-BR.md b/src/algorithms/sorting/radix-sort/README.pt-BR.md
new file mode 100644
index 0000000000..2274440984
--- /dev/null
+++ b/src/algorithms/sorting/radix-sort/README.pt-BR.md
@@ -0,0 +1,48 @@
+# Radix Sort
+
+_Leia isso em outros idiomas:_
+[_English_](README.md)
+
+Em ciência da computação, **radix sort** é uma classificação inteira não comparativa
+algoritmo que classifica os dados com chaves inteiras agrupando as chaves pelo indivíduo
+dígitos que compartilham a mesma posição e valor significativos. Uma notação posicional
+é necessário, mas porque os números inteiros podem representar cadeias de caracteres
+(por exemplo, nomes ou datas) e números de ponto flutuante especialmente formatados, base
+sort não está limitado a inteiros.
+
+*De onde vem o nome?*
+
+Em sistemas numéricos matemáticos, a *radix* ou base é o número de dígitos únicos,
+incluindo o dígito zero, usado para representar números em um sistema de numeração posicional.
+Por exemplo, um sistema binário (usando números 0 e 1) tem uma raiz de 2 e um decimal
+sistema (usando números de 0 a 9) tem uma raiz de 10.
+
+## Eficiência
+
+O tópico da eficiência do radix sort comparado a outros algoritmos de ordenação é
+um pouco complicado e sujeito a muitos mal-entendidos. Se raiz
+sort é igualmente eficiente, menos eficiente ou mais eficiente do que o melhor
+algoritmos baseados em comparação depende dos detalhes das suposições feitas.
+A complexidade de classificação de raiz é `O(wn)` para chaves `n` que são inteiros de tamanho de palavra `w`.
+Às vezes, `w` é apresentado como uma constante, o que tornaria a classificação radix melhor
+(para `n` suficientemente grande) do que os melhores algoritmos de ordenação baseados em comparação,
+que todos realizam comparações `O(n log n)` para classificar chaves `n`. No entanto, em
+geral `w` não pode ser considerado uma constante: se todas as chaves `n` forem distintas,
+então `w` tem que ser pelo menos `log n` para que uma máquina de acesso aleatório seja capaz de
+armazená-los na memória, o que dá na melhor das hipóteses uma complexidade de tempo `O(n log n)`. Este
+parece tornar a ordenação radix no máximo tão eficiente quanto a melhor
+ordenações baseadas em comparação (e pior se as chaves forem muito mais longas que `log n`).
+
+![Radix Sort](https://www.researchgate.net/publication/291086231/figure/fig1/AS:614214452404240@1523451545568/Simplistic-illustration-of-the-steps-performed-in-a-radix-sort-In-this-example-the.png)
+
+## Complexidade
+
+| Nome                  | Melhor            | Média             | Pior               | Memória    | Estável    | Comentários  |
+| --------------------- | :-------------: | :-----------------: | :-----------------: | :-------: | :-------: | :-------- |
+| **Radix sort**        | n * k           | n * k               | n * k               | n + k     | Sim       | k - comprimento da chave mais longa |
+
+## Referências
+
+- [Wikipedia](https://en.wikipedia.org/wiki/Radix_sort)
+- [YouTube](https://www.youtube.com/watch?v=XiuSW_mEn7g&index=62&t=0s&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
+- [ResearchGate](https://www.researchgate.net/figure/Simplistic-illustration-of-the-steps-performed-in-a-radix-sort-In-this-example-the_fig1_291086231)
diff --git a/src/algorithms/sorting/selection-sort/README.md b/src/algorithms/sorting/selection-sort/README.md
index b584777a59..005c616131 100644
--- a/src/algorithms/sorting/selection-sort/README.md
+++ b/src/algorithms/sorting/selection-sort/README.md
@@ -1,7 +1,7 @@
 # Selection Sort
 
 _Read this in other languages:_
-[Português brasileiro](README.pt-BR.md).
+[_Português_](README.pt-BR.md).
 
 Selection sort is a sorting algorithm, specifically an 
 in-place comparison sort. It has O(n2) time complexity, 
diff --git a/src/algorithms/sorting/selection-sort/README.pt-BR.md b/src/algorithms/sorting/selection-sort/README.pt-BR.md
index c9c1afd6a1..0c45b73f61 100644
--- a/src/algorithms/sorting/selection-sort/README.pt-BR.md
+++ b/src/algorithms/sorting/selection-sort/README.pt-BR.md
@@ -1,7 +1,7 @@
 # Selection Sort
 
-_Leia isso em outras línguas:_
-[english](README.md).
+_Leia isso em outros idiomas:_
+[_English_](README.md).
 
 Selection Sort é um algoritmo de ordenação, mais especificamente um algoritmo de ordenação por comparação in-place (requer uma quantidade constante de espaço de memória adicional). Tem complexidade O(n²), tornando-o ineficiente em listas grandes e, geralmente, tem desempenho inferior ao similar Insertion Sort. O Selection Sort é conhecido por sua simplicidade e tem vantagens de desempenho sobre algoritmos mais complexos em certas situações, particularmente quando a memória auxiliar é limitada.
 
diff --git a/src/algorithms/sorting/shell-sort/README.md b/src/algorithms/sorting/shell-sort/README.md
index 386fc9f066..f93338e2eb 100644
--- a/src/algorithms/sorting/shell-sort/README.md
+++ b/src/algorithms/sorting/shell-sort/README.md
@@ -1,5 +1,8 @@
 # Shellsort
 
+_Read this in other languages:_
+[_Português_](README.pt-BR.md).
+
 Shellsort, also known as Shell sort or Shell's method, 
 is an in-place comparison sort. It can be seen as either a 
 generalization of sorting by exchange (bubble sort) or sorting 
diff --git a/src/algorithms/sorting/shell-sort/README.pt-BR.md b/src/algorithms/sorting/shell-sort/README.pt-BR.md
new file mode 100644
index 0000000000..14de1a517e
--- /dev/null
+++ b/src/algorithms/sorting/shell-sort/README.pt-BR.md
@@ -0,0 +1,60 @@
+# Shellsort
+
+_Leia isso em outros idiomas:_
+[_English_](README.md).
+
+Shellsort, também conhecido como Shell sort ou método de Shell,
+é uma classificação de comparação in-loco. Pode ser visto tanto como um
+generalização da ordenação por troca (bubble sort) ou ordenação
+por inserção (ordenação por inserção). O método começa classificando
+pares de elementos distantes um do outro, então progressivamente
+reduzindo a distância entre os elementos a serem comparados. Iniciando
+com elementos distantes, pode mover alguns fora do lugar
+elementos em posição mais rápido do que um simples vizinho mais próximo
+intercâmbio
+
+![Shellsort](https://upload.wikimedia.org/wikipedia/commons/d/d8/Sorting_shellsort_anim.gif)
+
+## Como o Shellsort funciona?
+
+Para nosso exemplo e facilidade de compreensão, tomamos o intervalo
+de `4`. Faça uma sub-lista virtual de todos os valores localizados no
+intervalo de 4 posições. Aqui esses valores são
+`{35, 14}`, `{33, 19}`, `{42, 27}` e `{10, 44}`
+
+![Shellsort](https://www.tutorialspoint.com/data_structures_algorithms/images/shell_sort_gap_4.jpg)
+
+Comparamos valores em cada sublista e os trocamos (se necessário)
+na matriz original. Após esta etapa, o novo array deve
+parece com isso
+
+![Shellsort](https://www.tutorialspoint.com/data_structures_algorithms/images/shell_sort_step_1.jpg)
+
+Então, pegamos o intervalo de 2 e essa lacuna gera duas sub-listas
+- `{14, 27, 35, 42}`, `{19, 10, 33, 44}`
+
+![Shellsort](https://www.tutorialspoint.com/data_structures_algorithms/images/shell_sort_gap_2.jpg)
+
+Comparamos e trocamos os valores, se necessário, no array original.
+Após esta etapa, a matriz deve ficar assim
+
+![Shellsort](https://www.tutorialspoint.com/data_structures_algorithms/images/shell_sort_step_2.jpg)
+
+> OBS: Na imagem abaixo há um erro de digitação e a matriz de resultados deve ser `[14, 10, 27, 19, 35, 33, 42, 44]`.
+
+Finalmente, ordenamos o resto do array usando o intervalo de valor 1.
+A classificação de shell usa a classificação por inserção para classificar a matriz.
+
+![Shellsort](https://www.tutorialspoint.com/data_structures_algorithms/images/shell_sort.jpg)
+
+## Complexidade
+
+| Nome                  | Melhor            | Média             | Pior               | Memória    | Estável    | Comentários  |
+| --------------------- | :-------------: | :-----------------: | :-----------------: | :-------: | :-------: | :-------- |
+| **Shell sort**        | n&nbsp;log(n)   | depends on gap sequence   | n&nbsp;(log(n))<sup>2</sup>  | 1         | Não         |           |
+
+## Referências
+
+- [Tutorials Point](https://www.tutorialspoint.com/data_structures_algorithms/shell_sort_algorithm.htm)
+- [Wikipedia](https://en.wikipedia.org/wiki/Shellsort)
+- [YouTube by Rob Edwards](https://www.youtube.com/watch?v=ddeLSDsYVp8&index=79&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
diff --git a/src/data-structures/bloom-filter/README.pt-BR.md b/src/data-structures/bloom-filter/README.pt-BR.md
index 77c4232262..0c8522b958 100644
--- a/src/data-structures/bloom-filter/README.pt-BR.md
+++ b/src/data-structures/bloom-filter/README.pt-BR.md
@@ -3,7 +3,7 @@
 O **bloom filter** é uma estrutura de dados probabilística
 espaço-eficiente designada para testar se um elemento está
 ou não presente em um conjunto de dados. Foi projetado para ser
-incrivelmente rápido e utilizar o mínimo de memória ao 
+incrivelmente rápida e utilizar o mínimo de memória ao 
 potencial custo de um falso-positivo. Correspondências 
 _falsas positivas_ são possíveis, contudo _falsos negativos_ 
 não são - em outras palavras, a consulta retorna 
@@ -12,7 +12,7 @@ não são - em outras palavras, a consulta retorna
 Bloom propôs a técnica para aplicações onde a quantidade 
 de entrada de dados exigiria uma alocação de memória
 impraticavelmente grande se as "convencionais" técnicas
-error-free hashing fossem aplicado.
+error-free hashing fossem aplicadas.
 
 ## Descrição do algoritmo
 
diff --git a/src/data-structures/disjoint-set/README.pt-BR.md b/src/data-structures/disjoint-set/README.pt-BR.md
index 130b8aea6c..a7d827a8a2 100644
--- a/src/data-structures/disjoint-set/README.pt-BR.md
+++ b/src/data-structures/disjoint-set/README.pt-BR.md
@@ -1,8 +1,8 @@
-# Conjunto Disjuntor (Disjoint Set)
+# Conjunto Disjunto (Disjoint Set)
 
-**Conjunto Disjuntor**
+**Conjunto Disjunto**
 
-**Conjunto Disjuntor** é uma estrutura de dados (também chamado de
+**Conjunto Disjunto** é uma estrutura de dados (também chamado de
 estrutura de dados de union–find ou merge–find) é uma estrutura de dados
 que rastreia um conjunto de elementos particionados em um número de
 subconjuntos separados (sem sobreposição).
@@ -10,9 +10,9 @@ Ele fornece operações de tempo quase constante (limitadas pela função
 inversa de Ackermann) para *adicionar novos conjuntos*, para 
 *mesclar/fundir conjuntos existentes* e para *determinar se os elementos
 estão no mesmo conjunto*.
-Além de muitos outros usos (veja a seção Applications), conjunto disjuntor
+Além de muitos outros usos (veja a seção Applications), conjuntos disjuntos
 desempenham um papel fundamental no algoritmo de Kruskal para encontrar a
-árvore geradora mínima de um gráfico (graph).
+árvore geradora mínima de um grafo (graph).
 
 ![disjoint set](https://upload.wikimedia.org/wikipedia/commons/6/67/Dsu_disjoint_sets_init.svg)
 
diff --git a/src/data-structures/doubly-linked-list/README.pt-BR.md b/src/data-structures/doubly-linked-list/README.pt-BR.md
index 9ba3954d0b..c4294decf4 100644
--- a/src/data-structures/doubly-linked-list/README.pt-BR.md
+++ b/src/data-structures/doubly-linked-list/README.pt-BR.md
@@ -4,7 +4,7 @@ Na ciência da computação, uma **lista duplamente conectada** é uma estrutura
 de dados vinculada que se consistem em um conjunto de registros
 sequencialmente vinculados chamados de nós (nodes). Em cada nó contém dois
 campos, chamados de ligações, que são referenciados ao nó anterior e posterior
-de uma sequência de nós. O começo e o fim dos nós anteriormente e posteiormente
+de uma sequência de nós. O começo e o fim dos nós anteriormente e posteriormente
 ligados, respectiviamente, apontam para algum tipo de terminação, normalmente
 um nó sentinela ou nulo, para facilitar a travessia da lista. Se existe
 somente um nó sentinela, então a lista é ligada circularmente através do nó
@@ -20,7 +20,7 @@ Enquanto adicionar ou remover um nó de uma lista duplamente vinculada requer
 alterar mais ligações (conexões) do que em uma lista encadeada individualmente
 (singly linked list), as operações são mais simples e potencialmente mais
 eficientes (para nós que não sejam nós iniciais) porque não há necessidade
-de se manter rastreamento do nó anterior durante a travessia ou não há
+de manter um rastreamento do nó anterior durante a travessia ou não há
 necessidade de percorrer a lista para encontrar o nó anterior, para que
 então sua ligação/conexão possa ser modificada.
 
@@ -44,7 +44,7 @@ Add(value)
 end Add
 ```
 
-### Deletar
+### Remoção
 
 ```text
 Remove(head, value)
diff --git a/src/data-structures/hash-table/README.pt-BR.md b/src/data-structures/hash-table/README.pt-BR.md
index 9abbb48890..c89faf6ca1 100644
--- a/src/data-structures/hash-table/README.pt-BR.md
+++ b/src/data-structures/hash-table/README.pt-BR.md
@@ -1,6 +1,6 @@
 # Tabela de Hash (Hash Table)
 
-Na ciência da computação, uma **tabela de hash** (hash map) é uma
+Na ciência da computação, uma **tabela de hash** (hash table) é uma
 estrutura de dados pela qual implementa um tipo de dado abstrado de
 *array associativo*, uma estrutura que pode *mapear chaves para valores*.
 Uma tabela de hash utiliza uma *função de hash* para calcular um índice
@@ -10,7 +10,7 @@ pode ser encontrado.
 Idealmente, a função de hash irá atribuir a cada chave a um bucket único,
 mas a maioria dos designs de tabela de hash emprega uma função de hash
 imperfeita, pela qual poderá causar colisões de hashes onde a função de hash
-gera o mesmo índice para mais de uma chave.Tais colisões devem ser
+gera o mesmo índice para mais de uma chave. Tais colisões devem ser
 acomodados de alguma forma.
 
 ![Hash Table](./images/hash-table.jpeg)
diff --git a/src/data-structures/priority-queue/README.pt-BR.md b/src/data-structures/priority-queue/README.pt-BR.md
index 9e836bde7e..e6d84e263a 100644
--- a/src/data-structures/priority-queue/README.pt-BR.md
+++ b/src/data-structures/priority-queue/README.pt-BR.md
@@ -1,7 +1,7 @@
 # Fila de Prioridade (Priority Queue)
 
-Na ciência da computação, uma **fila de prioridade** é um tipo de dados
-abastrato que é como uma fila regular (regular queue) ou estrutura de
+Na ciência da computação, uma **fila de prioridade** é um tipo de estrutura de
+dados abastrata que é como uma fila regular (regular queue) ou estrutura de
 dados de pilha (stack), mas adicionalmente cada elemento possui uma
 "prioridade" associada.
 
@@ -10,11 +10,11 @@ antes de um elemento com baixa prioridade. Caso dois elementos posusam a
 mesma prioridade, eles serão servidos de acordo com sua ordem na fila.
 
 Enquanto as filas de prioridade são frequentemente implementadas com
-pilhas (heaps), elas são conceitualmente distintas das pilhas (heaps).
+pilhas (stacks), elas são conceitualmente distintas das pilhas (stacks).
 A fila de prioridade é um conceito abstrato como uma "lista" (list) ou
 um "mapa" (map); assim como uma lista pode ser implementada com uma
 lista encadeada (liked list) ou um array, a fila de prioridade pode ser
-implementada com uma pilha (heap) ou com uima variedade de outros métodos,
+implementada com uma pilha (stack) ou com uma variedade de outros métodos,
 como um array não ordenado (unordered array).
 
 ## Referências
diff --git a/src/data-structures/stack/README.pt-BR.md b/src/data-structures/stack/README.pt-BR.md
index d1269d2437..ee862fe43a 100644
--- a/src/data-structures/stack/README.pt-BR.md
+++ b/src/data-structures/stack/README.pt-BR.md
@@ -1,14 +1,14 @@
-# Stack
+# Pilha (Stack)
 
-Na ciência da computação, um **stack** é uma estrutura de dados abstrata
+Na ciência da computação, uma **pilha** é uma estrutura de dados abstrata
 que serve como uma coleção de elementos com duas operações principais:
 
 * **push**, pela qual adiciona um elemento à coleção, e
 * **pop**, pela qual remove o último elemento adicionado.
 
 A ordem em que os elementos saem de um _stack_ dá origem ao seu
-nome alternativo, LIFO (last in, first out). Adicionalmente, uma
-espiar a operação pode dar acesso ao topo sem modificar o _stack_.
+nome alternativo, LIFO (last in, first out). Adicionalmente, uma operação
+de espiada (peek) pode dar acesso ao topo sem modificar o _stack_.
 O nome "stack" para este tipo de estrutura vem da analogia de
 um conjunto de itens físicos empilhados uns sobre os outros,
 o que facilita retirar um item do topo da pilha, enquanto para chegar a
diff --git a/src/data-structures/tree/README.pt-BR.md b/src/data-structures/tree/README.pt-BR.md
index 173e096c48..7aade88caa 100644
--- a/src/data-structures/tree/README.pt-BR.md
+++ b/src/data-structures/tree/README.pt-BR.md
@@ -8,7 +8,7 @@
 
 Na ciência da computação, uma **árvore** é uma estrutura de dados
 abstrada (ADT) amplamente utilizada - ou uma estrutura de dados
-implementando este ADT que simula uma estrutura hierarquica de árvore,
+implementando este ADT que simula uma estrutura hierárquica de árvore,
 com valor raíz e sub-árvores de filhos com um nó pai, representado
 como um conjunto de nós conectados.
 
diff --git a/src/data-structures/trie/README.pt-BR.md b/src/data-structures/trie/README.pt-BR.md
index b0d49de1e1..50a294b77c 100644
--- a/src/data-structures/trie/README.pt-BR.md
+++ b/src/data-structures/trie/README.pt-BR.md
@@ -1,9 +1,9 @@
-# Trie
+# Árvore de Prefixos (Trie)
 
 Na ciência da computação, uma **trie**, também chamada de árvore digital (digital tree)
 e algumas vezes de _radix tree_ ou _prefix tree_ (tendo em vista que eles
-podem ser pesquisados por prefixos), é um tipo de árvore de pesquisa, uma
-uma estrutura de dados de árvore ordenada que é usado para armazenar um
+podem ser pesquisados por prefixos), é um tipo de árvore de pesquisa, uma 
+estrutura de dados de árvore ordenada que é usado para armazenar um
 conjunto dinâmico ou matriz associativa onde as chaves são geralmente _strings_.
 Ao contrário de uma árvore de pesquisa binária (binary search tree),
 nenhum nó na árvore armazena a chave associada a esse nó; em vez disso,

From c4164bf2240b1458252c3860f584bf01be4a85f8 Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Fri, 21 Oct 2022 22:21:11 +0200
Subject: [PATCH 210/264] Update README.md

---
 README.md | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/README.md b/README.md
index d2d0bc75a4..aa0c184424 100644
--- a/README.md
+++ b/README.md
@@ -363,3 +363,7 @@ Below is the list of some of the most used Big O notations and their performance
 [Folks who are backing this project](https://github.com/trekhleb/javascript-algorithms/blob/master/BACKERS.md) `∑ = 0`
 
 > ℹ️ A few more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev)
+
+## Author
+
+- [@trekhleb](https://trekhleb.dev)

From 5de9ca28e90cf860dbcb114441f72b5a4342ebb9 Mon Sep 17 00:00:00 2001
From: "David (Dato) Kadaria" <94402615+davidkadaria@users.noreply.github.com>
Date: Thu, 10 Nov 2022 18:00:21 +0400
Subject: [PATCH 211/264] Added Georgian translation && Added link to the
 translation from other files (#951)

---
 src/algorithms/math/fibonacci/README.fr-FR.md |  3 ++-
 src/algorithms/math/fibonacci/README.ka-GE.md | 20 +++++++++++++++++++
 src/algorithms/math/fibonacci/README.md       |  3 ++-
 src/algorithms/math/fibonacci/README.zh-CN.md |  3 ++-
 4 files changed, 26 insertions(+), 3 deletions(-)
 create mode 100644 src/algorithms/math/fibonacci/README.ka-GE.md

diff --git a/src/algorithms/math/fibonacci/README.fr-FR.md b/src/algorithms/math/fibonacci/README.fr-FR.md
index 1321ca24d7..81e3549b0d 100644
--- a/src/algorithms/math/fibonacci/README.fr-FR.md
+++ b/src/algorithms/math/fibonacci/README.fr-FR.md
@@ -1,7 +1,8 @@
 # Nombre de Fibonacci
 
 _Read this in other languages:_
-[english](README.md).
+[english](README.md),
+[ქართული](README.ka-GE.md).
 
 En mathématiques, la suite de Fibonacci est une suite d'entiers
 dans laquelle chaque terme (après les deux premiers)
diff --git a/src/algorithms/math/fibonacci/README.ka-GE.md b/src/algorithms/math/fibonacci/README.ka-GE.md
new file mode 100644
index 0000000000..ae7e11218b
--- /dev/null
+++ b/src/algorithms/math/fibonacci/README.ka-GE.md
@@ -0,0 +1,20 @@
+# ფიბონაჩის რიცხვი
+
+მათემატიკაში ფიბონაჩის მიმდევრობა წარმოადგენს მთელ რიცხვთა მიმდევრობას,
+რომელშიც ყოველი რიცხვი (პირველი ორი რიცხვის შემდეგ)
+მისი წინამორბედი ორი რიცხვის
+ჯამის ტოლია:
+
+`0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ...`
+
+კვადრატების წყობა, სადაც ყოველი კვადრატის გვერდების სიგრძე, თანმიმდევრობით, ფიბონაჩის რიცხვებს შეესაბამება
+
+![Fibonacci](https://upload.wikimedia.org/wikipedia/commons/d/db/34%2A21-FibonacciBlocks.png)
+
+ფიბონაჩის სპირალი: ოქროს სპირალის აპროქსიმაცია, რომელიც შექმნილია კვადრატების მოპირდაპირე კუთხეებს შორის შემაერთებელი რკალების გავლებით;[4] ამ შემთხვევაში, გამოყენებულ კვადრატთა [გვერდების] ზომებია: 1, 1, 2, 3, 5, 8, 13 და 21.
+
+![Fibonacci Spiral](https://upload.wikimedia.org/wikipedia/commons/2/2e/FibonacciSpiral.svg)
+
+## სქოლიო
+
+- [Wikipedia](https://en.wikipedia.org/wiki/Fibonacci_number)
diff --git a/src/algorithms/math/fibonacci/README.md b/src/algorithms/math/fibonacci/README.md
index 9a36887f71..3d476c5020 100644
--- a/src/algorithms/math/fibonacci/README.md
+++ b/src/algorithms/math/fibonacci/README.md
@@ -2,7 +2,8 @@
 
 _Read this in other languages:_
 [français](README.fr-FR.md),
-[简体中文](README.zh-CN.md).
+[简体中文](README.zh-CN.md),
+[ქართული](README.ka-GE.md).
 
 In mathematics, the Fibonacci numbers are the numbers in the following
 integer sequence, called the Fibonacci sequence, and characterized by
diff --git a/src/algorithms/math/fibonacci/README.zh-CN.md b/src/algorithms/math/fibonacci/README.zh-CN.md
index 70f74b533c..20378000d4 100644
--- a/src/algorithms/math/fibonacci/README.zh-CN.md
+++ b/src/algorithms/math/fibonacci/README.zh-CN.md
@@ -2,7 +2,8 @@
 
 _Read this in other languages:_
 [français](README.fr-FR.md),
-[english](README.md).
+[english](README.md),
+[ქართული](README.ka-GE.md).
 
 在数学中，斐波那契数是以下整数序列（称为斐波那契数列）中的数字，其特征在于前两个数字之后的每个数字都是前两个数字的和：
 

From e62572648c42b23b4e3a7ae68ce9529098eeca32 Mon Sep 17 00:00:00 2001
From: "Oleksandr (Sasha) Khivrych" <alexander.khivrych@gmail.com>
Date: Thu, 10 Nov 2022 14:02:29 +0000
Subject: [PATCH 212/264] feat: added ukr translations for bloom filter, 
 Disjoint Set, Doubly Linked List (#957)

Co-authored-by: Oleksii Trekhleb <trehleb@gmail.com>
---
 src/data-structures/bloom-filter/README.md    |  37 +++---
 .../bloom-filter/README.uk-UA.md              |  54 +++++++++
 src/data-structures/disjoint-set/README.md    |  16 +--
 .../disjoint-set/README.uk-UA.md              |  22 ++++
 .../doubly-linked-list/README.md              |   9 +-
 .../doubly-linked-list/README.uk-UA.md        | 109 ++++++++++++++++++
 6 files changed, 217 insertions(+), 30 deletions(-)
 create mode 100644 src/data-structures/bloom-filter/README.uk-UA.md
 create mode 100644 src/data-structures/disjoint-set/README.uk-UA.md
 create mode 100644 src/data-structures/doubly-linked-list/README.uk-UA.md

diff --git a/src/data-structures/bloom-filter/README.md b/src/data-structures/bloom-filter/README.md
index 17c666775e..e156310cb4 100644
--- a/src/data-structures/bloom-filter/README.md
+++ b/src/data-structures/bloom-filter/README.md
@@ -2,38 +2,39 @@
 
 _Read this in other languages:_
 [_Русский_](README.ru-RU.md),
-[_Português_](README.pt-BR.md)
+[_Português_](README.pt-BR.md),
+[_Українська_](README.uk-UA.md)
 
-A **bloom filter** is a space-efficient probabilistic 
-data structure designed to test whether an element 
-is present in a set. It is designed to be blazingly 
+A **bloom filter** is a space-efficient probabilistic
+data structure designed to test whether an element
+is present in a set. It is designed to be blazingly
 fast and use minimal memory at the cost of potential
 false positives. False positive matches are possible,
 but false negatives are not – in other words, a query
 returns either "possibly in set" or "definitely not in set".
 
-Bloom proposed the technique for applications where the 
+Bloom proposed the technique for applications where the
 amount of source data would require an impractically large
-amount of memory if "conventional" error-free hashing 
+amount of memory if "conventional" error-free hashing
 techniques were applied.
 
 ## Algorithm description
 
-An empty Bloom filter is a bit array of `m` bits, all 
+An empty Bloom filter is a bit array of `m` bits, all
 set to `0`. There must also be `k` different hash functions
-defined, each of which maps or hashes some set element to 
-one of the `m` array positions, generating a uniform random 
-distribution. Typically, `k` is a constant, much smaller 
-than `m`, which is proportional to the number of elements 
-to be added; the precise choice of `k` and the constant of 
-proportionality of `m` are determined by the intended 
+defined, each of which maps or hashes some set element to
+one of the `m` array positions, generating a uniform random
+distribution. Typically, `k` is a constant, much smaller
+than `m`, which is proportional to the number of elements
+to be added; the precise choice of `k` and the constant of
+proportionality of `m` are determined by the intended
 false positive rate of the filter.
 
-Here is an example of a Bloom filter, representing the 
-set `{x, y, z}`. The colored arrows show the positions 
-in the bit array that each set element is mapped to. The 
-element `w` is not in the set `{x, y, z}`, because it 
-hashes to one bit-array position containing `0`. For 
+Here is an example of a Bloom filter, representing the
+set `{x, y, z}`. The colored arrows show the positions
+in the bit array that each set element is mapped to. The
+element `w` is not in the set `{x, y, z}`, because it
+hashes to one bit-array position containing `0`. For
 this figure, `m = 18` and `k = 3`.
 
 ![Bloom Filter](https://upload.wikimedia.org/wikipedia/commons/a/ac/Bloom_filter.svg)
diff --git a/src/data-structures/bloom-filter/README.uk-UA.md b/src/data-structures/bloom-filter/README.uk-UA.md
new file mode 100644
index 0000000000..aa9075a094
--- /dev/null
+++ b/src/data-structures/bloom-filter/README.uk-UA.md
@@ -0,0 +1,54 @@
+# Фільтр Блума
+
+**Фільтр Блума** - це просторово-ефективна ймовірна структура даних, створена для перевірки наявності елемента
+у множині. Він спроектований неймовірно швидким за мінімального використання пам'яті ціною потенційних помилкових спрацьовувань.
+Існує можливість отримати хибнопозитивне спрацьовування (елемента в безлічі немає, але структура даних повідомляє,
+що він є), але не хибнонегативне. Іншими словами, черга повертає або "можливо в наборі", або "певно не
+у наборі". Фільтр Блума може використовувати будь-який обсяг пам'яті, проте чим він більший, тим менша вірогідність помилкового
+спрацьовування.
+
+Блум запропонував цю техніку для застосування в областях, де кількість вихідних даних потребувала б непрактично багато
+пам'яті, у разі застосування умовно безпомилкових технік хешування.
+
+## Опис алгоритму
+
+Порожній фільтр Блума представлений бітовим масивом з `m` бітів, всі біти якого обнулені. Має бути визначено `k`
+незалежних хеш-функцій, що відображають кожен елемент множини в одну з `m` позицій у масиві, генеруючи однакове
+випадковий розподіл. Зазвичай `k` задана константою, яка набагато менше `m` і пропорційна
+кількості елементів, що додаються; точний вибір `k` та постійної пропорційності `m` визначаються рівнем хибних
+спрацьовувань фільтра.
+
+Ось приклад Блум фільтра, що представляє набір `{x, y, z}`. Кольорові стрілки показують позиції в бітовому масиві,
+яким прив'язаний кожен елемент набору. Елемент `w` не в наборі `{x, y, z}`, тому що він прив'язаний до позиції в бітовому
+масиві, що дорівнює `0`. Для цієї форми, `m = 18`, а `k = 3`.
+
+Фільтр Блума є бітовий масив з `m` біт. Спочатку, коли структура даних зберігає порожню множину, всі
+m біт обнулені. Користувач повинен визначити `k` незалежних хеш-функцій `h1`, …, `hk`,
+що відображають кожен елемент в одну з m позицій бітового масиву досить рівномірним чином.
+
+Для додавання елемента e необхідно записати одиниці на кожну з позицій `h1(e)`, …, `hk(e)`
+бітового масиву.
+
+Для перевірки приналежності елемента `e` до безлічі елементів, що зберігаються, необхідно перевірити стан бітів
+`h1(e)`, …, `hk(e)`. Якщо хоча б один з них дорівнює нулю, елемент не може належати множині
+(інакше при його додаванні всі ці біти були встановлені). Якщо вони рівні одиниці, то структура даних повідомляє,
+що `е` належить безлічі. При цьому може виникнути дві ситуації: або елемент дійсно належить множині,
+або всі ці біти виявилися встановлені випадково при додаванні інших елементів, що і є джерелом помилкових
+спрацьовувань у цій структурі даних.
+
+![Фільтр Блума](https://upload.wikimedia.org/wikipedia/commons/a/ac/Bloom_filter.svg)
+
+## Застосування
+
+Фільтр Блума може бути використаний для блогів. Якщо мета полягає в тому, щоб показати читачам лише ті статті,
+які вони ще не бачили, фільтр блуму ідеальний. Він може містити значення, що хешуються, відповідні статті. Після
+того, як користувач прочитав кілька статей, вони можуть бути поміщені у фільтр. Наступного разу, коли користувач
+відвідає сайт, ці статті можуть бути вилучені з результатів за допомогою фільтра.
+
+Деякі статті неминуче будуть відфільтровані помилково, але ціна прийнятна. Те, що користувач не побачить дещо
+статей цілком прийнятно, беручи до уваги той факт, що йому завжди показуються інші нові статті при кожному
+новому відвідуванні.
+
+## Посилання
+
+- [Wikipedia](https://uk.wikipedia.org/wiki/%D0%A4%D1%96%D0%BB%D1%8C%D1%82%D1%80_%D0%91%D0%BB%D1%83%D0%BC%D0%B0)
diff --git a/src/data-structures/disjoint-set/README.md b/src/data-structures/disjoint-set/README.md
index 535960c7bb..44bcfa2769 100644
--- a/src/data-structures/disjoint-set/README.md
+++ b/src/data-structures/disjoint-set/README.md
@@ -2,22 +2,22 @@
 
 _Read this in other languages:_
 [_Русский_](README.ru-RU.md),
-[_Português_](README.pt-BR.md)
+[_Português_](README.pt-BR.md),
+[_Українська_](README.uk-UA.md)
 
-
-**Disjoint-set** data structure (also called a union–find data structure or merge–find set) is a data 
-structure that tracks a set of elements partitioned into a number of disjoint (non-overlapping) subsets. 
-It provides near-constant-time operations (bounded by the inverse Ackermann function) to *add new sets*, 
-to *merge existing sets*, and to *determine whether elements are in the same set*. 
+**Disjoint-set** data structure (also called a union–find data structure or merge–find set) is a data
+structure that tracks a set of elements partitioned into a number of disjoint (non-overlapping) subsets.
+It provides near-constant-time operations (bounded by the inverse Ackermann function) to _add new sets_,
+to _merge existing sets_, and to _determine whether elements are in the same set_.
 In addition to many other uses (see the Applications section), disjoint-sets play a key role in Kruskal's algorithm for finding the minimum spanning tree of a graph.
 
 ![disjoint set](https://upload.wikimedia.org/wikipedia/commons/6/67/Dsu_disjoint_sets_init.svg)
 
-*MakeSet* creates 8 singletons.
+_MakeSet_ creates 8 singletons.
 
 ![disjoint set](https://upload.wikimedia.org/wikipedia/commons/a/ac/Dsu_disjoint_sets_final.svg)
 
-After some operations of *Union*, some sets are grouped together.
+After some operations of _Union_, some sets are grouped together.
 
 ## References
 
diff --git a/src/data-structures/disjoint-set/README.uk-UA.md b/src/data-structures/disjoint-set/README.uk-UA.md
new file mode 100644
index 0000000000..f8c3be4df1
--- /dev/null
+++ b/src/data-structures/disjoint-set/README.uk-UA.md
@@ -0,0 +1,22 @@
+# Система неперетинних множин
+
+**Система неперетинних множин** це структура даних (також звана структурою даної пошуку перетину або
+безліччю пошуку злиття), яка управляє безліччю елементів, розбитих на кілька підмножин, що не перетинаються.
+Вона надає близько-константний час виконання операцій (обмежений зворотною функцією Акерманна) за додаванням
+нових множин, *злиття існуючих множин і *випередження, чи відносяться елементи до одного і того ж безлічі.
+
+Застосовується для зберігання компонентів зв'язності в графах, зокрема, алгоритму Фарбала необхідна подібна структура
+даних для ефективної реалізації.
+
+Основні операції:
+
+- _MakeSet(x)_ - створює одноелементне безліч {x},
+- _Find(x)_ - повертає ідентифікатор множини, що містить елемент x,
+- _Union(x,y)_ - об'єднання множин, що містять x та y.
+
+Після деяких операцій _об'єднання_, деякі множини зібрані разом
+
+## Посилання
+
+- [СНМ на Wikipedia](https://uk.wikipedia.org/wiki/%D0%A1%D0%B8%D1%81%D1%82%D0%B5%D0%BC%D0%B0_%D0%BD%D0%B5%D0%BF%D0%B5%D1%80%D0%B5%D1%82%D0%B8%D0%BD%D0%BD%D0%B8%D1%85_%D0%BC%D0%BD%D0%BE%D0%B6%D0%B8%D0%BD)
+- [СНМ на YouTube](https://www.youtube.com/watch?v=5XwRPwLnK6I)
diff --git a/src/data-structures/doubly-linked-list/README.md b/src/data-structures/doubly-linked-list/README.md
index 81c0797f73..1610d1e497 100644
--- a/src/data-structures/doubly-linked-list/README.md
+++ b/src/data-structures/doubly-linked-list/README.md
@@ -7,6 +7,7 @@ _Read this in other languages:_
 [_Português_](README.pt-BR.md),
 [_한국어_](README.ko-KR.md),
 [_Español_](README.es-ES.md),
+[_Українська_](README.uk-UA.md)
 
 In computer science, a **doubly linked list** is a linked data structure that
 consists of a set of sequentially linked records called nodes. Each node contains
@@ -20,7 +21,7 @@ but in opposite sequential orders.
 
 ![Doubly Linked List](./images/doubly-linked-list.jpeg)
 
-*Made with [okso.app](https://okso.app)*
+_Made with [okso.app](https://okso.app)_
 
 The two node links allow traversal of the list in either direction. While adding
 or removing a node in a doubly linked list requires changing more links than the
@@ -104,9 +105,9 @@ end Reverse Traversal
 
 ## Time Complexity
 
-| Access    | Search    | Insertion | Deletion  |
-| :-------: | :-------: | :-------: | :-------: |
-| O(n)      | O(n)      | O(1)      | O(n)      |
+| Access | Search | Insertion | Deletion |
+| :----: | :----: | :-------: | :------: |
+|  O(n)  |  O(n)  |   O(1)    |   O(n)   |
 
 ### Space Complexity
 
diff --git a/src/data-structures/doubly-linked-list/README.uk-UA.md b/src/data-structures/doubly-linked-list/README.uk-UA.md
new file mode 100644
index 0000000000..a52a8015e0
--- /dev/null
+++ b/src/data-structures/doubly-linked-list/README.uk-UA.md
@@ -0,0 +1,109 @@
+# Двобічно зв'язаний список
+
+**Двобічно зв'язаний список** — зв'язкова структура даних в інформатиці, що складається з набору
+послідовно пов'язаних записів, званих вузлами. Кожен вузол містить два поля,
+званих посиланнями, які вказують на попередній і наступний елементи
+послідовність вузлів. Посилання на попередній елемент кореневого вузла та посилання на
+Наступний елемент останнього вузла вказують на деякого роду переривник, зазвичай
+сторожовий вузол або null для полегшення обходу списку. Якщо у списку лише один
+сторожовий вузол, тоді перелік циклічно пов'язаний через нього.
+Двобічно зв'язаний список можна уявити, як два зв'язкові списки, які утворені з
+одних і тих самих даних, але розташованих у протилежному порядку.
+
+![Двобічно зв'язаний список](./images/doubly-linked-list.jpeg)
+
+_Made with [okso.app](https://okso.app)_
+
+Два посилання дозволяють обходити список в обох напрямках. Додавання та
+видалення вузла у двозв'язному списку вимагає зміни більшої кількості посилань,
+ніж аналогічні операції у зв'язковому списку. Однак дані операції простіше та потенційно
+більш ефективні (для некореневих вузлів) – при обході не потрібно стежити за попереднім
+вузлом або повторно обходити список у пошуку попереднього вузла, плюс його посилання
+може бути змінено.
+
+## Псевдокод основних операцій
+
+### Вставка
+
+```text
+Add(value)
+  Pre: value - значення, що додається
+  Post: value поміщено в кінець списку
+  n ← node(value)
+  if head = ø
+    head ← n
+    tail ← n
+  else
+    n.previous ← tail
+    tail.next ← n
+    tail ← n
+  end if
+end Add
+```
+
+### Видалення
+
+```text
+Remove(head, value)
+  Pre: head - перший вузол у списку
+       value - значення, яке слід видалити
+  Post: true - value видалено зі списку, інакше false
+  if head = ø
+    return false
+  end if
+  if value = head.value
+    if head = tail
+      head ← ø
+      tail ← ø
+    else
+      head ← head.next
+      head.previous ← ø
+    end if
+    return true
+  end if
+  n ← head.next
+  while n = ø and value = n.value
+    n ← n.next
+  end while
+  if n = tail
+    tail ← tail.previous
+    tail.next ← ø
+    return true
+  else if n = ø
+    n.previous.next ← n.next
+    n.next.previous ← n.previous
+    return true
+  end if
+  return false
+end Remove
+```
+
+### Зворотний обхід
+
+```text
+ReverseTraversal(tail)
+  Pre: tail - кінцевий елемент обхідного списку
+  Post: елементи списку пройдено у зворотному порядку
+  n ← tail
+  while n = ø
+    yield n.value
+    n ← n.previous
+  end while
+end Reverse Traversal
+```
+
+## Складність
+
+## Часова складність
+
+| Читання | Пошук | Вставка | Видалення |
+| :-----: | :---: | :-----: | :-------: |
+|  O(n)   | O(n)  |  O(1)   |   O(n)    |
+
+### Просторова складність
+
+O(n)
+
+## Посилання
+
+- [Wikipedia](https://uk.wikipedia.org/wiki/%D0%94%D0%B2%D0%BE%D0%B1%D1%96%D1%87%D0%BD%D0%BE_%D0%B7%D0%B2%27%D1%8F%D0%B7%D0%B0%D0%BD%D0%B8%D0%B9_%D1%81%D0%BF%D0%B8%D1%81%D0%BE%D0%BA#:~:text=%D0%94%D0%B2%D0%BE%D0%B1%D1%96%D1%87%D0%BD%D0%BE%20%D0%B7%D0%B2'%D1%8F%D0%B7%D0%B0%D0%BD%D0%B8%D0%B9%20%D1%81%D0%BF%D0%B8%D1%81%D0%BE%D0%BA%20%E2%80%94%20%D0%B2%D0%B8%D0%B4,%D0%BD%D0%B0%20%D0%BF%D0%BE%D0%B4%D0%B0%D0%BB%D1%8C%D1%88%D0%B8%D0%B9%20%D0%B2%D1%83%D0%B7%D0%BE%D0%BB%20%D1%83%20%D1%81%D0%BF%D0%B8%D1%81%D0%BA%D1%83.)

From 8e4225ac713fe2b0747b66ab1cd4206ea72b7791 Mon Sep 17 00:00:00 2001
From: Berkay <102474166+doandroidsdreamof@users.noreply.github.com>
Date: Thu, 10 Nov 2022 17:04:50 +0300
Subject: [PATCH 213/264] Update README.md (#953)

Co-authored-by: Oleksii Trekhleb <trehleb@gmail.com>
---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index aa0c184424..c9c6258769 100644
--- a/README.md
+++ b/README.md
@@ -27,7 +27,7 @@ _Read this in other languages:_
 [_Español_](README.es-ES.md),
 [_Português_](README.pt-BR.md),
 [_Русский_](README.ru-RU.md),
-[_Türk_](README.tr-TR.md),
+[_Türkçe_](README.tr-TR.md),
 [_Italiana_](README.it-IT.md),
 [_Bahasa Indonesia_](README.id-ID.md),
 [_Українська_](README.uk-UA.md),

From 565256088a1b99d3d7901b5d8db992fe9acabd2d Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Thu, 10 Nov 2022 15:06:33 +0100
Subject: [PATCH 214/264] README updates.

---
 src/data-structures/disjoint-set/README.uk-UA.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/data-structures/disjoint-set/README.uk-UA.md b/src/data-structures/disjoint-set/README.uk-UA.md
index f8c3be4df1..c721b66420 100644
--- a/src/data-structures/disjoint-set/README.uk-UA.md
+++ b/src/data-structures/disjoint-set/README.uk-UA.md
@@ -14,7 +14,7 @@
 - _Find(x)_ - повертає ідентифікатор множини, що містить елемент x,
 - _Union(x,y)_ - об'єднання множин, що містять x та y.
 
-Після деяких операцій _об'єднання_, деякі множини зібрані разом
+Після деяких операцій _об'єднання_, деякі множини зібрані разом.
 
 ## Посилання
 

From 025b9a390b5cde87d4d00604ee745e8ea83202ff Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Mon, 28 Nov 2022 16:43:30 +0100
Subject: [PATCH 215/264] Update Permutation and Combination cheatsheets.
 (#963)

---
 src/algorithms/sets/combinations/README.md    |  32 ++++++++----------
 .../images/combinations-overview.jpg          | Bin 0 -> 352932 bytes
 .../images/combinations-with-repetitions.jpg  | Bin 0 -> 331434 bytes
 .../combinations-without-repetitions.jpg      | Bin 0 -> 309391 bytes
 .../sets/combinations/images/overview.png     | Bin 0 -> 145014 bytes
 src/algorithms/sets/permutations/README.md    |  22 ++++++------
 .../sets/permutations/images/overview.png     | Bin 0 -> 145014 bytes
 .../images/permutations-overview.jpeg         | Bin 0 -> 314729 bytes
 .../images/permutations-with-repetitions.jpg  | Bin 0 -> 307854 bytes
 .../permutations-without-repetitions.jpg      | Bin 0 -> 373106 bytes
 10 files changed, 25 insertions(+), 29 deletions(-)
 create mode 100644 src/algorithms/sets/combinations/images/combinations-overview.jpg
 create mode 100644 src/algorithms/sets/combinations/images/combinations-with-repetitions.jpg
 create mode 100644 src/algorithms/sets/combinations/images/combinations-without-repetitions.jpg
 create mode 100644 src/algorithms/sets/combinations/images/overview.png
 create mode 100644 src/algorithms/sets/permutations/images/overview.png
 create mode 100644 src/algorithms/sets/permutations/images/permutations-overview.jpeg
 create mode 100644 src/algorithms/sets/permutations/images/permutations-with-repetitions.jpg
 create mode 100644 src/algorithms/sets/permutations/images/permutations-without-repetitions.jpg

diff --git a/src/algorithms/sets/combinations/README.md b/src/algorithms/sets/combinations/README.md
index 30243b8614..69fc0603f9 100644
--- a/src/algorithms/sets/combinations/README.md
+++ b/src/algorithms/sets/combinations/README.md
@@ -5,14 +5,14 @@ When the order doesn't matter, it is a **Combination**.
 When the order **does** matter it is a **Permutation**.
 
 **"My fruit salad is a combination of apples, grapes and bananas"**
-We don't care what order the fruits are in, they could also be 
-"bananas, grapes and apples" or "grapes, apples and bananas", 
+We don't care what order the fruits are in, they could also be
+"bananas, grapes and apples" or "grapes, apples and bananas",
 its the same fruit salad.
 
 ## Combinations without repetitions
 
-This is how lotteries work. The numbers are drawn one at a 
-time, and if we have the lucky numbers (no matter what order) 
+This is how lotteries work. The numbers are drawn one at a
+time, and if we have the lucky numbers (no matter what order)
 we win!
 
 No Repetition: such as lottery numbers `(2,14,15,27,30,33)`
@@ -30,12 +30,12 @@ It is often called "n choose r" (such as "16 choose 3"). And is also known as th
 
 Repetition is Allowed: such as coins in your pocket `(5,5,5,10,10)`
 
-Or let us say there are five flavours of ice cream: 
+Or let us say there are five flavours of ice cream:
 `banana`, `chocolate`, `lemon`, `strawberry` and `vanilla`.
 
 We can have three scoops. How many variations will there be?
 
-Let's use letters for the flavours: `{b, c, l, s, v}`. 
+Let's use letters for the flavours: `{b, c, l, s, v}`.
 Example selections include:
 
 - `{c, c, c}` (3 scoops of chocolate)
@@ -46,23 +46,21 @@ Example selections include:
 
 ![Formula](https://www.mathsisfun.com/combinatorics/images/combinations-repeat.gif)
 
-Where `n` is the number of things to choose from, and we 
-choose `r` of them. Repetition allowed, 
+Where `n` is the number of things to choose from, and we
+choose `r` of them. Repetition allowed,
 order doesn't matter.
 
-## Cheat Sheets
+## Cheatsheet
 
-Permutations cheat sheet
+![Permutations and Combinations Overview](./images/overview.png)
 
-![Permutations Cheat Sheet](https://cdn-images-1.medium.com/max/2000/1*JNK-n0Pt0Vbxk0lxVpgT5A.png)
+![Combinations overview](./images/combinations-overview.jpg)
 
-Combinations cheat sheet
+| | |
+| --- | --- |
+|![Combinations with repetition](./images/combinations-with-repetitions.jpg) | ![Combinations without repetition](./images/combinations-without-repetitions.jpg) |
 
-![Combinations Cheat Sheet](https://cdn-images-1.medium.com/max/2000/1*7cFRn8jW4g_91YgDAbmxRQ.png)
-
-Permutations/combinations algorithm ideas.
-
-![Algorithms Idea](https://cdn-images-1.medium.com/max/2000/1*vLsSsZMnesCFPCYTYMbxrQ.png)
+*Made with [okso.app](https://okso.app)*
 
 ## References
 
diff --git a/src/algorithms/sets/combinations/images/combinations-overview.jpg b/src/algorithms/sets/combinations/images/combinations-overview.jpg
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diff --git a/src/algorithms/sets/permutations/README.md b/src/algorithms/sets/permutations/README.md
index 8864af7240..4b6a268adc 100644
--- a/src/algorithms/sets/permutations/README.md
+++ b/src/algorithms/sets/permutations/README.md
@@ -4,13 +4,13 @@ When the order doesn't matter, it is a **Combination**.
 
 When the order **does** matter it is a **Permutation**.
 
-**"The combination to the safe is 472"**. We do care about the order. `724` won't work, nor will `247`. 
+**"The combination to the safe is 472"**. We do care about the order. `724` won't work, nor will `247`.
 It has to be exactly `4-7-2`.
 
 ## Permutations without repetitions
 
-A permutation, also called an “arrangement number” or “order”, is a rearrangement of 
-the elements of an ordered list `S` into a one-to-one correspondence with `S` itself. 
+A permutation, also called an “arrangement number” or “order”, is a rearrangement of
+the elements of an ordered list `S` into a one-to-one correspondence with `S` itself.
 
 Below are the permutations of string `ABC`.
 
@@ -37,19 +37,17 @@ For example the the lock below: it could be `333`.
 n * n * n ... (r times) = n^r
 ```
 
-## Cheat Sheets
+## Cheatsheet
 
-Permutations cheat sheet
+![Permutations and Combinations Overview](./images/overview.png)
 
-![Permutations Cheat Sheet](https://cdn-images-1.medium.com/max/2000/1*JNK-n0Pt0Vbxk0lxVpgT5A.png)
+![Permutations overview](./images/permutations-overview.jpeg)
 
-Combinations cheat sheet
+| | |
+| --- | --- |
+|![Permutations with repetition](./images/permutations-with-repetitions.jpg) | ![Permutations without repetition](./images/permutations-without-repetitions.jpg) |
 
-![Combinations Cheat Sheet](https://cdn-images-1.medium.com/max/2000/1*7cFRn8jW4g_91YgDAbmxRQ.png)
-
-Permutations/combinations algorithm ideas.
-
-![Algorithms Idea](https://cdn-images-1.medium.com/max/2000/1*vLsSsZMnesCFPCYTYMbxrQ.png)
+*Made with [okso.app](https://okso.app)*
 
 ## References
 
diff --git a/src/algorithms/sets/permutations/images/overview.png b/src/algorithms/sets/permutations/images/overview.png
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From a6a4d01f95a1f1f2243360d1fd7dbd2275f0fa79 Mon Sep 17 00:00:00 2001
From: "Oleksandr (Sasha) Khivrych" <alexander.khivrych@gmail.com>
Date: Mon, 5 Dec 2022 06:38:35 +0000
Subject: [PATCH 216/264] feat: added ukranian translations for graph, heap,
 linked-list, priority-queue, queue, stack. trie (#965)

---
 src/data-structures/graph/README.md           |   4 +-
 src/data-structures/graph/README.uk-UA.md     |  24 +++
 src/data-structures/heap/README.md            |   4 +-
 src/data-structures/heap/README.uk-UA.md      |  25 +++
 src/data-structures/linked-list/README.md     |   1 +
 .../linked-list/README.uk-UA.md               | 147 ++++++++++++++++++
 src/data-structures/priority-queue/README.md  |  19 +--
 .../priority-queue/README.uk-UA.md            |  21 +++
 src/data-structures/queue/README.md           |   3 +-
 src/data-structures/queue/README.uk-UA.md     |  21 +++
 src/data-structures/stack/README.md           |   3 +-
 src/data-structures/stack/README.uk-UA.md     |  25 +++
 src/data-structures/trie/README.md            |   3 +-
 src/data-structures/trie/README.uk-UA.md      |  27 ++++
 14 files changed, 313 insertions(+), 14 deletions(-)
 create mode 100644 src/data-structures/graph/README.uk-UA.md
 create mode 100644 src/data-structures/heap/README.uk-UA.md
 create mode 100644 src/data-structures/linked-list/README.uk-UA.md
 create mode 100644 src/data-structures/priority-queue/README.uk-UA.md
 create mode 100644 src/data-structures/queue/README.uk-UA.md
 create mode 100644 src/data-structures/stack/README.uk-UA.md
 create mode 100644 src/data-structures/trie/README.uk-UA.md

diff --git a/src/data-structures/graph/README.md b/src/data-structures/graph/README.md
index 9930053772..790602b536 100644
--- a/src/data-structures/graph/README.md
+++ b/src/data-structures/graph/README.md
@@ -4,7 +4,9 @@ _Read this in other languages:_
 [_简体中文_](README.zh-CN.md),
 [_Русский_](README.ru-RU.md),
 [_Français_](README.fr-FR.md),
-[_Português_](README.pt-BR.md)
+[_Português_](README.pt-BR.md),
+[_Українська_](README.uk-UA.md)
+
 
 In computer science, a **graph** is an abstract data type
 that is meant to implement the undirected graph and
diff --git a/src/data-structures/graph/README.uk-UA.md b/src/data-structures/graph/README.uk-UA.md
new file mode 100644
index 0000000000..9886cd904c
--- /dev/null
+++ b/src/data-structures/graph/README.uk-UA.md
@@ -0,0 +1,24 @@
+# Граф
+
+**Граф** в інформатиці - абстрактний тип даних, який має реалізовувати концепції спрямованого та неспрямованого
+графа у математиці, особливо у галузі теорії графів.
+
+Структура даних графа складається з кінцевого (і можливо, що змінюється) набору вершин або вузлів, або точок, спільно з
+набором ненаправлених пар цих вершин для ненаправленого графа або набором спрямованих пар для спрямованого графа.
+Ці пари відомі як ребра, арки або лінії для ненаправленого графа та як стрілки, спрямовані ребра, спрямовані
+арки чи спрямовані лінії для спрямованого графа. Ці вершини можуть бути частиною структури графа, або зовнішніми
+сутностями, представленими цілими індексами або посиланнями.
+
+Для різних областей застосування види графів можуть відрізнятися спрямованістю, обмеженнями на кількість зв'язків та
+додатковими даними про вершини або ребра. Багато структур, що становлять практичний інтерес у математиці та
+інформатики можуть бути представлені графами. Наприклад, будову Вікіпедії можна змоделювати за допомогою
+орієнтованого графа, в якому вершини – це статті, а дуги (орієнтовані ребра) – гіперпосилання.
+
+![Граф](./images/graph.jpeg)
+
+*Made with [okso.app](https://okso.app)*
+
+## Посилання
+
+- [Граф у математиці на Wikipedia](https://uk.wikipedia.org/wiki/%D0%93%D1%80%D0%B0%D1%84_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0))
+- [Структура даних Graph / Граф](https://www.youtube.com/watch?v=D0U8aFEhgKQ)
diff --git a/src/data-structures/heap/README.md b/src/data-structures/heap/README.md
index ef1d2e8b9a..db5f9e339f 100644
--- a/src/data-structures/heap/README.md
+++ b/src/data-structures/heap/README.md
@@ -7,7 +7,9 @@ _Read this in other languages:_
 [_Français_](README.fr-FR.md),
 [_Português_](README.pt-BR.md),
 [_Türkçe_](README.tr-TR.md),
-[_한국어_](README.ko-KR.md)
+[_한국어_](README.ko-KR.md),
+[_Українська_](README.uk-UA.md)
+
 
 In computer science, a **heap** is a specialized tree-based
 data structure that satisfies the heap property described
diff --git a/src/data-structures/heap/README.uk-UA.md b/src/data-structures/heap/README.uk-UA.md
new file mode 100644
index 0000000000..f35995d8ae
--- /dev/null
+++ b/src/data-structures/heap/README.uk-UA.md
@@ -0,0 +1,25 @@
+# Купа (структура даних)
+
+У комп'ютерних науках купа - це спеціалізована структура даних на кшталт дерева, яка задовольняє властивості купи:
+якщо B є вузлом-нащадком вузла A, то ключ (A) ≥ ключ (B). З цього випливає, що елемент із найбільшим ключем завжди
+є кореневим вузлом купи, тому іноді такі купи називають max-купами.
+
+![MaxHeap](./images/max-heap.jpeg)
+
+![Array Representation](./images/array-representation.jpeg)
+
+Якщо порівняння перевернути, то найменший елемент завжди буде кореневим вузлом, такі купи називають min-купами.
+
+![MinHeap](./images/min-heap.jpeg)
+
+*Made with [okso.app](https://okso.app)*
+
+Не існує жодних обмежень щодо того, скільки вузлів-нащадків має кожен вузол купи. На практиці їх
+число зазвичай трохи більше двох. Купа є максимально ефективною реалізацією абстрактного типу даних, який
+називається чергою із пріоритетом.
+
+Вузол на вершині купи, який не має батьків, називається кореневим вузлом.
+
+## Посилання
+
+- [Wikipedia](https://uk.wikipedia.org/wiki/%D0%9A%D1%83%D0%BF%D0%B0_(%D1%81%D1%82%D1%80%D1%83%D0%BA%D1%82%D1%83%D1%80%D0%B0_%D0%B4%D0%B0%D0%BD%D0%B8%D1%85))
diff --git a/src/data-structures/linked-list/README.md b/src/data-structures/linked-list/README.md
index 8819a390d3..bb30b07525 100644
--- a/src/data-structures/linked-list/README.md
+++ b/src/data-structures/linked-list/README.md
@@ -8,6 +8,7 @@ _Read this in other languages:_
 [_한국어_](README.ko-KR.md),
 [_Español_](README.es-ES.md),
 [_Turkish_](README.tr-TR.md),
+[_Українська_](README.uk-UA.md)
 
 In computer science, a **linked list** is a linear collection
 of data elements, in which linear order is not given by
diff --git a/src/data-structures/linked-list/README.uk-UA.md b/src/data-structures/linked-list/README.uk-UA.md
new file mode 100644
index 0000000000..5424c58db4
--- /dev/null
+++ b/src/data-structures/linked-list/README.uk-UA.md
@@ -0,0 +1,147 @@
+# Зв'язаний список
+
+Зв'язаний список — базова динамічна структура даних в інформатиці, що складається з вузлів, кожен з яких містить як дані, так посилання («зв'язку») на наступний вузол списку. Дана структура дозволяє ефективно додавати та видаляти елементи на довільній позиції у послідовності у процесі ітерації. Більш складні варіанти включають додаткові посилання, що дозволяють ефективно додавати та видаляти довільні елементи.
+
+Принциповою перевагою перед масивом є структурна гнучкість: порядок елементів зв'язкового списку може збігатися з порядком розташування елементів даних у пам'яті комп'ютера, а порядок обходу списку завжди явно задається його внутрішніми зв'язками. Суть переваги у тому, що у багатьох мовах створення масиву вимагає вказати його заздалегідь. Зв'язковий список дозволяє обійти це обмеження.
+
+Недоліком зв'язкових списків є те, що час доступу є лінійним (і важко для реалізації конвеєрів). Неможливий швидкий доступ (випадковий).
+
+![Linked List](./images/linked-list.jpeg)
+
+*Made with [okso.app](https://okso.app)*
+
+## Псевдокод основних операцій
+
+### Вставка
+
+```text
+Add(value)
+  Pre: value - значення, що додається
+  Post: value поміщено в кінець списку
+  n ← node(value)
+  if head = ø
+    head ← n
+    tail ← n
+  else
+    tail.next ← n
+    tail ← n
+  end if
+end Add
+```
+
+```text
+Prepend(value)
+ Pre: value - значення, що додається
+ Post: value поміщено на початок списку
+ n ← node(value)
+ n.next ← head
+ head ← n
+ if tail = ø
+   tail ← n
+ end
+end Prepend
+```
+
+### Поиск
+
+```text
+Contains(head, value)
+  Pre: head - перший вузол у списку
+         value - значення, яке слід знайти
+  Post: true - value знайдено у списку, інакше false
+  n ← head
+  while n != ø and n.value != value
+    n ← n.next
+  end while
+  if n = ø
+    return false
+  end if
+  return true
+end Contains
+```
+
+### Вилучення
+
+```text
+Remove(head, value)
+  Pre: head - перший вузол у списку
+       value - значення, яке слід видалити
+  Post: true - value видалено зі списку, інакше false
+  if head = ø
+    return false
+  end if
+  n ← head
+  if n.value = value
+    if head = tail
+      head ← ø
+      tail ← ø
+    else
+      head ← head.next
+    end if
+    return true
+  end if
+  while n.next != ø and n.next.value != value
+    n ← n.next
+  end while
+  if n.next != ø
+    if n.next = tail
+      tail ← n
+    end if
+    n.next ← n.next.next
+    return true
+  end if
+  return false
+end Remove
+```
+
+### Обход
+
+```text
+Traverse(head)
+  Pre: head - перший вузол у списку
+  Post: елементи списку пройдені
+  n ← head
+  while n != ø
+    yield n.value
+    n ← n.next
+  end while
+end Traverse
+```
+
+### Зворотний обхід
+
+```text
+ReverseTraversal(head, tail)
+  Pre: head и tail відносяться до одного списку
+  Post: елементи списку пройдено у зворотному порядку
+  if tail != ø
+    curr ← tail
+    while curr != head
+      prev ← head
+      while prev.next != curr
+        prev ← prev.next
+      end while
+      yield curr.value
+      curr ← prev
+    end while
+   yield curr.value
+  end if
+end ReverseTraversal
+```
+
+## Складність
+
+### Тимчасова складність
+
+| Читання    | Пошук     | Вставка    | Вилучення |
+| :--------: | :-------: | :--------: | :-------: |
+| O(n)       | O(n)      | O(1)       | O(n)      |
+
+### Просторова складність
+
+O(n)
+
+## Посилання
+
+- [Wikipedia](https://uk.wikipedia.org/wiki/%D0%97%D0%B2%27%D1%8F%D0%B7%D0%B0%D0%BD%D0%B8%D0%B9_%D1%81%D0%BF%D0%B8%D1%81%D0%BE%D0%BA)
+- [YouTube](https://www.youtube.com/watch?v=6snsMa4E1Os)
diff --git a/src/data-structures/priority-queue/README.md b/src/data-structures/priority-queue/README.md
index eb5ec72985..6d0901960d 100644
--- a/src/data-structures/priority-queue/README.md
+++ b/src/data-structures/priority-queue/README.md
@@ -6,20 +6,21 @@ _Read this in other languages:_
 [_日本語_](README.ja-JP.md),
 [_Français_](README.fr-FR.md),
 [_Português_](README.pt-BR.md),
-[_한국어_](README.ko-KR.md)
+[_한국어_](README.ko-KR.md),
+[_Українська_](README.uk-UA.md)
 
-In computer science, a **priority queue** is an abstract data type 
-which is like a regular queue or stack data structure, but where 
-additionally each element has a "priority" associated with it. 
-In a priority queue, an element with high priority is served before 
-an element with low priority. If two elements have the same 
+In computer science, a **priority queue** is an abstract data type
+which is like a regular queue or stack data structure, but where
+additionally each element has a "priority" associated with it.
+In a priority queue, an element with high priority is served before
+an element with low priority. If two elements have the same
 priority, they are served according to their order in the queue.
 
-While priority queues are often implemented with heaps, they are 
-conceptually distinct from heaps. A priority queue is an abstract 
+While priority queues are often implemented with heaps, they are
+conceptually distinct from heaps. A priority queue is an abstract
 concept like "a list" or "a map"; just as a list can be implemented
 with a linked list or an array, a priority queue can be implemented
-with a heap or a variety of other methods such as an unordered 
+with a heap or a variety of other methods such as an unordered
 array.
 
 ## References
diff --git a/src/data-structures/priority-queue/README.uk-UA.md b/src/data-structures/priority-queue/README.uk-UA.md
new file mode 100644
index 0000000000..2f0454479e
--- /dev/null
+++ b/src/data-structures/priority-queue/README.uk-UA.md
@@ -0,0 +1,21 @@
+# Черга з пріоритетом
+
+Черга з пріоритетом (англ. priority queue) - абстрактний тип даних в інформатиці,
+для кожного елемента якого можна визначити його пріоритет.
+
+У черзі з пріоритетами елемент із високим пріоритетом обслуговується раніше
+елемент з низьким пріоритетом. Якщо два елементи мають однаковий пріоритет, вони
+обслуговуються відповідно до їх порядку в черзі.
+
+Черга з пріоритетом підтримує дві обов'язкові операції – додати елемент та
+витягти максимум (мінімум).
+
+Хоча пріоритетні черги часто реалізуються у вигляді куп (heaps), вони
+концептуально відрізняються від куп. Черга пріоритетів є абстрактною
+концепцією на кшталт «списку» чи «карти»; так само, як список може бути реалізований
+у вигляді зв'язкового списку або масиву, так і черга з пріоритетом може бути реалізована
+у вигляді купи або безліччю інших методів, наприклад, у вигляді невпорядкованого масиву.
+
+## Посилання
+
+- [Wikipedia](https://uk.wikipedia.org/wiki/%D0%A7%D0%B5%D1%80%D0%B3%D0%B0_%D0%B7_%D0%BF%D1%80%D1%96%D0%BE%D1%80%D0%B8%D1%82%D0%B5%D1%82%D0%BE%D0%BC)
diff --git a/src/data-structures/queue/README.md b/src/data-structures/queue/README.md
index c1e40d735c..d8e0288b42 100644
--- a/src/data-structures/queue/README.md
+++ b/src/data-structures/queue/README.md
@@ -6,7 +6,8 @@ _Read this in other languages:_
 [_日本語_](README.ja-JP.md),
 [_Français_](README.fr-FR.md),
 [_Português_](README.pt-BR.md),
-[_한국어_](README.ko-KR.md)
+[_한국어_](README.ko-KR.md),
+[_Українська_](README.uk-UA.md)
 
 In computer science, a **queue** is a particular kind of abstract data
 type or collection in which the entities in the collection are
diff --git a/src/data-structures/queue/README.uk-UA.md b/src/data-structures/queue/README.uk-UA.md
new file mode 100644
index 0000000000..7934c7571a
--- /dev/null
+++ b/src/data-structures/queue/README.uk-UA.md
@@ -0,0 +1,21 @@
+# Черга
+
+Черга (англ. queue) – структура даних в інформатиці, в якій елементи
+зберігаються у порядку їх додавання. Додавання нових елементів(enqueue)
+здійснюється на кінець списку. А видалення елементів (dequeue)
+здійснюється із початку. Таким чином черга реалізує принцип
+"першим увійшов – першим вийшов" (FIFO). Часто реалізується операція читання
+головного елемента (peek), яка повертає перший у черзі елемент,
+при цьому не видаляючи його. Черга є прикладом лінійної структури
+даних чи послідовної колекції.
+
+Ілюстрація роботи з чергою.
+
+![Черга](./images/queue.jpeg)
+
+*Made with [okso.app](https://okso.app)*
+
+## Список літератури
+
+- [Wikipedia](https://uk.wikipedia.org/wiki/%D0%A7%D0%B5%D1%80%D0%B3%D0%B0_(%D1%81%D1%82%D1%80%D1%83%D0%BA%D1%82%D1%83%D1%80%D0%B0_%D0%B4%D0%B0%D0%BD%D0%B8%D1%85))
+- [YouTube](https://www.youtube.com/watch?v=ll4QLNSPn60)
diff --git a/src/data-structures/stack/README.md b/src/data-structures/stack/README.md
index 645e66c117..612f926736 100644
--- a/src/data-structures/stack/README.md
+++ b/src/data-structures/stack/README.md
@@ -6,7 +6,8 @@ _Read this in other languages:_
 [_日本語_](README.ja-JP.md),
 [_Français_](README.fr-FR.md),
 [_Português_](README.pt-BR.md),
-[_한국어_](README.ko-KR.md)
+[_한국어_](README.ko-KR.md),
+[_Українська_](README.uk-UA.md)
 
 In computer science, a **stack** is an abstract data type that serves
 as a collection of elements, with two principal operations:
diff --git a/src/data-structures/stack/README.uk-UA.md b/src/data-structures/stack/README.uk-UA.md
new file mode 100644
index 0000000000..9941114f5b
--- /dev/null
+++ b/src/data-structures/stack/README.uk-UA.md
@@ -0,0 +1,25 @@
+# Стек
+
+Стек (англ. stack - стопка) - абстрактний тип даних, що представляє собою
+список елементів, організованих за принципом LIFO (останнім прийшов – першим вийшов).
+
+Стек має дві ключові операції:
+* **додавання (push)** елемента в кінець стеку, та
+* **видалення (pop)**, останнього доданого елемента.
+
+Додаткова операція для читання головного елемента (peek) дає доступ
+до останнього елементу стека без зміни самого стека.
+
+Найчастіше принцип роботи стека порівнюють зі чаркою тарілок: щоб узяти другу
+зверху потрібно зняти верхню.
+
+Ілюстрація роботи зі стеком.
+
+![Стек](./images/stack.jpeg)
+
+*Made with [okso.app](https://okso.app)*
+
+## Посилання
+
+- [Wikipedia](https://uk.wikipedia.org/wiki/%D0%A1%D1%82%D0%B5%D0%BA)
+- [YouTube](https://www.youtube.com/watch?v=4jh1e1YCbYc)
diff --git a/src/data-structures/trie/README.md b/src/data-structures/trie/README.md
index f6f38ece09..2082fed903 100644
--- a/src/data-structures/trie/README.md
+++ b/src/data-structures/trie/README.md
@@ -3,7 +3,8 @@
 _Read this in other languages:_
 [_简体中文_](README.zh-CN.md),
 [_Русский_](README.ru-RU.md),
-[_Português_](README.pt-BR.md)
+[_Português_](README.pt-BR.md),
+[_Українська_](README.uk-UA.md)
 
 In computer science, a **trie**, also called digital tree and sometimes
 radix tree or prefix tree (as they can be searched by prefixes),
diff --git a/src/data-structures/trie/README.uk-UA.md b/src/data-structures/trie/README.uk-UA.md
new file mode 100644
index 0000000000..3b1f01f0aa
--- /dev/null
+++ b/src/data-structures/trie/README.uk-UA.md
@@ -0,0 +1,27 @@
+# Префіксне дерево
+
+**Префіксне дерево** (Також промінь, навантажене або суфіксне дерево) в інформатиці - впорядкована деревоподібна
+структура даних, яка використовується для зберігання динамічних множин або асоціативних масивів, де
+ключем зазвичай виступають рядки. Дерево називається префіксним, тому що пошук здійснюється за префіксами.
+
+На відміну від бінарного дерева, вузли не містять ключів, що відповідають вузлу. Являє собою кореневе дерево, кожне
+ребро якого позначено якимось символом так, що для будь-якого вузла всі ребра, що з'єднують цей вузол з його синами,
+позначені різними символами. Деякі вузли префіксного дерева виділені (на малюнку вони підписані цифрами) і вважається,
+що префіксне дерево містить цей рядок-ключ тоді і тільки тоді, коли цей рядок можна прочитати на шляху з
+кореня до певного виділеного вузла.
+
+Таким чином, на відміну від бінарних дерев пошуку, ключ, що ідентифікує конкретний вузол дерева, не явно зберігається в
+цьому вузлі, а неявно задається положенням цього вузла в дереві. Отримати ключ можна виписуванням поспіль символів,
+помічають ребра по дорозі від кореня до вузла. Ключ кореня дерева - порожній рядок. Часто у виділених вузлах зберігають
+додаткову інформацію, пов'язану з ключем, і зазвичай виділеними є тільки листя і, можливо, деякі
+внутрішні вузли.
+
+![Префіксне дерево](./images/trie.jpg)
+
+*Made with [okso.app](https://okso.app)*
+
+На малюнку представлено префіксне дерево, що містить ключі. «A», «to», «tea», «ted», «ten», «i», «in», «inn».
+
+## Посилання
+
+- [Wikipedia](https://uk.wikipedia.org/wiki/%D0%9F%D1%80%D0%B5%D1%84%D1%96%D0%BA%D1%81%D0%BD%D0%B5_%D0%B4%D0%B5%D1%80%D0%B5%D0%B2%D0%BE)

From 2a6f724589a1887a8ed6b665fa238e29acbf8c8c Mon Sep 17 00:00:00 2001
From: j0pgrm <109052480+j0pgrm@users.noreply.github.com>
Date: Sun, 4 Dec 2022 23:59:33 -0700
Subject: [PATCH 217/264] Malay readme (#927)

* update-readme

* deploy

* deploy

Co-authored-by: name <your mail>
Co-authored-by: Oleksii Trekhleb <trehleb@gmail.com>
---
 README.ma-MA.md                               | 364 ++++++++++++++++++
 README.md                                     |   2 +-
 .../graph/breadth-first-search/README.md      |   4 +-
 3 files changed, 367 insertions(+), 3 deletions(-)
 create mode 100644 README.ma-MA.md

diff --git a/README.ma-MA.md b/README.ma-MA.md
new file mode 100644
index 0000000000..0f75b78a12
--- /dev/null
+++ b/README.ma-MA.md
@@ -0,0 +1,364 @@
+# Algoritma JavaScript dan Struktur Data
+
+> 🇺🇦 UKRAINE [SEDANG DISERANG](https://twitter.com/MFA_Ukraine) OLEH TENTERA RUSIA. ORANG AWAM SEMAKIN DIBUNUH. KAWASAN KEDIAMAN SEMAKIN DIBOM.
+> - Bantu Ukraine melalui [Bank Negara Ukraine](https://bank.gov.ua/en/news/all/natsionalniy-bank-vidkriv-spetsrahunok-dlya-zboru-koshtiv-na-potrebi-armiyi)
+> - Bantu Ukraine melalui dana [SaveLife](https://savelife.in.ua/en/donate-en/)
+> - Maklumat lanjut tentang [war.ukraine.ua](https://war.ukraine.ua/)
+
+[![CI](https://github.com/trekhleb/javascript-algorithms/workflows/CI/badge.svg)](https://github.com/trekhleb/javascript-algorithms/actions?query=workflow% 3ACI+cawangan%3Amaster)
+[![codecov](https://codecov.io/gh/trekhleb/javascript-algorithms/branch/master/graph/badge.svg)](https://codecov.io/gh/trekhleb/javascript-algorithms)
+
+Repositori ini mengandungi banyak contoh berasaskan JavaScript
+algoritma dan struktur data yang popular.
+
+Setiap algoritma dan struktur data mempunyai README tersendiri
+dengan penjelasan dan pautan berkaitan untuk bacaan lanjut (termasuk yang
+kepada video YouTube).
+
+_Baca ini dalam bahasa lain:_
+[_简体中文_](README.zh-CN.md),
+[_繁體中文_](README.zh-TW.md),
+[_한국어_](README.ko-KR.md),
+[_日本語_](README.ja-JP.md),
+[_Polski_](README.pl-PL.md),
+[_Français_](README.fr-FR.md),
+[_Español_](README.es-ES.md),
+[_Português_](README.pt-BR.md),
+[_Русский_](README.ru-RU.md),
+[_Türk_](README.tr-TR.md),
+[_Italiana_](README.it-IT.md),
+[_Bahasa Indonesia_](README.id-ID.md),
+[_Українська_](README.uk-UA.md),
+[_Arab_](README.ar-AR.md),
+[_Tiếng Việt_](README.vi-VN.md),
+[_Deutsch_](README.de-DE.md)
+
+*☝ Ambil perhatian bahawa projek ini bertujuan untuk digunakan untuk tujuan pembelajaran dan penyelidikan
+sahaja, dan ia **tidak** bertujuan untuk digunakan untuk pengeluaran.*
+
+## Struktur Data
+
+Struktur data ialah cara tertentu untuk mengatur dan menyimpan data dalam komputer supaya ia boleh
+boleh diakses dan diubah suai dengan cekap. Lebih tepat lagi, struktur data ialah himpunan data
+nilai, hubungan di antara mereka, dan fungsi atau operasi yang boleh digunakan
+data itu.
+
+`B` - Pemula, `A` - Lanjutan
+
+* `B` [Senarai Terpaut](src/struktur-data/senarai-terpaut)
+* `B` [Senarai Terpaut Berganda](src/struktur-data/senarai-berpaut-dua)
+* `B` [Barisan](src/struktur-data/baris gilir)
+* `B` [Timbunan](src/struktur-data/tindanan)
+* `B` [Jadual Hash](src/struktur-data/jadual cincang)
+* `B` [Timbunan](src/struktur-data/timbunan) - versi timbunan maks dan min
+* `B` [Baris Keutamaan](src/struktur-data/baris gilir keutamaan)
+* `A` [Trie](src/data-structures/trie)
+* `A` [Pokok](src/struktur-data/pokok)
+  * `A` [Pokok Carian Perduaan](src/struktur-data/pokok/pokok-cari-perduaan)
+  * `A` [AVL Tree](src/data-structures/tree/avl-tree)
+  * `A` [Pokok Merah-Hitam](src/struktur-data/pokok/pokok-merah-hitam)
+  * `A` [Pokok Segmen](src/data-structures/tree/segment-tree) - dengan contoh pertanyaan julat min/maks/jumlah
+  * `A` [Pokok Fenwick](src/struktur-data/pokok/pokok-fenwick) (Pokok Berindeks Perduaan)
+* `A` [Graf](src/struktur-data/graf) (kedua-dua terarah dan tidak terarah)
+* `A` [Set Terpisah](src/struktur-data/set-terpisah)
+* `A` [Bloom Filter](src/data-structures/bloom-filter)
+
+## Algoritma
+
+Algoritma ialah spesifikasi yang tidak jelas tentang cara menyelesaikan kelas masalah. Ia adalah
+satu set peraturan yang mentakrifkan dengan tepat urutan operasi.
+
+`B` - Pemula, `A` - Lanjutan
+
+### Algoritma mengikut Topik
+
+* **Matematik**
+  * `B` [Manipulasi Bit](src/algoritma/matematik/bit) - set/dapatkan/kemas kini/kosongkan bit, darab/bahagi dengan dua, jadikan negatif dsb.
+  * `B` [Titik Terapung Perduaan](src/algoritma/matematik/titik terapung binari) - perwakilan binari nombor titik terapung.
+  * `B` [Factorial](src/algoritma/matematik/faktorial)
+  * `B` [Nombor Fibonacci](src/algoritma/matematik/fibonacci) - versi klasik dan bentuk tertutup
+  * `B` [Faktor Perdana](src/algoritma/matematik/faktor-prima) - mencari faktor perdana dan mengiranya menggunakan teorem Hardy-Ramanujan
+  * `B` [Ujian Primaliti](src/algoritma/matematik/ujian-primaliti) (kaedah pembahagian percubaan)
+  * `B` [Algoritma Euclidean](src/algorithm/math/euclidean-algorithm) - kira Pembahagi Sepunya Terhebat (GCD)
+  * `B` [Garab Sepunya Terkecil](src/algoritma/matematik/bilangan-paling-biasa) (LCM)
+  * `B` [Ayak Eratosthenes](src/algoritma/matematik/ayak-eratosthenes) - mencari semua nombor perdana sehingga mana-mana had tertentu
+  * `B` [Adalah Kuasa Dua](src/algoritma/math/is-power-of-two) - semak sama ada nombor itu kuasa dua (algoritma naif dan bitwise)
+  * `B` [Segitiga Pascal](src/algoritma/matematik/segitiga-pascal)
+  * `B` [Nombor Kompleks](src/algoritma/matematik/nombor-kompleks) - nombor kompleks dan operasi asas dengannya
+  * `B` [Radian & Darjah](src/algoritma/matematik/radian) - penukaran radian kepada darjah dan ke belakang
+  * `B` [Fast Powering](src/algorithm/math/fast-powering)
+  * `B` [Kaedah Horner](src/algoritma/matematik/kaedah-horner) - penilaian polinomial
+  * `B` [Matriks](src/algoritma/matematik/matriks) - matriks dan operasi matriks asas (pendaraban, transposisi, dsb.)
+  * `B` [Jarak Euclidean](src/algoritma/matematik/jarak-euclidean) - jarak antara dua titik/vektor/matriks
+  * `A` [Pembahagian Integer](src/algoritma/matematik/integer-partition)
+  * `A` [Akar Kuasa Dua](src/algoritma/matematik/akar-kuadrat) - Kaedah Newton
+  * `A` [Algoritma Liu Hui π](src/algoritma/math/liu-hui) - anggaran π pengiraan berdasarkan N-gons
+  * `A` [Transformasi Fourier Diskret](src/algoritma/matematik/fourier-transform) - menguraikan fungsi masa (suatu isyarat) kepada frekuensi yang membentuknya
+* **Set**
+  * `B` [Produk Cartesian](src/algoritma/set/produk cartesian) - hasil daripada berbilang set
+  * `B` [Fisher–Yates Shuffle](src/algoritma/sets/fisher-yates) - pilih atur rawak bagi urutan terhingga
+  * `A` [Set Kuasa](src/algoritma/set/set-kuasa) - semua subset set (penyelesaian bitwise dan backtracking)
+  * `A` [Permutasi](src/algoritma/set/permutasi) (dengan dan tanpa ulangan)
+  * `A` [Gabungan](src/algoritma/set/gabungan) (dengan dan tanpa ulangan)
+  * `A` [Turutan Sepunya Terpanjang](src/algoritma/set/susulan-biasa-terpanjang) (LCS)
+  * `A` [Surutan Bertambah Terpanjang](src/algoritma/set/susulan-bertambah-panjang)
+  * `A` [Jurutan Sepunya Terpendek](src/algoritma/set/jujukan-sepunya-terpendek) (SCS)
+  * `A` [Masalah Knapsack](src/algorithms/sets/knapsack-problem) - "0/1" dan "Unbound"
+  * `A` [Maximum Subarray](src/algorithm/sets/maximum-subarray) - versi "Brute Force" dan "Dynamic Programming" (Kadane's)
+  * `A` [Jumlah Gabungan](src/algoritma/set/jumlah-gabungan) - cari semua gabungan yang membentuk jumlah tertentu
+* **Rentetan**
+  * `B` [Jarak Hamming](src/algoritma/rentetan/jarak hamming) - bilangan kedudukan di mana simbol berbeza
+  * `B` [Palindrome](src/algorithm/string/palindrome) - semak sama ada rentetan adalah sama secara terbalik
+  * `A` [Jarak Levenshtein](src/algoritma/rentetan/levenshtein-jarak) - jarak edit minimum antara dua jujukan
+  * `A` [Algoritma Knuth–Morris–Pratt](src/algorithm/string/knuth-morris-pratt) (Algoritma KMP) - carian subrentetan (padanan corak)
+  * `A` [Z Algoritma](src/algorithm/string/z-algorithm) - carian subrentetan (padanan corak)
+  * `A` [Algoritma Rabin Karp](src/algorithm/string/rabin-karp) - carian subrentetan
+  * `A` [Subrentetan Biasa Terpanjang](src/algoritma/rentetan/subrentetan-biasa-terpanjang)
+  * `A` [Padanan Ungkapan Biasa](src/algoritma/rentetan/padanan-ungkapan-biasa)
+  * **Carian**
+  * `B` [Carian Linear](src/algorithm/search/linear-search)
+  * `B` [Cari Lompat](src/algorithm/search/jump-search) (atau Carian Sekat) - cari dalam tatasusunan yang diisih
+  * `B` [Carian Binari](src/algorithm/search/binary-search) - cari dalam tatasusunan yang diisih
+  * `B` [Carian Interpolasi](src/algoritma/search/interpolation-search) - cari dalam tatasusunan tersusun yang diedarkan secara seragam
+* **Menyusun**
+  * `B` [Isih Buih](src/algoritma/isih/isih-buih)
+  * `B` [Isih Pilihan](src/algoritma/isih/isih-pilihan)
+  * `B` [Isih Sisipan](src/algoritma/isih/isihan-sisipan)
+  * `B` [Isih Timbunan](src/algoritma/isih/isih-timbun)
+  * `B` [Isih Gabung](src/algoritma/isih/isih-gabung)
+  * `B` [Quicksort](src/algorithm/sorting/quick-sort) - pelaksanaan di tempat dan bukan di tempat
+  * `B` [Shellsort](src/algoritm/sorting/shell-sort)
+  * `B` [Isih Mengira](src/algoritma/isihan/isihan-kira)
+  * `B` [Isih Radix](src/algoritma/isih/isih-radix)
+* **Senarai Terpaut**
+  * `B` [Straight Traversal](src/algorithm/linked-list/traversal)
+  * `B` [Reverse Traversal](src/algorithm/linked-list/reverse-traversal)
+* **Pokok**
+  * `B` [Depth-First Search](src/algorithm/tree/depth-first-search) (DFS)
+  * `B` [Breadth-First-search](src/algorithm/tree/breadth-first-search) (BFS)
+* **Graf**
+  * `B` [Depth-First Search](src/algorithm/graph/depth-first-search) (DFS)
+  * `B` [Breadth-First Search](src/algorithm/graph/breadth-first-search) (BFS)
+  * `B` [Algoritma Kruskal](src/algoritma/graf/kruskal) - mencari Pokok Spanning Minimum (MST) untuk graf tidak berwajaran
+  * `A` [Algoritma Dijkstra](src/algorithm/graph/dijkstra) - mencari laluan terpendek ke semua bucu graf dari bucu tunggal
+  * `A` [Algoritma Bellman-Ford](src/algoritma/graf/bellman-ford) - mencari laluan terpendek ke semua bucu graf daripada bucu tunggal
+  * `A` [Algoritma Floyd-Warshall](src/algorithm/graph/floyd-warshall) - cari laluan terpendek antara semua pasangan bucu
+  * `A` [Detect Cycle](src/algorithm/graph/detect-cycle) - untuk kedua-dua graf terarah dan tidak terarah (versi berasaskan DFS dan Disjoint Set)
+  * `A` [Algoritma Prim](src/algoritma/graf/prim) - mencari Pokok Spanning Minimum (MST) untuk graf tidak berwajaran
+  * `A` [Isih Topologi](src/algoritma/graf/isihan-topologi) - Kaedah DFS
+  * `A` [Mata Artikulasi](src/algoritma/graf/titik-artikulasi) - Algoritma Tarjan (berasaskan DFS)
+  * `A` [Bridges](src/algorithm/graph/bridges) - algoritma berasaskan DFS
+  * `A` [Eulerian Path and Eulerian Circuit](src/algorithm/graph/eulerian-path) - Algoritma Fleury - Lawati setiap tepi tepat sekali
+  * `A` [Kitaran Hamiltonian](src/algoritma/graf/kitaran-hamilton) - Lawati setiap bucu tepat sekali
+  * `A` [Komponen Bersambung Kuat](src/algoritma/graf/komponen-kuat-bersambung) - Algoritma Kosaraju
+  * `A` [Masalah Jurujual Perjalanan](src/algoritma/graf/jurujual-perjalanan) - laluan terpendek mungkin yang melawati setiap bandar dan kembali ke bandar asal
+* **Kriptografi**
+  * `B` [Cincangan Polinomial](src/algoritma/kriptografi/cincang polinomial) - fungsi cincang bergolek berdasarkan polinomial
+  * `B` [Sifir Pagar Rel](src/algoritma/kriptografi/sifir-pagar-rel) - algoritma sifir transposisi untuk pengekodan mesej
+  * `B` [Caesar Cipher](src/algoritma/kriptografi/caesar-cipher) - sifir penggantian mudah
+  * `B` [Sifir Bukit](src/algoritma/kriptografi/sifir bukit) - sifir penggantian berdasarkan algebra linear
+* **Pembelajaran Mesin**
+  * `B` [NanoNeuron](https://github.com/trekhleb/nano-neuron) - 7 fungsi JS mudah yang menggambarkan bagaimana mesin sebenarnya boleh belajar (perambatan ke hadapan/belakang)
+  * `B` [k-NN](src/algoritma/ml/knn) - algoritma klasifikasi jiran terdekat k
+  * `B` [k-Means](src/algorithm/ml/k-means) - algoritma pengelompokan k-Means
+* **Pemprosesan imej**
+  * `B` [Ukiran Jahitan](src/algoritma/pemprosesan-imej/ukiran-jahitan) - algoritma saiz semula imej sedar kandungan
+* **Statistik**
+  * `B` [Rawak Berwajaran](src/algoritma/statistik/rawak-wajaran) - pilih item rawak daripada senarai berdasarkan berat item
+* **Algoritma evolusi**
+  * `A` [Algoritma genetik](https://github.com/trekhleb/self-parking-car-evolution) - contoh cara algoritma genetik boleh digunakan untuk melatih kereta letak sendiri
+  * **Tidak dikategorikan**
+  * `B` [Menara Hanoi](src/algoritma/tidak dikategorikan/menara-hanoi)
+  * `B` [Putaran Matriks Persegi](src/algoritma/tidak dikategorikan/putaran-matriks-persegi) - algoritma di tempat
+  * `B` [Permainan Lompat](src/algoritma/tidak dikategorikan/permainan lompat) - menjejak ke belakang, pengaturcaraan dinamik (atas ke bawah + bawah ke atas) dan contoh tamak
+  * `B` [Laluan Unik](src/algorithms/uncategorized/unique-paths) - penjejakan ke belakang, pengaturcaraan dinamik dan contoh berasaskan Segitiga Pascal
+  * `B` [Teres Hujan](src/algoritma/tidak dikategorikan/teres hujan) - memerangkap masalah air hujan (versi pengaturcaraan dinamik dan kekerasan)
+  * `B` [Tangga Rekursif](src/algoritma/tidak dikategorikan/tangga rekursif) - kira bilangan cara untuk sampai ke atas (4 penyelesaian)
+  * `B` [Masa Terbaik Untuk Membeli Saham Jual](src/algoritma/tidak dikategorikan/masa-terbaik-untuk-membeli-menjual-saham) - bahagikan dan takluk serta contoh satu laluan
+  * `A` [Masalah N-Queens](src/algoritma/uncategorized/n-queens)
+  * `A` [Lawatan Kesatria](src/algoritma/tidak dikategorikan/jelajah kesatria)
+
+### Algoritma mengikut Paradigma
+
+Paradigma algoritma ialah kaedah atau pendekatan generik yang mendasari reka bentuk kelas
+daripada algoritma. Ia adalah abstraksi yang lebih tinggi daripada tanggapan algoritma, sama seperti an
+algoritma adalah abstraksi yang lebih tinggi daripada program komputer.
+
+* **Brute Force** - lihat semua kemungkinan dan pilih penyelesaian terbaik
+  * `B` [Carian Linear](src/algorithm/search/linear-search)
+  * `B` [Rain Terraces](src/algoritma/uncategorized/rain-teres) - memerangkap masalah air hujan
+  * `B` [Tangga Rekursif](src/algoritma/tak berkategori/tangga rekursif) - kira bilangan cara untuk sampai ke atas
+  * `A` [Subarray Maksimum](src/algoritma/set/subarray maksimum)
+  * `A` [Masalah Jurujual Perjalanan](src/algoritma/graf/jurujual-perjalanan) - laluan terpendek mungkin yang melawati setiap bandar dan kembali ke bandar asal
+  * `A` [Transformasi Fourier Diskret](src/algoritma/matematik/fourier-transform) - menguraikan fungsi masa (suatu isyarat) kepada frekuensi yang membentuknya
+* **Rakus** - pilih pilihan terbaik pada masa semasa, tanpa sebarang pertimbangan untuk masa hadapan
+* `B` [Permainan Lompat](src/algoritma/tidak dikategorikan/permainan lompat)
+  * `A` [Masalah Knapsack Tidak Terikat](src/algoritma/set/masalah-knapsack)
+  * `A` [Algoritma Dijkstra](src/algoritma/graf/dijkstra) - mencari laluan terpendek ke semua bucu graf
+  * `A` [Algoritma Prim](src/algoritma/graf/prim) - mencari Pokok Spanning Minimum (MST) untuk graf tidak berwajaran
+  * `A` [Algoritma Kruskal](src/algoritma/graf/kruskal) - mencari Pokok Spanning Minimum (MST) untuk graf tidak berwajaran
+* **Divide and Conquer** - bahagikan masalah kepada bahagian yang lebih kecil dan kemudian selesaikan bahagian tersebut
+  * `B` [Carian Perduaan](src/algoritma/carian/pencarian-perduaan)
+  * `B` [Menara Hanoi](src/algoritma/tidak dikategorikan/menara-hanoi)
+  * `B` [Segitiga Pascal](src/algoritma/matematik/segitiga-pascal)
+  * `B` [Algoritma Euclidean](src/algorithm/math/euclidean-algorithm) - kira Pembahagi Sepunya Terhebat (GCD)
+  * `B` [Isih Gabung](src/algoritma/isih/isih-gabung)
+  * `B` [Isih Pantas](src/algoritma/isih/isih-pantas)
+  * `B` [Carian Kedalaman-Pertama Pokok](src/algoritma/pokok/carian-pertama-dalam) (DFS)
+  * `B` [Graph Depth-First Search](src/algorithm/graph/depth-first-search) (DFS)
+  * `B` [Matriks](src/algoritma/matematik/matriks) - menjana dan melintasi matriks pelbagai bentuk
+  * `B` [Permainan Lompat](src/algoritma/tidak dikategorikan/permainan lompat)
+  * `B` [Fast Powering](src/algorithm/math/fast-powering)
+  * `B` [Masa Terbaik Untuk Membeli Saham Jual](src/algoritma/tidak dikategorikan/masa-terbaik-untuk-membeli-menjual-saham) - bahagikan dan takluk serta contoh satu laluan
+  * `A` [Permutasi](src/algoritma/set/permutasi) (dengan dan tanpa ulangan)
+  * `A` [Gabungan](src/algoritma/set/gabungan) (dengan dan tanpa ulangan)
+  * `A` [Subarray Maksimum](src/algoritma/set/subarray maksimum)
+* **Pengaturcaraan Dinamik** - bina penyelesaian menggunakan sub-penyelesaian yang ditemui sebelum ini
+  * `B` [Nombor Fibonacci](src/algoritma/matematik/fibonacci)
+  * `B` [Permainan Lompat](src/algoritma/tidak dikategorikan/permainan lompat)
+  * `B` [Laluan Unik](src/algoritma/tidak dikategorikan/laluan-unik)
+  * `B` [Rain Terraces](src/algoritma/uncategorized/rain-teres) - memerangkap masalah air hujan
+
+  * `B` [Tangga Rekursif](src/algoritma/tak berkategori/tangga rekursif) - kira bilangan cara untuk sampai ke atas
+  * `B` [Ukiran Jahitan](src/algoritma/pemprosesan-imej/ukiran-jahitan) - algoritma saiz semula imej sedar kandungan
+  * `A` [Jarak Levenshtein](src/algoritma/rentetan/levenshtein-jarak) - jarak edit minimum antara dua jujukan
+  * `A` [Turutan Sepunya Terpanjang](src/algoritma/set/susulan-biasa-terpanjang) (LCS)
+  * `A` [Subrentetan Biasa Terpanjang](src/algoritma/rentetan/subrentetan-biasa-terpanjang)
+  * `A` [Surutan Bertambah Terpanjang](src/algoritma/set/susulan-bertambah-panjang)
+  * `A` [Jujukan Sepunya Terpendek](src/algoritma/set/jujukan-sepunya-terpendek)
+  * `A` [0/1 Masalah Knapsack](src/algoritma/set/knapsack-problem)
+  * `A` [Pembahagian Integer](src/algoritma/matematik/integer-partition)
+  * `A` [Subarray Maksimum](src/algoritma/set/subarray maksimum)
+  * `A` [Algoritma Bellman-Ford](src/algorithm/graph/bellman-ford) - mencari laluan terpendek ke semua bucu graf
+  * `A` [Algoritma Floyd-Warshall](src/algorithm/graph/floyd-warshall) - cari laluan terpendek antara semua pasangan bucu
+  * `A` [Padanan Ungkapan Biasa](src/algoritma/rentetan/padanan-ungkapan-biasa)
+* **Penjejakan Belakang** - sama seperti kekerasan, cuba jana semua penyelesaian yang mungkin, tetapi setiap kali anda menjana penyelesaian seterusnya anda menguji
+jika ia memenuhi semua syarat, dan hanya kemudian terus menjana penyelesaian seterusnya. Jika tidak, mundur, dan teruskan a
+jalan yang berbeza untuk mencari penyelesaian. Biasanya traversal DFS bagi ruang keadaan sedang digunakan.
+  * `B` [Permainan Lompat](src/algoritma/tidak dikategorikan/permainan lompat)
+  * `B` [Laluan Unik](src/algoritma/tidak dikategorikan/laluan-unik)
+  * `B` [Set Kuasa](src/algoritma/set/set-kuasa) - semua subset set
+  * `A` [Kitaran Hamiltonian](src/algoritma/graf/kitaran-hamilton) - Lawati setiap bucu tepat sekali
+  * `A` [Masalah N-Queens](src/algoritma/uncategorized/n-queens)
+  * `A` [Lawatan Kesatria](src/algoritma/tidak dikategorikan/jelajah kesatria)
+  * `A` [Jumlah Gabungan](src/algoritma/set/jumlah-gabungan) - cari semua gabungan yang membentuk jumlah tertentu
+
+  * **Branch & Bound** - ingat penyelesaian kos terendah yang terdapat pada setiap peringkat penjejakan ke belakang
+cari, dan gunakan kos penyelesaian kos terendah yang ditemui setakat ini sebagai had yang lebih rendah pada kos
+penyelesaian kos termurah untuk masalah, untuk membuang penyelesaian separa dengan kos lebih besar daripada
+penyelesaian kos terendah ditemui setakat ini. Biasanya traversal BFS digabungkan dengan traversal DFS of state-space
+pokok sedang digunakan.
+
+## Cara menggunakan repositori ini
+
+**Pasang semua kebergantungan**
+
+```
+pemasangan npm
+```
+
+**Jalankan ESLint**
+
+Anda mungkin mahu menjalankannya untuk menyemak kualiti kod.
+
+```
+npm run lint
+```
+
+**Jalankan semua ujian**
+
+```
+ujian npm
+```
+
+**Jalankan ujian mengikut nama**
+
+```
+ujian npm -- 'LinkedList'
+```
+
+**Penyelesaian masalah**
+
+Jika linting atau ujian gagal, cuba padamkan folder `node_modules` dan pasang semula pakej npm:
+
+```
+rm -rf ./node_modules
+npm i
+```
+
+Juga pastikan anda menggunakan versi Nod yang betul (`>=14.16.0`). Jika anda menggunakan [nvm](https://github.com/nvm-sh/nvm) untuk pengurusan versi Nod, anda boleh menjalankan `nvm use` daripada folder akar projek dan versi yang betul akan diambil.
+
+**Taman permainan**
+
+Anda boleh bermain dengan struktur data dan algoritma dalam fail `./src/playground/playground.js` dan tulis
+mengujinya dalam `./src/playground/__test__/playground.test.js`.
+
+Kemudian hanya jalankan arahan berikut untuk menguji sama ada kod taman permainan anda berfungsi seperti yang diharapkan:
+
+```
+ujian npm -- 'taman permainan'
+```
+
+## Informasi berguna
+
+### Rujukan
+
+[▶ Struktur Data dan Algoritma di YouTube](https://www.youtube.com/playlist?list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
+
+### Notasi O Besar
+
+*Notasi O Besar* digunakan untuk mengklasifikasikan algoritma mengikut cara masa berjalan atau keperluan ruang mereka berkembang apabila saiz input bertambah.
+Pada carta di bawah anda mungkin menemui susunan pertumbuhan algoritma yang paling biasa yang dinyatakan dalam tatatanda Big O.
+
+![Graf O Besar](./assets/big-o-graph.png)
+
+Sumber: [Big O Cheat Sheet](http://bigocheatsheet.com/).
+
+Di bawah ialah senarai beberapa tatatanda Big O yang paling banyak digunakan dan perbandingan prestasinya terhadap saiz data input yang berbeza.
+
+| Notasi O Besar | Taip | Pengiraan untuk 10 elemen | Pengiraan untuk 100 elemen | Pengiraan untuk 1000 elemen |
+| -------------- | ----------- | ---------------------------- | ---------------------------- | ------------------------------- |
+| **O(1)** | Malar | 1 | 1 | 1 |
+| **O(log N)** | Logaritma | 3 | 6 | 9 |
+| **O(N)** | Linear | 10 | 100 | 1000 |
+| **O(N log N)** | n log(n) | 30 | 600 | 9000 |
+| **O(N^2)** | Kuadratik | 100 | 10000 | 1000000 |
+| **O(2^N)** | Eksponen | 1024 | 1.26e+29 | 1.07e+301 |
+| **O(N!)** | Faktorial | 3628800 | 9.3e+157 | 4.02e+2567
+
+### Kerumitan Operasi Struktur Data
+
+| Struktur Data | Akses | Cari | Sisipan | Pemadaman | Komen |
+| ------------------------ | :-------: | :-------: | :-------: | :-------: | :-------- |
+| **Array** | 1 | n | n | n | |
+| **Timbunan** | n | n | 1 | 1 | |
+| **Beratur** | n | n | 1 | 1 | |
+| **Senarai Terpaut** | n | n | 1 | n | |
+| **Jadual Hash** | - | n | n | n | Dalam kes kos fungsi cincang yang sempurna ialah O(1) |
+| **Pokok Carian Binari** | n | n | n | n | Dalam kes kos pokok seimbang ialah O(log(n)) |
+| **B-Tree** | log(n) | log(n) | log(n) | log(n) | |
+| **Pokok Merah-Hitam** | log(n) | log(n) | log(n) | log(n) | |
+| **Pokok AVL** | log(n) | log(n) | log(n) | log(n) | |
+| **Penapis Bloom** | - | 1 | 1 | - | Positif palsu mungkin semasa mencari |
+
+### Kerumitan Algoritma Pengisihan Tatasusunan
+
+| Nama | Terbaik | Purata | Paling teruk | Memori | Stabil | Komen |
+| ---------------------- | :-------------: | :-----------------: | :-----------------: | :-------: | :-------: | :-------- |
+| **Isih gelembung** | n | n<sup>2</sup> | n<sup>2</sup> | 1 | Ya | |
+| **Isihan sisipan** | n | n<sup>2</sup> | n<sup>2</sup> | 1 | Ya | |
+| **Isih pilihan** | n<sup>2</sup> | n<sup>2</sup> | n<sup>2</sup> | 1 | Tidak | |
+| **Isihan timbunan** | n&nbsp;log(n) | n&nbsp;log(n) | n&nbsp;log(n) | 1 | Tidak | |
+| **Isih gabung** | n&nbsp;log(n) | n&nbsp;log(n) | n&nbsp;log(n) | n | Ya | |
+| **Isih cepat** | n&nbsp;log(n) | n&nbsp;log(n) | n<sup>2</sup> | log(n) | Tidak | Quicksort biasanya dilakukan di tempat dengan ruang tindanan O(log(n)) |
+| **Isih cangkerang** | n&nbsp;log(n) | bergantung pada jujukan jurang | n&nbsp;(log(n))<sup>2</sup> | 1 | Tidak | |
+| **Isih mengira** | n + r | n + r | n + r | n + r | Ya | r - nombor terbesar dalam tatasusunan |
+| **Isih Radix** | n * k | n * k | n * k | n + k | Ya | k - panjang kunci terpanjang |
+
+## Penyokong Projek
+
+> Anda boleh menyokong projek ini melalui ❤️️ [GitHub](https://github.com/sponsors/trekhleb) atau ❤️️ [Patreon](https://www.patreon.com/trekhleb).
+
+[Orang yang menyokong projek ini](https://github.com/trekhleb/javascript-algorithms/blob/master/BACKERS.md) `∑ = 0`
+
+> ℹ️ Beberapa lagi [projek](https://trekhleb.dev/projects/) dan [artikel](https://trekhleb.dev/blog/) tentang JavaScript dan algoritma pada [trekhleb.dev](https:/ /trekhleb.dev)
\ No newline at end of file
diff --git a/README.md b/README.md
index c9c6258769..0392aefb96 100644
--- a/README.md
+++ b/README.md
@@ -279,7 +279,7 @@ npm test -- 'LinkedList'
 
 **Troubleshooting**
 
-In case if linting or testing is failing try to delete the `node_modules` folder and re-install npm packages:
+If linting or testing is failing, try to delete the `node_modules` folder and re-install npm packages:
 
 ```
 rm -rf ./node_modules
diff --git a/src/algorithms/graph/breadth-first-search/README.md b/src/algorithms/graph/breadth-first-search/README.md
index 32ec3e815c..06073abd8b 100644
--- a/src/algorithms/graph/breadth-first-search/README.md
+++ b/src/algorithms/graph/breadth-first-search/README.md
@@ -1,7 +1,7 @@
 # Breadth-First Search (BFS)
 
-Breadth-first search (BFS) is an algorithm for traversing 
-or searching tree or graph data structures. It starts at
+Breadth-first search (BFS) is an algorithm for traversing, 
+searching tree, or graph data structures. It starts at
 the tree root (or some arbitrary node of a graph, sometimes 
 referred to as a 'search key') and explores the neighbor
 nodes first, before moving to the next level neighbors.

From a123b9017d53a54853401b21382828b65c712e71 Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Mon, 5 Dec 2022 08:06:38 +0100
Subject: [PATCH 218/264] Reverting Malay translation since most of the links
 are not working

---
 README.ma-MA.md | 364 ------------------------------------------------
 1 file changed, 364 deletions(-)
 delete mode 100644 README.ma-MA.md

diff --git a/README.ma-MA.md b/README.ma-MA.md
deleted file mode 100644
index 0f75b78a12..0000000000
--- a/README.ma-MA.md
+++ /dev/null
@@ -1,364 +0,0 @@
-# Algoritma JavaScript dan Struktur Data
-
-> 🇺🇦 UKRAINE [SEDANG DISERANG](https://twitter.com/MFA_Ukraine) OLEH TENTERA RUSIA. ORANG AWAM SEMAKIN DIBUNUH. KAWASAN KEDIAMAN SEMAKIN DIBOM.
-> - Bantu Ukraine melalui [Bank Negara Ukraine](https://bank.gov.ua/en/news/all/natsionalniy-bank-vidkriv-spetsrahunok-dlya-zboru-koshtiv-na-potrebi-armiyi)
-> - Bantu Ukraine melalui dana [SaveLife](https://savelife.in.ua/en/donate-en/)
-> - Maklumat lanjut tentang [war.ukraine.ua](https://war.ukraine.ua/)
-
-[![CI](https://github.com/trekhleb/javascript-algorithms/workflows/CI/badge.svg)](https://github.com/trekhleb/javascript-algorithms/actions?query=workflow% 3ACI+cawangan%3Amaster)
-[![codecov](https://codecov.io/gh/trekhleb/javascript-algorithms/branch/master/graph/badge.svg)](https://codecov.io/gh/trekhleb/javascript-algorithms)
-
-Repositori ini mengandungi banyak contoh berasaskan JavaScript
-algoritma dan struktur data yang popular.
-
-Setiap algoritma dan struktur data mempunyai README tersendiri
-dengan penjelasan dan pautan berkaitan untuk bacaan lanjut (termasuk yang
-kepada video YouTube).
-
-_Baca ini dalam bahasa lain:_
-[_简体中文_](README.zh-CN.md),
-[_繁體中文_](README.zh-TW.md),
-[_한국어_](README.ko-KR.md),
-[_日本語_](README.ja-JP.md),
-[_Polski_](README.pl-PL.md),
-[_Français_](README.fr-FR.md),
-[_Español_](README.es-ES.md),
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-
-*☝ Ambil perhatian bahawa projek ini bertujuan untuk digunakan untuk tujuan pembelajaran dan penyelidikan
-sahaja, dan ia **tidak** bertujuan untuk digunakan untuk pengeluaran.*
-
-## Struktur Data
-
-Struktur data ialah cara tertentu untuk mengatur dan menyimpan data dalam komputer supaya ia boleh
-boleh diakses dan diubah suai dengan cekap. Lebih tepat lagi, struktur data ialah himpunan data
-nilai, hubungan di antara mereka, dan fungsi atau operasi yang boleh digunakan
-data itu.
-
-`B` - Pemula, `A` - Lanjutan
-
-* `B` [Senarai Terpaut](src/struktur-data/senarai-terpaut)
-* `B` [Senarai Terpaut Berganda](src/struktur-data/senarai-berpaut-dua)
-* `B` [Barisan](src/struktur-data/baris gilir)
-* `B` [Timbunan](src/struktur-data/tindanan)
-* `B` [Jadual Hash](src/struktur-data/jadual cincang)
-* `B` [Timbunan](src/struktur-data/timbunan) - versi timbunan maks dan min
-* `B` [Baris Keutamaan](src/struktur-data/baris gilir keutamaan)
-* `A` [Trie](src/data-structures/trie)
-* `A` [Pokok](src/struktur-data/pokok)
-  * `A` [Pokok Carian Perduaan](src/struktur-data/pokok/pokok-cari-perduaan)
-  * `A` [AVL Tree](src/data-structures/tree/avl-tree)
-  * `A` [Pokok Merah-Hitam](src/struktur-data/pokok/pokok-merah-hitam)
-  * `A` [Pokok Segmen](src/data-structures/tree/segment-tree) - dengan contoh pertanyaan julat min/maks/jumlah
-  * `A` [Pokok Fenwick](src/struktur-data/pokok/pokok-fenwick) (Pokok Berindeks Perduaan)
-* `A` [Graf](src/struktur-data/graf) (kedua-dua terarah dan tidak terarah)
-* `A` [Set Terpisah](src/struktur-data/set-terpisah)
-* `A` [Bloom Filter](src/data-structures/bloom-filter)
-
-## Algoritma
-
-Algoritma ialah spesifikasi yang tidak jelas tentang cara menyelesaikan kelas masalah. Ia adalah
-satu set peraturan yang mentakrifkan dengan tepat urutan operasi.
-
-`B` - Pemula, `A` - Lanjutan
-
-### Algoritma mengikut Topik
-
-* **Matematik**
-  * `B` [Manipulasi Bit](src/algoritma/matematik/bit) - set/dapatkan/kemas kini/kosongkan bit, darab/bahagi dengan dua, jadikan negatif dsb.
-  * `B` [Titik Terapung Perduaan](src/algoritma/matematik/titik terapung binari) - perwakilan binari nombor titik terapung.
-  * `B` [Factorial](src/algoritma/matematik/faktorial)
-  * `B` [Nombor Fibonacci](src/algoritma/matematik/fibonacci) - versi klasik dan bentuk tertutup
-  * `B` [Faktor Perdana](src/algoritma/matematik/faktor-prima) - mencari faktor perdana dan mengiranya menggunakan teorem Hardy-Ramanujan
-  * `B` [Ujian Primaliti](src/algoritma/matematik/ujian-primaliti) (kaedah pembahagian percubaan)
-  * `B` [Algoritma Euclidean](src/algorithm/math/euclidean-algorithm) - kira Pembahagi Sepunya Terhebat (GCD)
-  * `B` [Garab Sepunya Terkecil](src/algoritma/matematik/bilangan-paling-biasa) (LCM)
-  * `B` [Ayak Eratosthenes](src/algoritma/matematik/ayak-eratosthenes) - mencari semua nombor perdana sehingga mana-mana had tertentu
-  * `B` [Adalah Kuasa Dua](src/algoritma/math/is-power-of-two) - semak sama ada nombor itu kuasa dua (algoritma naif dan bitwise)
-  * `B` [Segitiga Pascal](src/algoritma/matematik/segitiga-pascal)
-  * `B` [Nombor Kompleks](src/algoritma/matematik/nombor-kompleks) - nombor kompleks dan operasi asas dengannya
-  * `B` [Radian & Darjah](src/algoritma/matematik/radian) - penukaran radian kepada darjah dan ke belakang
-  * `B` [Fast Powering](src/algorithm/math/fast-powering)
-  * `B` [Kaedah Horner](src/algoritma/matematik/kaedah-horner) - penilaian polinomial
-  * `B` [Matriks](src/algoritma/matematik/matriks) - matriks dan operasi matriks asas (pendaraban, transposisi, dsb.)
-  * `B` [Jarak Euclidean](src/algoritma/matematik/jarak-euclidean) - jarak antara dua titik/vektor/matriks
-  * `A` [Pembahagian Integer](src/algoritma/matematik/integer-partition)
-  * `A` [Akar Kuasa Dua](src/algoritma/matematik/akar-kuadrat) - Kaedah Newton
-  * `A` [Algoritma Liu Hui π](src/algoritma/math/liu-hui) - anggaran π pengiraan berdasarkan N-gons
-  * `A` [Transformasi Fourier Diskret](src/algoritma/matematik/fourier-transform) - menguraikan fungsi masa (suatu isyarat) kepada frekuensi yang membentuknya
-* **Set**
-  * `B` [Produk Cartesian](src/algoritma/set/produk cartesian) - hasil daripada berbilang set
-  * `B` [Fisher–Yates Shuffle](src/algoritma/sets/fisher-yates) - pilih atur rawak bagi urutan terhingga
-  * `A` [Set Kuasa](src/algoritma/set/set-kuasa) - semua subset set (penyelesaian bitwise dan backtracking)
-  * `A` [Permutasi](src/algoritma/set/permutasi) (dengan dan tanpa ulangan)
-  * `A` [Gabungan](src/algoritma/set/gabungan) (dengan dan tanpa ulangan)
-  * `A` [Turutan Sepunya Terpanjang](src/algoritma/set/susulan-biasa-terpanjang) (LCS)
-  * `A` [Surutan Bertambah Terpanjang](src/algoritma/set/susulan-bertambah-panjang)
-  * `A` [Jurutan Sepunya Terpendek](src/algoritma/set/jujukan-sepunya-terpendek) (SCS)
-  * `A` [Masalah Knapsack](src/algorithms/sets/knapsack-problem) - "0/1" dan "Unbound"
-  * `A` [Maximum Subarray](src/algorithm/sets/maximum-subarray) - versi "Brute Force" dan "Dynamic Programming" (Kadane's)
-  * `A` [Jumlah Gabungan](src/algoritma/set/jumlah-gabungan) - cari semua gabungan yang membentuk jumlah tertentu
-* **Rentetan**
-  * `B` [Jarak Hamming](src/algoritma/rentetan/jarak hamming) - bilangan kedudukan di mana simbol berbeza
-  * `B` [Palindrome](src/algorithm/string/palindrome) - semak sama ada rentetan adalah sama secara terbalik
-  * `A` [Jarak Levenshtein](src/algoritma/rentetan/levenshtein-jarak) - jarak edit minimum antara dua jujukan
-  * `A` [Algoritma Knuth–Morris–Pratt](src/algorithm/string/knuth-morris-pratt) (Algoritma KMP) - carian subrentetan (padanan corak)
-  * `A` [Z Algoritma](src/algorithm/string/z-algorithm) - carian subrentetan (padanan corak)
-  * `A` [Algoritma Rabin Karp](src/algorithm/string/rabin-karp) - carian subrentetan
-  * `A` [Subrentetan Biasa Terpanjang](src/algoritma/rentetan/subrentetan-biasa-terpanjang)
-  * `A` [Padanan Ungkapan Biasa](src/algoritma/rentetan/padanan-ungkapan-biasa)
-  * **Carian**
-  * `B` [Carian Linear](src/algorithm/search/linear-search)
-  * `B` [Cari Lompat](src/algorithm/search/jump-search) (atau Carian Sekat) - cari dalam tatasusunan yang diisih
-  * `B` [Carian Binari](src/algorithm/search/binary-search) - cari dalam tatasusunan yang diisih
-  * `B` [Carian Interpolasi](src/algoritma/search/interpolation-search) - cari dalam tatasusunan tersusun yang diedarkan secara seragam
-* **Menyusun**
-  * `B` [Isih Buih](src/algoritma/isih/isih-buih)
-  * `B` [Isih Pilihan](src/algoritma/isih/isih-pilihan)
-  * `B` [Isih Sisipan](src/algoritma/isih/isihan-sisipan)
-  * `B` [Isih Timbunan](src/algoritma/isih/isih-timbun)
-  * `B` [Isih Gabung](src/algoritma/isih/isih-gabung)
-  * `B` [Quicksort](src/algorithm/sorting/quick-sort) - pelaksanaan di tempat dan bukan di tempat
-  * `B` [Shellsort](src/algoritm/sorting/shell-sort)
-  * `B` [Isih Mengira](src/algoritma/isihan/isihan-kira)
-  * `B` [Isih Radix](src/algoritma/isih/isih-radix)
-* **Senarai Terpaut**
-  * `B` [Straight Traversal](src/algorithm/linked-list/traversal)
-  * `B` [Reverse Traversal](src/algorithm/linked-list/reverse-traversal)
-* **Pokok**
-  * `B` [Depth-First Search](src/algorithm/tree/depth-first-search) (DFS)
-  * `B` [Breadth-First-search](src/algorithm/tree/breadth-first-search) (BFS)
-* **Graf**
-  * `B` [Depth-First Search](src/algorithm/graph/depth-first-search) (DFS)
-  * `B` [Breadth-First Search](src/algorithm/graph/breadth-first-search) (BFS)
-  * `B` [Algoritma Kruskal](src/algoritma/graf/kruskal) - mencari Pokok Spanning Minimum (MST) untuk graf tidak berwajaran
-  * `A` [Algoritma Dijkstra](src/algorithm/graph/dijkstra) - mencari laluan terpendek ke semua bucu graf dari bucu tunggal
-  * `A` [Algoritma Bellman-Ford](src/algoritma/graf/bellman-ford) - mencari laluan terpendek ke semua bucu graf daripada bucu tunggal
-  * `A` [Algoritma Floyd-Warshall](src/algorithm/graph/floyd-warshall) - cari laluan terpendek antara semua pasangan bucu
-  * `A` [Detect Cycle](src/algorithm/graph/detect-cycle) - untuk kedua-dua graf terarah dan tidak terarah (versi berasaskan DFS dan Disjoint Set)
-  * `A` [Algoritma Prim](src/algoritma/graf/prim) - mencari Pokok Spanning Minimum (MST) untuk graf tidak berwajaran
-  * `A` [Isih Topologi](src/algoritma/graf/isihan-topologi) - Kaedah DFS
-  * `A` [Mata Artikulasi](src/algoritma/graf/titik-artikulasi) - Algoritma Tarjan (berasaskan DFS)
-  * `A` [Bridges](src/algorithm/graph/bridges) - algoritma berasaskan DFS
-  * `A` [Eulerian Path and Eulerian Circuit](src/algorithm/graph/eulerian-path) - Algoritma Fleury - Lawati setiap tepi tepat sekali
-  * `A` [Kitaran Hamiltonian](src/algoritma/graf/kitaran-hamilton) - Lawati setiap bucu tepat sekali
-  * `A` [Komponen Bersambung Kuat](src/algoritma/graf/komponen-kuat-bersambung) - Algoritma Kosaraju
-  * `A` [Masalah Jurujual Perjalanan](src/algoritma/graf/jurujual-perjalanan) - laluan terpendek mungkin yang melawati setiap bandar dan kembali ke bandar asal
-* **Kriptografi**
-  * `B` [Cincangan Polinomial](src/algoritma/kriptografi/cincang polinomial) - fungsi cincang bergolek berdasarkan polinomial
-  * `B` [Sifir Pagar Rel](src/algoritma/kriptografi/sifir-pagar-rel) - algoritma sifir transposisi untuk pengekodan mesej
-  * `B` [Caesar Cipher](src/algoritma/kriptografi/caesar-cipher) - sifir penggantian mudah
-  * `B` [Sifir Bukit](src/algoritma/kriptografi/sifir bukit) - sifir penggantian berdasarkan algebra linear
-* **Pembelajaran Mesin**
-  * `B` [NanoNeuron](https://github.com/trekhleb/nano-neuron) - 7 fungsi JS mudah yang menggambarkan bagaimana mesin sebenarnya boleh belajar (perambatan ke hadapan/belakang)
-  * `B` [k-NN](src/algoritma/ml/knn) - algoritma klasifikasi jiran terdekat k
-  * `B` [k-Means](src/algorithm/ml/k-means) - algoritma pengelompokan k-Means
-* **Pemprosesan imej**
-  * `B` [Ukiran Jahitan](src/algoritma/pemprosesan-imej/ukiran-jahitan) - algoritma saiz semula imej sedar kandungan
-* **Statistik**
-  * `B` [Rawak Berwajaran](src/algoritma/statistik/rawak-wajaran) - pilih item rawak daripada senarai berdasarkan berat item
-* **Algoritma evolusi**
-  * `A` [Algoritma genetik](https://github.com/trekhleb/self-parking-car-evolution) - contoh cara algoritma genetik boleh digunakan untuk melatih kereta letak sendiri
-  * **Tidak dikategorikan**
-  * `B` [Menara Hanoi](src/algoritma/tidak dikategorikan/menara-hanoi)
-  * `B` [Putaran Matriks Persegi](src/algoritma/tidak dikategorikan/putaran-matriks-persegi) - algoritma di tempat
-  * `B` [Permainan Lompat](src/algoritma/tidak dikategorikan/permainan lompat) - menjejak ke belakang, pengaturcaraan dinamik (atas ke bawah + bawah ke atas) dan contoh tamak
-  * `B` [Laluan Unik](src/algorithms/uncategorized/unique-paths) - penjejakan ke belakang, pengaturcaraan dinamik dan contoh berasaskan Segitiga Pascal
-  * `B` [Teres Hujan](src/algoritma/tidak dikategorikan/teres hujan) - memerangkap masalah air hujan (versi pengaturcaraan dinamik dan kekerasan)
-  * `B` [Tangga Rekursif](src/algoritma/tidak dikategorikan/tangga rekursif) - kira bilangan cara untuk sampai ke atas (4 penyelesaian)
-  * `B` [Masa Terbaik Untuk Membeli Saham Jual](src/algoritma/tidak dikategorikan/masa-terbaik-untuk-membeli-menjual-saham) - bahagikan dan takluk serta contoh satu laluan
-  * `A` [Masalah N-Queens](src/algoritma/uncategorized/n-queens)
-  * `A` [Lawatan Kesatria](src/algoritma/tidak dikategorikan/jelajah kesatria)
-
-### Algoritma mengikut Paradigma
-
-Paradigma algoritma ialah kaedah atau pendekatan generik yang mendasari reka bentuk kelas
-daripada algoritma. Ia adalah abstraksi yang lebih tinggi daripada tanggapan algoritma, sama seperti an
-algoritma adalah abstraksi yang lebih tinggi daripada program komputer.
-
-* **Brute Force** - lihat semua kemungkinan dan pilih penyelesaian terbaik
-  * `B` [Carian Linear](src/algorithm/search/linear-search)
-  * `B` [Rain Terraces](src/algoritma/uncategorized/rain-teres) - memerangkap masalah air hujan
-  * `B` [Tangga Rekursif](src/algoritma/tak berkategori/tangga rekursif) - kira bilangan cara untuk sampai ke atas
-  * `A` [Subarray Maksimum](src/algoritma/set/subarray maksimum)
-  * `A` [Masalah Jurujual Perjalanan](src/algoritma/graf/jurujual-perjalanan) - laluan terpendek mungkin yang melawati setiap bandar dan kembali ke bandar asal
-  * `A` [Transformasi Fourier Diskret](src/algoritma/matematik/fourier-transform) - menguraikan fungsi masa (suatu isyarat) kepada frekuensi yang membentuknya
-* **Rakus** - pilih pilihan terbaik pada masa semasa, tanpa sebarang pertimbangan untuk masa hadapan
-* `B` [Permainan Lompat](src/algoritma/tidak dikategorikan/permainan lompat)
-  * `A` [Masalah Knapsack Tidak Terikat](src/algoritma/set/masalah-knapsack)
-  * `A` [Algoritma Dijkstra](src/algoritma/graf/dijkstra) - mencari laluan terpendek ke semua bucu graf
-  * `A` [Algoritma Prim](src/algoritma/graf/prim) - mencari Pokok Spanning Minimum (MST) untuk graf tidak berwajaran
-  * `A` [Algoritma Kruskal](src/algoritma/graf/kruskal) - mencari Pokok Spanning Minimum (MST) untuk graf tidak berwajaran
-* **Divide and Conquer** - bahagikan masalah kepada bahagian yang lebih kecil dan kemudian selesaikan bahagian tersebut
-  * `B` [Carian Perduaan](src/algoritma/carian/pencarian-perduaan)
-  * `B` [Menara Hanoi](src/algoritma/tidak dikategorikan/menara-hanoi)
-  * `B` [Segitiga Pascal](src/algoritma/matematik/segitiga-pascal)
-  * `B` [Algoritma Euclidean](src/algorithm/math/euclidean-algorithm) - kira Pembahagi Sepunya Terhebat (GCD)
-  * `B` [Isih Gabung](src/algoritma/isih/isih-gabung)
-  * `B` [Isih Pantas](src/algoritma/isih/isih-pantas)
-  * `B` [Carian Kedalaman-Pertama Pokok](src/algoritma/pokok/carian-pertama-dalam) (DFS)
-  * `B` [Graph Depth-First Search](src/algorithm/graph/depth-first-search) (DFS)
-  * `B` [Matriks](src/algoritma/matematik/matriks) - menjana dan melintasi matriks pelbagai bentuk
-  * `B` [Permainan Lompat](src/algoritma/tidak dikategorikan/permainan lompat)
-  * `B` [Fast Powering](src/algorithm/math/fast-powering)
-  * `B` [Masa Terbaik Untuk Membeli Saham Jual](src/algoritma/tidak dikategorikan/masa-terbaik-untuk-membeli-menjual-saham) - bahagikan dan takluk serta contoh satu laluan
-  * `A` [Permutasi](src/algoritma/set/permutasi) (dengan dan tanpa ulangan)
-  * `A` [Gabungan](src/algoritma/set/gabungan) (dengan dan tanpa ulangan)
-  * `A` [Subarray Maksimum](src/algoritma/set/subarray maksimum)
-* **Pengaturcaraan Dinamik** - bina penyelesaian menggunakan sub-penyelesaian yang ditemui sebelum ini
-  * `B` [Nombor Fibonacci](src/algoritma/matematik/fibonacci)
-  * `B` [Permainan Lompat](src/algoritma/tidak dikategorikan/permainan lompat)
-  * `B` [Laluan Unik](src/algoritma/tidak dikategorikan/laluan-unik)
-  * `B` [Rain Terraces](src/algoritma/uncategorized/rain-teres) - memerangkap masalah air hujan
-
-  * `B` [Tangga Rekursif](src/algoritma/tak berkategori/tangga rekursif) - kira bilangan cara untuk sampai ke atas
-  * `B` [Ukiran Jahitan](src/algoritma/pemprosesan-imej/ukiran-jahitan) - algoritma saiz semula imej sedar kandungan
-  * `A` [Jarak Levenshtein](src/algoritma/rentetan/levenshtein-jarak) - jarak edit minimum antara dua jujukan
-  * `A` [Turutan Sepunya Terpanjang](src/algoritma/set/susulan-biasa-terpanjang) (LCS)
-  * `A` [Subrentetan Biasa Terpanjang](src/algoritma/rentetan/subrentetan-biasa-terpanjang)
-  * `A` [Surutan Bertambah Terpanjang](src/algoritma/set/susulan-bertambah-panjang)
-  * `A` [Jujukan Sepunya Terpendek](src/algoritma/set/jujukan-sepunya-terpendek)
-  * `A` [0/1 Masalah Knapsack](src/algoritma/set/knapsack-problem)
-  * `A` [Pembahagian Integer](src/algoritma/matematik/integer-partition)
-  * `A` [Subarray Maksimum](src/algoritma/set/subarray maksimum)
-  * `A` [Algoritma Bellman-Ford](src/algorithm/graph/bellman-ford) - mencari laluan terpendek ke semua bucu graf
-  * `A` [Algoritma Floyd-Warshall](src/algorithm/graph/floyd-warshall) - cari laluan terpendek antara semua pasangan bucu
-  * `A` [Padanan Ungkapan Biasa](src/algoritma/rentetan/padanan-ungkapan-biasa)
-* **Penjejakan Belakang** - sama seperti kekerasan, cuba jana semua penyelesaian yang mungkin, tetapi setiap kali anda menjana penyelesaian seterusnya anda menguji
-jika ia memenuhi semua syarat, dan hanya kemudian terus menjana penyelesaian seterusnya. Jika tidak, mundur, dan teruskan a
-jalan yang berbeza untuk mencari penyelesaian. Biasanya traversal DFS bagi ruang keadaan sedang digunakan.
-  * `B` [Permainan Lompat](src/algoritma/tidak dikategorikan/permainan lompat)
-  * `B` [Laluan Unik](src/algoritma/tidak dikategorikan/laluan-unik)
-  * `B` [Set Kuasa](src/algoritma/set/set-kuasa) - semua subset set
-  * `A` [Kitaran Hamiltonian](src/algoritma/graf/kitaran-hamilton) - Lawati setiap bucu tepat sekali
-  * `A` [Masalah N-Queens](src/algoritma/uncategorized/n-queens)
-  * `A` [Lawatan Kesatria](src/algoritma/tidak dikategorikan/jelajah kesatria)
-  * `A` [Jumlah Gabungan](src/algoritma/set/jumlah-gabungan) - cari semua gabungan yang membentuk jumlah tertentu
-
-  * **Branch & Bound** - ingat penyelesaian kos terendah yang terdapat pada setiap peringkat penjejakan ke belakang
-cari, dan gunakan kos penyelesaian kos terendah yang ditemui setakat ini sebagai had yang lebih rendah pada kos
-penyelesaian kos termurah untuk masalah, untuk membuang penyelesaian separa dengan kos lebih besar daripada
-penyelesaian kos terendah ditemui setakat ini. Biasanya traversal BFS digabungkan dengan traversal DFS of state-space
-pokok sedang digunakan.
-
-## Cara menggunakan repositori ini
-
-**Pasang semua kebergantungan**
-
-```
-pemasangan npm
-```
-
-**Jalankan ESLint**
-
-Anda mungkin mahu menjalankannya untuk menyemak kualiti kod.
-
-```
-npm run lint
-```
-
-**Jalankan semua ujian**
-
-```
-ujian npm
-```
-
-**Jalankan ujian mengikut nama**
-
-```
-ujian npm -- 'LinkedList'
-```
-
-**Penyelesaian masalah**
-
-Jika linting atau ujian gagal, cuba padamkan folder `node_modules` dan pasang semula pakej npm:
-
-```
-rm -rf ./node_modules
-npm i
-```
-
-Juga pastikan anda menggunakan versi Nod yang betul (`>=14.16.0`). Jika anda menggunakan [nvm](https://github.com/nvm-sh/nvm) untuk pengurusan versi Nod, anda boleh menjalankan `nvm use` daripada folder akar projek dan versi yang betul akan diambil.
-
-**Taman permainan**
-
-Anda boleh bermain dengan struktur data dan algoritma dalam fail `./src/playground/playground.js` dan tulis
-mengujinya dalam `./src/playground/__test__/playground.test.js`.
-
-Kemudian hanya jalankan arahan berikut untuk menguji sama ada kod taman permainan anda berfungsi seperti yang diharapkan:
-
-```
-ujian npm -- 'taman permainan'
-```
-
-## Informasi berguna
-
-### Rujukan
-
-[▶ Struktur Data dan Algoritma di YouTube](https://www.youtube.com/playlist?list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
-
-### Notasi O Besar
-
-*Notasi O Besar* digunakan untuk mengklasifikasikan algoritma mengikut cara masa berjalan atau keperluan ruang mereka berkembang apabila saiz input bertambah.
-Pada carta di bawah anda mungkin menemui susunan pertumbuhan algoritma yang paling biasa yang dinyatakan dalam tatatanda Big O.
-
-![Graf O Besar](./assets/big-o-graph.png)
-
-Sumber: [Big O Cheat Sheet](http://bigocheatsheet.com/).
-
-Di bawah ialah senarai beberapa tatatanda Big O yang paling banyak digunakan dan perbandingan prestasinya terhadap saiz data input yang berbeza.
-
-| Notasi O Besar | Taip | Pengiraan untuk 10 elemen | Pengiraan untuk 100 elemen | Pengiraan untuk 1000 elemen |
-| -------------- | ----------- | ---------------------------- | ---------------------------- | ------------------------------- |
-| **O(1)** | Malar | 1 | 1 | 1 |
-| **O(log N)** | Logaritma | 3 | 6 | 9 |
-| **O(N)** | Linear | 10 | 100 | 1000 |
-| **O(N log N)** | n log(n) | 30 | 600 | 9000 |
-| **O(N^2)** | Kuadratik | 100 | 10000 | 1000000 |
-| **O(2^N)** | Eksponen | 1024 | 1.26e+29 | 1.07e+301 |
-| **O(N!)** | Faktorial | 3628800 | 9.3e+157 | 4.02e+2567
-
-### Kerumitan Operasi Struktur Data
-
-| Struktur Data | Akses | Cari | Sisipan | Pemadaman | Komen |
-| ------------------------ | :-------: | :-------: | :-------: | :-------: | :-------- |
-| **Array** | 1 | n | n | n | |
-| **Timbunan** | n | n | 1 | 1 | |
-| **Beratur** | n | n | 1 | 1 | |
-| **Senarai Terpaut** | n | n | 1 | n | |
-| **Jadual Hash** | - | n | n | n | Dalam kes kos fungsi cincang yang sempurna ialah O(1) |
-| **Pokok Carian Binari** | n | n | n | n | Dalam kes kos pokok seimbang ialah O(log(n)) |
-| **B-Tree** | log(n) | log(n) | log(n) | log(n) | |
-| **Pokok Merah-Hitam** | log(n) | log(n) | log(n) | log(n) | |
-| **Pokok AVL** | log(n) | log(n) | log(n) | log(n) | |
-| **Penapis Bloom** | - | 1 | 1 | - | Positif palsu mungkin semasa mencari |
-
-### Kerumitan Algoritma Pengisihan Tatasusunan
-
-| Nama | Terbaik | Purata | Paling teruk | Memori | Stabil | Komen |
-| ---------------------- | :-------------: | :-----------------: | :-----------------: | :-------: | :-------: | :-------- |
-| **Isih gelembung** | n | n<sup>2</sup> | n<sup>2</sup> | 1 | Ya | |
-| **Isihan sisipan** | n | n<sup>2</sup> | n<sup>2</sup> | 1 | Ya | |
-| **Isih pilihan** | n<sup>2</sup> | n<sup>2</sup> | n<sup>2</sup> | 1 | Tidak | |
-| **Isihan timbunan** | n&nbsp;log(n) | n&nbsp;log(n) | n&nbsp;log(n) | 1 | Tidak | |
-| **Isih gabung** | n&nbsp;log(n) | n&nbsp;log(n) | n&nbsp;log(n) | n | Ya | |
-| **Isih cepat** | n&nbsp;log(n) | n&nbsp;log(n) | n<sup>2</sup> | log(n) | Tidak | Quicksort biasanya dilakukan di tempat dengan ruang tindanan O(log(n)) |
-| **Isih cangkerang** | n&nbsp;log(n) | bergantung pada jujukan jurang | n&nbsp;(log(n))<sup>2</sup> | 1 | Tidak | |
-| **Isih mengira** | n + r | n + r | n + r | n + r | Ya | r - nombor terbesar dalam tatasusunan |
-| **Isih Radix** | n * k | n * k | n * k | n + k | Ya | k - panjang kunci terpanjang |
-
-## Penyokong Projek
-
-> Anda boleh menyokong projek ini melalui ❤️️ [GitHub](https://github.com/sponsors/trekhleb) atau ❤️️ [Patreon](https://www.patreon.com/trekhleb).
-
-[Orang yang menyokong projek ini](https://github.com/trekhleb/javascript-algorithms/blob/master/BACKERS.md) `∑ = 0`
-
-> ℹ️ Beberapa lagi [projek](https://trekhleb.dev/projects/) dan [artikel](https://trekhleb.dev/blog/) tentang JavaScript dan algoritma pada [trekhleb.dev](https:/ /trekhleb.dev)
\ No newline at end of file

From 65e4a7c8b35914e70bfc2b7cbc58c5a9f654db53 Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Fri, 6 Jan 2023 14:37:36 +0100
Subject: [PATCH 219/264] Adding a simple cascading solution to generate a
 Power Set (#975)

* Add a simple cascading version of generating a PowerSet.

* Update README.

* Update README.

* Update README.
---
 README.md                                     |  2 +-
 src/algorithms/sets/power-set/README.md       | 60 +++++++++++++++----
 .../power-set/__test__/caPowerSet.test.js     | 28 +++++++++
 src/algorithms/sets/power-set/caPowerSet.js   | 37 ++++++++++++
 4 files changed, 115 insertions(+), 12 deletions(-)
 create mode 100644 src/algorithms/sets/power-set/__test__/caPowerSet.test.js
 create mode 100644 src/algorithms/sets/power-set/caPowerSet.js

diff --git a/README.md b/README.md
index 0392aefb96..8836940696 100644
--- a/README.md
+++ b/README.md
@@ -99,7 +99,7 @@ a set of rules that precisely define a sequence of operations.
 * **Sets**
   * `B` [Cartesian Product](src/algorithms/sets/cartesian-product) - product of multiple sets
   * `B` [Fisher–Yates Shuffle](src/algorithms/sets/fisher-yates) - random permutation of a finite sequence
-  * `A` [Power Set](src/algorithms/sets/power-set) - all subsets of a set (bitwise and backtracking solutions)
+  * `A` [Power Set](src/algorithms/sets/power-set) - all subsets of a set (bitwise, backtracking, and cascading solutions)
   * `A` [Permutations](src/algorithms/sets/permutations) (with and without repetitions)
   * `A` [Combinations](src/algorithms/sets/combinations) (with and without repetitions)
   * `A` [Longest Common Subsequence](src/algorithms/sets/longest-common-subsequence) (LCS)
diff --git a/src/algorithms/sets/power-set/README.md b/src/algorithms/sets/power-set/README.md
index cfe791aeb2..e96961dd8f 100644
--- a/src/algorithms/sets/power-set/README.md
+++ b/src/algorithms/sets/power-set/README.md
@@ -1,7 +1,7 @@
 # Power Set
 
 Power set of a set `S` is the set of all of the subsets of `S`, including the
-empty set and `S` itself. Power set of set `S` is denoted as `P(S)`. 
+empty set and `S` itself. Power set of set `S` is denoted as `P(S)`.
 
 For example for `{x, y, z}`, the subsets
 are:
@@ -21,37 +21,37 @@ are:
 
 ![Power Set](https://www.mathsisfun.com/sets/images/power-set.svg)
 
-Here is how we may illustrate the elements of the power set of the set `{x, y, z}` ordered with respect to 
+Here is how we may illustrate the elements of the power set of the set `{x, y, z}` ordered with respect to
 inclusion:
 
 ![](https://upload.wikimedia.org/wikipedia/commons/e/ea/Hasse_diagram_of_powerset_of_3.svg)
 
 **Number of Subsets**
 
-If `S` is a finite set with `|S| = n` elements, then the number of subsets 
-of `S` is `|P(S)| = 2^n`. This fact, which is the motivation for the 
+If `S` is a finite set with `|S| = n` elements, then the number of subsets
+of `S` is `|P(S)| = 2^n`. This fact, which is the motivation for the
 notation `2^S`, may be demonstrated simply as follows:
 
-> First, order the elements of `S` in any manner. We write any subset of `S` in 
-the format `{γ1, γ2, ..., γn}` where `γi , 1 ≤ i ≤ n`, can take the value 
+> First, order the elements of `S` in any manner. We write any subset of `S` in
+the format `{γ1, γ2, ..., γn}` where `γi , 1 ≤ i ≤ n`, can take the value
 of `0` or `1`. If `γi = 1`, the `i`-th element of `S` is in the subset;
-otherwise, the `i`-th element is not in the subset. Clearly the number of 
+otherwise, the `i`-th element is not in the subset. Clearly the number of
 distinct subsets that can be constructed this way is `2^n` as `γi ∈ {0, 1}`.
 
 ## Algorithms
 
 ### Bitwise Solution
 
-Each number in binary representation in a range from `0` to `2^n` does exactly 
-what we need: it shows by its bits (`0` or `1`) whether to include related 
-element from the set or not. For example, for the set `{1, 2, 3}` the binary 
+Each number in binary representation in a range from `0` to `2^n` does exactly
+what we need: it shows by its bits (`0` or `1`) whether to include related
+element from the set or not. For example, for the set `{1, 2, 3}` the binary
 number of `0b010` would mean that we need to include only `2` to the current set.
 
 |       | `abc` | Subset        |
 | :---: | :---: | :-----------: |
 | `0`   | `000` | `{}`          |
 | `1`   | `001` | `{c}`         |
-| `2`   | `010` | `{b}`         | 
+| `2`   | `010` | `{b}`         |
 | `3`   | `011` | `{c, b}`      |
 | `4`   | `100` | `{a}`         |
 | `5`   | `101` | `{a, c}`      |
@@ -68,6 +68,44 @@ element.
 
 > See [btPowerSet.js](./btPowerSet.js) file for backtracking solution.
 
+### Cascading Solution
+
+This is, arguably, the simplest solution to generate a Power Set.
+
+We start with an empty set:
+
+```text
+powerSets = [[]]
+```
+
+Now, let's say:
+
+```text
+originalSet = [1, 2, 3]
+```
+
+Let's add the 1st element from the originalSet to all existing sets:
+
+```text
+[[]] ← 1 = [[], [1]]
+```
+
+Adding the 2nd element to all existing sets:
+
+```text
+[[], [1]] ← 2 = [[], [1], [2], [1, 2]]
+```
+
+Adding the 3nd element to all existing sets:
+
+```
+[[], [1], [2], [1, 2]] ← 3 = [[], [1], [2], [1, 2], [3], [1, 3], [2, 3], [1, 2, 3]]
+```
+
+And so on, for the rest of the elements from the `originalSet`. On every iteration the number of sets is doubled, so we'll get `2^n` sets.
+
+> See [caPowerSet.js](./caPowerSet.js) file for cascading solution.
+
 ## References
 
 * [Wikipedia](https://en.wikipedia.org/wiki/Power_set)
diff --git a/src/algorithms/sets/power-set/__test__/caPowerSet.test.js b/src/algorithms/sets/power-set/__test__/caPowerSet.test.js
new file mode 100644
index 0000000000..4fad5efe20
--- /dev/null
+++ b/src/algorithms/sets/power-set/__test__/caPowerSet.test.js
@@ -0,0 +1,28 @@
+import caPowerSet from '../caPowerSet';
+
+describe('caPowerSet', () => {
+  it('should calculate power set of given set using cascading approach', () => {
+    expect(caPowerSet([1])).toEqual([
+      [],
+      [1],
+    ]);
+
+    expect(caPowerSet([1, 2])).toEqual([
+      [],
+      [1],
+      [2],
+      [1, 2],
+    ]);
+
+    expect(caPowerSet([1, 2, 3])).toEqual([
+      [],
+      [1],
+      [2],
+      [1, 2],
+      [3],
+      [1, 3],
+      [2, 3],
+      [1, 2, 3],
+    ]);
+  });
+});
diff --git a/src/algorithms/sets/power-set/caPowerSet.js b/src/algorithms/sets/power-set/caPowerSet.js
new file mode 100644
index 0000000000..45b9eb6169
--- /dev/null
+++ b/src/algorithms/sets/power-set/caPowerSet.js
@@ -0,0 +1,37 @@
+/**
+ * Find power-set of a set using CASCADING approach.
+ *
+ * @param {*[]} originalSet
+ * @return {*[][]}
+ */
+export default function caPowerSet(originalSet) {
+  // Let's start with an empty set.
+  const sets = [[]];
+
+  /*
+    Now, let's say:
+    originalSet = [1, 2, 3].
+
+    Let's add the first element from the originalSet to all existing sets:
+    [[]] ← 1 = [[], [1]]
+
+    Adding the 2nd element to all existing sets:
+    [[], [1]] ← 2 = [[], [1], [2], [1, 2]]
+
+    Adding the 3nd element to all existing sets:
+    [[], [1], [2], [1, 2]] ← 3 = [[], [1], [2], [1, 2], [3], [1, 3], [2, 3], [1, 2, 3]]
+
+    And so on for the rest of the elements from originalSet.
+    On every iteration the number of sets is doubled, so we'll get 2^n sets.
+  */
+  for (let numIdx = 0; numIdx < originalSet.length; numIdx += 1) {
+    const existingSetsNum = sets.length;
+
+    for (let setIdx = 0; setIdx < existingSetsNum; setIdx += 1) {
+      const set = [...sets[setIdx], originalSet[numIdx]];
+      sets.push(set);
+    }
+  }
+
+  return sets;
+}

From 6c335c5d833fd2a68342cf3648a3174bed8c01ad Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Fri, 6 Jan 2023 14:45:04 +0100
Subject: [PATCH 220/264] Fixing the broken link for QuickSort

---
 src/algorithms/sorting/quick-sort/QuickSortInPlace.js | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/algorithms/sorting/quick-sort/QuickSortInPlace.js b/src/algorithms/sorting/quick-sort/QuickSortInPlace.js
index cc1f5e5068..d02298b230 100644
--- a/src/algorithms/sorting/quick-sort/QuickSortInPlace.js
+++ b/src/algorithms/sorting/quick-sort/QuickSortInPlace.js
@@ -4,7 +4,7 @@ export default class QuickSortInPlace extends Sort {
   /** Sorting in place avoids unnecessary use of additional memory, but modifies input array.
    *
    * This process is difficult to describe, but much clearer with a visualization:
-   * @see: http://www.algomation.com/algorithm/quick-sort-visualization
+   * @see: https://www.hackerearth.com/practice/algorithms/sorting/quick-sort/visualize/
    *
    * @param {*[]} originalArray - Not sorted array.
    * @param {number} inputLowIndex

From e4f2ccdbece78d44d3f4bd908c828408b1c0c791 Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Mon, 23 Jan 2023 18:03:40 +0100
Subject: [PATCH 221/264] Add an example of the LRU (Least Recently Used) Cache
 implementation (#980)

* Add an example of the LRU Cache implementation.

* Promote the node on set() as well.

* Add LRU Cache images.
---
 README.md                                     |   1 +
 src/data-structures/lru-cache/LRUCache.js     | 134 ++++++++++++++++
 .../lru-cache/LinkedListNode.js               |  17 ++
 src/data-structures/lru-cache/README.md       |  37 +++++
 .../lru-cache/__test__/LRUCache.test.js       | 150 ++++++++++++++++++
 .../lru-cache/images/lru-cache.jpg            | Bin 0 -> 677600 bytes
 6 files changed, 339 insertions(+)
 create mode 100644 src/data-structures/lru-cache/LRUCache.js
 create mode 100644 src/data-structures/lru-cache/LinkedListNode.js
 create mode 100644 src/data-structures/lru-cache/README.md
 create mode 100644 src/data-structures/lru-cache/__test__/LRUCache.test.js
 create mode 100644 src/data-structures/lru-cache/images/lru-cache.jpg

diff --git a/README.md b/README.md
index 8836940696..2c83a70b71 100644
--- a/README.md
+++ b/README.md
@@ -64,6 +64,7 @@ the data.
 * `A` [Graph](src/data-structures/graph) (both directed and undirected)
 * `A` [Disjoint Set](src/data-structures/disjoint-set)
 * `A` [Bloom Filter](src/data-structures/bloom-filter)
+* `A` [LRU Cache](src/data-structures/lru-cache/) - Least Recently Used (LRU) cache
 
 ## Algorithms
 
diff --git a/src/data-structures/lru-cache/LRUCache.js b/src/data-structures/lru-cache/LRUCache.js
new file mode 100644
index 0000000000..dc27d1b4b0
--- /dev/null
+++ b/src/data-structures/lru-cache/LRUCache.js
@@ -0,0 +1,134 @@
+/* eslint-disable no-param-reassign */
+import LinkedListNode from './LinkedListNode';
+
+/**
+ * Implementation of the LRU (Least Recently Used) Cache
+ * based on the HashMap and Doubly Linked List data-structures.
+ *
+ * Current implementation allows to have fast (O(1)) read and write operations.
+ *
+ * At any moment in time the LRU Cache holds not more that "capacity" number of items in it.
+ */
+class LRUCache {
+  /**
+   * Creates a cache instance of a specific capacity.
+   * @param {number} capacity
+   */
+  constructor(capacity) {
+    this.capacity = capacity; // How many items to store in cache at max.
+    this.nodesMap = {}; // The quick links to each linked list node in cache.
+    this.size = 0; // The number of items that is currently stored in the cache.
+    this.head = new LinkedListNode(); // The Head (first) linked list node.
+    this.tail = new LinkedListNode(); // The Tail (last) linked list node.
+  }
+
+  /**
+   * Returns the cached value by its key.
+   * Time complexity: O(1).
+   * @param {string} key
+   * @returns {any}
+   */
+  get(key) {
+    if (this.nodesMap[key] === undefined) return undefined;
+    const node = this.nodesMap[key];
+    this.promote(node);
+    return node.val;
+  }
+
+  /**
+   * Sets the value to cache by its key.
+   * Time complexity: O(1).
+   * @param {string} key
+   * @param {any} val
+   */
+  set(key, val) {
+    if (this.nodesMap[key]) {
+      const node = this.nodesMap[key];
+      node.val = val;
+      this.promote(node);
+    } else {
+      const node = new LinkedListNode(key, val);
+      this.append(node);
+    }
+  }
+
+  /**
+   * Promotes the node to the end of the linked list.
+   * It means that the node is most frequently used.
+   * It also reduces the chance for such node to get evicted from cache.
+   * @param {LinkedListNode} node
+   */
+  promote(node) {
+    this.evict(node);
+    this.append(node);
+  }
+
+  /**
+   * Appends a new node to the end of the cache linked list.
+   * @param {LinkedListNode} node
+   */
+  append(node) {
+    this.nodesMap[node.key] = node;
+
+    if (!this.head.next) {
+      // First node to append.
+      this.head.next = node;
+      this.tail.prev = node;
+      node.prev = this.head;
+      node.next = this.tail;
+    } else {
+      // Append to an existing tail.
+      const oldTail = this.tail.prev;
+      oldTail.next = node;
+      node.prev = oldTail;
+      node.next = this.tail;
+      this.tail.prev = node;
+    }
+
+    this.size += 1;
+
+    if (this.size > this.capacity) {
+      this.evict(this.head.next);
+    }
+  }
+
+  /**
+   * Evicts (removes) the node from cache linked list.
+   * @param {LinkedListNode} node
+   */
+  evict(node) {
+    delete this.nodesMap[node.key];
+    this.size -= 1;
+
+    const prevNode = node.prev;
+    const nextNode = node.next;
+
+    // If one and only node.
+    if (prevNode === this.head && nextNode === this.tail) {
+      this.head.next = null;
+      this.tail.prev = null;
+      this.size = 0;
+      return;
+    }
+
+    // If this is a Head node.
+    if (prevNode === this.head) {
+      nextNode.prev = this.head;
+      this.head.next = nextNode;
+      return;
+    }
+
+    // If this is a Tail node.
+    if (nextNode === this.tail) {
+      prevNode.next = this.tail;
+      this.tail.prev = prevNode;
+      return;
+    }
+
+    // If the node is in the middle.
+    prevNode.next = nextNode;
+    nextNode.prev = prevNode;
+  }
+}
+
+export default LRUCache;
diff --git a/src/data-structures/lru-cache/LinkedListNode.js b/src/data-structures/lru-cache/LinkedListNode.js
new file mode 100644
index 0000000000..6c2b3cd6ff
--- /dev/null
+++ b/src/data-structures/lru-cache/LinkedListNode.js
@@ -0,0 +1,17 @@
+class LinkedListNode {
+  /**
+   * Creates a doubly-linked list node.
+   * @param {string} key
+   * @param {any} val
+   * @param {LinkedListNode} prev
+   * @param {LinkedListNode} next
+   */
+  constructor(key, val, prev = null, next = null) {
+    this.key = key;
+    this.val = val;
+    this.prev = prev;
+    this.next = next;
+  }
+}
+
+export default LinkedListNode;
diff --git a/src/data-structures/lru-cache/README.md b/src/data-structures/lru-cache/README.md
new file mode 100644
index 0000000000..b9175ba36d
--- /dev/null
+++ b/src/data-structures/lru-cache/README.md
@@ -0,0 +1,37 @@
+# Least Recently Used (LRU) Cache
+
+A **Least Recently Used (LRU) Cache** organizes items in order of use, allowing you to quickly identify which item hasn't been used for the longest amount of time.
+
+Picture a clothes rack, where clothes are always hung up on one side. To find the least-recently used item, look at the item on the other end of the rack.
+
+## The problem statement
+
+Implement the LRUCache class:
+
+- `LRUCache(int capacity)` Initialize the LRU cache with **positive** size `capacity`.
+- `int get(int key)` Return the value of the `key` if the `key` exists, otherwise return `undefined`.
+- `void set(int key, int value)` Update the value of the `key` if the `key` exists. Otherwise, add the `key-value` pair to the cache. If the number of keys exceeds the `capacity` from this operation, **evict** the least recently used key.
+
+The functions `get()` and `set()` must each run in `O(1)` average time complexity.
+
+## Implementation
+
+See the `LRUCache` implementation example in [LRUCache.js](./LRUCache.js). The solution uses a `HashMap` for fast `O(1)` cache items access, and a `DoublyLinkedList` for fast `O(1)` cache items promotions and eviction (to keep the maximum allowed cache capacity).
+
+![Linked List](./images/lru-cache.jpg)
+
+*Made with [okso.app](https://okso.app)*
+
+## Costs
+
+|   | Worst Case |
+|---|---|
+| Space |`O(n)`|
+| Get item | `O(1)` |
+| Set item | `O(1)` |
+
+## References
+
+- [LRU Cache on LeetCode](https://leetcode.com/problems/lru-cache/solutions/244744/lru-cache/)
+- [LRU Cache on InterviewCake](https://www.interviewcake.com/concept/java/lru-cache)
+- [LRU Cache on Wiki](https://en.wikipedia.org/wiki/Cache_replacement_policies)
diff --git a/src/data-structures/lru-cache/__test__/LRUCache.test.js b/src/data-structures/lru-cache/__test__/LRUCache.test.js
new file mode 100644
index 0000000000..438fd50378
--- /dev/null
+++ b/src/data-structures/lru-cache/__test__/LRUCache.test.js
@@ -0,0 +1,150 @@
+import LRUCache from '../LRUCache';
+
+describe('LRUCache', () => {
+  it('should set and get values to and from the cache', () => {
+    const cache = new LRUCache(100);
+    expect(cache.get('key-1')).toBeUndefined();
+
+    cache.set('key-1', 15);
+    cache.set('key-2', 16);
+    cache.set('key-3', 17);
+    expect(cache.get('key-1')).toBe(15);
+    expect(cache.get('key-2')).toBe(16);
+    expect(cache.get('key-3')).toBe(17);
+    expect(cache.get('key-3')).toBe(17);
+    expect(cache.get('key-2')).toBe(16);
+    expect(cache.get('key-1')).toBe(15);
+
+    cache.set('key-1', 5);
+    cache.set('key-2', 6);
+    cache.set('key-3', 7);
+    expect(cache.get('key-1')).toBe(5);
+    expect(cache.get('key-2')).toBe(6);
+    expect(cache.get('key-3')).toBe(7);
+  });
+
+  it('should evict least recently used items from cache with cache size of 1', () => {
+    const cache = new LRUCache(1);
+    expect(cache.get('key-1')).toBeUndefined();
+
+    cache.set('key-1', 15);
+    expect(cache.get('key-1')).toBe(15);
+
+    cache.set('key-2', 16);
+    expect(cache.get('key-1')).toBeUndefined();
+    expect(cache.get('key-2')).toBe(16);
+
+    cache.set('key-2', 17);
+    expect(cache.get('key-2')).toBe(17);
+
+    cache.set('key-3', 18);
+    cache.set('key-4', 19);
+    expect(cache.get('key-2')).toBeUndefined();
+    expect(cache.get('key-3')).toBeUndefined();
+    expect(cache.get('key-4')).toBe(19);
+  });
+
+  it('should evict least recently used items from cache with cache size of 2', () => {
+    const cache = new LRUCache(2);
+    expect(cache.get('key-21')).toBeUndefined();
+
+    cache.set('key-21', 15);
+    expect(cache.get('key-21')).toBe(15);
+
+    cache.set('key-22', 16);
+    expect(cache.get('key-21')).toBe(15);
+    expect(cache.get('key-22')).toBe(16);
+
+    cache.set('key-22', 17);
+    expect(cache.get('key-22')).toBe(17);
+
+    cache.set('key-23', 18);
+    expect(cache.size).toBe(2);
+    expect(cache.get('key-21')).toBeUndefined();
+    expect(cache.get('key-22')).toBe(17);
+    expect(cache.get('key-23')).toBe(18);
+
+    cache.set('key-24', 19);
+    expect(cache.size).toBe(2);
+    expect(cache.get('key-21')).toBeUndefined();
+    expect(cache.get('key-22')).toBeUndefined();
+    expect(cache.get('key-23')).toBe(18);
+    expect(cache.get('key-24')).toBe(19);
+  });
+
+  it('should evict least recently used items from cache with cache size of 3', () => {
+    const cache = new LRUCache(3);
+
+    cache.set('key-1', 1);
+    cache.set('key-2', 2);
+    cache.set('key-3', 3);
+    expect(cache.get('key-1')).toBe(1);
+    expect(cache.get('key-2')).toBe(2);
+    expect(cache.get('key-3')).toBe(3);
+
+    cache.set('key-3', 4);
+    expect(cache.get('key-1')).toBe(1);
+    expect(cache.get('key-2')).toBe(2);
+    expect(cache.get('key-3')).toBe(4);
+
+    cache.set('key-4', 5);
+    expect(cache.get('key-1')).toBeUndefined();
+    expect(cache.get('key-2')).toBe(2);
+    expect(cache.get('key-3')).toBe(4);
+    expect(cache.get('key-4')).toBe(5);
+  });
+
+  it('should promote the node while calling set() method', () => {
+    const cache = new LRUCache(2);
+
+    cache.set('2', 1);
+    cache.set('1', 1);
+    cache.set('2', 3);
+    cache.set('4', 1);
+    expect(cache.get('1')).toBeUndefined();
+    expect(cache.get('2')).toBe(3);
+  });
+
+  it('should promote the recently accessed item with cache size of 3', () => {
+    const cache = new LRUCache(3);
+
+    cache.set('key-1', 1);
+    cache.set('key-2', 2);
+    cache.set('key-3', 3);
+    expect(cache.get('key-1')).toBe(1);
+
+    cache.set('key-4', 4);
+    expect(cache.get('key-1')).toBe(1);
+    expect(cache.get('key-3')).toBe(3);
+    expect(cache.get('key-4')).toBe(4);
+    expect(cache.get('key-2')).toBeUndefined();
+  });
+
+  it('should promote the recently accessed item with cache size of 4', () => {
+    const cache = new LRUCache(4);
+
+    cache.set('key-1', 1);
+    cache.set('key-2', 2);
+    cache.set('key-3', 3);
+    cache.set('key-4', 4);
+    expect(cache.get('key-4')).toBe(4);
+    expect(cache.get('key-3')).toBe(3);
+    expect(cache.get('key-2')).toBe(2);
+    expect(cache.get('key-1')).toBe(1);
+
+    cache.set('key-5', 5);
+    expect(cache.get('key-1')).toBe(1);
+    expect(cache.get('key-2')).toBe(2);
+    expect(cache.get('key-3')).toBe(3);
+    expect(cache.get('key-4')).toBeUndefined();
+    expect(cache.get('key-5')).toBe(5);
+
+    cache.set('key-6', 6);
+    expect(cache.get('key-1')).toBeUndefined();
+    expect(cache.get('key-2')).toBe(2);
+    expect(cache.get('key-3')).toBe(3);
+    expect(cache.get('key-4')).toBeUndefined();
+    expect(cache.get('key-5')).toBe(5);
+    expect(cache.get('key-6')).toBe(6);
+  });
+});
diff --git a/src/data-structures/lru-cache/images/lru-cache.jpg b/src/data-structures/lru-cache/images/lru-cache.jpg
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HcmV?d00001


From d408abd833181c5866166ce6b6af073576bd5708 Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Mon, 23 Jan 2023 18:07:24 +0100
Subject: [PATCH 222/264] Update LRU Cache image.

---
 .../lru-cache/images/lru-cache.jpg            | Bin 677600 -> 665297 bytes
 1 file changed, 0 insertions(+), 0 deletions(-)

diff --git a/src/data-structures/lru-cache/images/lru-cache.jpg b/src/data-structures/lru-cache/images/lru-cache.jpg
index be851b2f1d468f3608529460a43dd808a85418c9..6a2fcfceb42a0539d58f17816d67d4e73ae5fc70 100644
GIT binary patch
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From 3d8dd9a67f7e17ff892dd3186e351a5d9caee329 Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Mon, 23 Jan 2023 18:15:13 +0100
Subject: [PATCH 223/264] Update LRU Cache README.

---
 src/data-structures/lru-cache/README.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/src/data-structures/lru-cache/README.md b/src/data-structures/lru-cache/README.md
index b9175ba36d..866afa1e60 100644
--- a/src/data-structures/lru-cache/README.md
+++ b/src/data-structures/lru-cache/README.md
@@ -22,6 +22,8 @@ See the `LRUCache` implementation example in [LRUCache.js](./LRUCache.js). The s
 
 *Made with [okso.app](https://okso.app)*
 
+You may also find more test-case examples of how the LRU Cache works in [LRUCache.test.js](./__test__/LRUCache.test.js) file.
+
 ## Costs
 
 |   | Worst Case |

From 6c4aa1b6a26c45e75d22a92adf1fcdcbc95cd401 Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Mon, 23 Jan 2023 18:43:00 +0100
Subject: [PATCH 224/264] Update time complexity table for LRU.

---
 src/data-structures/lru-cache/README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/data-structures/lru-cache/README.md b/src/data-structures/lru-cache/README.md
index 866afa1e60..231656ae3d 100644
--- a/src/data-structures/lru-cache/README.md
+++ b/src/data-structures/lru-cache/README.md
@@ -26,7 +26,7 @@ You may also find more test-case examples of how the LRU Cache works in [LRUCach
 
 ## Costs
 
-|   | Worst Case |
+|   | Average |
 |---|---|
 | Space |`O(n)`|
 | Get item | `O(1)` |

From f6a0ed42bcaba0607fb2cc1d843f90d78ea340c3 Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Mon, 23 Jan 2023 18:43:52 +0100
Subject: [PATCH 225/264] Update time complexity table for LRU.

---
 src/data-structures/lru-cache/README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/data-structures/lru-cache/README.md b/src/data-structures/lru-cache/README.md
index 231656ae3d..2076115fa3 100644
--- a/src/data-structures/lru-cache/README.md
+++ b/src/data-structures/lru-cache/README.md
@@ -24,7 +24,7 @@ See the `LRUCache` implementation example in [LRUCache.js](./LRUCache.js). The s
 
 You may also find more test-case examples of how the LRU Cache works in [LRUCache.test.js](./__test__/LRUCache.test.js) file.
 
-## Costs
+## Complexities
 
 |   | Average |
 |---|---|

From fbd77551b3196b15f7ea3373ad0efebc13fd47c1 Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Mon, 23 Jan 2023 18:44:46 +0100
Subject: [PATCH 226/264] Update time complexity table for LRU.

---
 src/data-structures/lru-cache/README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/data-structures/lru-cache/README.md b/src/data-structures/lru-cache/README.md
index 2076115fa3..2e964239d2 100644
--- a/src/data-structures/lru-cache/README.md
+++ b/src/data-structures/lru-cache/README.md
@@ -16,7 +16,7 @@ The functions `get()` and `set()` must each run in `O(1)` average time complexit
 
 ## Implementation
 
-See the `LRUCache` implementation example in [LRUCache.js](./LRUCache.js). The solution uses a `HashMap` for fast `O(1)` cache items access, and a `DoublyLinkedList` for fast `O(1)` cache items promotions and eviction (to keep the maximum allowed cache capacity).
+See the `LRUCache` implementation example in [LRUCache.js](./LRUCache.js). The solution uses a `HashMap` for fast `O(1)` (in average) cache items access, and a `DoublyLinkedList` for fast `O(1)` (in average) cache items promotions and eviction (to keep the maximum allowed cache capacity).
 
 ![Linked List](./images/lru-cache.jpg)
 

From 69c3a16f75175fa6f49cd936e0049fdc6ede1da4 Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Tue, 24 Jan 2023 09:04:02 +0100
Subject: [PATCH 227/264] Refactor LRU Cache.

---
 src/data-structures/lru-cache/LRUCache.js     | 23 +++++++++++++++++--
 .../lru-cache/LinkedListNode.js               | 17 --------------
 2 files changed, 21 insertions(+), 19 deletions(-)
 delete mode 100644 src/data-structures/lru-cache/LinkedListNode.js

diff --git a/src/data-structures/lru-cache/LRUCache.js b/src/data-structures/lru-cache/LRUCache.js
index dc27d1b4b0..09bf58e434 100644
--- a/src/data-structures/lru-cache/LRUCache.js
+++ b/src/data-structures/lru-cache/LRUCache.js
@@ -1,5 +1,24 @@
-/* eslint-disable no-param-reassign */
-import LinkedListNode from './LinkedListNode';
+/* eslint-disable no-param-reassign, max-classes-per-file */
+
+/**
+ * Simple implementation of the Doubly-Linked List Node
+ * that is used in LRUCache class below.
+ */
+class LinkedListNode {
+  /**
+   * Creates a doubly-linked list node.
+   * @param {string} key
+   * @param {any} val
+   * @param {LinkedListNode} prev
+   * @param {LinkedListNode} next
+   */
+  constructor(key, val, prev = null, next = null) {
+    this.key = key;
+    this.val = val;
+    this.prev = prev;
+    this.next = next;
+  }
+}
 
 /**
  * Implementation of the LRU (Least Recently Used) Cache
diff --git a/src/data-structures/lru-cache/LinkedListNode.js b/src/data-structures/lru-cache/LinkedListNode.js
deleted file mode 100644
index 6c2b3cd6ff..0000000000
--- a/src/data-structures/lru-cache/LinkedListNode.js
+++ /dev/null
@@ -1,17 +0,0 @@
-class LinkedListNode {
-  /**
-   * Creates a doubly-linked list node.
-   * @param {string} key
-   * @param {any} val
-   * @param {LinkedListNode} prev
-   * @param {LinkedListNode} next
-   */
-  constructor(key, val, prev = null, next = null) {
-    this.key = key;
-    this.val = val;
-    this.prev = prev;
-    this.next = next;
-  }
-}
-
-export default LinkedListNode;

From 4b4d77071cee9c6ba50390ec3635a9755828daa3 Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Tue, 24 Jan 2023 09:43:12 +0100
Subject: [PATCH 228/264] Add an example of the LRU Cache based on the Map.

---
 src/data-structures/lru-cache/LRUCache.js     |   6 +-
 .../lru-cache/LRUCacheOnMap.js                |  53 +++++++
 src/data-structures/lru-cache/README.md       |  12 ++
 .../lru-cache/__test__/LRUCacheOnMap.test.js  | 148 ++++++++++++++++++
 4 files changed, 216 insertions(+), 3 deletions(-)
 create mode 100644 src/data-structures/lru-cache/LRUCacheOnMap.js
 create mode 100644 src/data-structures/lru-cache/__test__/LRUCacheOnMap.test.js

diff --git a/src/data-structures/lru-cache/LRUCache.js b/src/data-structures/lru-cache/LRUCache.js
index 09bf58e434..d6b4b3c6be 100644
--- a/src/data-structures/lru-cache/LRUCache.js
+++ b/src/data-structures/lru-cache/LRUCache.js
@@ -24,7 +24,7 @@ class LinkedListNode {
  * Implementation of the LRU (Least Recently Used) Cache
  * based on the HashMap and Doubly Linked List data-structures.
  *
- * Current implementation allows to have fast (O(1)) read and write operations.
+ * Current implementation allows to have fast O(1) (in average) read and write operations.
  *
  * At any moment in time the LRU Cache holds not more that "capacity" number of items in it.
  */
@@ -43,7 +43,7 @@ class LRUCache {
 
   /**
    * Returns the cached value by its key.
-   * Time complexity: O(1).
+   * Time complexity: O(1) in average.
    * @param {string} key
    * @returns {any}
    */
@@ -56,7 +56,7 @@ class LRUCache {
 
   /**
    * Sets the value to cache by its key.
-   * Time complexity: O(1).
+   * Time complexity: O(1) in average.
    * @param {string} key
    * @param {any} val
    */
diff --git a/src/data-structures/lru-cache/LRUCacheOnMap.js b/src/data-structures/lru-cache/LRUCacheOnMap.js
new file mode 100644
index 0000000000..8e4e226129
--- /dev/null
+++ b/src/data-structures/lru-cache/LRUCacheOnMap.js
@@ -0,0 +1,53 @@
+/* eslint-disable no-restricted-syntax, no-unreachable-loop */
+
+/**
+ * Implementation of the LRU (Least Recently Used) Cache
+ * based on the (ordered) Map data-structure.
+ *
+ * Current implementation allows to have fast O(1) (in average) read and write operations.
+ *
+ * At any moment in time the LRU Cache holds not more that "capacity" number of items in it.
+ */
+class LRUCacheOnMap {
+  /**
+   * Creates a cache instance of a specific capacity.
+   * @param {number} capacity
+   */
+  constructor(capacity) {
+    this.capacity = capacity; // How many items to store in cache at max.
+    this.items = new Map(); // The ordered hash map of all cached items.
+  }
+
+  /**
+   * Returns the cached value by its key.
+   * Time complexity: O(1) in average.
+   * @param {string} key
+   * @returns {any}
+   */
+  get(key) {
+    if (!this.items.has(key)) return undefined;
+    const val = this.items.get(key);
+    this.items.delete(key);
+    this.items.set(key, val);
+    return val;
+  }
+
+  /**
+   * Sets the value to cache by its key.
+   * Time complexity: O(1).
+   * @param {string} key
+   * @param {any} val
+   */
+  set(key, val) {
+    this.items.delete(key);
+    this.items.set(key, val);
+    if (this.items.size > this.capacity) {
+      for (const headKey of this.items.keys()) {
+        this.items.delete(headKey);
+        break;
+      }
+    }
+  }
+}
+
+export default LRUCacheOnMap;
diff --git a/src/data-structures/lru-cache/README.md b/src/data-structures/lru-cache/README.md
index 2e964239d2..05bcc0a0f7 100644
--- a/src/data-structures/lru-cache/README.md
+++ b/src/data-structures/lru-cache/README.md
@@ -16,6 +16,8 @@ The functions `get()` and `set()` must each run in `O(1)` average time complexit
 
 ## Implementation
 
+### Version 1: Doubly Linked List + Hash Map
+
 See the `LRUCache` implementation example in [LRUCache.js](./LRUCache.js). The solution uses a `HashMap` for fast `O(1)` (in average) cache items access, and a `DoublyLinkedList` for fast `O(1)` (in average) cache items promotions and eviction (to keep the maximum allowed cache capacity).
 
 ![Linked List](./images/lru-cache.jpg)
@@ -24,6 +26,16 @@ See the `LRUCache` implementation example in [LRUCache.js](./LRUCache.js). The s
 
 You may also find more test-case examples of how the LRU Cache works in [LRUCache.test.js](./__test__/LRUCache.test.js) file.
 
+### Version 2: Ordered Map
+
+The first implementation that uses doubly linked list is good for learning purposes and for better understanding of how the average `O(1)` time complexity is achievable while doing `set()` and `get()`.
+
+However, the simpler approach might be to use a JavaScript [Map](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Map) object. The `Map` object holds key-value pairs and **remembers the original insertion order** of the keys. We can use this fact in order to keep the recently-used items in the "end" of the map by removing and re-adding items. The item at the beginning of the `Map` is the first one to be evicted if cache capacity overflows. The order of the items may checked by using the `IterableIterator` like `map.keys()`.
+
+See the `LRUCacheOnMap` implementation example in [LRUCacheOnMap.js](./LRUCacheOnMap.js).
+
+You may also find more test-case examples of how the LRU Cache works in [LRUCacheOnMap.test.js](./__test__/LRUCacheOnMap.test.js) file.
+
 ## Complexities
 
 |   | Average |
diff --git a/src/data-structures/lru-cache/__test__/LRUCacheOnMap.test.js b/src/data-structures/lru-cache/__test__/LRUCacheOnMap.test.js
new file mode 100644
index 0000000000..8912a1199a
--- /dev/null
+++ b/src/data-structures/lru-cache/__test__/LRUCacheOnMap.test.js
@@ -0,0 +1,148 @@
+import LRUCache from '../LRUCacheOnMap';
+
+describe('LRUCacheOnMap', () => {
+  it('should set and get values to and from the cache', () => {
+    const cache = new LRUCache(100);
+    expect(cache.get('key-1')).toBeUndefined();
+
+    cache.set('key-1', 15);
+    cache.set('key-2', 16);
+    cache.set('key-3', 17);
+    expect(cache.get('key-1')).toBe(15);
+    expect(cache.get('key-2')).toBe(16);
+    expect(cache.get('key-3')).toBe(17);
+    expect(cache.get('key-3')).toBe(17);
+    expect(cache.get('key-2')).toBe(16);
+    expect(cache.get('key-1')).toBe(15);
+
+    cache.set('key-1', 5);
+    cache.set('key-2', 6);
+    cache.set('key-3', 7);
+    expect(cache.get('key-1')).toBe(5);
+    expect(cache.get('key-2')).toBe(6);
+    expect(cache.get('key-3')).toBe(7);
+  });
+
+  it('should evict least recently used items from cache with cache size of 1', () => {
+    const cache = new LRUCache(1);
+    expect(cache.get('key-1')).toBeUndefined();
+
+    cache.set('key-1', 15);
+    expect(cache.get('key-1')).toBe(15);
+
+    cache.set('key-2', 16);
+    expect(cache.get('key-1')).toBeUndefined();
+    expect(cache.get('key-2')).toBe(16);
+
+    cache.set('key-2', 17);
+    expect(cache.get('key-2')).toBe(17);
+
+    cache.set('key-3', 18);
+    cache.set('key-4', 19);
+    expect(cache.get('key-2')).toBeUndefined();
+    expect(cache.get('key-3')).toBeUndefined();
+    expect(cache.get('key-4')).toBe(19);
+  });
+
+  it('should evict least recently used items from cache with cache size of 2', () => {
+    const cache = new LRUCache(2);
+    expect(cache.get('key-21')).toBeUndefined();
+
+    cache.set('key-21', 15);
+    expect(cache.get('key-21')).toBe(15);
+
+    cache.set('key-22', 16);
+    expect(cache.get('key-21')).toBe(15);
+    expect(cache.get('key-22')).toBe(16);
+
+    cache.set('key-22', 17);
+    expect(cache.get('key-22')).toBe(17);
+
+    cache.set('key-23', 18);
+    expect(cache.get('key-21')).toBeUndefined();
+    expect(cache.get('key-22')).toBe(17);
+    expect(cache.get('key-23')).toBe(18);
+
+    cache.set('key-24', 19);
+    expect(cache.get('key-21')).toBeUndefined();
+    expect(cache.get('key-22')).toBeUndefined();
+    expect(cache.get('key-23')).toBe(18);
+    expect(cache.get('key-24')).toBe(19);
+  });
+
+  it('should evict least recently used items from cache with cache size of 3', () => {
+    const cache = new LRUCache(3);
+
+    cache.set('key-1', 1);
+    cache.set('key-2', 2);
+    cache.set('key-3', 3);
+    expect(cache.get('key-1')).toBe(1);
+    expect(cache.get('key-2')).toBe(2);
+    expect(cache.get('key-3')).toBe(3);
+
+    cache.set('key-3', 4);
+    expect(cache.get('key-1')).toBe(1);
+    expect(cache.get('key-2')).toBe(2);
+    expect(cache.get('key-3')).toBe(4);
+
+    cache.set('key-4', 5);
+    expect(cache.get('key-1')).toBeUndefined();
+    expect(cache.get('key-2')).toBe(2);
+    expect(cache.get('key-3')).toBe(4);
+    expect(cache.get('key-4')).toBe(5);
+  });
+
+  it('should promote the node while calling set() method', () => {
+    const cache = new LRUCache(2);
+
+    cache.set('2', 1);
+    cache.set('1', 1);
+    cache.set('2', 3);
+    cache.set('4', 1);
+    expect(cache.get('1')).toBeUndefined();
+    expect(cache.get('2')).toBe(3);
+  });
+
+  it('should promote the recently accessed item with cache size of 3', () => {
+    const cache = new LRUCache(3);
+
+    cache.set('key-1', 1);
+    cache.set('key-2', 2);
+    cache.set('key-3', 3);
+    expect(cache.get('key-1')).toBe(1);
+
+    cache.set('key-4', 4);
+    expect(cache.get('key-1')).toBe(1);
+    expect(cache.get('key-3')).toBe(3);
+    expect(cache.get('key-4')).toBe(4);
+    expect(cache.get('key-2')).toBeUndefined();
+  });
+
+  it('should promote the recently accessed item with cache size of 4', () => {
+    const cache = new LRUCache(4);
+
+    cache.set('key-1', 1);
+    cache.set('key-2', 2);
+    cache.set('key-3', 3);
+    cache.set('key-4', 4);
+    expect(cache.get('key-4')).toBe(4);
+    expect(cache.get('key-3')).toBe(3);
+    expect(cache.get('key-2')).toBe(2);
+    expect(cache.get('key-1')).toBe(1);
+
+    cache.set('key-5', 5);
+    expect(cache.get('key-1')).toBe(1);
+    expect(cache.get('key-2')).toBe(2);
+    expect(cache.get('key-3')).toBe(3);
+    expect(cache.get('key-4')).toBeUndefined();
+    expect(cache.get('key-5')).toBe(5);
+
+    cache.set('key-6', 6);
+    expect(cache.get('key-1')).toBeUndefined();
+    expect(cache.get('key-2')).toBe(2);
+    expect(cache.get('key-3')).toBe(3);
+    expect(cache.get('key-4')).toBeUndefined();
+    expect(cache.get('key-5')).toBe(5);
+    expect(cache.get('key-6')).toBe(6);
+  });
+});

From 1d6249d552240794c4ea66e97cd91ae5b062392e Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Fri, 27 Jan 2023 08:05:56 +0100
Subject: [PATCH 229/264] Update README.

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 2c83a70b71..b1bc690479 100644
--- a/README.md
+++ b/README.md
@@ -62,7 +62,7 @@ the data.
   * `A` [Segment Tree](src/data-structures/tree/segment-tree) - with min/max/sum range queries examples
   * `A` [Fenwick Tree](src/data-structures/tree/fenwick-tree) (Binary Indexed Tree)
 * `A` [Graph](src/data-structures/graph) (both directed and undirected)
-* `A` [Disjoint Set](src/data-structures/disjoint-set)
+* `A` [Disjoint Set](src/data-structures/disjoint-set) - a union–find data structure or merge–find set
 * `A` [Bloom Filter](src/data-structures/bloom-filter)
 * `A` [LRU Cache](src/data-structures/lru-cache/) - Least Recently Used (LRU) cache
 

From bcd1cc1b008100098a906b610f79074db2edea0e Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Mon, 30 Jan 2023 08:19:38 +0100
Subject: [PATCH 230/264] Upgrade packages and Node versions. (#989)

* Upgrade to Node 16

* Upgrade packages and Node versions.
---
 .eslintrc                |     2 +-
 .github/workflows/CI.yml |     2 +-
 .nvmrc                   |     2 +-
 README.md                |     2 +-
 jest.config.js           |     4 +-
 package-lock.json        | 14190 +++++++++++++++++++++++++++++++------
 package.json             |    25 +-
 7 files changed, 11859 insertions(+), 2368 deletions(-)

diff --git a/.eslintrc b/.eslintrc
index e1c40a0adb..cf3245bf37 100644
--- a/.eslintrc
+++ b/.eslintrc
@@ -14,7 +14,7 @@
   },
   "settings": {
     "react": {
-      "version": "latest"
+      "version": "18.2.0"
     }
   }
 }
diff --git a/.github/workflows/CI.yml b/.github/workflows/CI.yml
index 912c719df3..e007b6c910 100644
--- a/.github/workflows/CI.yml
+++ b/.github/workflows/CI.yml
@@ -11,7 +11,7 @@ jobs:
     runs-on: ubuntu-latest
     strategy:
       matrix:
-        node-version: [ 14.x ]
+        node-version: [ 16.x ]
 
     steps:
       - name: Checkout repository
diff --git a/.nvmrc b/.nvmrc
index 958b5a36e1..7fd023741b 100644
--- a/.nvmrc
+++ b/.nvmrc
@@ -1 +1 @@
-v14
+v16.15.0
diff --git a/README.md b/README.md
index b1bc690479..9666335e35 100644
--- a/README.md
+++ b/README.md
@@ -287,7 +287,7 @@ rm -rf ./node_modules
 npm i
 ```
 
-Also make sure that you're using a correct Node version (`>=14.16.0`). If you're using [nvm](https://github.com/nvm-sh/nvm) for Node version management you may run `nvm use` from the root folder of the project and the correct version will be picked up.
+Also make sure that you're using a correct Node version (`>=16`). If you're using [nvm](https://github.com/nvm-sh/nvm) for Node version management you may run `nvm use` from the root folder of the project and the correct version will be picked up.
 
 **Playground**
 
diff --git a/jest.config.js b/jest.config.js
index 3fec225237..78568a1e94 100644
--- a/jest.config.js
+++ b/jest.config.js
@@ -24,7 +24,9 @@ module.exports = {
   // This option sets the URL for the jsdom environment.
   // It is reflected in properties such as location.href.
   // @see: https://github.com/facebook/jest/issues/6769
-  testURL: 'http://localhost/',
+  testEnvironmentOptions: {
+    url: 'http://localhost/',
+  },
 
   // @see: https://jestjs.io/docs/en/configuration#coveragethreshold-object
   coverageThreshold: {
diff --git a/package-lock.json b/package-lock.json
index a1e4b4f8ca..3cfe2e3571 100644
--- a/package-lock.json
+++ b/package-lock.json
@@ -1,555 +1,10145 @@
 {
   "name": "javascript-algorithms-and-data-structures",
   "version": "0.0.4",
-  "lockfileVersion": 1,
+  "lockfileVersion": 2,
   "requires": true,
+  "packages": {
+    "": {
+      "name": "javascript-algorithms-and-data-structures",
+      "version": "0.0.4",
+      "license": "MIT",
+      "devDependencies": {
+        "@babel/cli": "7.20.7",
+        "@babel/preset-env": "7.20.2",
+        "@types/jest": "29.4.0",
+        "canvas": "2.11.0",
+        "eslint": "8.33.0",
+        "eslint-config-airbnb": "19.0.4",
+        "eslint-plugin-import": "2.27.5",
+        "eslint-plugin-jest": "27.2.1",
+        "eslint-plugin-jsx-a11y": "6.7.1",
+        "husky": "8.0.3",
+        "jest": "29.4.1"
+      },
+      "engines": {
+        "node": ">=16.15.0",
+        "npm": ">=8.5.5"
+      }
+    },
+    "node_modules/@ampproject/remapping": {
+      "version": "2.2.0",
+      "resolved": "https://registry.npmjs.org/@ampproject/remapping/-/remapping-2.2.0.tgz",
+      "integrity": "sha512-qRmjj8nj9qmLTQXXmaR1cck3UXSRMPrbsLJAasZpF+t3riI71BXed5ebIOYwQntykeZuhjsdweEc9BxH5Jc26w==",
+      "dev": true,
+      "dependencies": {
+        "@jridgewell/gen-mapping": "^0.1.0",
+        "@jridgewell/trace-mapping": "^0.3.9"
+      },
+      "engines": {
+        "node": ">=6.0.0"
+      }
+    },
+    "node_modules/@babel/cli": {
+      "version": "7.20.7",
+      "resolved": "https://registry.npmjs.org/@babel/cli/-/cli-7.20.7.tgz",
+      "integrity": "sha512-WylgcELHB66WwQqItxNILsMlaTd8/SO6SgTTjMp4uCI7P4QyH1r3nqgFmO3BfM4AtfniHgFMH3EpYFj/zynBkQ==",
+      "dev": true,
+      "dependencies": {
+        "@jridgewell/trace-mapping": "^0.3.8",
+        "commander": "^4.0.1",
+        "convert-source-map": "^1.1.0",
+        "fs-readdir-recursive": "^1.1.0",
+        "glob": "^7.2.0",
+        "make-dir": "^2.1.0",
+        "slash": "^2.0.0"
+      },
+      "bin": {
+        "babel": "bin/babel.js",
+        "babel-external-helpers": "bin/babel-external-helpers.js"
+      },
+      "engines": {
+        "node": ">=6.9.0"
+      },
+      "optionalDependencies": {
+        "@nicolo-ribaudo/chokidar-2": "2.1.8-no-fsevents.3",
+        "chokidar": "^3.4.0"
+      },
+      "peerDependencies": {
+        "@babel/core": "^7.0.0-0"
+      }
+    },
+    "node_modules/@babel/code-frame": {
+      "version": "7.18.6",
+      "resolved": "https://registry.npmjs.org/@babel/code-frame/-/code-frame-7.18.6.tgz",
+      "integrity": "sha512-TDCmlK5eOvH+eH7cdAFlNXeVJqWIQ7gW9tY1GJIpUtFb6CmjVyq2VM3u71bOyR8CRihcCgMUYoDNyLXao3+70Q==",
+      "dev": true,
+      "dependencies": {
+        "@babel/highlight": "^7.18.6"
+      },
+      "engines": {
+        "node": ">=6.9.0"
+      }
+    },
+    "node_modules/@babel/compat-data": {
+      "version": "7.20.14",
+      "resolved": "https://registry.npmjs.org/@babel/compat-data/-/compat-data-7.20.14.tgz",
+      "integrity": "sha512-0YpKHD6ImkWMEINCyDAD0HLLUH/lPCefG8ld9it8DJB2wnApraKuhgYTvTY1z7UFIfBTGy5LwncZ+5HWWGbhFw==",
+      "dev": true,
+      "engines": {
+        "node": ">=6.9.0"
+      }
+    },
+    "node_modules/@babel/core": {
+      "version": "7.20.12",
+      "resolved": "https://registry.npmjs.org/@babel/core/-/core-7.20.12.tgz",
+      "integrity": "sha512-XsMfHovsUYHFMdrIHkZphTN/2Hzzi78R08NuHfDBehym2VsPDL6Zn/JAD/JQdnRvbSsbQc4mVaU1m6JgtTEElg==",
+      "dev": true,
+      "dependencies": {
+        "@ampproject/remapping": "^2.1.0",
+        "@babel/code-frame": "^7.18.6",
+        "@babel/generator": "^7.20.7",
+        "@babel/helper-compilation-targets": "^7.20.7",
+        "@babel/helper-module-transforms": "^7.20.11",
+        "@babel/helpers": "^7.20.7",
+        "@babel/parser": "^7.20.7",
+        "@babel/template": "^7.20.7",
+        "@babel/traverse": "^7.20.12",
+        "@babel/types": "^7.20.7",
+        "convert-source-map": "^1.7.0",
+        "debug": "^4.1.0",
+        "gensync": "^1.0.0-beta.2",
+        "json5": "^2.2.2",
+        "semver": "^6.3.0"
+      },
+      "engines": {
+        "node": ">=6.9.0"
+      },
+      "funding": {
+        "type": "opencollective",
+        "url": "https://opencollective.com/babel"
+      }
+    },
+    "node_modules/@babel/generator": {
+      "version": "7.20.14",
+      "resolved": "https://registry.npmjs.org/@babel/generator/-/generator-7.20.14.tgz",
+      "integrity": "sha512-AEmuXHdcD3A52HHXxaTmYlb8q/xMEhoRP67B3T4Oq7lbmSoqroMZzjnGj3+i1io3pdnF8iBYVu4Ilj+c4hBxYg==",
+      "dev": true,
+      "dependencies": {
+        "@babel/types": "^7.20.7",
+        "@jridgewell/gen-mapping": "^0.3.2",
+        "jsesc": "^2.5.1"
+      },
+      "engines": {
+        "node": ">=6.9.0"
+      }
+    },
+    "node_modules/@babel/generator/node_modules/@jridgewell/gen-mapping": {
+      "version": "0.3.2",
+      "resolved": "https://registry.npmjs.org/@jridgewell/gen-mapping/-/gen-mapping-0.3.2.tgz",
+      "integrity": "sha512-mh65xKQAzI6iBcFzwv28KVWSmCkdRBWoOh+bYQGW3+6OZvbbN3TqMGo5hqYxQniRcH9F2VZIoJCm4pa3BPDK/A==",
+      "dev": true,
+      "dependencies": {
+        "@jridgewell/set-array": "^1.0.1",
+        "@jridgewell/sourcemap-codec": "^1.4.10",
+        "@jridgewell/trace-mapping": "^0.3.9"
+      },
+      "engines": {
+        "node": ">=6.0.0"
+      }
+    },
+    "node_modules/@babel/helper-annotate-as-pure": {
+      "version": "7.18.6",
+      "resolved": "https://registry.npmjs.org/@babel/helper-annotate-as-pure/-/helper-annotate-as-pure-7.18.6.tgz",
+      "integrity": "sha512-duORpUiYrEpzKIop6iNbjnwKLAKnJ47csTyRACyEmWj0QdUrm5aqNJGHSSEQSUAvNW0ojX0dOmK9dZduvkfeXA==",
+      "dev": true,
+      "dependencies": {
+        "@babel/types": "^7.18.6"
+      },
+      "engines": {
+        "node": ">=6.9.0"
+      }
+    },
+    "node_modules/@babel/helper-builder-binary-assignment-operator-visitor": {
+      "version": "7.18.9",
+      "resolved": "https://registry.npmjs.org/@babel/helper-builder-binary-assignment-operator-visitor/-/helper-builder-binary-assignment-operator-visitor-7.18.9.tgz",
+      "integrity": "sha512-yFQ0YCHoIqarl8BCRwBL8ulYUaZpz3bNsA7oFepAzee+8/+ImtADXNOmO5vJvsPff3qi+hvpkY/NYBTrBQgdNw==",
+      "dev": true,
+      "dependencies": {
+        "@babel/helper-explode-assignable-expression": "^7.18.6",
+        "@babel/types": "^7.18.9"
+      },
+      "engines": {
+        "node": ">=6.9.0"
+      }
+    },
+    "node_modules/@babel/helper-compilation-targets": {
+      "version": "7.20.7",
+      "resolved": "https://registry.npmjs.org/@babel/helper-compilation-targets/-/helper-compilation-targets-7.20.7.tgz",
+      "integrity": "sha512-4tGORmfQcrc+bvrjb5y3dG9Mx1IOZjsHqQVUz7XCNHO+iTmqxWnVg3KRygjGmpRLJGdQSKuvFinbIb0CnZwHAQ==",
+      "dev": true,
+      "dependencies": {
+        "@babel/compat-data": "^7.20.5",
+        "@babel/helper-validator-option": "^7.18.6",
+        "browserslist": "^4.21.3",
+        "lru-cache": "^5.1.1",
+        "semver": "^6.3.0"
+      },
+      "engines": {
+        "node": ">=6.9.0"
+      },
+      "peerDependencies": {
+        "@babel/core": "^7.0.0"
+      }
+    },
+    "node_modules/@babel/helper-create-class-features-plugin": {
+      "version": "7.20.12",
+      "resolved": "https://registry.npmjs.org/@babel/helper-create-class-features-plugin/-/helper-create-class-features-plugin-7.20.12.tgz",
+      "integrity": "sha512-9OunRkbT0JQcednL0UFvbfXpAsUXiGjUk0a7sN8fUXX7Mue79cUSMjHGDRRi/Vz9vYlpIhLV5fMD5dKoMhhsNQ==",
+      "dev": true,
+      "dependencies": {
+        "@babel/helper-annotate-as-pure": "^7.18.6",
+        "@babel/helper-environment-visitor": "^7.18.9",
+        "@babel/helper-function-name": "^7.19.0",
+        "@babel/helper-member-expression-to-functions": "^7.20.7",
+        "@babel/helper-optimise-call-expression": "^7.18.6",
+        "@babel/helper-replace-supers": "^7.20.7",
+        "@babel/helper-skip-transparent-expression-wrappers": "^7.20.0",
+        "@babel/helper-split-export-declaration": "^7.18.6"
+      },
+      "engines": {
+        "node": ">=6.9.0"
+      },
+      "peerDependencies": {
+        "@babel/core": "^7.0.0"
+      }
+    },
+    "node_modules/@babel/helper-create-regexp-features-plugin": {
+      "version": "7.20.5",
+      "resolved": "https://registry.npmjs.org/@babel/helper-create-regexp-features-plugin/-/helper-create-regexp-features-plugin-7.20.5.tgz",
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+      "dev": true,
+      "dependencies": {
+        "@babel/helper-annotate-as-pure": "^7.18.6",
+        "regexpu-core": "^5.2.1"
+      },
+      "engines": {
+        "node": ">=6.9.0"
+      },
+      "peerDependencies": {
+        "@babel/core": "^7.0.0"
+      }
+    },
+    "node_modules/@babel/helper-define-polyfill-provider": {
+      "version": "0.3.3",
+      "resolved": "https://registry.npmjs.org/@babel/helper-define-polyfill-provider/-/helper-define-polyfill-provider-0.3.3.tgz",
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+      "dev": true,
+      "dependencies": {
+        "@babel/helper-compilation-targets": "^7.17.7",
+        "@babel/helper-plugin-utils": "^7.16.7",
+        "debug": "^4.1.1",
+        "lodash.debounce": "^4.0.8",
+        "resolve": "^1.14.2",
+        "semver": "^6.1.2"
+      },
+      "peerDependencies": {
+        "@babel/core": "^7.4.0-0"
+      }
+    },
+    "node_modules/@babel/helper-environment-visitor": {
+      "version": "7.18.9",
+      "resolved": "https://registry.npmjs.org/@babel/helper-environment-visitor/-/helper-environment-visitor-7.18.9.tgz",
+      "integrity": "sha512-3r/aACDJ3fhQ/EVgFy0hpj8oHyHpQc+LPtJoY9SzTThAsStm4Ptegq92vqKoE3vD706ZVFWITnMnxucw+S9Ipg==",
+      "dev": true,
+      "engines": {
+        "node": ">=6.9.0"
+      }
+    },
+    "node_modules/@babel/helper-explode-assignable-expression": {
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+    },
+    "yocto-queue": {
+      "version": "0.1.0",
+      "resolved": "https://registry.npmjs.org/yocto-queue/-/yocto-queue-0.1.0.tgz",
+      "integrity": "sha512-rVksvsnNCdJ/ohGc6xgPwyN8eheCxsiLM8mxuE/t/mOVqJewPuO1miLpTHQiRgTKCLexL4MeAFVagts7HmNZ2Q==",
       "dev": true
     }
   }
diff --git a/package.json b/package.json
index 6d29c89e11..80e64db3c7 100644
--- a/package.json
+++ b/package.json
@@ -35,21 +35,20 @@
     "prepare": "husky install"
   },
   "devDependencies": {
-    "@babel/cli": "7.16.8",
-    "@babel/preset-env": "7.16.11",
-    "@types/jest": "27.4.0",
-    "canvas": "2.9.0",
-    "eslint": "8.7.0",
+    "@babel/cli": "7.20.7",
+    "@babel/preset-env": "7.20.2",
+    "@types/jest": "29.4.0",
+    "canvas": "2.11.0",
+    "eslint": "8.33.0",
     "eslint-config-airbnb": "19.0.4",
-    "eslint-plugin-import": "2.25.4",
-    "eslint-plugin-jest": "25.7.0",
-    "eslint-plugin-jsx-a11y": "6.5.1",
-    "eslint-plugin-react": "7.28.0",
-    "husky": "7.0.4",
-    "jest": "27.4.7"
+    "eslint-plugin-import": "2.27.5",
+    "eslint-plugin-jest": "27.2.1",
+    "eslint-plugin-jsx-a11y": "6.7.1",
+    "husky": "8.0.3",
+    "jest": "29.4.1"
   },
   "engines": {
-    "node": ">=14.16.0",
-    "npm": ">=6.14.0"
+    "node": ">=16.15.0",
+    "npm": ">=8.5.5"
   }
 }

From c9f1caf1ca87cfa23a5a12046a8359f93f337971 Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Mon, 30 Jan 2023 09:01:49 +0100
Subject: [PATCH 231/264] Add a recursive version of the Longest Common
 Substring.

---
 .../__test__/longestCommonSubstring.test.js   |  2 ++
 .../longestCommonSubstringRecursive.test.js   | 17 +++++++++
 .../longestCommonSubstring.js                 |  2 ++
 .../longestCommonSubstringRecursive.js        | 36 +++++++++++++++++++
 4 files changed, 57 insertions(+)
 create mode 100644 src/algorithms/string/longest-common-substring/__test__/longestCommonSubstringRecursive.test.js
 create mode 100644 src/algorithms/string/longest-common-substring/longestCommonSubstringRecursive.js

diff --git a/src/algorithms/string/longest-common-substring/__test__/longestCommonSubstring.test.js b/src/algorithms/string/longest-common-substring/__test__/longestCommonSubstring.test.js
index a24c0df55c..8c1cb20703 100644
--- a/src/algorithms/string/longest-common-substring/__test__/longestCommonSubstring.test.js
+++ b/src/algorithms/string/longest-common-substring/__test__/longestCommonSubstring.test.js
@@ -7,6 +7,8 @@ describe('longestCommonSubstring', () => {
     expect(longestCommonSubstring('', 'ABC')).toBe('');
     expect(longestCommonSubstring('ABABC', 'BABCA')).toBe('BABC');
     expect(longestCommonSubstring('BABCA', 'ABCBA')).toBe('ABC');
+    expect(longestCommonSubstring('sea', 'eat')).toBe('ea');
+    expect(longestCommonSubstring('algorithms', 'rithm')).toBe('rithm');
     expect(longestCommonSubstring(
       'Algorithms and data structures implemented in JavaScript',
       'Here you may find Algorithms and data structures that are implemented in JavaScript',
diff --git a/src/algorithms/string/longest-common-substring/__test__/longestCommonSubstringRecursive.test.js b/src/algorithms/string/longest-common-substring/__test__/longestCommonSubstringRecursive.test.js
new file mode 100644
index 0000000000..d8428033c8
--- /dev/null
+++ b/src/algorithms/string/longest-common-substring/__test__/longestCommonSubstringRecursive.test.js
@@ -0,0 +1,17 @@
+import longestCommonSubstring from '../longestCommonSubstringRecursive';
+
+describe('longestCommonSubstringRecursive', () => {
+  it('should find longest common substring between two strings', () => {
+    expect(longestCommonSubstring('', '')).toBe('');
+    expect(longestCommonSubstring('ABC', '')).toBe('');
+    expect(longestCommonSubstring('', 'ABC')).toBe('');
+    expect(longestCommonSubstring('ABABC', 'BABCA')).toBe('BABC');
+    expect(longestCommonSubstring('BABCA', 'ABCBA')).toBe('ABCA');
+    expect(longestCommonSubstring('sea', 'eat')).toBe('ea');
+    expect(longestCommonSubstring('algorithms', 'rithm')).toBe('rithm');
+    expect(longestCommonSubstring(
+      'Algorithms and data structures implemented in JavaScript',
+      'Here you may find Algorithms and data structures that are implemented in JavaScript',
+    )).toBe('Algorithms and data structures implemented in JavaScript');
+  });
+});
diff --git a/src/algorithms/string/longest-common-substring/longestCommonSubstring.js b/src/algorithms/string/longest-common-substring/longestCommonSubstring.js
index 1d68ede9e3..6afeccf398 100644
--- a/src/algorithms/string/longest-common-substring/longestCommonSubstring.js
+++ b/src/algorithms/string/longest-common-substring/longestCommonSubstring.js
@@ -1,4 +1,6 @@
 /**
+ * Longest Common Substring (LCS) (Dynamic Programming Approach).
+ *
  * @param {string} string1
  * @param {string} string2
  * @return {string}
diff --git a/src/algorithms/string/longest-common-substring/longestCommonSubstringRecursive.js b/src/algorithms/string/longest-common-substring/longestCommonSubstringRecursive.js
new file mode 100644
index 0000000000..88cb08aa00
--- /dev/null
+++ b/src/algorithms/string/longest-common-substring/longestCommonSubstringRecursive.js
@@ -0,0 +1,36 @@
+/* eslint-disable no-param-reassign */
+/**
+ * Longest Common Substring (LCS) (Recursive Approach).
+ *
+ * @param {string} string1
+ * @param {string} string2
+ * @return {number}
+ */
+export default function longestCommonSubstringRecursive(string1, string2) {
+  /**
+   *
+   * @param {string} s1
+   * @param {string} s2
+   * @return {string} - returns the LCS (Longest Common Substring)
+   */
+  const lcs = (s1, s2, memo = {}) => {
+    if (!s1 || !s2) return '';
+
+    if (memo[`${s1}:${s2}`]) return memo[`${s1}:${s2}`];
+
+    if (s1[0] === s2[0]) {
+      return s1[0] + lcs(s1.substring(1), s2.substring(1), memo);
+    }
+
+    const nextLcs1 = lcs(s1.substring(1), s2, memo);
+    const nextLcs2 = lcs(s1, s2.substring(1), memo);
+
+    const nextLongest = nextLcs1.length >= nextLcs2.length ? nextLcs1 : nextLcs2;
+
+    memo[`${s1}:${s2}`] = nextLongest;
+
+    return nextLongest;
+  };
+
+  return lcs(string1, string2);
+}

From 5fc33c0f0ae5c6ccddaf8c40a8af483fb750a3ad Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Mon, 30 Jan 2023 09:08:17 +0100
Subject: [PATCH 232/264] Add a recursive version of the Longest Common
 Subsequence.

---
 .../longestCommonSubsequenceRecursive.test.js   | 17 +++++++++++++++++
 .../longestCommonSubsequenceRecursive.js}       |  6 +++---
 .../longestCommonSubstringRecursive.test.js     | 17 -----------------
 3 files changed, 20 insertions(+), 20 deletions(-)
 create mode 100644 src/algorithms/sets/longest-common-subsequence/__test__/longestCommonSubsequenceRecursive.test.js
 rename src/algorithms/{string/longest-common-substring/longestCommonSubstringRecursive.js => sets/longest-common-subsequence/longestCommonSubsequenceRecursive.js} (77%)
 delete mode 100644 src/algorithms/string/longest-common-substring/__test__/longestCommonSubstringRecursive.test.js

diff --git a/src/algorithms/sets/longest-common-subsequence/__test__/longestCommonSubsequenceRecursive.test.js b/src/algorithms/sets/longest-common-subsequence/__test__/longestCommonSubsequenceRecursive.test.js
new file mode 100644
index 0000000000..3d5c9d802a
--- /dev/null
+++ b/src/algorithms/sets/longest-common-subsequence/__test__/longestCommonSubsequenceRecursive.test.js
@@ -0,0 +1,17 @@
+import longestCommonSubsequence from '../longestCommonSubsequenceRecursive';
+
+describe('longestCommonSubsequenceRecursive', () => {
+  it('should find longest common substring between two strings', () => {
+    expect(longestCommonSubsequence('', '')).toBe('');
+    expect(longestCommonSubsequence('ABC', '')).toBe('');
+    expect(longestCommonSubsequence('', 'ABC')).toBe('');
+    expect(longestCommonSubsequence('ABABC', 'BABCA')).toBe('BABC');
+    expect(longestCommonSubsequence('BABCA', 'ABCBA')).toBe('ABCA');
+    expect(longestCommonSubsequence('sea', 'eat')).toBe('ea');
+    expect(longestCommonSubsequence('algorithms', 'rithm')).toBe('rithm');
+    expect(longestCommonSubsequence(
+      'Algorithms and data structures implemented in JavaScript',
+      'Here you may find Algorithms and data structures that are implemented in JavaScript',
+    )).toBe('Algorithms and data structures implemented in JavaScript');
+  });
+});
diff --git a/src/algorithms/string/longest-common-substring/longestCommonSubstringRecursive.js b/src/algorithms/sets/longest-common-subsequence/longestCommonSubsequenceRecursive.js
similarity index 77%
rename from src/algorithms/string/longest-common-substring/longestCommonSubstringRecursive.js
rename to src/algorithms/sets/longest-common-subsequence/longestCommonSubsequenceRecursive.js
index 88cb08aa00..580ba8c72f 100644
--- a/src/algorithms/string/longest-common-substring/longestCommonSubstringRecursive.js
+++ b/src/algorithms/sets/longest-common-subsequence/longestCommonSubsequenceRecursive.js
@@ -1,17 +1,17 @@
 /* eslint-disable no-param-reassign */
 /**
- * Longest Common Substring (LCS) (Recursive Approach).
+ * Longest Common Subsequence (LCS) (Recursive Approach).
  *
  * @param {string} string1
  * @param {string} string2
  * @return {number}
  */
-export default function longestCommonSubstringRecursive(string1, string2) {
+export default function longestCommonSubsequenceRecursive(string1, string2) {
   /**
    *
    * @param {string} s1
    * @param {string} s2
-   * @return {string} - returns the LCS (Longest Common Substring)
+   * @return {string} - returns the LCS (Longest Common Subsequence)
    */
   const lcs = (s1, s2, memo = {}) => {
     if (!s1 || !s2) return '';
diff --git a/src/algorithms/string/longest-common-substring/__test__/longestCommonSubstringRecursive.test.js b/src/algorithms/string/longest-common-substring/__test__/longestCommonSubstringRecursive.test.js
deleted file mode 100644
index d8428033c8..0000000000
--- a/src/algorithms/string/longest-common-substring/__test__/longestCommonSubstringRecursive.test.js
+++ /dev/null
@@ -1,17 +0,0 @@
-import longestCommonSubstring from '../longestCommonSubstringRecursive';
-
-describe('longestCommonSubstringRecursive', () => {
-  it('should find longest common substring between two strings', () => {
-    expect(longestCommonSubstring('', '')).toBe('');
-    expect(longestCommonSubstring('ABC', '')).toBe('');
-    expect(longestCommonSubstring('', 'ABC')).toBe('');
-    expect(longestCommonSubstring('ABABC', 'BABCA')).toBe('BABC');
-    expect(longestCommonSubstring('BABCA', 'ABCBA')).toBe('ABCA');
-    expect(longestCommonSubstring('sea', 'eat')).toBe('ea');
-    expect(longestCommonSubstring('algorithms', 'rithm')).toBe('rithm');
-    expect(longestCommonSubstring(
-      'Algorithms and data structures implemented in JavaScript',
-      'Here you may find Algorithms and data structures that are implemented in JavaScript',
-    )).toBe('Algorithms and data structures implemented in JavaScript');
-  });
-});

From af08253a956c994f098f84e5fdd700b6ce99b344 Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Wed, 1 Feb 2023 08:11:25 +0100
Subject: [PATCH 233/264] Adding Heap time complexities

---
 src/data-structures/heap/README.md | 25 +++++++++++++++++++++++++
 1 file changed, 25 insertions(+)

diff --git a/src/data-structures/heap/README.md b/src/data-structures/heap/README.md
index db5f9e339f..824d646043 100644
--- a/src/data-structures/heap/README.md
+++ b/src/data-structures/heap/README.md
@@ -33,6 +33,31 @@ to the key of `C`
 The node at the "top" of the heap with no parents is
 called the root node.
 
+## Time Complexities
+
+Here are time complexities of various heap data structures. Function names assume a max-heap.
+
+| Operation | find-max | delete-max | insert| increase-key| meld |
+| --------- | -------- | ---------- | ----- | ----------- | ---- |
+| [Binary](https://en.wikipedia.org/wiki/Binary_heap) | `Θ(1)` | `Θ(log n)` | `O(log n)` | `O(log n)` | `Θ(n)` |
+| [Leftist](https://en.wikipedia.org/wiki/Leftist_tree) | `Θ(1)` | `Θ(log n)` | `Θ(log n)` | `O(log n)` | `Θ(log n)` |
+| [Binomial](https://en.wikipedia.org/wiki/Binomial_heap) | `Θ(1)` | `Θ(log n)` | `Θ(1)` | `O(log n)` | `O(log n)` |
+| [Fibonacci](https://en.wikipedia.org/wiki/Fibonacci_heap) | `Θ(1)` | `Θ(log n)` | `Θ(1)` | `Θ(1)` | `Θ(1)` |
+| [Pairing](https://en.wikipedia.org/wiki/Pairing_heap) | `Θ(1)` | `Θ(log n)` | `Θ(1)` | `o(log n)` | `Θ(1)` |
+| [Brodal](https://en.wikipedia.org/wiki/Brodal_queue) | `Θ(1)` | `Θ(log n)` | `Θ(1)` | `Θ(1)` | `Θ(1)` |
+| [Rank-pairing](https://en.wikipedia.org/w/index.php?title=Rank-pairing_heap&action=edit&redlink=1) | `Θ(1)` | `Θ(log n)` | `Θ(1)` | `Θ(1)` | `Θ(1)` |
+| [Strict Fibonacci](https://en.wikipedia.org/wiki/Fibonacci_heap) | `Θ(1)` | `Θ(log n)` | `Θ(1)` | `Θ(1)` | `Θ(1)` |
+| [2-3 heap](https://en.wikipedia.org/wiki/2%E2%80%933_heap) | `O(log n)` | `O(log n)` | `O(log n)` | `Θ(1)` | `?` |
+
+Where:
+- **find-max (or find-min):** find a maximum item of a max-heap, or a minimum item of a min-heap, respectively (a.k.a. *peek*)
+- **delete-max (or delete-min):** removing the root node of a max heap (or min heap), respectively
+- **insert:** adding a new key to the heap (a.k.a., *push*)
+- **increase-key or decrease-key:** updating a key within a max- or min-heap, respectively
+- **meld:** joining two heaps to form a valid new heap containing all the elements of both, destroying the original heaps.
+
+> In this repository, the [MaxHeap.js](./MaxHeap.js) and [MinHeap.js](./MinHeap.js) are examples of the **Binary** heap.
+
 ## References
 
 - [Wikipedia](https://en.wikipedia.org/wiki/Heap_(data_structure))

From 5a41865787350d1270ae07b2086604caf7d16454 Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Mon, 20 Feb 2023 18:41:58 +0100
Subject: [PATCH 234/264] Add links for code examples for K-Means clustering

---
 src/algorithms/ml/k-means/README.md | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/src/algorithms/ml/k-means/README.md b/src/algorithms/ml/k-means/README.md
index 4221880054..fb58c1bfa4 100644
--- a/src/algorithms/ml/k-means/README.md
+++ b/src/algorithms/ml/k-means/README.md
@@ -30,6 +30,11 @@ _Image source: [Wikipedia](https://en.wikipedia.org/wiki/K-means_clustering)_
 
 The centroids are moving continuously in order to create better distinction between the different set of data points. As we can see, after a few iterations, the difference in centroids is quite low between iterations. For example between iterations `13` and `14` the difference is quite small because there the optimizer is tuning boundary cases.
 
+## Code Examples
+
+- [kMeans.js](./kMeans.js)
+- [kMeans.test.js](./__test__/kMeans.test.js) (test cases)
+
 ## References
 
 - [k-Means neighbors algorithm on Wikipedia](https://en.wikipedia.org/wiki/K-means_clustering)

From 46aae1d708f077ad229f200053cab8276fd6317c Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Fri, 24 Feb 2023 23:04:35 -0100
Subject: [PATCH 235/264] Add bakers

---
 BACKERS.md | 31 ++++++++++++++++++++++++++++++-
 README.md  | 24 ++++++++++++++++++++----
 2 files changed, 50 insertions(+), 5 deletions(-)

diff --git a/BACKERS.md b/BACKERS.md
index 62c397a38c..ccd5a2d287 100644
--- a/BACKERS.md
+++ b/BACKERS.md
@@ -8,12 +8,41 @@
 
 ## `O(n²)` Backers
 
-`null`
+<ul>
+  <li>
+    <a href="https://github.com/newrelic">
+      <img
+        src="https://avatars.githubusercontent.com/u/31739?s=200&v=4"
+        width="30"
+        height="30"
+      /></a>
+    &thinsp;
+    <a href="https://github.com/newrelic">newrelic</a>
+  </li>
+</ul>
 
 ## `O(n×log(n))` Backers
 
 `null`
 
+<!--
+<table>
+  <tr>
+    <td align="center">
+      <a href="http://github.com/[PROFILE_URL]">
+        <img
+          src="http://github.com/[PROFILE_IMG_SRC]"
+          width="50"
+          height="50"
+        />
+      </a>
+      <br />
+      <a href="http://github.com/[PROFILE_URL]">[PROFILE_NAME]</a>
+    </td>
+  </tr>
+</table>
+-->
+
 <!--
 <ul>
   <li>
diff --git a/README.md b/README.md
index 9666335e35..f7f4827c0f 100644
--- a/README.md
+++ b/README.md
@@ -361,10 +361,26 @@ Below is the list of some of the most used Big O notations and their performance
 
 > You may support this project via ❤️️ [GitHub](https://github.com/sponsors/trekhleb) or ❤️️ [Patreon](https://www.patreon.com/trekhleb).
 
-[Folks who are backing this project](https://github.com/trekhleb/javascript-algorithms/blob/master/BACKERS.md) `∑ = 0`
-
-> ℹ️ A few more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev)
+[Folks who are backing this project](https://github.com/trekhleb/javascript-algorithms/blob/master/BACKERS.md) `∑ = 1`
+
+<table>
+  <tr>
+    <td align="center">
+      <a href="https://github.com/newrelic">
+        <img
+          src="https://avatars.githubusercontent.com/u/31739?s=200&v=4"
+          width="50"
+          height="50"
+        />
+      </a>
+      <br />
+      <a href="https://github.com/newrelic">newrelic</a>
+    </td>
+  </tr>
+</table>
 
 ## Author
 
-- [@trekhleb](https://trekhleb.dev)
+[@trekhleb](https://trekhleb.dev)
+
+A few more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev)

From e95d856e6781fdb3a727f139bbc12249d814a80e Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Fri, 24 Feb 2023 23:06:02 -0100
Subject: [PATCH 236/264] Add bakers

---
 BACKERS.md | 27 +++++++++++++++------------
 1 file changed, 15 insertions(+), 12 deletions(-)

diff --git a/BACKERS.md b/BACKERS.md
index ccd5a2d287..718475fe3a 100644
--- a/BACKERS.md
+++ b/BACKERS.md
@@ -8,18 +8,21 @@
 
 ## `O(n²)` Backers
 
-<ul>
-  <li>
-    <a href="https://github.com/newrelic">
-      <img
-        src="https://avatars.githubusercontent.com/u/31739?s=200&v=4"
-        width="30"
-        height="30"
-      /></a>
-    &thinsp;
-    <a href="https://github.com/newrelic">newrelic</a>
-  </li>
-</ul>
+<table>
+  <tr>
+    <td align="center">
+      <a href="https://github.com/newrelic">
+        <img
+          src="https://avatars.githubusercontent.com/u/31739?s=200&v=4"
+          width="50"
+          height="50"
+        />
+      </a>
+      <br />
+      <a href="https://github.com/newrelic">newrelic</a>
+    </td>
+  </tr>
+</table>
 
 ## `O(n×log(n))` Backers
 

From 1ad60dc5107216e1f6febf7255e5fc915588c94b Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Mon, 13 Mar 2023 14:12:43 +0100
Subject: [PATCH 237/264] Add Bucket Sort.

---
 README.md                                     |   1 +
 .../sorting/bucket-sort/BucketSort.js         |  46 ++++++++++++++++++
 src/algorithms/sorting/bucket-sort/README.md  |  35 +++++++++++++
 .../bucket-sort/__test__/BucketSort.test.js   |  33 +++++++++++++
 .../bucket-sort/images/bucket_sort_1.png      | Bin 0 -> 11151 bytes
 .../bucket-sort/images/bucket_sort_2.png      | Bin 0 -> 12936 bytes
 src/algorithms/sorting/radix-sort/README.md   |  38 +++++++--------
 .../sorting/radix-sort/images/radix-sort.png  | Bin 0 -> 12619 bytes
 8 files changed, 134 insertions(+), 19 deletions(-)
 create mode 100644 src/algorithms/sorting/bucket-sort/BucketSort.js
 create mode 100644 src/algorithms/sorting/bucket-sort/README.md
 create mode 100644 src/algorithms/sorting/bucket-sort/__test__/BucketSort.test.js
 create mode 100644 src/algorithms/sorting/bucket-sort/images/bucket_sort_1.png
 create mode 100644 src/algorithms/sorting/bucket-sort/images/bucket_sort_2.png
 create mode 100644 src/algorithms/sorting/radix-sort/images/radix-sort.png

diff --git a/README.md b/README.md
index f7f4827c0f..443ee953c7 100644
--- a/README.md
+++ b/README.md
@@ -133,6 +133,7 @@ a set of rules that precisely define a sequence of operations.
   * `B` [Shellsort](src/algorithms/sorting/shell-sort)
   * `B` [Counting Sort](src/algorithms/sorting/counting-sort)
   * `B` [Radix Sort](src/algorithms/sorting/radix-sort)
+  * `B` [Bucket Sort](src/algorithms/sorting/bucket-sort)
 * **Linked Lists**
   * `B` [Straight Traversal](src/algorithms/linked-list/traversal)
   * `B` [Reverse Traversal](src/algorithms/linked-list/reverse-traversal)
diff --git a/src/algorithms/sorting/bucket-sort/BucketSort.js b/src/algorithms/sorting/bucket-sort/BucketSort.js
new file mode 100644
index 0000000000..a41e5892d2
--- /dev/null
+++ b/src/algorithms/sorting/bucket-sort/BucketSort.js
@@ -0,0 +1,46 @@
+import RadixSort from '../radix-sort/RadixSort';
+
+/**
+ * Bucket Sort
+ *
+ * @param {number[]} arr
+ * @param {number} bucketsNum
+ * @return {number[]}
+ */
+export default function BucketSort(arr, bucketsNum = 1) {
+  const buckets = new Array(bucketsNum).fill(null).map(() => []);
+
+  const minValue = Math.min(...arr);
+  const maxValue = Math.max(...arr);
+
+  const bucketSize = Math.ceil(Math.max(1, (maxValue - minValue) / bucketsNum));
+
+  // Place elements into buckets.
+  for (let i = 0; i < arr.length; i += 1) {
+    const currValue = arr[i];
+    const bucketIndex = Math.floor((currValue - minValue) / bucketSize);
+
+    // Edge case for max value.
+    if (bucketIndex === bucketsNum) {
+      buckets[bucketsNum - 1].push(currValue);
+    } else {
+      buckets[bucketIndex].push(currValue);
+    }
+  }
+
+  // Sort individual buckets.
+  for (let i = 0; i < buckets.length; i += 1) {
+    // Let's use the Radix Sorter here. This may give us
+    // the average O(n + k) time complexity to sort one bucket
+    // (where k is a number of digits in the longest number).
+    buckets[i] = new RadixSort().sort(buckets[i]);
+  }
+
+  // Merge sorted buckets into final output.
+  const sortedArr = [];
+  for (let i = 0; i < buckets.length; i += 1) {
+    sortedArr.push(...buckets[i]);
+  }
+
+  return sortedArr;
+}
diff --git a/src/algorithms/sorting/bucket-sort/README.md b/src/algorithms/sorting/bucket-sort/README.md
new file mode 100644
index 0000000000..673ba80b71
--- /dev/null
+++ b/src/algorithms/sorting/bucket-sort/README.md
@@ -0,0 +1,35 @@
+# Bucket Sort
+
+**Bucket sort**, or **bin sort**, is a sorting algorithm that works by distributing the elements of an array into a number of buckets. Each bucket is then sorted individually, either using a different sorting algorithm, or by recursively applying the bucket sorting algorithm.
+
+## Algorithm
+
+Bucket sort works as follows:
+
+1. Set up an array of initially empty `buckets`.
+2. **Scatter:** Go over the original array, putting each object in its `bucket`.
+3. Sort each non-empty `bucket`.
+4. **Gather:** Visit the `buckets` in order and put all elements back into the original array.
+
+Elements are distributed among bins:
+
+![Elements are distributed among bins](./images/bucket_sort_1.png)
+
+Then, elements are sorted within each bin:
+
+![Elements are sorted within each bin](./images/bucket_sort_2.png)
+
+
+## Complexity
+
+The computational complexity depends on the algorithm used to sort each bucket, the number of buckets to use, and whether the input is uniformly distributed.
+
+The **worst-case** time complexity of bucket sort is
+`O(n^2)` if the sorting algorithm used on the bucket is *insertion sort*, which is the most common use case since the expectation is that buckets will not have too many elements relative to the entire list. In the worst case, all elements are placed in one bucket, causing the running time to reduce to the worst-case complexity of insertion sort (all elements are in reverse order). If the worst-case running time of the intermediate sort used is `O(n * log(n))`, then the worst-case running time of bucket sort will also be
+`O(n * log(n))`.
+
+On **average**, when the distribution of elements across buckets is reasonably uniform, it can be shown that bucket sort runs on average `O(n + k)` for `k` buckets.
+
+## References
+
+- [Bucket Sort on Wikipedia](https://en.wikipedia.org/wiki/Bucket_sort)
diff --git a/src/algorithms/sorting/bucket-sort/__test__/BucketSort.test.js b/src/algorithms/sorting/bucket-sort/__test__/BucketSort.test.js
new file mode 100644
index 0000000000..9cab525d9b
--- /dev/null
+++ b/src/algorithms/sorting/bucket-sort/__test__/BucketSort.test.js
@@ -0,0 +1,33 @@
+import BucketSort from '../BucketSort';
+import {
+  equalArr,
+  notSortedArr,
+  reverseArr,
+  sortedArr,
+} from '../../SortTester';
+
+describe('BucketSort', () => {
+  it('should sort the array of numbers with different buckets amounts', () => {
+    expect(BucketSort(notSortedArr, 4)).toEqual(sortedArr);
+    expect(BucketSort(equalArr, 4)).toEqual(equalArr);
+    expect(BucketSort(reverseArr, 4)).toEqual(sortedArr);
+    expect(BucketSort(sortedArr, 4)).toEqual(sortedArr);
+
+    expect(BucketSort(notSortedArr, 10)).toEqual(sortedArr);
+    expect(BucketSort(equalArr, 10)).toEqual(equalArr);
+    expect(BucketSort(reverseArr, 10)).toEqual(sortedArr);
+    expect(BucketSort(sortedArr, 10)).toEqual(sortedArr);
+
+    expect(BucketSort(notSortedArr, 50)).toEqual(sortedArr);
+    expect(BucketSort(equalArr, 50)).toEqual(equalArr);
+    expect(BucketSort(reverseArr, 50)).toEqual(sortedArr);
+    expect(BucketSort(sortedArr, 50)).toEqual(sortedArr);
+  });
+
+  it('should sort the array of numbers with the default buckets of 1', () => {
+    expect(BucketSort(notSortedArr)).toEqual(sortedArr);
+    expect(BucketSort(equalArr)).toEqual(equalArr);
+    expect(BucketSort(reverseArr)).toEqual(sortedArr);
+    expect(BucketSort(sortedArr)).toEqual(sortedArr);
+  });
+});
diff --git a/src/algorithms/sorting/bucket-sort/images/bucket_sort_1.png b/src/algorithms/sorting/bucket-sort/images/bucket_sort_1.png
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diff --git a/src/algorithms/sorting/radix-sort/README.md b/src/algorithms/sorting/radix-sort/README.md
index 80129278d1..108d7d19b6 100644
--- a/src/algorithms/sorting/radix-sort/README.md
+++ b/src/algorithms/sorting/radix-sort/README.md
@@ -3,37 +3,37 @@
 _Read this in other languages:_
 [_Português_](README.pt-BR.md),
 
-In computer science, **radix sort** is a non-comparative integer sorting 
-algorithm that sorts data with integer keys by grouping keys by the individual 
+In computer science, **radix sort** is a non-comparative integer sorting
+algorithm that sorts data with integer keys by grouping keys by the individual
 digits which share the same significant position and value. A positional notation
-is required, but because integers can represent strings of characters 
-(e.g., names or dates) and specially formatted floating point numbers, radix 
+is required, but because integers can represent strings of characters
+(e.g., names or dates) and specially formatted floating point numbers, radix
 sort is not limited to integers.
 
 *Where does the name come from?*
 
 In mathematical numeral systems, the *radix* or base is the number of unique digits,
-including the digit zero, used to represent numbers in a positional numeral system. 
-For example, a binary system (using numbers 0 and 1) has a radix of 2 and a decimal 
+including the digit zero, used to represent numbers in a positional numeral system.
+For example, a binary system (using numbers 0 and 1) has a radix of 2 and a decimal
 system (using numbers 0 to 9) has a radix of 10.
 
 ## Efficiency
 
-The topic of the efficiency of radix sort compared to other sorting algorithms is 
-somewhat tricky and subject to quite a lot of misunderstandings. Whether radix 
-sort is equally efficient, less efficient or more efficient than the best 
-comparison-based algorithms depends on the details of the assumptions made. 
-Radix sort complexity is `O(wn)` for `n` keys which are integers of word size `w`. 
-Sometimes `w` is presented as a constant, which would make radix sort better 
-(for sufficiently large `n`) than the best comparison-based sorting algorithms, 
-which all perform `O(n log n)` comparisons to sort `n` keys. However, in 
-general `w` cannot be considered a constant: if all `n` keys are distinct, 
-then `w` has to be at least `log n` for a random-access machine to be able to 
-store them in memory, which gives at best a time complexity `O(n log n)`. That 
-would seem to make radix sort at most equally efficient as the best 
+The topic of the efficiency of radix sort compared to other sorting algorithms is
+somewhat tricky and subject to quite a lot of misunderstandings. Whether radix
+sort is equally efficient, less efficient or more efficient than the best
+comparison-based algorithms depends on the details of the assumptions made.
+Radix sort complexity is `O(wn)` for `n` keys which are integers of word size `w`.
+Sometimes `w` is presented as a constant, which would make radix sort better
+(for sufficiently large `n`) than the best comparison-based sorting algorithms,
+which all perform `O(n log n)` comparisons to sort `n` keys. However, in
+general `w` cannot be considered a constant: if all `n` keys are distinct,
+then `w` has to be at least `log n` for a random-access machine to be able to
+store them in memory, which gives at best a time complexity `O(n log n)`. That
+would seem to make radix sort at most equally efficient as the best
 comparison-based sorts (and worse if keys are much longer than `log n`).
 
-![Radix Sort](https://www.researchgate.net/publication/291086231/figure/fig1/AS:614214452404240@1523451545568/Simplistic-illustration-of-the-steps-performed-in-a-radix-sort-In-this-example-the.png)
+![Radix Sort](./images/radix-sort.png)
 
 ## Complexity
 
diff --git a/src/algorithms/sorting/radix-sort/images/radix-sort.png b/src/algorithms/sorting/radix-sort/images/radix-sort.png
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From b9304f4787c9586ad146f24e305244d0df95e080 Mon Sep 17 00:00:00 2001
From: Yaroslav Podorvanov
 <63663261+YaroslavPodorvanov@users.noreply.github.com>
Date: Thu, 16 Mar 2023 21:40:41 +0200
Subject: [PATCH 238/264] feat: added Ukrainian translation for factorial
 (#1006)
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

* added Ukrainian translations for factorial

* added links to other languages

* formatting

* delete link

* Türkçe

---------

Co-authored-by: VictorPoprozhuk <victor.poprozhuk@gmail.com>
---
 src/algorithms/math/factorial/README.md       |  2 +-
 src/algorithms/math/factorial/README.uk-UA.md | 33 +++++++++++++++++++
 src/data-structures/linked-list/README.md     |  2 +-
 3 files changed, 35 insertions(+), 2 deletions(-)
 create mode 100644 src/algorithms/math/factorial/README.uk-UA.md

diff --git a/src/algorithms/math/factorial/README.md b/src/algorithms/math/factorial/README.md
index 5f7f0e1129..9c75b41aae 100644
--- a/src/algorithms/math/factorial/README.md
+++ b/src/algorithms/math/factorial/README.md
@@ -1,7 +1,7 @@
 # Factorial
 
 _Read this in other languages:_
-[_简体中文_](README.zh-CN.md), [français](README.fr-FR.md), [turkish](README.tr-TR.md), [ქართული](README.ka-GE.md).
+[_简体中文_](README.zh-CN.md), [_Français_](README.fr-FR.md), [_Türkçe_](README.tr-TR.md), [_ქართული_](README.ka-GE.md), [_Українська_](README.uk-UA.md).
 
 In mathematics, the factorial of a non-negative integer `n`,
 denoted by `n!`, is the product of all positive integers less
diff --git a/src/algorithms/math/factorial/README.uk-UA.md b/src/algorithms/math/factorial/README.uk-UA.md
new file mode 100644
index 0000000000..bf75963113
--- /dev/null
+++ b/src/algorithms/math/factorial/README.uk-UA.md
@@ -0,0 +1,33 @@
+# Факторіал
+
+_Прочитайте це іншими мовами:_
+[_English_](README.md), [_简体中文_](README.zh-CN.md), [_Français_](README.fr-FR.md), [_Türkçe_](README.tr-TR.md), [_ქართული_](README.ka-GE.md).
+
+У математиці факторіал невід'ємного цілого числа `n`, позначений `n!`, є добутком усіх натуральних чисел, менших або рівних `n`. Наприклад:
+
+```
+5! = 5 * 4 * 3 * 2 * 1 = 120
+```
+
+| n   |                n! |
+| --- | ----------------: |
+| 0   |                 1 |
+| 1   |                 1 |
+| 2   |                 2 |
+| 3   |                 6 |
+| 4   |                24 |
+| 5   |               120 |
+| 6   |               720 |
+| 7   |             5 040 |
+| 8   |            40 320 |
+| 9   |           362 880 |
+| 10  |         3 628 800 |
+| 11  |        39 916 800 |
+| 12  |       479 001 600 |
+| 13  |     6 227 020 800 |
+| 14  |    87 178 291 200 |
+| 15  | 1 307 674 368 000 |
+
+## Посилання
+
+[Wikipedia](https://uk.wikipedia.org/wiki/%D0%A4%D0%B0%D0%BA%D1%82%D0%BE%D1%80%D1%96%D0%B0%D0%BB)
diff --git a/src/data-structures/linked-list/README.md b/src/data-structures/linked-list/README.md
index bb30b07525..825a0272f4 100644
--- a/src/data-structures/linked-list/README.md
+++ b/src/data-structures/linked-list/README.md
@@ -7,7 +7,7 @@ _Read this in other languages:_
 [_Português_](README.pt-BR.md),
 [_한국어_](README.ko-KR.md),
 [_Español_](README.es-ES.md),
-[_Turkish_](README.tr-TR.md),
+[_Türkçe_](README.tr-TR.md),
 [_Українська_](README.uk-UA.md)
 
 In computer science, a **linked list** is a linear collection

From bbbfd32a45a677950554a91c4ece8976b8b31c38 Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Sat, 25 Mar 2023 17:02:02 +0100
Subject: [PATCH 239/264] Update Bakers.

---
 BACKERS.md | 16 +---------------
 README.md  | 16 ----------------
 2 files changed, 1 insertion(+), 31 deletions(-)

diff --git a/BACKERS.md b/BACKERS.md
index 718475fe3a..a244d3bed3 100644
--- a/BACKERS.md
+++ b/BACKERS.md
@@ -8,21 +8,7 @@
 
 ## `O(n²)` Backers
 
-<table>
-  <tr>
-    <td align="center">
-      <a href="https://github.com/newrelic">
-        <img
-          src="https://avatars.githubusercontent.com/u/31739?s=200&v=4"
-          width="50"
-          height="50"
-        />
-      </a>
-      <br />
-      <a href="https://github.com/newrelic">newrelic</a>
-    </td>
-  </tr>
-</table>
+`null`
 
 ## `O(n×log(n))` Backers
 
diff --git a/README.md b/README.md
index 443ee953c7..747508235b 100644
--- a/README.md
+++ b/README.md
@@ -364,22 +364,6 @@ Below is the list of some of the most used Big O notations and their performance
 
 [Folks who are backing this project](https://github.com/trekhleb/javascript-algorithms/blob/master/BACKERS.md) `∑ = 1`
 
-<table>
-  <tr>
-    <td align="center">
-      <a href="https://github.com/newrelic">
-        <img
-          src="https://avatars.githubusercontent.com/u/31739?s=200&v=4"
-          width="50"
-          height="50"
-        />
-      </a>
-      <br />
-      <a href="https://github.com/newrelic">newrelic</a>
-    </td>
-  </tr>
-</table>
-
 ## Author
 
 [@trekhleb](https://trekhleb.dev)

From 14c563619c300145de3d07d8e67024dc05869606 Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Mon, 10 Apr 2023 18:31:06 +0200
Subject: [PATCH 240/264] Fix repo build for M1 MacBooks (#1029)

---
 package-lock.json                             | 3416 ++++++-----------
 package.json                                  |    4 +-
 .../__tests__/resizeImageWidth.node.js        |   85 +
 .../__tests__/resizeImageWidth.test.js        |   91 -
 .../__tests__/test-image-after.jpg            |  Bin 6088 -> 0 bytes
 .../__tests__/test-image-after.png            |  Bin 0 -> 6725 bytes
 .../__tests__/test-image-before.jpg           |  Bin 3395 -> 0 bytes
 .../__tests__/test-image-before.png           |  Bin 0 -> 11746 bytes
 8 files changed, 1365 insertions(+), 2231 deletions(-)
 create mode 100644 src/algorithms/image-processing/seam-carving/__tests__/resizeImageWidth.node.js
 delete mode 100644 src/algorithms/image-processing/seam-carving/__tests__/resizeImageWidth.test.js
 delete mode 100644 src/algorithms/image-processing/seam-carving/__tests__/test-image-after.jpg
 create mode 100644 src/algorithms/image-processing/seam-carving/__tests__/test-image-after.png
 delete mode 100644 src/algorithms/image-processing/seam-carving/__tests__/test-image-before.jpg
 create mode 100644 src/algorithms/image-processing/seam-carving/__tests__/test-image-before.png

diff --git a/package-lock.json b/package-lock.json
index 3cfe2e3571..b61d279d87 100644
--- a/package-lock.json
+++ b/package-lock.json
@@ -12,14 +12,14 @@
         "@babel/cli": "7.20.7",
         "@babel/preset-env": "7.20.2",
         "@types/jest": "29.4.0",
-        "canvas": "2.11.0",
         "eslint": "8.33.0",
         "eslint-config-airbnb": "19.0.4",
         "eslint-plugin-import": "2.27.5",
         "eslint-plugin-jest": "27.2.1",
         "eslint-plugin-jsx-a11y": "6.7.1",
         "husky": "8.0.3",
-        "jest": "29.4.1"
+        "jest": "29.4.1",
+        "pngjs": "^7.0.0"
       },
       "engines": {
         "node": ">=16.15.0",
@@ -27,12 +27,12 @@
       }
     },
     "node_modules/@ampproject/remapping": {
-      "version": "2.2.0",
-      "resolved": "https://registry.npmjs.org/@ampproject/remapping/-/remapping-2.2.0.tgz",
-      "integrity": "sha512-qRmjj8nj9qmLTQXXmaR1cck3UXSRMPrbsLJAasZpF+t3riI71BXed5ebIOYwQntykeZuhjsdweEc9BxH5Jc26w==",
+      "version": "2.2.1",
+      "resolved": "https://registry.npmjs.org/@ampproject/remapping/-/remapping-2.2.1.tgz",
+      "integrity": "sha512-lFMjJTrFL3j7L9yBxwYfCq2k6qqwHyzuUl/XBnif78PWTJYyL/dfowQHWE3sp6U6ZzqWiiIZnpTMO96zhkjwtg==",
       "dev": true,
       "dependencies": {
-        "@jridgewell/gen-mapping": "^0.1.0",
+        "@jridgewell/gen-mapping": "^0.3.0",
         "@jridgewell/trace-mapping": "^0.3.9"
       },
       "engines": {
@@ -69,9 +69,9 @@
       }
     },
     "node_modules/@babel/code-frame": {
-      "version": "7.18.6",
-      "resolved": "https://registry.npmjs.org/@babel/code-frame/-/code-frame-7.18.6.tgz",
-      "integrity": "sha512-TDCmlK5eOvH+eH7cdAFlNXeVJqWIQ7gW9tY1GJIpUtFb6CmjVyq2VM3u71bOyR8CRihcCgMUYoDNyLXao3+70Q==",
+      "version": "7.21.4",
+      "resolved": "https://registry.npmjs.org/@babel/code-frame/-/code-frame-7.21.4.tgz",
+      "integrity": "sha512-LYvhNKfwWSPpocw8GI7gpK2nq3HSDuEPC/uSYaALSJu9xjsalaaYFOq0Pwt5KmVqwEbZlDu81aLXwBOmD/Fv9g==",
       "dev": true,
       "dependencies": {
         "@babel/highlight": "^7.18.6"
@@ -81,30 +81,30 @@
       }
     },
     "node_modules/@babel/compat-data": {
-      "version": "7.20.14",
-      "resolved": "https://registry.npmjs.org/@babel/compat-data/-/compat-data-7.20.14.tgz",
-      "integrity": "sha512-0YpKHD6ImkWMEINCyDAD0HLLUH/lPCefG8ld9it8DJB2wnApraKuhgYTvTY1z7UFIfBTGy5LwncZ+5HWWGbhFw==",
+      "version": "7.21.4",
+      "resolved": "https://registry.npmjs.org/@babel/compat-data/-/compat-data-7.21.4.tgz",
+      "integrity": "sha512-/DYyDpeCfaVinT40FPGdkkb+lYSKvsVuMjDAG7jPOWWiM1ibOaB9CXJAlc4d1QpP/U2q2P9jbrSlClKSErd55g==",
       "dev": true,
       "engines": {
         "node": ">=6.9.0"
       }
     },
     "node_modules/@babel/core": {
-      "version": "7.20.12",
-      "resolved": "https://registry.npmjs.org/@babel/core/-/core-7.20.12.tgz",
-      "integrity": "sha512-XsMfHovsUYHFMdrIHkZphTN/2Hzzi78R08NuHfDBehym2VsPDL6Zn/JAD/JQdnRvbSsbQc4mVaU1m6JgtTEElg==",
-      "dev": true,
-      "dependencies": {
-        "@ampproject/remapping": "^2.1.0",
-        "@babel/code-frame": "^7.18.6",
-        "@babel/generator": "^7.20.7",
-        "@babel/helper-compilation-targets": "^7.20.7",
-        "@babel/helper-module-transforms": "^7.20.11",
-        "@babel/helpers": "^7.20.7",
-        "@babel/parser": "^7.20.7",
+      "version": "7.21.4",
+      "resolved": "https://registry.npmjs.org/@babel/core/-/core-7.21.4.tgz",
+      "integrity": "sha512-qt/YV149Jman/6AfmlxJ04LMIu8bMoyl3RB91yTFrxQmgbrSvQMy7cI8Q62FHx1t8wJ8B5fu0UDoLwHAhUo1QA==",
+      "dev": true,
+      "dependencies": {
+        "@ampproject/remapping": "^2.2.0",
+        "@babel/code-frame": "^7.21.4",
+        "@babel/generator": "^7.21.4",
+        "@babel/helper-compilation-targets": "^7.21.4",
+        "@babel/helper-module-transforms": "^7.21.2",
+        "@babel/helpers": "^7.21.0",
+        "@babel/parser": "^7.21.4",
         "@babel/template": "^7.20.7",
-        "@babel/traverse": "^7.20.12",
-        "@babel/types": "^7.20.7",
+        "@babel/traverse": "^7.21.4",
+        "@babel/types": "^7.21.4",
         "convert-source-map": "^1.7.0",
         "debug": "^4.1.0",
         "gensync": "^1.0.0-beta.2",
@@ -120,33 +120,20 @@
       }
     },
     "node_modules/@babel/generator": {
-      "version": "7.20.14",
-      "resolved": "https://registry.npmjs.org/@babel/generator/-/generator-7.20.14.tgz",
-      "integrity": "sha512-AEmuXHdcD3A52HHXxaTmYlb8q/xMEhoRP67B3T4Oq7lbmSoqroMZzjnGj3+i1io3pdnF8iBYVu4Ilj+c4hBxYg==",
+      "version": "7.21.4",
+      "resolved": "https://registry.npmjs.org/@babel/generator/-/generator-7.21.4.tgz",
+      "integrity": "sha512-NieM3pVIYW2SwGzKoqfPrQsf4xGs9M9AIG3ThppsSRmO+m7eQhmI6amajKMUeIO37wFfsvnvcxQFx6x6iqxDnA==",
       "dev": true,
       "dependencies": {
-        "@babel/types": "^7.20.7",
+        "@babel/types": "^7.21.4",
         "@jridgewell/gen-mapping": "^0.3.2",
+        "@jridgewell/trace-mapping": "^0.3.17",
         "jsesc": "^2.5.1"
       },
       "engines": {
         "node": ">=6.9.0"
       }
     },
-    "node_modules/@babel/generator/node_modules/@jridgewell/gen-mapping": {
-      "version": "0.3.2",
-      "resolved": "https://registry.npmjs.org/@jridgewell/gen-mapping/-/gen-mapping-0.3.2.tgz",
-      "integrity": "sha512-mh65xKQAzI6iBcFzwv28KVWSmCkdRBWoOh+bYQGW3+6OZvbbN3TqMGo5hqYxQniRcH9F2VZIoJCm4pa3BPDK/A==",
-      "dev": true,
-      "dependencies": {
-        "@jridgewell/set-array": "^1.0.1",
-        "@jridgewell/sourcemap-codec": "^1.4.10",
-        "@jridgewell/trace-mapping": "^0.3.9"
-      },
-      "engines": {
-        "node": ">=6.0.0"
-      }
-    },
     "node_modules/@babel/helper-annotate-as-pure": {
       "version": "7.18.6",
       "resolved": "https://registry.npmjs.org/@babel/helper-annotate-as-pure/-/helper-annotate-as-pure-7.18.6.tgz",
@@ -173,13 +160,13 @@
       }
     },
     "node_modules/@babel/helper-compilation-targets": {
-      "version": "7.20.7",
-      "resolved": "https://registry.npmjs.org/@babel/helper-compilation-targets/-/helper-compilation-targets-7.20.7.tgz",
-      "integrity": "sha512-4tGORmfQcrc+bvrjb5y3dG9Mx1IOZjsHqQVUz7XCNHO+iTmqxWnVg3KRygjGmpRLJGdQSKuvFinbIb0CnZwHAQ==",
+      "version": "7.21.4",
+      "resolved": "https://registry.npmjs.org/@babel/helper-compilation-targets/-/helper-compilation-targets-7.21.4.tgz",
+      "integrity": "sha512-Fa0tTuOXZ1iL8IeDFUWCzjZcn+sJGd9RZdH9esYVjEejGmzf+FFYQpMi/kZUk2kPy/q1H3/GPw7np8qar/stfg==",
       "dev": true,
       "dependencies": {
-        "@babel/compat-data": "^7.20.5",
-        "@babel/helper-validator-option": "^7.18.6",
+        "@babel/compat-data": "^7.21.4",
+        "@babel/helper-validator-option": "^7.21.0",
         "browserslist": "^4.21.3",
         "lru-cache": "^5.1.1",
         "semver": "^6.3.0"
@@ -192,15 +179,15 @@
       }
     },
     "node_modules/@babel/helper-create-class-features-plugin": {
-      "version": "7.20.12",
-      "resolved": "https://registry.npmjs.org/@babel/helper-create-class-features-plugin/-/helper-create-class-features-plugin-7.20.12.tgz",
-      "integrity": "sha512-9OunRkbT0JQcednL0UFvbfXpAsUXiGjUk0a7sN8fUXX7Mue79cUSMjHGDRRi/Vz9vYlpIhLV5fMD5dKoMhhsNQ==",
+      "version": "7.21.4",
+      "resolved": "https://registry.npmjs.org/@babel/helper-create-class-features-plugin/-/helper-create-class-features-plugin-7.21.4.tgz",
+      "integrity": "sha512-46QrX2CQlaFRF4TkwfTt6nJD7IHq8539cCL7SDpqWSDeJKY1xylKKY5F/33mJhLZ3mFvKv2gGrVS6NkyF6qs+Q==",
       "dev": true,
       "dependencies": {
         "@babel/helper-annotate-as-pure": "^7.18.6",
         "@babel/helper-environment-visitor": "^7.18.9",
-        "@babel/helper-function-name": "^7.19.0",
-        "@babel/helper-member-expression-to-functions": "^7.20.7",
+        "@babel/helper-function-name": "^7.21.0",
+        "@babel/helper-member-expression-to-functions": "^7.21.0",
         "@babel/helper-optimise-call-expression": "^7.18.6",
         "@babel/helper-replace-supers": "^7.20.7",
         "@babel/helper-skip-transparent-expression-wrappers": "^7.20.0",
@@ -214,13 +201,13 @@
       }
     },
     "node_modules/@babel/helper-create-regexp-features-plugin": {
-      "version": "7.20.5",
-      "resolved": "https://registry.npmjs.org/@babel/helper-create-regexp-features-plugin/-/helper-create-regexp-features-plugin-7.20.5.tgz",
-      "integrity": "sha512-m68B1lkg3XDGX5yCvGO0kPx3v9WIYLnzjKfPcQiwntEQa5ZeRkPmo2X/ISJc8qxWGfwUr+kvZAeEzAwLec2r2w==",
+      "version": "7.21.4",
+      "resolved": "https://registry.npmjs.org/@babel/helper-create-regexp-features-plugin/-/helper-create-regexp-features-plugin-7.21.4.tgz",
+      "integrity": "sha512-M00OuhU+0GyZ5iBBN9czjugzWrEq2vDpf/zCYHxxf93ul/Q5rv+a5h+/+0WnI1AebHNVtl5bFV0qsJoH23DbfA==",
       "dev": true,
       "dependencies": {
         "@babel/helper-annotate-as-pure": "^7.18.6",
-        "regexpu-core": "^5.2.1"
+        "regexpu-core": "^5.3.1"
       },
       "engines": {
         "node": ">=6.9.0"
@@ -268,13 +255,13 @@
       }
     },
     "node_modules/@babel/helper-function-name": {
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-        "is-core-module": "^2.9.0",
+        "is-core-module": "^2.11.0",
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+      "version": "2.0.2",
+      "resolved": "https://registry.npmjs.org/resolve.exports/-/resolve.exports-2.0.2.tgz",
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@@ -15982,12 +15208,6 @@
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@@ -16175,6 +15363,17 @@
         "side-channel": "^1.0.4"
       }
     },
+    "string.prototype.trim": {
+      "version": "1.2.7",
+      "resolved": "https://registry.npmjs.org/string.prototype.trim/-/string.prototype.trim-1.2.7.tgz",
+      "integrity": "sha512-p6TmeT1T3411M8Cgg9wBTMRtY2q9+PNy9EV1i2lIXUN/btt763oIfxwN3RR8VU6wHX8j/1CFy0L+YuThm6bgOg==",
+      "dev": true,
+      "requires": {
+        "call-bind": "^1.0.2",
+        "define-properties": "^1.1.4",
+        "es-abstract": "^1.20.4"
+      }
+    },
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       "version": "1.0.6",
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-        "minipass": "^4.0.0",
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@@ -16299,20 +15476,14 @@
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-      "resolved": "https://registry.npmjs.org/tsconfig-paths/-/tsconfig-paths-3.14.1.tgz",
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+      "version": "3.14.2",
+      "resolved": "https://registry.npmjs.org/tsconfig-paths/-/tsconfig-paths-3.14.2.tgz",
+      "integrity": "sha512-o/9iXgCYc5L/JxCHPe3Hvh8Q/2xm5Z+p18PESBU6Ff33695QnCHBEjcytY2q19ua7Mbl/DavtBOLq+oG0RCL+g==",
       "dev": true,
       "requires": {
         "@types/json5": "^0.0.29",
-        "json5": "^1.0.1",
+        "json5": "^1.0.2",
         "minimist": "^1.2.6",
         "strip-bom": "^3.0.0"
       },
@@ -16382,9 +15553,9 @@
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-      "version": "4.9.4",
-      "resolved": "https://registry.npmjs.org/typescript/-/typescript-4.9.4.tgz",
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+      "version": "5.0.4",
+      "resolved": "https://registry.npmjs.org/typescript/-/typescript-5.0.4.tgz",
+      "integrity": "sha512-cW9T5W9xY37cc+jfEnaUvX91foxtHkza3Nw3wkoF4sSlKn0MONdkdEndig/qPBWXNkmplh3NzayQzCiHM4/hqw==",
       "dev": true,
       "peer": true
     },
@@ -16447,16 +15618,10 @@
         "punycode": "^2.1.0"
       }
     },
-    "util-deprecate": {
-      "version": "1.0.2",
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-      "dev": true
-    },
     "v8-to-istanbul": {
-      "version": "9.0.1",
-      "resolved": "https://registry.npmjs.org/v8-to-istanbul/-/v8-to-istanbul-9.0.1.tgz",
-      "integrity": "sha512-74Y4LqY74kLE6IFyIjPtkSTWzUZmj8tdHT9Ii/26dvQ6K9Dl2NbEfj0XgU2sHCtKgt5VupqhlO/5aWuqS+IY1w==",
+      "version": "9.1.0",
+      "resolved": "https://registry.npmjs.org/v8-to-istanbul/-/v8-to-istanbul-9.1.0.tgz",
+      "integrity": "sha512-6z3GW9x8G1gd+JIIgQQQxXuiJtCXeAjp6RaPEPLv62mH3iPHPxV6W3robxtCzNErRo6ZwTmzWhsbNvjyEBKzKA==",
       "dev": true,
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@@ -16473,22 +15638,6 @@
         "makeerror": "1.0.12"
       }
     },
-    "webidl-conversions": {
-      "version": "3.0.1",
-      "resolved": "https://registry.npmjs.org/webidl-conversions/-/webidl-conversions-3.0.1.tgz",
-      "integrity": "sha512-2JAn3z8AR6rjK8Sm8orRC0h/bcl/DqL7tRPdGZ4I1CjdF+EaMLmYxBHyXuKL849eucPFhvBoxMsflfOb8kxaeQ==",
-      "dev": true
-    },
-    "whatwg-url": {
-      "version": "5.0.0",
-      "resolved": "https://registry.npmjs.org/whatwg-url/-/whatwg-url-5.0.0.tgz",
-      "integrity": "sha512-saE57nupxk6v3HY35+jzBwYa0rKSy0XR8JSxZPwgLr7ys0IBzhGviA1/TUGJLmSVqs8pb9AnvICXEuOHLprYTw==",
-      "dev": true,
-      "requires": {
-        "tr46": "~0.0.3",
-        "webidl-conversions": "^3.0.0"
-      }
-    },
     "which": {
       "version": "2.0.2",
       "resolved": "https://registry.npmjs.org/which/-/which-2.0.2.tgz",
@@ -16537,15 +15686,6 @@
         "is-typed-array": "^1.1.10"
       }
     },
-    "wide-align": {
-      "version": "1.1.5",
-      "resolved": "https://registry.npmjs.org/wide-align/-/wide-align-1.1.5.tgz",
-      "integrity": "sha512-eDMORYaPNZ4sQIuuYPDHdQvf4gyCF9rEEV/yPxGfwPkRodwEgiMUUXTx/dex+Me0wxx53S+NgUHaP7y3MGlDmg==",
-      "dev": true,
-      "requires": {
-        "string-width": "^1.0.2 || 2 || 3 || 4"
-      }
-    },
     "word-wrap": {
       "version": "1.2.3",
       "resolved": "https://registry.npmjs.org/word-wrap/-/word-wrap-1.2.3.tgz",
@@ -16596,9 +15736,9 @@
       "dev": true
     },
     "write-file-atomic": {
-      "version": "5.0.0",
-      "resolved": "https://registry.npmjs.org/write-file-atomic/-/write-file-atomic-5.0.0.tgz",
-      "integrity": "sha512-R7NYMnHSlV42K54lwY9lvW6MnSm1HSJqZL3xiSgi9E7//FYaI74r2G0rd+/X6VAMkHEdzxQaU5HUOXWUz5kA/w==",
+      "version": "4.0.2",
+      "resolved": "https://registry.npmjs.org/write-file-atomic/-/write-file-atomic-4.0.2.tgz",
+      "integrity": "sha512-7KxauUdBmSdWnmpaGFg+ppNjKF8uNLry8LyzjauQDOVONfFLNKrKvQOxZ/VuTIcS/gge/YNahf5RIIQWTSarlg==",
       "dev": true,
       "requires": {
         "imurmurhash": "^0.1.4",
@@ -16618,9 +15758,9 @@
       "dev": true
     },
     "yargs": {
-      "version": "17.6.2",
-      "resolved": "https://registry.npmjs.org/yargs/-/yargs-17.6.2.tgz",
-      "integrity": "sha512-1/9UrdHjDZc0eOU0HxOHoS78C69UD3JRMvzlJ7S79S2nTaWRA/whGCTV8o9e/N/1Va9YIV7Q4sOxD8VV4pCWOw==",
+      "version": "17.7.1",
+      "resolved": "https://registry.npmjs.org/yargs/-/yargs-17.7.1.tgz",
+      "integrity": "sha512-cwiTb08Xuv5fqF4AovYacTFNxk62th7LKJ6BL9IGUpTJrWoU7/7WdQGTP2SjKf1dUNBGzDd28p/Yfs/GI6JrLw==",
       "dev": true,
       "requires": {
         "cliui": "^8.0.1",
diff --git a/package.json b/package.json
index 80e64db3c7..95d6d28942 100644
--- a/package.json
+++ b/package.json
@@ -38,14 +38,14 @@
     "@babel/cli": "7.20.7",
     "@babel/preset-env": "7.20.2",
     "@types/jest": "29.4.0",
-    "canvas": "2.11.0",
     "eslint": "8.33.0",
     "eslint-config-airbnb": "19.0.4",
     "eslint-plugin-import": "2.27.5",
     "eslint-plugin-jest": "27.2.1",
     "eslint-plugin-jsx-a11y": "6.7.1",
     "husky": "8.0.3",
-    "jest": "29.4.1"
+    "jest": "29.4.1",
+    "pngjs": "^7.0.0"
   },
   "engines": {
     "node": ">=16.15.0",
diff --git a/src/algorithms/image-processing/seam-carving/__tests__/resizeImageWidth.node.js b/src/algorithms/image-processing/seam-carving/__tests__/resizeImageWidth.node.js
new file mode 100644
index 0000000000..e4f78b7a52
--- /dev/null
+++ b/src/algorithms/image-processing/seam-carving/__tests__/resizeImageWidth.node.js
@@ -0,0 +1,85 @@
+import fs from 'fs';
+import { PNG } from 'pngjs';
+
+import resizeImageWidth from '../resizeImageWidth';
+
+const testImageBeforePath = './src/algorithms/image-processing/seam-carving/__tests__/test-image-before.png';
+const testImageAfterPath = './src/algorithms/image-processing/seam-carving/__tests__/test-image-after.png';
+
+/**
+ * Compares two images and finds the number of different pixels.
+ *
+ * @param {ImageData} imgA - ImageData for the first image.
+ * @param {ImageData} imgB - ImageData for the second image.
+ * @param {number} threshold - Color difference threshold [0..255]. Smaller - stricter.
+ * @returns {number} - Number of different pixels.
+ */
+function pixelsDiff(imgA, imgB, threshold = 0) {
+  if (imgA.width !== imgB.width || imgA.height !== imgB.height) {
+    throw new Error('Images must have the same size');
+  }
+
+  let differentPixels = 0;
+  const numColorParams = 4; // RGBA
+
+  for (let pixelIndex = 0; pixelIndex < imgA.data.length; pixelIndex += numColorParams) {
+    // Get pixel's color for each image.
+    const [aR, aG, aB] = imgA.data.subarray(pixelIndex, pixelIndex + numColorParams);
+    const [bR, bG, bB] = imgB.data.subarray(pixelIndex, pixelIndex + numColorParams);
+
+    // Get average pixel's color for each image (make them greyscale).
+    const aAvgColor = Math.floor((aR + aG + aB) / 3);
+    const bAvgColor = Math.floor((bR + bG + bB) / 3);
+
+    // Compare pixel colors.
+    if (Math.abs(aAvgColor - bAvgColor) > threshold) {
+      differentPixels += 1;
+    }
+  }
+
+  return differentPixels;
+}
+
+const pngLoad = (path) => new Promise((resolve) => {
+  fs.createReadStream(path)
+    .pipe(new PNG())
+    .on('parsed', function Parsed() {
+      /** @type {ImageData} */
+      const imageData = {
+        colorSpace: 'srgb',
+        width: this.width,
+        height: this.height,
+        data: this.data,
+      };
+      resolve(imageData);
+    });
+});
+
+describe('resizeImageWidth', () => {
+  it('should perform content-aware image width reduction', async () => {
+    const imgBefore = await pngLoad(testImageBeforePath);
+    const imgAfter = await pngLoad(testImageAfterPath);
+
+    const toWidth = Math.floor(imgBefore.width / 2);
+
+    const {
+      img: imgResized,
+      size: resizedSize,
+    } = resizeImageWidth({ img: imgBefore, toWidth });
+
+    expect(imgResized).toBeDefined();
+    expect(resizedSize).toBeDefined();
+
+    expect(resizedSize).toEqual({ w: toWidth, h: imgBefore.height });
+    expect(imgResized.width).toBe(imgAfter.width);
+    expect(imgResized.height).toBe(imgAfter.height);
+
+    const colorThreshold = 50;
+    const differentPixels = pixelsDiff(imgResized, imgAfter, colorThreshold);
+
+    // Allow 10% of pixels to be different
+    const pixelsThreshold = Math.floor((imgAfter.width * imgAfter.height) / 10);
+
+    expect(differentPixels).toBeLessThanOrEqual(pixelsThreshold);
+  });
+});
diff --git a/src/algorithms/image-processing/seam-carving/__tests__/resizeImageWidth.test.js b/src/algorithms/image-processing/seam-carving/__tests__/resizeImageWidth.test.js
deleted file mode 100644
index 9afed97123..0000000000
--- a/src/algorithms/image-processing/seam-carving/__tests__/resizeImageWidth.test.js
+++ /dev/null
@@ -1,91 +0,0 @@
-import { createCanvas, loadImage } from 'canvas';
-import resizeImageWidth from '../resizeImageWidth';
-
-const testImageBeforePath = './src/algorithms/image-processing/seam-carving/__tests__/test-image-before.jpg';
-const testImageAfterPath = './src/algorithms/image-processing/seam-carving/__tests__/test-image-after.jpg';
-
-/**
- * Compares two images and finds the number of different pixels.
- *
- * @param {ImageData} imgA - ImageData for the first image.
- * @param {ImageData} imgB - ImageData for the second image.
- * @param {number} threshold - Color difference threshold [0..255]. Smaller - stricter.
- * @returns {number} - Number of different pixels.
- */
-function pixelsDiff(imgA, imgB, threshold = 0) {
-  if (imgA.width !== imgB.width || imgA.height !== imgB.height) {
-    throw new Error('Images must have the same size');
-  }
-
-  let differentPixels = 0;
-  const numColorParams = 4; // RGBA
-
-  for (let pixelIndex = 0; pixelIndex < imgA.data.length; pixelIndex += numColorParams) {
-    // Get pixel's color for each image.
-    const [aR, aG, aB] = imgA.data.subarray(pixelIndex, pixelIndex + numColorParams);
-    const [bR, bG, bB] = imgB.data.subarray(pixelIndex, pixelIndex + numColorParams);
-
-    // Get average pixel's color for each image (make them greyscale).
-    const aAvgColor = Math.floor((aR + aG + aB) / 3);
-    const bAvgColor = Math.floor((bR + bG + bB) / 3);
-
-    // Compare pixel colors.
-    if (Math.abs(aAvgColor - bAvgColor) > threshold) {
-      differentPixels += 1;
-    }
-  }
-
-  return differentPixels;
-}
-
-describe('resizeImageWidth', () => {
-  it('should perform content-aware image width reduction', () => {
-    // @see: https://jestjs.io/docs/asynchronous
-    return Promise.all([
-      loadImage(testImageBeforePath),
-      loadImage(testImageAfterPath),
-    ]).then(([imgBefore, imgAfter]) => {
-      // Original image.
-      const canvasBefore = createCanvas(imgBefore.width, imgBefore.height);
-      const ctxBefore = canvasBefore.getContext('2d');
-      ctxBefore.drawImage(imgBefore, 0, 0, imgBefore.width, imgBefore.height);
-      const imgDataBefore = ctxBefore.getImageData(0, 0, imgBefore.width, imgBefore.height);
-
-      // Resized image saved.
-      const canvasAfter = createCanvas(imgAfter.width, imgAfter.height);
-      const ctxAfter = canvasAfter.getContext('2d');
-      ctxAfter.drawImage(imgAfter, 0, 0, imgAfter.width, imgAfter.height);
-      const imgDataAfter = ctxAfter.getImageData(0, 0, imgAfter.width, imgAfter.height);
-
-      const toWidth = Math.floor(imgBefore.width / 2);
-
-      const {
-        img: resizedImg,
-        size: resizedSize,
-      } = resizeImageWidth({ img: imgDataBefore, toWidth });
-
-      expect(resizedImg).toBeDefined();
-      expect(resizedSize).toBeDefined();
-
-      // Resized image generated.
-      const canvasTest = createCanvas(resizedSize.w, resizedSize.h);
-      const ctxTest = canvasTest.getContext('2d');
-      ctxTest.putImageData(resizedImg, 0, 0, 0, 0, resizedSize.w, resizedSize.h);
-      const imgDataTest = ctxTest.getImageData(0, 0, resizedSize.w, resizedSize.h);
-
-      expect(resizedSize).toEqual({ w: toWidth, h: imgBefore.height });
-      expect(imgDataTest.width).toBe(toWidth);
-      expect(imgDataTest.height).toBe(imgBefore.height);
-      expect(imgDataTest.width).toBe(imgAfter.width);
-      expect(imgDataTest.height).toBe(imgAfter.height);
-
-      const colorThreshold = 50;
-      const differentPixels = pixelsDiff(imgDataTest, imgDataAfter, colorThreshold);
-
-      // Allow 10% of pixels to be different
-      const pixelsThreshold = Math.floor((imgAfter.width * imgAfter.height) / 10);
-
-      expect(differentPixels).toBeLessThanOrEqual(pixelsThreshold);
-    });
-  });
-});
diff --git a/src/algorithms/image-processing/seam-carving/__tests__/test-image-after.jpg b/src/algorithms/image-processing/seam-carving/__tests__/test-image-after.jpg
deleted file mode 100644
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diff --git a/src/algorithms/image-processing/seam-carving/__tests__/test-image-before.png b/src/algorithms/image-processing/seam-carving/__tests__/test-image-before.png
new file mode 100644
index 0000000000000000000000000000000000000000..20a53207ddf19ed3ace2b29abbe714b2b409e204
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From 8c5e5f4f0d5bb94439e02fe6ad6bb92b37a23834 Mon Sep 17 00:00:00 2001
From: trekhleb <trehleb@gmail.com>
Date: Mon, 10 Apr 2023 18:47:10 +0200
Subject: [PATCH 241/264] Add repo size

---
 README.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/README.md b/README.md
index 747508235b..38fab68bd6 100644
--- a/README.md
+++ b/README.md
@@ -9,6 +9,7 @@
 
 [![CI](https://github.com/trekhleb/javascript-algorithms/workflows/CI/badge.svg)](https://github.com/trekhleb/javascript-algorithms/actions?query=workflow%3ACI+branch%3Amaster)
 [![codecov](https://codecov.io/gh/trekhleb/javascript-algorithms/branch/master/graph/badge.svg)](https://codecov.io/gh/trekhleb/javascript-algorithms)
+![repo size](https://img.shields.io/github/repo-size/trekhleb/javascript-algorithms.svg)
 
 This repository contains JavaScript based examples of many
 popular algorithms and data structures.

From 76617fa83ac9a8519f20c7a9c938e2d8ef2fd512 Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Fri, 21 Jul 2023 20:08:01 +0200
Subject: [PATCH 242/264] Update README.md

---
 README.md | 6 ++++--
 1 file changed, 4 insertions(+), 2 deletions(-)

diff --git a/README.md b/README.md
index 38fab68bd6..e06cfb9075 100644
--- a/README.md
+++ b/README.md
@@ -1,8 +1,10 @@
 # JavaScript Algorithms and Data Structures
 
 > 🇺🇦 UKRAINE [IS BEING ATTACKED](https://war.ukraine.ua/) BY RUSSIAN ARMY. CIVILIANS ARE GETTING KILLED. RESIDENTIAL AREAS ARE GETTING BOMBED.
-> - Help Ukraine via [National Bank of Ukraine](https://bank.gov.ua/en/news/all/natsionalniy-bank-vidkriv-spetsrahunok-dlya-zboru-koshtiv-na-potrebi-armiyi)
-> - Help Ukraine via [SaveLife](https://savelife.in.ua/en/donate-en/) fund
+> - Help Ukraine via:
+>   - [Serhiy Prytula Charity Foundation](https://prytulafoundation.org/en/)
+>   - [Come Back Alive Charity Foundation](https://savelife.in.ua/en/donate-en/)
+>   - [National Bank of Ukraine](https://bank.gov.ua/en/news/all/natsionalniy-bank-vidkriv-spetsrahunok-dlya-zboru-koshtiv-na-potrebi-armiyi)
 > - More info on [war.ukraine.ua](https://war.ukraine.ua/) and [MFA of Ukraine](https://twitter.com/MFA_Ukraine)
 
 <hr/>

From 111ea3dbd30a5c596143a3b69bfd356bbc870d7a Mon Sep 17 00:00:00 2001
From: Arpit Goyal <50814175+Arpitgoyalgg@users.noreply.github.com>
Date: Sat, 9 Mar 2024 21:32:29 +0530
Subject: [PATCH 243/264] Update README.md (#1093)

---
 src/data-structures/tree/README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/data-structures/tree/README.md b/src/data-structures/tree/README.md
index 7eb7ec1db1..e492257d33 100644
--- a/src/data-structures/tree/README.md
+++ b/src/data-structures/tree/README.md
@@ -23,7 +23,7 @@ together with a list of references to nodes (the "children"),
 with the constraints that no reference is duplicated, and none
 points to the root.
 
-A simple unordered tree; in this diagram, the node labeled 7 has
+A simple unordered tree; in this diagram, the node labeled 3 has
 two children, labeled 2 and 6, and one parent, labeled 2. The
 root node, at the top, has no parent.
 

From 8d1f473610f173713179fcfd4f628b3d67591ac3 Mon Sep 17 00:00:00 2001
From: Vi Truong <103717482+vivitruong@users.noreply.github.com>
Date: Sat, 9 Mar 2024 10:06:47 -0600
Subject: [PATCH 244/264] Vietsub (#1088)

* translate readme from linked list

* add linked list for viet sub

* add vietnamese readme translation for queue

* add readme in vietnamese for Stack
---
 .../linked-list/README.vi-VN.md               | 155 ++++++++++++++++++
 src/data-structures/queue/README.vi-VN.md     |  22 +++
 src/data-structures/stack/README.vi-VN.md     |  27 +++
 3 files changed, 204 insertions(+)
 create mode 100644 src/data-structures/linked-list/README.vi-VN.md
 create mode 100644 src/data-structures/queue/README.vi-VN.md
 create mode 100644 src/data-structures/stack/README.vi-VN.md

diff --git a/src/data-structures/linked-list/README.vi-VN.md b/src/data-structures/linked-list/README.vi-VN.md
new file mode 100644
index 0000000000..005838c6c1
--- /dev/null
+++ b/src/data-structures/linked-list/README.vi-VN.md
@@ -0,0 +1,155 @@
+# Danh sách liên kết (Linked List)
+
+_Đọc bằng ngôn ngữ khác:_
+[_简体中文_](README.zh-CN.md),
+[_Русский_](README.ru-RU.md),
+[_日本語_](README.ja-JP.md),
+[_Português_](README.pt-BR.md),
+[_한국어_](README.ko-KR.md),
+[_Español_](README.es-ES.md),
+[_Türkçe_](README.tr-TR.md),
+[_Українська_](README.uk-UA.md)
+
+
+Trong khoa học máy tính, một danh sách liên kết là một bộ sưu tập tuyến tính
+các phần tử dữ liệu, trong đó thứ tự tuyến tính không được xác định bởi
+vị trí vật lý của chúng trong bộ nhớ. Thay vào đó, mỗi
+phần tử trỏ đến phần tử tiếp theo. Đây là một cấu trúc dữ liệu
+bao gồm một nhóm các nút cùng đại diện cho
+một chuỗi. Dưới dạng đơn giản nhất, mỗi nút
+bao gồm dữ liệu và một tham chiếu (nói cách khác,
+một liên kết) đến nút tiếp theo trong chuỗi. Cấu trúc này
+cho phép việc chèn hoặc loại bỏ các phần tử một cách hiệu quả
+từ bất kỳ vị trí nào trong chuỗi trong quá trình lặp.
+Các biến thể phức tạp hơn thêm các liên kết bổ sung, cho phép
+việc chèn hoặc loại bỏ một cách hiệu quả từ bất kỳ phần tử nào
+trong chuỗi dựa trên tham chiếu. Một nhược điểm của danh sách liên kết
+là thời gian truy cập tuyến tính (và khó điều chỉnh). Truy cập nhanh hơn,
+như truy cập ngẫu nhiên, là không khả thi. Mảng
+có độ tương phản cache tốt hơn so với danh sách liên kết.
+
+![Linked List](./images/linked-list.jpeg)
+*Được làm từ [okso.app](https://okso.app)*
+
+## Mã giải (Pseudocode) cho Các Hoạt Động Cơ Bản
+  *head = đầu,
+  *tail = đuôi,
+  *next = kế tiếp,
+  *node = nút,
+  *value = giá trị
+
+### Chèn (Insert)
+
+```
+ThêmGiáTrị(giá trị) (Add(value))
+  Trước(Pre): giá trị là giá trị muốn thêm vào danh sách
+  Sau(Post): giá trị đã được đặt ở cuối danh sách
+
+ n ← node(value)
+  if head = ø
+    head ← n
+    tail ← n
+  else
+    tail.next ← n
+    tail ← n
+  end if
+end ThêmGiáTrị(Add)
+```
+
+```
+ChènVàoĐầu(giá trị)
+  Trước(Pre): giá trị là giá trị muốn thêm vào danh sách
+  Sau(Post): giá trị đã được đặt ở đầu danh sách
+
+ n ← node(value)
+ n.next ← head
+ head ← n
+ if tail = ø
+   tail ← n
+ end
+end ChènVàoĐầu
+```
+
+### Tìm Kiếm (Search)
+```
+Chứa(đầu, giá trị)
+  Trước: đầu là nút đầu trong danh sách
+       giá trị là giá trị cần tìm kiếm
+  Sau: mục đó có thể ở trong danh sách liên kết, true; nếu không, là false
+  n ← head
+  while n != ø and n.value != value
+    n ← n.next
+  end while
+  if n = ø
+    return false
+  end if
+  return true
+end Contains
+```
+
+### Xóa (Delete)
+```
+Xóa(đầu, giá trị)
+  Trước: đầu là nút đầu trong danh sách
+       giá trị là giá trị cần xóa khỏi danh sách
+  Sau: giá trị đã được xóa khỏi danh sách, true; nếu không, là false
+  if head = ø
+    return false
+  end if
+  n ← head
+  if n.value = value
+    if head = tail
+      head ← ø
+      tail ← ø
+    else
+      head ← head.next
+    end if
+    return true
+  end if
+  while n.next != ø and n.next.value != value
+    n ← n.next
+  end while
+  if n.next != ø
+    if n.next = tail
+      tail ← n
+      tail.next = null
+    else
+      n.next ← n.next.next
+    end if
+    return true
+  end if
+  return false
+end Remove
+```
+
+### Duyệt(raverse)
+Duyệt(đầu)
+  Trước: đầu là nút đầu trong danh sách
+  Sau: các mục trong danh sách đã được duyệt
+  n ← head
+  while n != ø
+    yield n.value
+    n ← n.next
+  end while
+end Traverse
+
+### Duyệt Ngược (Traverse in Reverse)
+DuyệtNgược(đầu, đuôi)
+  Trước: đầu và đuôi thuộc cùng một danh sách
+  Sau: các mục trong danh sách đã được duyệt theo thứ tự ngược lại
+
+## Độ Phức Tạp
+
+### Độ Phức Tạp Thời Gian (Time Complexity)
+
+| Access    | Search    | Insertion | Deletion  |
+| :-------: | :-------: | :-------: | :-------: |
+| O(n)      | O(n)      | O(1)      | O(n)      |
+
+## Độ Phức Tạp Không Gian (Space Complexity)
+O(n)
+
+## Tham Khảo
+
+- [Wikipedia](https://en.wikipedia.org/wiki/Linked_list)
+- [YouTube](https://www.youtube.com/watch?v=njTh_OwMljA&index=2&t=1s&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
diff --git a/src/data-structures/queue/README.vi-VN.md b/src/data-structures/queue/README.vi-VN.md
new file mode 100644
index 0000000000..84b3bdbfa6
--- /dev/null
+++ b/src/data-structures/queue/README.vi-VN.md
@@ -0,0 +1,22 @@
+# Hàng đợi (Queue)
+
+_Đọc bằng ngôn ngữ khác:_
+[_简体中文_](README.zh-CN.md),
+[_Русский_](README.ru-RU.md),
+[_日本語_](README.ja-JP.md),
+[_Português_](README.pt-BR.md),
+[_한국어_](README.ko-KR.md),
+[_Українська_](README.uk-UA.md)
+
+Trong khoa học máy tính, một **hàng đợi** là một loại cụ thể của kiểu dữ liệu trừu tượng hoặc bộ sưu tập trong đó các phần tử trong bộ sưu tập được giữ theo thứ tự và nguyên tắc (hoặc chỉ) các hoạt động trên bộ sưu tập là thêm các phần tử vào vị trí cuối cùng, được gọi là đưa vào hàng đợi (enqueue), và loại bỏ các phần tử từ vị trí đầu tiên, được gọi là đưa ra khỏi hàng đợi (dequeue). Điều này khiến cho hàng đợi trở thành một cấu trúc dữ liệu First-In-First-Out (FIFO). Trong cấu trúc dữ liệu FIFO, phần tử đầu tiên được thêm vào hàng đợi sẽ là phần tử đầu tiên được loại bỏ. Điều này tương đương với yêu cầu rằng sau khi một phần tử mới được thêm vào, tất cả các phần tử đã được thêm vào trước đó phải được loại bỏ trước khi có thể loại bỏ phần tử mới. Thường thì cũng có thêm một hoạt động nhìn hay lấy phần đầu, trả về giá trị của phần tử đầu tiên mà không loại bỏ nó. Hàng đợi là một ví dụ về cấu trúc dữ liệu tuyến tính, hoặc trừu tượng hơn là một bộ sưu tập tuần tự.
+
+Hàng đợi FIFO (First-In-First-Out) có thể được biểu diễn như sau:
+
+![Queue](./images/queue.jpeg)
+
+*Made with [okso.app](https://okso.app)*
+
+## Tham Khảo
+
+- [Wikipedia](https://en.wikipedia.org/wiki/Queue_(abstract_data_type))
+- [YouTube](https://www.youtube.com/watch?v=wjI1WNcIntg&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8&index=3&)
diff --git a/src/data-structures/stack/README.vi-VN.md b/src/data-structures/stack/README.vi-VN.md
new file mode 100644
index 0000000000..f051f3201f
--- /dev/null
+++ b/src/data-structures/stack/README.vi-VN.md
@@ -0,0 +1,27 @@
+# Ngăn xếp (stack)
+
+_Đọc bằng ngôn ngữ khác:_
+[_简体中文_](README.zh-CN.md),
+[_Русский_](README.ru-RU.md),
+[_日本語_](README.ja-JP.md),
+[_Português_](README.pt-BR.md),
+[_한국어_](README.ko-KR.md),
+[_Español_](README.es-ES.md),
+[_Українська_](README.uk-UA.md)
+
+Trong khoa học máy tính, một ngăn xếp (stack) là một kiểu dữ liệu trừu tượng phục vụ như một bộ sưu tập các phần tử, với hai hoạt động chính:
+
+đẩy (push), thêm một phần tử vào bộ sưu tập, và
+lấy (pop), loại bỏ phần tử được thêm gần nhất mà chưa được loại bỏ.
+Thứ tự mà các phần tử được lấy ra khỏi ngăn xếp dẫn đến tên gọi thay thế của nó, là LIFO (last in, first out). Ngoài ra, một hoạt động nhìn có thể cung cấp quyền truy cập vào phần trên mà không làm thay đổi ngăn xếp. Tên "ngăn xếp" cho loại cấu trúc này đến từ sự tương tự với một bộ sưu tập các vật phẩm vật lý được xếp chồng lên nhau, điều này làm cho việc lấy một vật phẩm ra khỏi đỉnh của ngăn xếp dễ dàng, trong khi để đến được một vật phẩm sâu hơn trong ngăn xếp có thể đòi hỏi việc lấy ra nhiều vật phẩm khác trước đó.
+
+Biểu diễn đơn giản về thời gian chạy của một ngăn xếp với các hoạt động đẩy và lấy.
+
+![Stack](./images/stack.jpeg)
+
+*Made with [okso.app](https://okso.app)*
+
+## Tham Khảo
+
+- [Wikipedia](https://en.wikipedia.org/wiki/Linked_list)
+- [YouTube](https://www.youtube.com/watch?v=njTh_OwMljA&index=2&t=1s&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)

From 729bc4d78a2e7f15204bcc406a00605c6251c727 Mon Sep 17 00:00:00 2001
From: Vi Truong <103717482+vivitruong@users.noreply.github.com>
Date: Sat, 9 Mar 2024 10:09:21 -0600
Subject: [PATCH 245/264] Add Vietnamese translation for LinkedList (#1086)

* translate readme from linked list

* add linked list for viet sub

---------

Co-authored-by: Oleksii Trekhleb <trehleb@gmail.com>

From 8959566a36b3b7c28064da04c1522f3920956e22 Mon Sep 17 00:00:00 2001
From: "irene (Irene Tomaini)" <irene.tomaini@gmail.com>
Date: Sat, 9 Mar 2024 17:11:53 +0100
Subject: [PATCH 246/264] fix binary search typo (#1079)

Co-authored-by: Oleksii Trekhleb <trehleb@gmail.com>
---
 src/algorithms/search/binary-search/binarySearch.js | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/algorithms/search/binary-search/binarySearch.js b/src/algorithms/search/binary-search/binarySearch.js
index b9e18aab7b..5c8d48fbea 100644
--- a/src/algorithms/search/binary-search/binarySearch.js
+++ b/src/algorithms/search/binary-search/binarySearch.js
@@ -11,7 +11,7 @@ import Comparator from '../../../utils/comparator/Comparator';
 
 export default function binarySearch(sortedArray, seekElement, comparatorCallback) {
   // Let's create comparator from the comparatorCallback function.
-  // Comparator object will give us common comparison methods like equal() and lessThen().
+  // Comparator object will give us common comparison methods like equal() and lessThan().
   const comparator = new Comparator(comparatorCallback);
 
   // These two indices will contain current array (sub-array) boundaries.

From ac78353e3cbc73befb7db1ffd748764ec59d6a50 Mon Sep 17 00:00:00 2001
From: Mira Kwak <kk5448599@gmail.com>
Date: Sun, 10 Mar 2024 01:13:54 +0900
Subject: [PATCH 247/264] feat: added korean translation for trie (#1071)

Co-authored-by: Oleksii Trekhleb <trehleb@gmail.com>
---
 src/data-structures/trie/README.ko-KO.md | 19 +++++++++++++++++++
 src/data-structures/trie/README.md       |  3 ++-
 2 files changed, 21 insertions(+), 1 deletion(-)
 create mode 100644 src/data-structures/trie/README.ko-KO.md

diff --git a/src/data-structures/trie/README.ko-KO.md b/src/data-structures/trie/README.ko-KO.md
new file mode 100644
index 0000000000..e57142ece4
--- /dev/null
+++ b/src/data-structures/trie/README.ko-KO.md
@@ -0,0 +1,19 @@
+# Trie
+
+_Read this in other languages:_
+[_简体中文_](README.zh-CN.md),
+[_Русский_](README.ru-RU.md),
+[_Português_](README.pt-BR.md),
+[_Українська_](README.uk-UA.md),
+[_한국어_](README.ko-KO.md)
+
+컴퓨터 과학에서 **트라이**는 디지털 트리라고도 불리며 때로는 기수 트리 또는 접두사 트리(접두사로 검색할 수 있기 때문에)라고도 불리며 일종의 검색 트리입니다. 키가 보통 문자열인 동적 집합 또는 연관 배열을 저장하는 데 사용되는 순서가 지정된 트리 데이터 구조입니다. 이진 검색 트리와 달리 트리의 어떤 노드도 해당 노드와 연결된 키를 저장하지 않으며 대신 트리의 위치가 해당 노드와 연결된 키를 정의합니다. 노드의 모든 하위 항목은 해당 노드와 연결된 문자열의 공통 접두사를 가지며 루트는 빈 문자열과 연결됩니다. 값은 모든 노드와 반드시 연결되지는 않습니다. 오히려 값은 나뭇잎과 관심 있는 키에 해당하는 일부 내부 노드에만 연결되는 경향이 있습니다. 접두사 트리의 공간에 최적화된 표현은 콤팩트 접두사 트리를 참조하십시오.
+
+![Trie](./images/trie.jpg)
+
+_Made with [okso.app](https://okso.app)_
+
+## 참조
+
+- [Wikipedia](<https://ko.wikipedia.org/wiki/%ED%8A%B8%EB%9D%BC%EC%9D%B4_(%EC%BB%B4%ED%93%A8%ED%8C%85)>)
+- [YouTube](https://www.youtube.com/watch?v=zIjfhVPRZCg&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8&index=7&t=0s)
diff --git a/src/data-structures/trie/README.md b/src/data-structures/trie/README.md
index 2082fed903..b3bba5de1e 100644
--- a/src/data-structures/trie/README.md
+++ b/src/data-structures/trie/README.md
@@ -4,7 +4,8 @@ _Read this in other languages:_
 [_简体中文_](README.zh-CN.md),
 [_Русский_](README.ru-RU.md),
 [_Português_](README.pt-BR.md),
-[_Українська_](README.uk-UA.md)
+[_Українська_](README.uk-UA.md),
+[_한국어_](README.ko-KO.md)
 
 In computer science, a **trie**, also called digital tree and sometimes
 radix tree or prefix tree (as they can be searched by prefixes),

From 2c67b48c21eed86aafbb4d09065ffe391b4fc7e4 Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Sat, 9 Mar 2024 17:15:19 +0100
Subject: [PATCH 248/264] Ad hoc versions of MinHeap, MaxHeap, and DisjointSet
 (#1117)

* Add DisjointSetMinimalistic

* Add MinHeapMinimalistic and MaxHeapMinimalistic

* Rename minimalistic to adhoc

* Update README
---
 .../disjoint-set/DisjointSetAdhoc.js          |  78 ++++++++++++
 src/data-structures/disjoint-set/README.md    |   5 +
 .../__test__/DisjointSetAdhoc.test.js         |  50 ++++++++
 src/data-structures/heap/MaxHeapAdhoc.js      | 115 +++++++++++++++++
 src/data-structures/heap/MinHeapAdhoc.js      | 117 ++++++++++++++++++
 src/data-structures/heap/README.md            |   5 +
 .../heap/__test__/MaxHeapAdhoc.test.js        |  91 ++++++++++++++
 .../heap/__test__/MinHeapAdhoc.test.js        |  91 ++++++++++++++
 8 files changed, 552 insertions(+)
 create mode 100644 src/data-structures/disjoint-set/DisjointSetAdhoc.js
 create mode 100644 src/data-structures/disjoint-set/__test__/DisjointSetAdhoc.test.js
 create mode 100644 src/data-structures/heap/MaxHeapAdhoc.js
 create mode 100644 src/data-structures/heap/MinHeapAdhoc.js
 create mode 100644 src/data-structures/heap/__test__/MaxHeapAdhoc.test.js
 create mode 100644 src/data-structures/heap/__test__/MinHeapAdhoc.test.js

diff --git a/src/data-structures/disjoint-set/DisjointSetAdhoc.js b/src/data-structures/disjoint-set/DisjointSetAdhoc.js
new file mode 100644
index 0000000000..9653418042
--- /dev/null
+++ b/src/data-structures/disjoint-set/DisjointSetAdhoc.js
@@ -0,0 +1,78 @@
+/**
+ * The minimalistic (ad hoc) version of a DisjointSet (or a UnionFind) data structure
+ * that doesn't have external dependencies and that is easy to copy-paste and
+ * use during the coding interview if allowed by the interviewer (since many
+ * data structures in JS are missing).
+ *
+ * Time Complexity:
+ *
+ * - Constructor: O(N)
+ * - Find: O(α(N))
+ * - Union: O(α(N))
+ * - Connected: O(α(N))
+ *
+ * Where N is the number of vertices in the graph.
+ * α refers to the Inverse Ackermann function.
+ * In practice, we assume it's a constant.
+ * In other words, O(α(N)) is regarded as O(1) on average.
+ */
+class DisjointSetAdhoc {
+  /**
+   * Initializes the set of specified size.
+   * @param {number} size
+   */
+  constructor(size) {
+    // The index of a cell is an id of the node in a set.
+    // The value of a cell is an id (index) of the root node.
+    // By default, the node is a parent of itself.
+    this.roots = new Array(size).fill(0).map((_, i) => i);
+
+    // Using the heights array to record the height of each node.
+    // By default each node has a height of 1 because it has no children.
+    this.heights = new Array(size).fill(1);
+  }
+
+  /**
+   * Finds the root of node `a`
+   * @param {number} a
+   * @returns {number}
+   */
+  find(a) {
+    if (a === this.roots[a]) return a;
+    this.roots[a] = this.find(this.roots[a]);
+    return this.roots[a];
+  }
+
+  /**
+   * Joins the `a` and `b` nodes into same set.
+   * @param {number} a
+   * @param {number} b
+   * @returns {number}
+   */
+  union(a, b) {
+    const aRoot = this.find(a);
+    const bRoot = this.find(b);
+
+    if (aRoot === bRoot) return;
+
+    if (this.heights[aRoot] > this.heights[bRoot]) {
+      this.roots[bRoot] = aRoot;
+    } else if (this.heights[aRoot] < this.heights[bRoot]) {
+      this.roots[aRoot] = bRoot;
+    } else {
+      this.roots[bRoot] = aRoot;
+      this.heights[aRoot] += 1;
+    }
+  }
+
+  /**
+   * Checks if `a` and `b` belong to the same set.
+   * @param {number} a
+   * @param {number} b
+   */
+  connected(a, b) {
+    return this.find(a) === this.find(b);
+  }
+}
+
+export default DisjointSetAdhoc;
diff --git a/src/data-structures/disjoint-set/README.md b/src/data-structures/disjoint-set/README.md
index 44bcfa2769..772f68191b 100644
--- a/src/data-structures/disjoint-set/README.md
+++ b/src/data-structures/disjoint-set/README.md
@@ -19,6 +19,11 @@ _MakeSet_ creates 8 singletons.
 
 After some operations of _Union_, some sets are grouped together.
 
+## Implementation
+
+- [DisjointSet.js](./DisjointSet.js)
+- [DisjointSetAdhoc.js](./DisjointSetAdhoc.js) - The minimalistic (ad hoc) version of a DisjointSet (or a UnionFind) data structure that doesn't have external dependencies and that is easy to copy-paste and use during the coding interview if allowed by the interviewer (since many data structures in JS are missing).
+
 ## References
 
 - [Wikipedia](https://en.wikipedia.org/wiki/Disjoint-set_data_structure)
diff --git a/src/data-structures/disjoint-set/__test__/DisjointSetAdhoc.test.js b/src/data-structures/disjoint-set/__test__/DisjointSetAdhoc.test.js
new file mode 100644
index 0000000000..f7be0fcde9
--- /dev/null
+++ b/src/data-structures/disjoint-set/__test__/DisjointSetAdhoc.test.js
@@ -0,0 +1,50 @@
+import DisjointSetAdhoc from '../DisjointSetAdhoc';
+
+describe('DisjointSetAdhoc', () => {
+  it('should create unions and find connected elements', () => {
+    const set = new DisjointSetAdhoc(10);
+
+    // 1-2-5-6-7 3-8-9 4
+    set.union(1, 2);
+    set.union(2, 5);
+    set.union(5, 6);
+    set.union(6, 7);
+
+    set.union(3, 8);
+    set.union(8, 9);
+
+    expect(set.connected(1, 5)).toBe(true);
+    expect(set.connected(5, 7)).toBe(true);
+    expect(set.connected(3, 8)).toBe(true);
+
+    expect(set.connected(4, 9)).toBe(false);
+    expect(set.connected(4, 7)).toBe(false);
+
+    // 1-2-5-6-7 3-8-9-4
+    set.union(9, 4);
+
+    expect(set.connected(4, 9)).toBe(true);
+    expect(set.connected(4, 3)).toBe(true);
+    expect(set.connected(8, 4)).toBe(true);
+
+    expect(set.connected(8, 7)).toBe(false);
+    expect(set.connected(2, 3)).toBe(false);
+  });
+
+  it('should keep the height of the tree small', () => {
+    const set = new DisjointSetAdhoc(10);
+
+    // 1-2-6-7-9 1 3 4 5
+    set.union(7, 6);
+    set.union(1, 2);
+    set.union(2, 6);
+    set.union(1, 7);
+    set.union(9, 1);
+
+    expect(set.connected(1, 7)).toBe(true);
+    expect(set.connected(6, 9)).toBe(true);
+    expect(set.connected(4, 9)).toBe(false);
+
+    expect(Math.max(...set.heights)).toBe(3);
+  });
+});
diff --git a/src/data-structures/heap/MaxHeapAdhoc.js b/src/data-structures/heap/MaxHeapAdhoc.js
new file mode 100644
index 0000000000..b9d69c59e0
--- /dev/null
+++ b/src/data-structures/heap/MaxHeapAdhoc.js
@@ -0,0 +1,115 @@
+/**
+ * The minimalistic (ad hoc) version of a MaxHeap data structure that doesn't have
+ * external dependencies and that is easy to copy-paste and use during the
+ * coding interview if allowed by the interviewer (since many data
+ * structures in JS are missing).
+ */
+class MaxHeapAdhoc {
+  constructor(heap = []) {
+    this.heap = [];
+    heap.forEach(this.add);
+  }
+
+  add(num) {
+    this.heap.push(num);
+    this.heapifyUp();
+  }
+
+  peek() {
+    return this.heap[0];
+  }
+
+  poll() {
+    if (this.heap.length === 0) return undefined;
+    const top = this.heap[0];
+    this.heap[0] = this.heap[this.heap.length - 1];
+    this.heap.pop();
+    this.heapifyDown();
+    return top;
+  }
+
+  isEmpty() {
+    return this.heap.length === 0;
+  }
+
+  toString() {
+    return this.heap.join(',');
+  }
+
+  heapifyUp() {
+    let nodeIndex = this.heap.length - 1;
+    while (nodeIndex > 0) {
+      const parentIndex = this.getParentIndex(nodeIndex);
+      if (this.heap[parentIndex] >= this.heap[nodeIndex]) break;
+      this.swap(parentIndex, nodeIndex);
+      nodeIndex = parentIndex;
+    }
+  }
+
+  heapifyDown() {
+    let nodeIndex = 0;
+
+    while (
+      (
+        this.hasLeftChild(nodeIndex) && this.heap[nodeIndex] < this.leftChild(nodeIndex)
+      )
+      || (
+        this.hasRightChild(nodeIndex) && this.heap[nodeIndex] < this.rightChild(nodeIndex)
+      )
+    ) {
+      const leftIndex = this.getLeftChildIndex(nodeIndex);
+      const rightIndex = this.getRightChildIndex(nodeIndex);
+      const left = this.leftChild(nodeIndex);
+      const right = this.rightChild(nodeIndex);
+
+      if (this.hasLeftChild(nodeIndex) && this.hasRightChild(nodeIndex)) {
+        if (left >= right) {
+          this.swap(leftIndex, nodeIndex);
+          nodeIndex = leftIndex;
+        } else {
+          this.swap(rightIndex, nodeIndex);
+          nodeIndex = rightIndex;
+        }
+      } else if (this.hasLeftChild(nodeIndex)) {
+        this.swap(leftIndex, nodeIndex);
+        nodeIndex = leftIndex;
+      }
+    }
+  }
+
+  getLeftChildIndex(parentIndex) {
+    return (2 * parentIndex) + 1;
+  }
+
+  getRightChildIndex(parentIndex) {
+    return (2 * parentIndex) + 2;
+  }
+
+  getParentIndex(childIndex) {
+    return Math.floor((childIndex - 1) / 2);
+  }
+
+  hasLeftChild(parentIndex) {
+    return this.getLeftChildIndex(parentIndex) < this.heap.length;
+  }
+
+  hasRightChild(parentIndex) {
+    return this.getRightChildIndex(parentIndex) < this.heap.length;
+  }
+
+  leftChild(parentIndex) {
+    return this.heap[this.getLeftChildIndex(parentIndex)];
+  }
+
+  rightChild(parentIndex) {
+    return this.heap[this.getRightChildIndex(parentIndex)];
+  }
+
+  swap(indexOne, indexTwo) {
+    const tmp = this.heap[indexTwo];
+    this.heap[indexTwo] = this.heap[indexOne];
+    this.heap[indexOne] = tmp;
+  }
+}
+
+export default MaxHeapAdhoc;
diff --git a/src/data-structures/heap/MinHeapAdhoc.js b/src/data-structures/heap/MinHeapAdhoc.js
new file mode 100644
index 0000000000..c70692f3de
--- /dev/null
+++ b/src/data-structures/heap/MinHeapAdhoc.js
@@ -0,0 +1,117 @@
+/**
+ * The minimalistic (ad hoc) version of a MinHeap data structure that doesn't have
+ * external dependencies and that is easy to copy-paste and use during the
+ * coding interview if allowed by the interviewer (since many data
+ * structures in JS are missing).
+ */
+class MinHeapAdhoc {
+  constructor(heap = []) {
+    this.heap = [];
+    heap.forEach(this.add);
+  }
+
+  add(num) {
+    this.heap.push(num);
+    this.heapifyUp();
+  }
+
+  peek() {
+    return this.heap[0];
+  }
+
+  poll() {
+    if (this.heap.length === 0) return undefined;
+    const top = this.heap[0];
+    this.heap[0] = this.heap[this.heap.length - 1];
+    this.heap.pop();
+    this.heapifyDown();
+    return top;
+  }
+
+  isEmpty() {
+    return this.heap.length === 0;
+  }
+
+  toString() {
+    return this.heap.join(',');
+  }
+
+  heapifyUp() {
+    let nodeIndex = this.heap.length - 1;
+    while (nodeIndex > 0) {
+      const parentIndex = this.getParentIndex(nodeIndex);
+      if (this.heap[parentIndex] <= this.heap[nodeIndex]) break;
+      this.swap(parentIndex, nodeIndex);
+      nodeIndex = parentIndex;
+    }
+  }
+
+  heapifyDown() {
+    let nodeIndex = 0;
+
+    while (
+      (
+        this.hasLeftChild(nodeIndex)
+        && this.heap[nodeIndex] > this.leftChild(nodeIndex)
+      )
+      || (
+        this.hasRightChild(nodeIndex)
+        && this.heap[nodeIndex] > this.rightChild(nodeIndex)
+      )
+    ) {
+      const leftIndex = this.getLeftChildIndex(nodeIndex);
+      const rightIndex = this.getRightChildIndex(nodeIndex);
+      const left = this.leftChild(nodeIndex);
+      const right = this.rightChild(nodeIndex);
+
+      if (this.hasLeftChild(nodeIndex) && this.hasRightChild(nodeIndex)) {
+        if (left <= right) {
+          this.swap(leftIndex, nodeIndex);
+          nodeIndex = leftIndex;
+        } else {
+          this.swap(rightIndex, nodeIndex);
+          nodeIndex = rightIndex;
+        }
+      } else if (this.hasLeftChild(nodeIndex)) {
+        this.swap(leftIndex, nodeIndex);
+        nodeIndex = leftIndex;
+      }
+    }
+  }
+
+  getLeftChildIndex(parentIndex) {
+    return 2 * parentIndex + 1;
+  }
+
+  getRightChildIndex(parentIndex) {
+    return 2 * parentIndex + 2;
+  }
+
+  getParentIndex(childIndex) {
+    return Math.floor((childIndex - 1) / 2);
+  }
+
+  hasLeftChild(parentIndex) {
+    return this.getLeftChildIndex(parentIndex) < this.heap.length;
+  }
+
+  hasRightChild(parentIndex) {
+    return this.getRightChildIndex(parentIndex) < this.heap.length;
+  }
+
+  leftChild(parentIndex) {
+    return this.heap[this.getLeftChildIndex(parentIndex)];
+  }
+
+  rightChild(parentIndex) {
+    return this.heap[this.getRightChildIndex(parentIndex)];
+  }
+
+  swap(indexOne, indexTwo) {
+    const tmp = this.heap[indexTwo];
+    this.heap[indexTwo] = this.heap[indexOne];
+    this.heap[indexOne] = tmp;
+  }
+}
+
+export default MinHeapAdhoc;
diff --git a/src/data-structures/heap/README.md b/src/data-structures/heap/README.md
index 824d646043..392c5c96bc 100644
--- a/src/data-structures/heap/README.md
+++ b/src/data-structures/heap/README.md
@@ -58,6 +58,11 @@ Where:
 
 > In this repository, the [MaxHeap.js](./MaxHeap.js) and [MinHeap.js](./MinHeap.js) are examples of the **Binary** heap.
 
+## Implementation
+
+- [MaxHeap.js](./MaxHeap.js) and [MinHeap.js](./MinHeap.js)
+- [MaxHeapAdhoc.js](./MaxHeapAdhoc.js) and [MinHeapAdhoc.js](./MinHeapAdhoc.js) - The minimalistic (ad hoc) version of a MinHeap/MaxHeap data structure that doesn't have external dependencies and that is easy to copy-paste and use during the coding interview if allowed by the interviewer (since many data structures in JS are missing).
+
 ## References
 
 - [Wikipedia](https://en.wikipedia.org/wiki/Heap_(data_structure))
diff --git a/src/data-structures/heap/__test__/MaxHeapAdhoc.test.js b/src/data-structures/heap/__test__/MaxHeapAdhoc.test.js
new file mode 100644
index 0000000000..0217a98ddf
--- /dev/null
+++ b/src/data-structures/heap/__test__/MaxHeapAdhoc.test.js
@@ -0,0 +1,91 @@
+import MaxHeap from '../MaxHeapAdhoc';
+
+describe('MaxHeapAdhoc', () => {
+  it('should create an empty max heap', () => {
+    const maxHeap = new MaxHeap();
+
+    expect(maxHeap).toBeDefined();
+    expect(maxHeap.peek()).toBe(undefined);
+    expect(maxHeap.isEmpty()).toBe(true);
+  });
+
+  it('should add items to the heap and heapify it up', () => {
+    const maxHeap = new MaxHeap();
+
+    maxHeap.add(5);
+    expect(maxHeap.isEmpty()).toBe(false);
+    expect(maxHeap.peek()).toBe(5);
+    expect(maxHeap.toString()).toBe('5');
+
+    maxHeap.add(3);
+    expect(maxHeap.peek()).toBe(5);
+    expect(maxHeap.toString()).toBe('5,3');
+
+    maxHeap.add(10);
+    expect(maxHeap.peek()).toBe(10);
+    expect(maxHeap.toString()).toBe('10,3,5');
+
+    maxHeap.add(1);
+    expect(maxHeap.peek()).toBe(10);
+    expect(maxHeap.toString()).toBe('10,3,5,1');
+
+    maxHeap.add(1);
+    expect(maxHeap.peek()).toBe(10);
+    expect(maxHeap.toString()).toBe('10,3,5,1,1');
+
+    expect(maxHeap.poll()).toBe(10);
+    expect(maxHeap.toString()).toBe('5,3,1,1');
+
+    expect(maxHeap.poll()).toBe(5);
+    expect(maxHeap.toString()).toBe('3,1,1');
+
+    expect(maxHeap.poll()).toBe(3);
+    expect(maxHeap.toString()).toBe('1,1');
+  });
+
+  it('should poll items from the heap and heapify it down', () => {
+    const maxHeap = new MaxHeap();
+
+    maxHeap.add(5);
+    maxHeap.add(3);
+    maxHeap.add(10);
+    maxHeap.add(11);
+    maxHeap.add(1);
+
+    expect(maxHeap.toString()).toBe('11,10,5,3,1');
+
+    expect(maxHeap.poll()).toBe(11);
+    expect(maxHeap.toString()).toBe('10,3,5,1');
+
+    expect(maxHeap.poll()).toBe(10);
+    expect(maxHeap.toString()).toBe('5,3,1');
+
+    expect(maxHeap.poll()).toBe(5);
+    expect(maxHeap.toString()).toBe('3,1');
+
+    expect(maxHeap.poll()).toBe(3);
+    expect(maxHeap.toString()).toBe('1');
+
+    expect(maxHeap.poll()).toBe(1);
+    expect(maxHeap.toString()).toBe('');
+
+    expect(maxHeap.poll()).toBe(undefined);
+    expect(maxHeap.toString()).toBe('');
+  });
+
+  it('should heapify down through the right branch as well', () => {
+    const maxHeap = new MaxHeap();
+
+    maxHeap.add(3);
+    maxHeap.add(12);
+    maxHeap.add(10);
+
+    expect(maxHeap.toString()).toBe('12,3,10');
+
+    maxHeap.add(11);
+    expect(maxHeap.toString()).toBe('12,11,10,3');
+
+    expect(maxHeap.poll()).toBe(12);
+    expect(maxHeap.toString()).toBe('11,3,10');
+  });
+});
diff --git a/src/data-structures/heap/__test__/MinHeapAdhoc.test.js b/src/data-structures/heap/__test__/MinHeapAdhoc.test.js
new file mode 100644
index 0000000000..766b307ff0
--- /dev/null
+++ b/src/data-structures/heap/__test__/MinHeapAdhoc.test.js
@@ -0,0 +1,91 @@
+import MinHeapAdhoc from '../MinHeapAdhoc';
+
+describe('MinHeapAdhoc', () => {
+  it('should create an empty min heap', () => {
+    const minHeap = new MinHeapAdhoc();
+
+    expect(minHeap).toBeDefined();
+    expect(minHeap.peek()).toBe(undefined);
+    expect(minHeap.isEmpty()).toBe(true);
+  });
+
+  it('should add items to the heap and heapify it up', () => {
+    const minHeap = new MinHeapAdhoc();
+
+    minHeap.add(5);
+    expect(minHeap.isEmpty()).toBe(false);
+    expect(minHeap.peek()).toBe(5);
+    expect(minHeap.toString()).toBe('5');
+
+    minHeap.add(3);
+    expect(minHeap.peek()).toBe(3);
+    expect(minHeap.toString()).toBe('3,5');
+
+    minHeap.add(10);
+    expect(minHeap.peek()).toBe(3);
+    expect(minHeap.toString()).toBe('3,5,10');
+
+    minHeap.add(1);
+    expect(minHeap.peek()).toBe(1);
+    expect(minHeap.toString()).toBe('1,3,10,5');
+
+    minHeap.add(1);
+    expect(minHeap.peek()).toBe(1);
+    expect(minHeap.toString()).toBe('1,1,10,5,3');
+
+    expect(minHeap.poll()).toBe(1);
+    expect(minHeap.toString()).toBe('1,3,10,5');
+
+    expect(minHeap.poll()).toBe(1);
+    expect(minHeap.toString()).toBe('3,5,10');
+
+    expect(minHeap.poll()).toBe(3);
+    expect(minHeap.toString()).toBe('5,10');
+  });
+
+  it('should poll items from the heap and heapify it down', () => {
+    const minHeap = new MinHeapAdhoc();
+
+    minHeap.add(5);
+    minHeap.add(3);
+    minHeap.add(10);
+    minHeap.add(11);
+    minHeap.add(1);
+
+    expect(minHeap.toString()).toBe('1,3,10,11,5');
+
+    expect(minHeap.poll()).toBe(1);
+    expect(minHeap.toString()).toBe('3,5,10,11');
+
+    expect(minHeap.poll()).toBe(3);
+    expect(minHeap.toString()).toBe('5,11,10');
+
+    expect(minHeap.poll()).toBe(5);
+    expect(minHeap.toString()).toBe('10,11');
+
+    expect(minHeap.poll()).toBe(10);
+    expect(minHeap.toString()).toBe('11');
+
+    expect(minHeap.poll()).toBe(11);
+    expect(minHeap.toString()).toBe('');
+
+    expect(minHeap.poll()).toBe(undefined);
+    expect(minHeap.toString()).toBe('');
+  });
+
+  it('should heapify down through the right branch as well', () => {
+    const minHeap = new MinHeapAdhoc();
+
+    minHeap.add(3);
+    minHeap.add(12);
+    minHeap.add(10);
+
+    expect(minHeap.toString()).toBe('3,12,10');
+
+    minHeap.add(11);
+    expect(minHeap.toString()).toBe('3,11,10,12');
+
+    expect(minHeap.poll()).toBe(3);
+    expect(minHeap.toString()).toBe('10,11,12');
+  });
+});

From e5b5944c6849389bbfc39f476fa7a1f97d8ce4c6 Mon Sep 17 00:00:00 2001
From: Alexander Cyon <Sajjon@users.noreply.github.com>
Date: Sat, 13 Jul 2024 20:56:39 +0200
Subject: [PATCH 249/264] Fix four typos (#1139)

---
 .../uncategorized/best-time-to-buy-sell-stocks/README.md        | 2 +-
 src/algorithms/uncategorized/n-queens/README.md                 | 2 +-
 src/data-structures/bloom-filter/README.md                      | 2 +-
 src/data-structures/heap/Heap.js                                | 2 +-
 4 files changed, 4 insertions(+), 4 deletions(-)

diff --git a/src/algorithms/uncategorized/best-time-to-buy-sell-stocks/README.md b/src/algorithms/uncategorized/best-time-to-buy-sell-stocks/README.md
index 9446993e98..975eade3a4 100644
--- a/src/algorithms/uncategorized/best-time-to-buy-sell-stocks/README.md
+++ b/src/algorithms/uncategorized/best-time-to-buy-sell-stocks/README.md
@@ -46,7 +46,7 @@ Let's say we have an array of prices `[7, 6, 4, 3, 1]` and we're on the _1st_ da
 1. _Option 1: Keep the money_ → profit would equal to the profit from buying/selling the rest of the stocks → `keepProfit = profit([6, 4, 3, 1])`.
 2. _Option 2: Buy/sell at current price_ → profit in this case would equal to the profit from buying/selling the rest of the stocks plus (or minus, depending on whether we're selling or buying) the current stock price → `buySellProfit = -7 + profit([6, 4, 3, 1])`.
 
-The overall profit would be equal to → `overalProfit = Max(keepProfit, buySellProfit)`.
+The overall profit would be equal to → `overallProfit = Max(keepProfit, buySellProfit)`.
 
 As you can see the `profit([6, 4, 3, 1])` task is being solved in the same recursive manner.
 
diff --git a/src/algorithms/uncategorized/n-queens/README.md b/src/algorithms/uncategorized/n-queens/README.md
index 077e26d73d..399256768e 100644
--- a/src/algorithms/uncategorized/n-queens/README.md
+++ b/src/algorithms/uncategorized/n-queens/README.md
@@ -59,7 +59,7 @@ and return false.
         queen here leads to a solution.
     b) If placing queen in [row, column] leads to a solution then return 
         true.
-    c) If placing queen doesn't lead to a solution then umark this [row, 
+    c) If placing queen doesn't lead to a solution then unmark this [row, 
         column] (Backtrack) and go to step (a) to try other rows.
 3) If all rows have been tried and nothing worked, return false to trigger 
     backtracking.
diff --git a/src/data-structures/bloom-filter/README.md b/src/data-structures/bloom-filter/README.md
index e156310cb4..7880a7f7be 100644
--- a/src/data-structures/bloom-filter/README.md
+++ b/src/data-structures/bloom-filter/README.md
@@ -93,7 +93,7 @@ three factors: the size of the bloom filter, the
 number of hash functions we use, and the number
 of items that have been inserted into the filter.
 
-The formula to calculate probablity of a false positive is:
+The formula to calculate probability of a false positive is:
 
 ( 1 - e <sup>-kn/m</sup> ) <sup>k</sup>
 
diff --git a/src/data-structures/heap/Heap.js b/src/data-structures/heap/Heap.js
index 45dfcfa267..b978739ec8 100644
--- a/src/data-structures/heap/Heap.js
+++ b/src/data-structures/heap/Heap.js
@@ -279,7 +279,7 @@ export default class Heap {
   /* istanbul ignore next */
   pairIsInCorrectOrder(firstElement, secondElement) {
     throw new Error(`
-      You have to implement heap pair comparision method
+      You have to implement heap pair comparison method
       for ${firstElement} and ${secondElement} values.
     `);
   }

From 9046d80bdb9e5c2e65c87369575a3e47e9c01978 Mon Sep 17 00:00:00 2001
From: Mahdi Azarboon <21277296+azarboon@users.noreply.github.com>
Date: Sun, 14 Jul 2024 02:58:45 +0800
Subject: [PATCH 250/264] Update README.md (#1141)

Before diving into any of the data structures, readers should be reminded of two fundamental laws in software architecture:

1.Everything is a trade-ff
2."Why is more important than the how"

So, readers face the nuances and reality of these data structures from the beginning. These two laws are coined by two thought leaders in software architecture: Mark Richards and Neal Ford. They have explained these two laws in various conference talks and books. For example, here you can read about these two laws here:

https://www.infoq.com/podcasts/software-architecture-hard-parts/


Also, here is a book for reference:
https://a.co/d/fKOodW9

Co-authored-by: Oleksii Trekhleb <3000285+trekhleb@users.noreply.github.com>
---
 README.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/README.md b/README.md
index e06cfb9075..8fa631425d 100644
--- a/README.md
+++ b/README.md
@@ -48,6 +48,8 @@ be accessed and modified efficiently. More precisely, a data structure is a coll
 values, the relationships among them, and the functions or operations that can be applied to
 the data.
 
+Remember that each data has its own trade-offs. And you need to pay attention more to why you're choosing a certain data structure than to how to implement it.
+
 `B` - Beginner, `A` - Advanced
 
 * `B` [Linked List](src/data-structures/linked-list)

From d7a41a64610db25caa4525d61e9f8545fcb491c5 Mon Sep 17 00:00:00 2001
From: Qudratillo <80141037+softXengineer@users.noreply.github.com>
Date: Sun, 14 Jul 2024 00:09:06 +0500
Subject: [PATCH 251/264] feat: added uzbek language (#1082)

Co-authored-by: Oleksii Trekhleb <3000285+trekhleb@users.noreply.github.com>
---
 README.ar-AR.md |   3 +-
 README.de-DE.md |   3 +-
 README.es-ES.md |   3 +-
 README.fr-FR.md |   3 +-
 README.id-ID.md |   3 +-
 README.it-IT.md |   3 +-
 README.ja-JP.md |   3 +-
 README.ko-KR.md |   3 +-
 README.md       |   3 +-
 README.pl-PL.md |   3 +-
 README.pt-BR.md |   3 +-
 README.ru-RU.md |   3 +-
 README.tr-TR.md |   3 +-
 README.uk-UA.md |   3 +-
 README.uz-UZ.md | 358 ++++++++++++++++++++++++++++++++++++++++++++++++
 README.zh-CN.md |   3 +-
 README.zh-TW.md |   3 +-
 17 files changed, 390 insertions(+), 16 deletions(-)
 create mode 100644 README.uz-UZ.md

diff --git a/README.ar-AR.md b/README.ar-AR.md
index cbcfd02409..fedd29c0e5 100644
--- a/README.ar-AR.md
+++ b/README.ar-AR.md
@@ -23,7 +23,8 @@ _اقرأ هذا في لغات أخرى:_
 [_Türk_](README.tr-TR.md),
 [_Italiana_](README.it-IT.md),
 [_Tiếng Việt_](README.vi-VN.md),
-[_Deutsch_](README.de-DE.md)
+[_Deutsch_](README.de-DE.md),
+[_Uzbek_](README.uz-UZ.md)
 
  ☝ ملاحضة هذا المشروع مخصص للاستخدام لأغراض التعلم والبحث
 فقط ، و ** ليست ** معدة للاستخدام في **الإنتاج**
diff --git a/README.de-DE.md b/README.de-DE.md
index b34ad3563f..9663f7b06b 100644
--- a/README.de-DE.md
+++ b/README.de-DE.md
@@ -24,7 +24,8 @@ _Lies dies in anderen Sprachen:_
 [_Italiana_](README.it-IT.md),
 [_Bahasa Indonesia_](README.id-ID.md),
 [_Українська_](README.uk-UA.md),
-[_Arabic_](README.ar-AR.md)
+[_Arabic_](README.ar-AR.md),
+[_Uzbek_](README.uz-UZ.md)
 
 _☝ Beachte, dass dieses Projekt nur für Lern- und Forschungszwecke gedacht ist und **nicht** für den produktiven Einsatz verwendet werden soll_
 
diff --git a/README.es-ES.md b/README.es-ES.md
index d79baf6022..24d1990a41 100644
--- a/README.es-ES.md
+++ b/README.es-ES.md
@@ -25,7 +25,8 @@ _Léelo en otros idiomas:_
 [_Українська_](README.uk-UA.md),
 [_Arabic_](README.ar-AR.md),
 [_Tiếng Việt_](README.vi-VN.md),
-[_Deutsch_](README.de-DE.md)
+[_Deutsch_](README.de-DE.md),
+[_Uzbek_](README.uz-UZ.md)
 
 *☝ Nótese que este proyecto está pensado con fines de aprendizaje e investigación,
 y **no** para ser usado en producción.*
diff --git a/README.fr-FR.md b/README.fr-FR.md
index 469a4f52d9..be8258befd 100644
--- a/README.fr-FR.md
+++ b/README.fr-FR.md
@@ -26,7 +26,8 @@ _Lisez ceci dans d'autres langues:_
 [_Українська_](README.uk-UA.md),
 [_Arabic_](README.ar-AR.md),
 [_Tiếng Việt_](README.vi-VN.md),
-[_Deutsch_](README.de-DE.md)
+[_Deutsch_](README.de-DE.md),
+[_Uzbek_](README.uz-UZ.md)
 
 ## Data Structures
 
diff --git a/README.id-ID.md b/README.id-ID.md
index b204f2a8f8..2f4310fee3 100644
--- a/README.id-ID.md
+++ b/README.id-ID.md
@@ -23,7 +23,8 @@ _Baca ini dalam bahasa yang lain:_
 [_Українська_](README.uk-UA.md),
 [_Arabic_](README.ar-AR.md),
 [_Tiếng Việt_](README.vi-VN.md),
-[_Deutsch_](README.de-DE.md)
+[_Deutsch_](README.de-DE.md),
+[_Uzbek_](README.uz-UZ.md)
 
 _☝ Perhatikan bahwa proyek ini hanya dimaksudkan untuk tujuan pembelajaran dan riset, dan **tidak** dimaksudkan untuk digunakan sebagai produksi._
 
diff --git a/README.it-IT.md b/README.it-IT.md
index 6ac47fa5bc..a86c52cfbb 100644
--- a/README.it-IT.md
+++ b/README.it-IT.md
@@ -22,7 +22,8 @@ _Leggilo in altre lingue:_
 [_Українська_](README.uk-UA.md),
 [_Arabic_](README.ar-AR.md),
 [_Tiếng Việt_](README.vi-VN.md),
-[_Deutsch_](README.de-DE.md)
+[_Deutsch_](README.de-DE.md),
+[_Uzbek_](README.uz-UZ.md)
 
 *☝ Si noti che questo progetto è destinato ad essere utilizzato solo per l'apprendimento e la ricerca e non è destinato ad essere utilizzato per il commercio.*
 
diff --git a/README.ja-JP.md b/README.ja-JP.md
index e10bb94083..6e3a8b8192 100644
--- a/README.ja-JP.md
+++ b/README.ja-JP.md
@@ -25,7 +25,8 @@ _Read this in other languages:_
 [_Українська_](README.uk-UA.md),
 [_Arabic_](README.ar-AR.md),
 [_Tiếng Việt_](README.vi-VN.md),
-[_Deutsch_](README.de-DE.md)
+[_Deutsch_](README.de-DE.md),
+[_Uzbek_](README.uz-UZ.md)
 
 ## データ構造
 
diff --git a/README.ko-KR.md b/README.ko-KR.md
index b48c43aa56..9aac387e8d 100644
--- a/README.ko-KR.md
+++ b/README.ko-KR.md
@@ -24,7 +24,8 @@ _Read this in other languages:_
 [_Українська_](README.uk-UA.md),
 [_Arabic_](README.ar-AR.md),
 [_Tiếng Việt_](README.vi-VN.md),
-[_Deutsch_](README.de-DE.md)
+[_Deutsch_](README.de-DE.md),
+[_Uzbek_](README.uz-UZ.md)
 
 ## 자료 구조
 
diff --git a/README.md b/README.md
index 8fa631425d..a20673989c 100644
--- a/README.md
+++ b/README.md
@@ -36,7 +36,8 @@ _Read this in other languages:_
 [_Українська_](README.uk-UA.md),
 [_Arabic_](README.ar-AR.md),
 [_Tiếng Việt_](README.vi-VN.md),
-[_Deutsch_](README.de-DE.md)
+[_Deutsch_](README.de-DE.md),
+[_Uzbek_](README.uz-UZ.md)
 
 *☝ Note that this project is meant to be used for learning and researching purposes
 only, and it is **not** meant to be used for production.*
diff --git a/README.pl-PL.md b/README.pl-PL.md
index 52ba75a5e4..9fac028aa3 100644
--- a/README.pl-PL.md
+++ b/README.pl-PL.md
@@ -26,7 +26,8 @@ _Read this in other languages:_
 [_Українська_](README.uk-UA.md),
 [_Arabic_](README.ar-AR.md),
 [_Tiếng Việt_](README.vi-VN.md),
-[_Deutsch_](README.de-DE.md)
+[_Deutsch_](README.de-DE.md),
+[_Uzbek_](README.uz-UZ.md)
 
 ## Struktury Danych
 
diff --git a/README.pt-BR.md b/README.pt-BR.md
index a937e8c0bf..edb2bd4417 100644
--- a/README.pt-BR.md
+++ b/README.pt-BR.md
@@ -26,7 +26,8 @@ _Leia isto em outros idiomas:_
 [_Українська_](README.uk-UA.md),
 [_Arabic_](README.ar-AR.md),
 [_Tiếng Việt_](README.vi-VN.md),
-[_Deutsch_](README.de-DE.md)
+[_Deutsch_](README.de-DE.md),
+[_Uzbek_](README.uz-UZ.md)
 
 ## Estrutura de Dados
 
diff --git a/README.ru-RU.md b/README.ru-RU.md
index 541e1d2703..b926b5eab3 100644
--- a/README.ru-RU.md
+++ b/README.ru-RU.md
@@ -23,7 +23,8 @@ _Читать на других языках:_
 [_Українська_](README.uk-UA.md),
 [_Arabic_](README.ar-AR.md),
 [_Tiếng Việt_](README.vi-VN.md),
-[_Deutsch_](README.de-DE.md)
+[_Deutsch_](README.de-DE.md),
+[_Uzbek_](README.uz-UZ.md)
 
 *☝ Замечание: этот репозиторий предназначен для учебно-исследовательских целей (**не** для использования в продакшн-системах).*
 
diff --git a/README.tr-TR.md b/README.tr-TR.md
index 805bf7b431..fada4e0b48 100644
--- a/README.tr-TR.md
+++ b/README.tr-TR.md
@@ -23,7 +23,8 @@ _Read this in other languages:_
 [_Українська_](README.uk-UA.md),
 [_Arabic_](README.ar-AR.md),
 [_Tiếng Việt_](README.vi-VN.md),
-[_Deutsch_](README.de-DE.md)
+[_Deutsch_](README.de-DE.md),
+[_Uzbek_](README.uz-UZ.md)
 
 *☝ Not, bu proje araştırma ve öğrenme amacı ile yapılmış
 olup üretim için **yapılmamıştır**.*
diff --git a/README.uk-UA.md b/README.uk-UA.md
index dd129b2c3c..e79a8ae845 100644
--- a/README.uk-UA.md
+++ b/README.uk-UA.md
@@ -23,7 +23,8 @@ _Вивчення матеріалу на інших мовах:_
 [_Bahasa Indonesia_](README.id-ID.md),
 [_Arabic_](README.ar-AR.md),
 [_Tiếng Việt_](README.vi-VN.md),
-[_Deutsch_](README.de-DE.md)
+[_Deutsch_](README.de-DE.md),
+[_Uzbek_](README.uz-UZ.md)
 
 *☝ Зверніть увагу! Даний проект призначений лише для навчальних та дослідницьких цілей, і він **не** призначений для виробництва (продакшн).*
 
diff --git a/README.uz-UZ.md b/README.uz-UZ.md
new file mode 100644
index 0000000000..130c1f99d3
--- /dev/null
+++ b/README.uz-UZ.md
@@ -0,0 +1,358 @@
+# JavaScript algoritmlari va ma'lumotlar tuzilmalari
+
+[![CI](https://github.com/trekhleb/javascript-algorithms/workflows/CI/badge.svg)](https://github.com/trekhleb/javascript-algorithms/actions?query=workflow%3ACI+branch%3Amaster)
+[![codecov](https://codecov.io/gh/trekhleb/javascript-algorithms/branch/master/graph/badge.svg)](https://codecov.io/gh/trekhleb/javascript-algorithms)
+![repo size](https://img.shields.io/github/repo-size/trekhleb/javascript-algorithms.svg)
+
+Bu repozitoriyada JavaScript-ga asoslangan ko'plab mashhur algoritmlar
+va ma'lumotlar tuzilmalarining namunalari mavjud.
+
+Har bir algoritm va ma'lumotlar tuzilmasining alohida README fayli
+bo'lib, unda tegishli tushuntirishlar va qo'shimcha o'qish uchun
+havolalar (shu jumladan YouTube videolariga ham havolalar) mavjud.
+
+_Read this in other languages:_
+[_简体中文_](README.zh-CN.md),
+[_繁體中文_](README.zh-TW.md),
+[_한국어_](README.ko-KR.md),
+[_日本語_](README.ja-JP.md),
+[_Polski_](README.pl-PL.md),
+[_Français_](README.fr-FR.md),
+[_Español_](README.es-ES.md),
+[_Português_](README.pt-BR.md),
+[_Русский_](README.ru-RU.md),
+[_Türkçe_](README.tr-TR.md),
+[_Italiana_](README.it-IT.md),
+[_Bahasa Indonesia_](README.id-ID.md),
+[_Українська_](README.uk-UA.md),
+[_Arabic_](README.ar-AR.md),
+[_Tiếng Việt_](README.vi-VN.md),
+[_Deutsch_](README.de-DE.md),
+[_Uzbek_](README.uz-UZ.md)
+
+Yodda tuting, bu loyiha faqat o'quv va tadqiqot maqsadida ishlatilishi
+uchun mo'ljallangan va ishlab chiqarishda ishlatilishi **mumkin emas**.
+
+## Ma'lumotlar tuzilmalari
+
+Ma'lumotlar tuzilmasi - bu kompyuterda ma'lumotlarni samarali tarzda
+olish va o'zgartirish uchun ularni tashkil etish va saqlashning ma'lum
+bir usuli. Ayniqsa, ma'lumotlar tuzilmasi ma'lumot qiymatlarining
+to'plami, ular orasidagi munosabatlar va ma'lumotlarga qo'llanilishi
+mumkin bo'lgan funksiyalar yoki operatsiyalardir.
+
+`B` - Boshlang'ich, `A` - Ilg'or
+
+- `B` [Bog'langan ro'yxat](src/data-structures/linked-list)
+- `B` [Ikki marta bog'langan ro'yxat](src/data-structures/doubly-linked-list)
+- `B` [Navbat](src/data-structures/queue)
+- `B` [Stek](src/data-structures/stack)
+- `B` [Hash jadvali](src/data-structures/hash-table)
+- `B` [Heap](src/data-structures/heap) - maksimal va minimal heap versiyalari
+- `B` [Ustuvor navbat](src/data-structures/priority-queue)
+- `A` [Trie](src/data-structures/trie)
+- `A` [Daraxt](src/data-structures/tree)
+  - `A` [Ikkilik qidiruv daraxt](src/data-structures/tree/binary-search-tree)
+  - `A` [AVL daraxt](src/data-structures/tree/avl-tree)
+  - `A` [Qizil-qora daraxt](src/data-structures/tree/red-black-tree)
+  - `A` [Segment daraxt](src/data-structures/tree/segment-tree) - min/max/sum diapazon so'rovlari bilan misollar
+  - `A` [Fenwick daraxt](src/data-structures/tree/fenwick-tree) (ikkilik indeksli daraxt)
+- `A` [Graf](src/data-structures/graph) (yo'naltirilgan hamda yo'naltirilmagan)
+- `A` [Ajratilgan to'plam](src/data-structures/disjoint-set) - union-find ma'lumotlar strukturasi yoki merge-find to'plami
+- `A` [Bloom filtri](src/data-structures/bloom-filter)
+- `A` [LRU keshi](src/data-structures/lru-cache/) - Eng kam ishlatilgan (LRU) keshi
+
+## Algoritmlar
+
+Algoritm muammolar sinfini qanday hal qilishning aniq spetsifikatsiyasi. Bu operatsiyalar ketma-ketligini aniqlaydigan qoidalar to'plami.
+
+`B` - Boshlang'ich, `A` - Ilg'or
+
+### Mavzu bo'yicha algoritmlar
+
+- **Matematika**
+  - `B` [Bit manipulatsiyasi](src/algorithms/math/bits) - bitlarni qo'yish/olish/yangilash/tozalash, ikkilikka ko'paytirish/bo'lish, manfiy qilish va hokazo.
+  - `B` [Ikkilik suzuvchi nuqta](src/algorithms/math/binary-floating-point) - suzuvchi nuqtali sonlarning ikkilik tasviri.
+  - `B` [Faktorial](src/algorithms/math/factorial)
+  - `B` [Fibonachchi raqam](src/algorithms/math/fibonacci) - klassik va yopiq shakldagi versiyalar
+  - `B` [Asosiy omillar](src/algorithms/math/prime-factors) - tub omillarni topish va ularni Xardi-Ramanujan teoremasi yordamida sanash
+  - `B` [Birlamchilik testi](src/algorithms/math/primality-test) (sinov bo'linish usuli)
+  - `B` [Evklid algoritmi](src/algorithms/math/euclidean-algorithm) - eng katta umumiy bo'luvchini (EKUB) hisoblash
+  - `B` [Eng kichik umumiy karrali](src/algorithms/math/least-common-multiple) (EKUK)
+  - `B` [Eratosfen elagi](src/algorithms/math/sieve-of-eratosthenes) - berilgan chegaragacha barcha tub sonlarni topish
+  - `B` [Ikkining darajasimi](src/algorithms/math/is-power-of-two) - raqamning ikkining darajasi ekanligini tekshirish (sodda va bitli algoritmlar)
+  - `B` [Paskal uchburchagi](src/algorithms/math/pascal-triangle)
+  - `B` [Kompleks sonlar](src/algorithms/math/complex-number) - kompleks sonlar va ular bilan asosiy amallar
+  - `B` [Radian & Daraja](src/algorithms/math/radian) - radianlarni darajaga va orqaga aylantirish
+  - `B` [Tez ko'tarish](src/algorithms/math/fast-powering)
+  - `B` [Horner metodi](src/algorithms/math/horner-method) - polinomlarni baholash
+  - `B` [Matritsalar](src/algorithms/math/matrix) - matritsalar va asosiy matritsa operatsiyalari (ko'paytirish, transpozitsiya va boshqalar).
+  - `B` [Evklid masofasi](src/algorithms/math/euclidean-distance) - ikki nuqta/vektor/matritsa orasidagi masofa
+  - `A` [Butun sonlarni bo'lish](src/algorithms/math/integer-partition)
+  - `A` [Kvadrat ildiz](src/algorithms/math/square-root) - Nyuton metodi
+  - `A` [Liu Hui π algoritmi](src/algorithms/math/liu-hui) - N-gonlarga asoslangan π ning taxminiy hisoblari
+  - `A` [Diskret Furye transformatsiyasi](src/algorithms/math/fourier-transform) - vaqt funksiyasini (signalni) uni tashkil etuvchi chastotalarga ajratish
+- **Sets**
+  - `B` [Karteziya maxsuloti](src/algorithms/sets/cartesian-product) - bir nechta to'plamlarning ko'paytmasi
+  - `B` [Fisher–Yates Shuffle](src/algorithms/sets/fisher-yates) - chekli ketma-ketlikni tasodifiy almashtirish
+  - `A` [Power Set](src/algorithms/sets/power-set) - to'plamning barcha kichik to'plamlari (bitwise, backtracking va kaskadli echimlar)
+  - `A` [Permutatsiyalar](src/algorithms/sets/permutations) (takroriyalash bilan va takroriyalashsiz)
+  - `A` [Kombinatsiyalar](src/algorithms/sets/combinations) (takroriyalash bilan va takroriyalashsiz)
+  - `A` [Eng uzun umumiy ketma-ketlik](src/algorithms/sets/longest-common-subsequence) (LCS)
+  - `A` [Eng uzun ortib boruvchi ketma-ketlik](src/algorithms/sets/longest-increasing-subsequence)
+  - `A` [Eng qisqa umumiy ketma-ketlik](src/algorithms/sets/shortest-common-supersequence) (SCS)
+  - `A` [Knapsack muammosi](src/algorithms/sets/knapsack-problem) - "0/1" va "Bir-biriga bog'lanmagan"
+  - `A` [Maksimal kichik massiv](src/algorithms/sets/maximum-subarray) - Toʻliq kuch va dinamik dasturlash (Kadane usuli) versiyalari
+  - `A` [Kombinatsiya yig'indisi](src/algorithms/sets/combination-sum) - ma'lum summani tashkil etuvchi barcha kombinatsiyalarni topish
+- **Stringlar**
+  - `B` [Hamming masofasi](src/algorithms/string/hamming-distance) - belgilarning bir-biridan farq qiladigan pozitsiyalar soni
+  - `B` [Palindrom](src/algorithms/string/palindrome) - satrning teskari tomoni ham bir xil ekanligini tekshirish
+  - `A` [Levenshtein masofasi](src/algorithms/string/levenshtein-distance) - ikki ketma-ketlik o'rtasidagi minimal tahrirlash masofasi
+  - `A` [Knuth–Morris–Pratt Algoritmi](src/algorithms/string/knuth-morris-pratt) (KMP Algoritmi) - kichik qatorlarni qidirish (mosh keluvchi naqshni qidirish)
+  - `A` [Z Algoritmi](src/algorithms/string/z-algorithm) - kichik qatorlarni qidirish (mosh keluvchi naqshni qidirish)
+  - `A` [Rabin Karp Algoritmi](src/algorithms/string/rabin-karp) - kichik qatorlarni qidirish
+  - `A` [Eng uzun umumiy kichik matn](src/algorithms/string/longest-common-substring)
+  - `A` [Regulyar ifoda moslashuvi](src/algorithms/string/regular-expression-matching) (RegEx)
+- **Qidiruvlar**
+  - `B` [Linear qidirish](src/algorithms/search/linear-search)
+  - `B` [Jump qidirish](src/algorithms/search/jump-search) (yoki Blok qidirish) - saralangan qatorda qidirish
+  - `B` [Ikkilik qidirish](src/algorithms/search/binary-search) - saralangan qatorda qidirish
+  - `B` [Interpolatsiya qidirish](src/algorithms/search/interpolation-search) - bir tekis taqsimlangan saralangan qatorda qidirish
+- **Tartiblash**
+  - `B` [Pufakcha tartiblash](src/algorithms/sorting/bubble-sort)
+  - `B` [Tanlash tartibi](src/algorithms/sorting/selection-sort)
+  - `B` [Kiritish tartibi](src/algorithms/sorting/insertion-sort)
+  - `B` [Heap tartibi](src/algorithms/sorting/heap-sort)
+  - `B` [Birlashtirish tartibi](src/algorithms/sorting/merge-sort)
+  - `B` [Tezkor saralash](src/algorithms/sorting/quick-sort) - joyida va joyida bo'lmagan amalga oshirish
+  - `B` [Shell tartiblash](src/algorithms/sorting/shell-sort)
+  - `B` [Sanash tartibi](src/algorithms/sorting/counting-sort)
+  - `B` [Radiksli tartiblash](src/algorithms/sorting/radix-sort)
+  - `B` [Bucket tartiblash](src/algorithms/sorting/bucket-sort)
+- **Bog'langan ro'yhatlar**
+  - `B` [To'g'ri traversal](src/algorithms/linked-list/traversal)
+  - `B` [Teskari traversal](src/algorithms/linked-list/reverse-traversal)
+- **Daraxtlar**
+  - `B` [Birinchi-pastga qarab qidirish](src/algorithms/tree/depth-first-search) (Depth-First Search)
+  - `B` [Birinchi-yonga qarab qidirish](src/algorithms/tree/breadth-first-search) (Breadth-First Search)
+- **Grafiklar**
+  - `B` [Birinchi-pastga qarab qidirish](src/algorithms/graph/depth-first-search) (Depth-First Search)
+  - `B` [Birinchi-yonga qarab qidirish](src/algorithms/graph/breadth-first-search) (Breadth-First Search)
+  - `B` [Kruskal Algoritmi](src/algorithms/graph/kruskal) - og'irlikdagi yo'naltirilmagan grafik uchun Minimal kengayuvchi daraxtni (MST) topish
+  - `A` [Dijkstra Algoritmi](src/algorithms/graph/dijkstra) - grafikning bir cho'qqisidan qolgan barcha nuqtalarga eng qisqa yo'llarni topish
+  - `A` [Bellman-Ford Algoritmi](src/algorithms/graph/bellman-ford) - grafikning bir cho'qqisidan qolgan barcha nuqtalarga eng qisqa yo'llarni topish
+  - `A` [Floyd-Warshall Algoritmi](src/algorithms/graph/floyd-warshall) - grafikning barcha uchlari orasidagi eng qisqa masofalarni topish
+  - `A` [Siklni aniqlash](src/algorithms/graph/detect-cycle) - yo'naltirilgan va yo'naltirilmagan grafiklar uchun (DFS va Disjoint Set-ga asoslangan versiyalar)
+  - `A` [Prim Algoritmi](src/algorithms/graph/prim) - og'irlikdagi yo'naltirilmagan grafik uchun Minimal kengayuvchi daraxtni (MST) topish
+  - `A` [Topologik saralash](src/algorithms/graph/topological-sorting) - DFS metodi
+  - `A` [Artikulyatsiya nuqtalari](src/algorithms/graph/articulation-points) - Tarjan algoritmi (DFS asosida)
+  - `A` [Ko'priklar](src/algorithms/graph/bridges) - DFS asosidagi algoritm
+  - `A` [Eyler yo'li va Eyler sxemasi](src/algorithms/graph/eulerian-path) - Fleury algoritmi - Har bir chekkaga bir marta tashrif buyurish
+  - `A` [Gamilton sikli](src/algorithms/graph/hamiltonian-cycle) - Har bir cho'qqiga bir marta tashrif buyurish
+  - `A` [Kuchli bog'langan komponentlar](src/algorithms/graph/strongly-connected-components) - Kosaraju algoritmi
+  - `A` [Sayohatchi sotuvchi muammosi](src/algorithms/graph/travelling-salesman) - har bir shaharga tashrif buyuradigan va kelib chiqqan shaharga qaytib keladigan eng qisqa yo'l
+- **Kriptografiya**
+  - `B` [Polynomial Hash](src/algorithms/cryptography/polynomial-hash) - polinomga asoslangan hash funktsiyasi
+  - `B` [Rail Fence Cipher](src/algorithms/cryptography/rail-fence-cipher) - xabarlarni kodlash uchun transpozitsiya shifrlash algoritmi
+  - `B` [Caesar Cipher](src/algorithms/cryptography/caesar-cipher) - oddiy almashtirish shifridir
+  - `B` [Hill Cipher](src/algorithms/cryptography/hill-cipher) - chiziqli algebraga asoslangan almashtirish shifri
+- **Machine Learning**
+  - `B` [NanoNeuron](https://github.com/trekhleb/nano-neuron) - Mashinalar aslida qanday o'rganishi mumkinligini ko'rsatadigan 7 ta oddiy JS funksiyasi (forward/backward tarqalish)
+  - `B` [k-NN](src/algorithms/ml/knn) - eng yaqin qo'shnilarni tasniflash algoritmi
+  - `B` [k-Means](src/algorithms/ml/k-means) - k-Means kalsterlash algoritmi
+- **Tasvirga ishlov berish**
+  - `B` [Seam Carving](src/algorithms/image-processing/seam-carving) - kontentga moslashuvchan rasm o'lchamini o'zgartirish algoritmi
+- **Statistikalar**
+  - `B` [Weighted Random](src/algorithms/statistics/weighted-random) - elementlarning og'irligi asosida ro'yxatdan tasodifiy elementni tanlash
+- **Evolyutsion algoritmlar**
+  - `A` [Genetik algoritm](https://github.com/trekhleb/self-parking-car-evolution) - avtoturargohni o'rgatish uchun genetik algoritm qanday qo'llanilishiga misol.
+- **Kategoriyasiz**
+  - `B` [Xanoy minorasi](src/algorithms/uncategorized/hanoi-tower)
+  - `B` [Kvadrat matritsaning aylanishi](src/algorithms/uncategorized/square-matrix-rotation) - joyidagi algoritm
+  - `B` [Sakrash o'yini](src/algorithms/uncategorized/jump-game) - orqaga qaytish, dinamik dasturlash (yuqoridan pastga + pastdan yuqoriga) va ochko'z misollar
+  - `B` [Noyob yo'llar](src/algorithms/uncategorized/unique-paths) - orqaga qaytish, dinamik dasturlash va Paskal uchburchagiga asoslangan misolla
+  - `B` [Yomg'ir teraslari](src/algorithms/uncategorized/rain-terraces) - yomg'ir suvini ushlab turish muammosi (dinamik dasturlash va qo'pol kuch versiyalari)
+  - `B` [Rekursiv zinapoya](src/algorithms/uncategorized/recursive-staircase) - yuqoriga chiqish yo'llari sonini hisoblash (4 ta echim)
+  - `B` [Aksiyalarni sotib olish va sotish uchun eng yaxshi vaqt](src/algorithms/uncategorized/best-time-to-buy-sell-stocks) - bo'linib-zabt etish va bir marta o'tish misollari
+  - `A` [N-Queens Muommosi](src/algorithms/uncategorized/n-queens)
+  - `A` [Ritsar sayohati](src/algorithms/uncategorized/knight-tour)
+
+### Paradigma bo'yicha algoritmlar
+
+Algorithmic paradigm - bu algoritmlar sinfini loyihalashtirishga asos bo'lib xizmat qiladigan umumiy usul yoki yondashuv. Bu algoritm tushunchasidan yuqori darajadagi abstraktsiya bo'lib, algoritm kompyuter dasturi tushunchasidan yuqori darajadagi abstraktsiya bo'lgani kabi.
+
+- **Brute Force** - barcha imkoniyatlarni ko'rib chiqib va eng yaxshi echimni tanlash
+  - `B` [Chiziqli qidirish](src/algorithms/search/linear-search)
+  - `B` [Yomg'irli teraslar](src/algorithms/uncategorized/rain-terraces) - yomg'ir suvini to'plash muammosi
+  - `B` [Rekursiv zinapoya](src/algorithms/uncategorized/recursive-staircase) - cho'qqiga chiqish yo'llari sonini hisoblash
+  - `A` [Maksimal kichik massiv](src/algorithms/sets/maximum-subarray)
+  - `A` [Sayohatchi sotuvchi muammosi](src/algorithms/graph/travelling-salesman) - har bir shaharga tashrif buyuradigan va kelib chiqqan shaharga qaytib keladigan eng qisqa yo'l
+  - `A` [Diskret Furye transformatsiyasi](src/algorithms/math/fourier-transform) - vaqt funksiyasini (signalni) uni tashkil etuvchi chastotalarga ajratish
+- **Greedy** - kelajakni o'ylamasdan, hozirgi vaqtda eng yaxshi variantni tanlash
+  - `B` [Sakrash o'yini](src/algorithms/uncategorized/jump-game)
+  - `A` [Bog'lanmagan yukxalta muammosi](src/algorithms/sets/knapsack-problem)
+  - `A` [Dijkstra Algoritmi](src/algorithms/graph/dijkstra) - grafikning bir cho'qqisidan qolgan barcha nuqtalarga eng qisqa yo'llarni topish
+  - `A` [Prim Algoritmi](src/algorithms/graph/prim) - og'irlikdagi yo'naltirilmagan grafik uchun Minimal kengayuvchi daraxtni (MST) topish
+  - `A` [Kruskal Algoritmi](src/algorithms/graph/kruskal) - og'irlikdagi yo'naltirilmagan grafik uchun Minimal kengayuvchi daraxtni (MST) topish
+- **Divide and Conquer** - muammoni kichikroq qismlarga bo'lib va keyin bu qismlarni hal qilish
+
+  - `B` [Ikkilik qidiruv](src/algorithms/search/binary-search)
+  - `B` [Xanoy minorasi](src/algorithms/uncategorized/hanoi-tower)
+  - `B` [Paskal uchburchagi](src/algorithms/math/pascal-triangle)
+  - `B` [Evklid Algoritmi](src/algorithms/math/euclidean-algorithm) - eng katta umumiy bo'luvchini (EKUB) hisoblash
+  - `B` [Birlashtirish tartibi](src/algorithms/sorting/merge-sort)
+  - `B` [Tezkor saralash](src/algorithms/sorting/quick-sort)
+  - `B` [Birinchi-pastga qarab qidirish daraxti](src/algorithms/tree/depth-first-search) (DFS)
+  - `B` [Birinchi-pastga qarab qidirish grafigi](src/algorithms/graph/depth-first-search) (DFS)
+  - `B` [Matritsalar](src/algorithms/math/matrix) - turli shakldagi matritsalarni hosil qilish va kesib o'tish
+  - `B` [Sakrash o'yini](src/algorithms/uncategorized/jump-game)
+  - `B` [Tez ko'tarish](src/algorithms/math/fast-powering)
+  - `B` [Aksiyalarni sotib olish va sotish uchun eng yaxshi vaqt](src/algorithms/uncategorized/best-time-to-buy-sell-stocks) - bo'linib-zabt etish va bir marta o'tish misollari
+  - `A` [Permutatsiyalar](src/algorithms/sets/permutations) (takroriyalash bilan va takroriyalashsiz)
+  - `A` [Kombinatsiyalar](src/algorithms/sets/combinations) (takroriyalash bilan va takroriyalashsiz)
+  - `A` [Maksimal kichik massiv](src/algorithms/sets/maximum-subarray)
+
+- **Dinamik dasturlash** - ilgari topilgan kichik yechimlar yordamida yechim yaratish
+  - `B` [Fibonachchi raqam](src/algorithms/math/fibonacci)
+  - `B` [Sakrash o'yini](src/algorithms/uncategorized/jump-game)
+  - `B` [Noyob yo'llar](src/algorithms/uncategorized/unique-paths)
+  - `B` [Yomg'ir teraslari](src/algorithms/uncategorized/rain-terraces) - yomg'ir suvini to'plash muammosi
+  - `B` [Recursive Staircase](src/algorithms/uncategorized/recursive-staircase) - count the number of ways to reach to the top
+  - `B` [Seam Carving](src/algorithms/image-processing/seam-carving) - kontentga moslashuvchan rasm o'lchamini o'zgartirish algoritmi
+  - `A` [Levenshtein masofasi](src/algorithms/string/levenshtein-distance) - ikki ketma-ketlik o'rtasidagi minimal tahrirlash masofasi
+  - `A` [Eng uzun umumiy ketma-ketlik](src/algorithms/sets/longest-common-subsequence) (LCS)
+  - `A` [Eng uzun umumiy kichik matn](src/algorithms/string/longest-common-substring)
+  - `A` [Eng uzun ortib boruvchi ketma-ketlik](src/algorithms/sets/longest-increasing-subsequence)
+  - `A` [Eng qisqa umumiy ketma-ketlik](src/algorithms/sets/shortest-common-supersequence)
+  - `A` [0/1 Knapsak muommosi](src/algorithms/sets/knapsack-problem)
+  - `A` [Butun sonlarni bo'lish](src/algorithms/math/integer-partition)
+  - `A` [Maksimal kichik massiv](src/algorithms/sets/maximum-subarray)
+  - `A` [Bellman-Ford Algoritmi](src/algorithms/graph/bellman-ford) - grafikning bir cho'qqisidan qolgan barcha nuqtalarga eng qisqa yo'llarni topish
+  - `A` [Floyd-Warshall Algoritmi](src/algorithms/graph/floyd-warshall) -grafikning barcha uchlari orasidagi eng qisqa masofalarni topish
+  - `A` [Regulyar ifoda moslashuvi](src/algorithms/string/regular-expression-matching)
+- **Backtracking** - brute forcega o'xshab, barcha mumkin bo'lgan yechimlarni generatsiya qilishga harakat qiladi, lekin har safar keyingi yechimni yaratganingizda, yechim barcha shartlarga javob beradimi yoki yo'qligini tekshirasiz va shundan keyingina keyingi yechimlarni ishlab chiqarishni davom ettirasiz. Aks holda, orqaga qaytib, yechim topishning boshqa yo'liga o'tasiz. Odatda state-space ning DFS-qidiruvi ishlatiladi.
+  - `B` [Sakrash o'yini](src/algorithms/uncategorized/jump-game)
+  - `B` [Noyob yo'llar](src/algorithms/uncategorized/unique-paths)
+  - `B` [Power Set](src/algorithms/sets/power-set) - to'plamning barcha kichik to'plamlari
+  - `A` [Gamilton sikli](src/algorithms/graph/hamiltonian-cycle) - Har bir cho'qqiga bir marta tashrif buyurish
+  - `A` [N-Queens muommosi](src/algorithms/uncategorized/n-queens)
+  - `A` [Ritsar sayohati](src/algorithms/uncategorized/knight-tour)
+  - `A` [Kombinatsiya yig'indisi](src/algorithms/sets/combination-sum) - ma'lum summani tashkil etuvchi barcha kombinatsiyalarni topish
+- **Branch & Bound** - shu paytgacha topilgan eng arzon echimdan kattaroq xarajatlarga ega qisman echimlarni bekor qilish uchun, backtracking qidiruvining har bir bosqichida topilgan eng arzon echimni eslab qoling va shu paytgacha topilgan eng arzon yechim narxidan muammoni eng kam xarajatli yechim narxining past chegarasi sifatida foydalaning. Odatda state-space daraxtining DFS o'tishi bilan birgalikda BFS traversal qo'llaniladi.
+
+## Ushbu repozitoriyadan qanday foydalanish kerak
+
+**Barcha dependensiylarni o'rnating**
+
+```
+npm install
+```
+
+**ESLint ni ishga tushiring**
+
+Kod sifatini tekshirish uchun ESLint ni ishga tushirishingiz mumkin.
+
+```
+npm run lint
+```
+
+**Barcha testlarni ishga tushuring**
+
+```
+npm test
+```
+
+**Testlarni nom bo'yicha ishga tushirish**
+
+```
+npm test -- 'LinkedList'
+```
+
+**Muammolarni bartaraf qilish (Troubleshooting)**
+
+Agar linting yoki sinov muvaffaqiyatsiz bo'lsa, `node_modules` papkasini o'chirib, npm paketlarini qayta o'rnatishga harakat qiling:
+
+```
+rm -rf ./node_modules
+npm i
+```
+
+Shuningdek, to'g'ri Node versiyasidan foydalanayotganingizga ishonch hosil qiling (`>=16`). Agar Node versiyasini boshqarish uchun [nvm](https://github.com/nvm-sh/nvm) dan foydalanayotgan bo'lsangiz, loyihaning ildiz papkasidan `nvm use` ni ishga tushiring va to'g'ri versiya tanlanadi.
+
+**O'yin maydoni (Playground)**
+
+`./src/playground/playground.js` faylida ma'lumotlar strukturalari va algoritmlar bilan o'ynashingiz, `./src/playground/test/playground.test.js` faylida esa ular uchun testlar yozishingiz mumkin.
+
+Shundan so'ng, playground kodingiz kutilgandek ishlashini tekshirish uchun quyidagi buyruqni ishga tushirishingiz kifoya:
+
+```
+npm test -- 'playground'
+```
+
+## Foydali ma'lumotlar
+
+### Manbalar
+
+- [▶ Data Structures and Algorithms on YouTube](https://www.youtube.com/playlist?list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
+- [✍🏻 Data Structure Sketches](https://okso.app/showcase/data-structures)
+
+### Big O Notation
+
+_Big O notation_ algoritmlarni kirish hajmi oshgani sayin ularning ishlash vaqti yoki bo'sh joy talablari qanday o'sishiga qarab tasniflash uchun ishlatiladi. Quyidagi jadvalda siz Big O notatsiyasida ko'rsatilgan algoritmlarning o'sishining eng keng tarqalgan tartiblarini topishingiz mumkin.
+
+![Big O grafiklar](./assets/big-o-graph.png)
+
+Manba: [Big O Cheat Sheet](http://bigocheatsheet.com/).
+
+Quyida eng ko'p qo'llaniladigan Big O notatsiyalarining ro'yxati va ularning kirish ma'lumotlarining turli o'lchamlariga nisbatan ishlashini taqqoslash keltirilgan.
+
+| Big O Notatsiya | Turi         | 10 ta element uchun hisob-kitoblar | 100 ta element uchun hisob-kitoblar | 1000 ta element uchun hisob-kitoblar |
+| --------------- | ------------ | ---------------------------------- | ----------------------------------- | ------------------------------------ |
+| **O(1)**        | O'zgarmas    | 1                                  | 1                                   | 1                                    |
+| **O(log N)**    | Logarifmik   | 3                                  | 6                                   | 9                                    |
+| **O(N)**        | Chiziqli     | 10                                 | 100                                 | 1000                                 |
+| **O(N log N)**  | n log(n)     | 30                                 | 600                                 | 9000                                 |
+| **O(N^2)**      | Kvadrat      | 100                                | 10000                               | 1000000                              |
+| **O(2^N)**      | Eksponensial | 1024                               | 1.26e+29                            | 1.07e+301                            |
+| **O(N!)**       | Faktorial    | 3628800                            | 9.3e+157                            | 4.02e+2567                           |
+
+### Ma'lumotlar tuzilmalarining operatsiyalari murakkabligi
+
+| Ma'lumotlar tuzilmalari     | Kirish | Qidirish | Kiritish | O'chirish | Izohlar                                                    |
+| --------------------------- | :----: | :------: | :------: | :-------: | :--------------------------------------------------------- |
+| **Massiv**                  |   1    |    n     |    n     |     n     |                                                            |
+| **Stak**                    |   n    |    n     |    1     |     1     |                                                            |
+| **Navbat**                  |   n    |    n     |    1     |     1     |                                                            |
+| **Bog'langan ro'yhat**      |   n    |    n     |    1     |     n     |                                                            |
+| **Hash jadval**             |   -    |    n     |    n     |     n     | Mukammal xash funksiyasi bo'lsa, xarajatlar O (1) bo'ladi. |
+| **Ikkilik qidiruv daraxti** |   n    |    n     |    n     |     n     | Balanslangan daraxt narxida O(log(n)) bo'ladi.             |
+| **B-daraxti**               | log(n) |  log(n)  |  log(n)  |  log(n)   |                                                            |
+| **Qizil-qora daraxt**       | log(n) |  log(n)  |  log(n)  |  log(n)   |                                                            |
+| **AVL Daraxt**              | log(n) |  log(n)  |  log(n)  |  log(n)   |                                                            |
+| **Bloom filtri**            |   -    |    1     |    1     |     -     | Qidiruv paytida noto'g'ri pozitivlar bo'lishi mumkin       |
+
+### Massivlarni saralash algoritmlarining murakkabligi
+
+| Nomi                      |  Eng yaxshi   |          O'rta          |          Eng yomon          | Xotira | Barqaror | Izohlar                                                                      |
+| ------------------------- | :-----------: | :---------------------: | :-------------------------: | :----: | :------: | :--------------------------------------------------------------------------- |
+| **Pufakcha tartiblash**   |       n       |      n<sup>2</sup>      |        n<sup>2</sup>        |   1    |    Ha    |                                                                              |
+| **Kiritish tartibi**      |       n       |      n<sup>2</sup>      |        n<sup>2</sup>        |   1    |    Ha    |                                                                              |
+| **Tanlash tartibi**       | n<sup>2</sup> |      n<sup>2</sup>      |        n<sup>2</sup>        |   1    |   Yo'q   |                                                                              |
+| **Heap tartibi**          | n&nbsp;log(n) |      n&nbsp;log(n)      |        n&nbsp;log(n)        |   1    |   Yo'q   |                                                                              |
+| **Birlashtirish tartibi** | n&nbsp;log(n) |      n&nbsp;log(n)      |        n&nbsp;log(n)        |   n    |    Ha    |                                                                              |
+| **Tezkor saralash**       | n&nbsp;log(n) |      n&nbsp;log(n)      |        n<sup>2</sup>        | log(n) |   Yo'q   | Tezkor saralash odatda O(log(n)) stek maydoni bilan joyida amalga oshiriladi |
+| **Shell tartiblash**      | n&nbsp;log(n) | depends on gap sequence | n&nbsp;(log(n))<sup>2</sup> |   1    |   Yo'q   |                                                                              |
+| **Sanash tartibi**        |     n + r     |          n + r          |            n + r            | n + r  |    Ha    | r - massivdagi eng katta raqam                                               |
+| **Radiksli tartiblash**   |    n \* k     |         n \* k          |           n \* k            | n + k  |    Ha    | k - eng uzun kalitning uzunligi                                              |
+
+## Loyihani qo'llab-quvvatlovchilar
+
+> Siz ushbu loyihani ❤️️ [GitHub](https://github.com/sponsors/trekhleb) yoki ❤️️ [Patreon](https://www.patreon.com/trekhleb) orqali qo'llab-quvvatlashingiz mumkin.
+
+[Ushbu loyihani qo'llab-quvvatlagan odamlar](https://github.com/trekhleb/javascript-algorithms/blob/master/BACKERS.md) `∑ = 1`
+
+## Muallif
+
+[@trekhleb](https://trekhleb.dev)
+
+A few more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev)
diff --git a/README.zh-CN.md b/README.zh-CN.md
index cdef9cabea..27982c6553 100644
--- a/README.zh-CN.md
+++ b/README.zh-CN.md
@@ -23,7 +23,8 @@ _Read this in other languages:_
 [_Українська_](README.uk-UA.md),
 [_Arabic_](README.ar-AR.md),
 [_Tiếng Việt_](README.vi-VN.md),
-[_Deutsch_](README.de-DE.md)
+[_Deutsch_](README.de-DE.md),
+[_Uzbek_](README.uz-UZ.md)
 
 *注意：这个项目仅用于学习和研究，**不是**用于生产环境。*
 
diff --git a/README.zh-TW.md b/README.zh-TW.md
index 20d4381a2a..aeb0547d2e 100644
--- a/README.zh-TW.md
+++ b/README.zh-TW.md
@@ -22,7 +22,8 @@ _Read this in other languages:_
 [_Українська_](README.uk-UA.md),
 [_Arabic_](README.ar-AR.md),
 [_Tiếng Việt_](README.vi-VN.md),
-[_Deutsch_](README.de-DE.md)
+[_Deutsch_](README.de-DE.md),
+[_Uzbek_](README.uz-UZ.md)
 
 ## 資料結構
 

From 09afeb58d820ae32d6f3ccfa4042981fae4e1a9d Mon Sep 17 00:00:00 2001
From: Stanislav Dolgachov <s.dolgachov@gmail.com>
Date: Sat, 13 Jul 2024 22:13:11 +0300
Subject: [PATCH 252/264] Update .eslintrc, improve UK translation for
 LinkedList (#1128)

* Add ignore patterns to eslint config

* Improve UK translation for LinkedList

---------

Co-authored-by: Oleksii Trekhleb <3000285+trekhleb@users.noreply.github.com>
---
 .eslintrc                                     |  1 +
 .../linked-list/README.uk-UA.md               | 26 +++++++++----------
 2 files changed, 14 insertions(+), 13 deletions(-)

diff --git a/.eslintrc b/.eslintrc
index cf3245bf37..88af3ecf32 100644
--- a/.eslintrc
+++ b/.eslintrc
@@ -12,6 +12,7 @@
     "arrow-body-style": "off",
     "no-loop-func": "off"
   },
+  "ignorePatterns": ["*.md", "*.png", "*.jpeg", "*.jpg"],
   "settings": {
     "react": {
       "version": "18.2.0"
diff --git a/src/data-structures/linked-list/README.uk-UA.md b/src/data-structures/linked-list/README.uk-UA.md
index 5424c58db4..9b34a6d828 100644
--- a/src/data-structures/linked-list/README.uk-UA.md
+++ b/src/data-structures/linked-list/README.uk-UA.md
@@ -1,10 +1,10 @@
 # Зв'язаний список
 
-Зв'язаний список — базова динамічна структура даних в інформатиці, що складається з вузлів, кожен з яких містить як дані, так посилання («зв'язку») на наступний вузол списку. Дана структура дозволяє ефективно додавати та видаляти елементи на довільній позиції у послідовності у процесі ітерації. Більш складні варіанти включають додаткові посилання, що дозволяють ефективно додавати та видаляти довільні елементи.
+Зв'язаний список — базова динамічна структура даних в інформатиці, що складається з вузлів, кожен з яких містить як дані, так і посилання («зв'язку») на наступний вузол списку. Ця структура даних дозволяє ефективно додавати та видаляти елементи на довільній позиції у послідовності у процесі ітерації. Більш складні варіанти включають додаткові посилання, що дозволяють ефективно додавати та видаляти довільні елементи.
 
-Принциповою перевагою перед масивом є структурна гнучкість: порядок елементів зв'язкового списку може збігатися з порядком розташування елементів даних у пам'яті комп'ютера, а порядок обходу списку завжди явно задається його внутрішніми зв'язками. Суть переваги у тому, що у багатьох мовах створення масиву вимагає вказати його заздалегідь. Зв'язковий список дозволяє обійти це обмеження.
+Принциповою перевагою перед масивом є структурна гнучкість: порядок елементів зв'язаного списку може збігатися з порядком розташування елементів даних у пам'яті комп'ютера, а порядок обходу списку завжди явно задається його внутрішніми зв'язками. Це важливо, бо у багатьох мовах створення масиву вимагає вказати його розмір заздалегідь. Зв'язаний список дозволяє обійти це обмеження.
 
-Недоліком зв'язкових списків є те, що час доступу є лінійним (і важко для реалізації конвеєрів). Неможливий швидкий доступ (випадковий).
+Недоліком зв'язаних списків є те, що час доступу є лінійним (і важко для реалізації конвеєрів). Неможливий швидкий доступ (випадковий).
 
 ![Linked List](./images/linked-list.jpeg)
 
@@ -17,7 +17,7 @@
 ```text
 Add(value)
   Pre: value - значення, що додається
-  Post: value поміщено в кінець списку
+  Post: value додано в кінець списку
   n ← node(value)
   if head = ø
     head ← n
@@ -32,7 +32,7 @@ end Add
 ```text
 Prepend(value)
  Pre: value - значення, що додається
- Post: value поміщено на початок списку
+ Post: value додано на початку списку
  n ← node(value)
  n.next ← head
  head ← n
@@ -42,7 +42,7 @@ Prepend(value)
 end Prepend
 ```
 
-### Поиск
+### Пошук
 
 ```text
 Contains(head, value)
@@ -60,7 +60,7 @@ Contains(head, value)
 end Contains
 ```
 
-### Вилучення
+### Видалення
 
 ```text
 Remove(head, value)
@@ -94,7 +94,7 @@ Remove(head, value)
 end Remove
 ```
 
-### Обход
+### Обхід
 
 ```text
 Traverse(head)
@@ -108,12 +108,12 @@ Traverse(head)
 end Traverse
 ```
 
-### Зворотний обхід
+### Зворотній обхід
 
 ```text
 ReverseTraversal(head, tail)
-  Pre: head и tail відносяться до одного списку
-  Post: елементи списку пройдено у зворотному порядку
+  Pre: head і tail відносяться до одного списку
+  Post: елементи списку пройдено у зворотньому порядку
   if tail != ø
     curr ← tail
     while curr != head
@@ -131,7 +131,7 @@ end ReverseTraversal
 
 ## Складність
 
-### Тимчасова складність
+### Часова складність
 
 | Читання    | Пошук     | Вставка    | Вилучення |
 | :--------: | :-------: | :--------: | :-------: |
@@ -143,5 +143,5 @@ O(n)
 
 ## Посилання
 
-- [Wikipedia](https://uk.wikipedia.org/wiki/%D0%97%D0%B2%27%D1%8F%D0%B7%D0%B0%D0%BD%D0%B8%D0%B9_%D1%81%D0%BF%D0%B8%D1%81%D0%BE%D0%BA)
+- [Wikipedia](https://uk.wikipedia.org/wiki/Зв'язаний_список)
 - [YouTube](https://www.youtube.com/watch?v=6snsMa4E1Os)

From 6509304ff613f88191155f1f9834aace8db1c149 Mon Sep 17 00:00:00 2001
From: JungHyunLah <leahincom@gmail.com>
Date: Sun, 14 Jul 2024 04:20:23 +0900
Subject: [PATCH 253/264] update LRU Cache translation for ko-KR (#987)

* feat: LRU cache translation in ko-KR

* chore: add readInAnotherLan for ko-KR

---------

Co-authored-by: Oleksii Trekhleb <3000285+trekhleb@users.noreply.github.com>
---
 src/data-structures/lru-cache/README.ko-KR.md | 51 +++++++++++++++++++
 src/data-structures/lru-cache/README.md       | 15 +++---
 2 files changed, 60 insertions(+), 6 deletions(-)
 create mode 100644 src/data-structures/lru-cache/README.ko-KR.md

diff --git a/src/data-structures/lru-cache/README.ko-KR.md b/src/data-structures/lru-cache/README.ko-KR.md
new file mode 100644
index 0000000000..93957bc0ed
--- /dev/null
+++ b/src/data-structures/lru-cache/README.ko-KR.md
@@ -0,0 +1,51 @@
+# LRU 캐시 알고리즘
+
+**LRU 캐시 알고리즘** 은 사용된 순서대로 아이템을 정리함으로써, 오랜 시간 동안 사용되지 않은 아이템을 빠르게 찾아낼 수 있도록 한다.
+
+한방향으로만 옷을 걸 수 있는 옷걸이 행거를 생각해봅시다. 가장 오랫동안 입지 않은 옷을 찾기 위해서는, 행거의 반대쪽 끝을 보면 됩니다.
+
+## 문제 정의
+
+LRUCache 클래스를 구현해봅시다:
+
+- `LRUCache(int capacity)` LRU 캐시를 **양수** 의 `capacity` 로 초기화합니다.
+- `int get(int key)` `key` 가 존재할 경우 `key` 값을 반환하고, 그렇지 않으면 `undefined` 를 반환합니다.
+- `void set(int key, int value)` `key` 가 존재할 경우 `key` 값을 업데이트 하고, 그렇지 않으면 `key-value` 쌍을 캐시에 추가합니다. 만약 이 동작으로 인해 키 개수가 `capacity` 를 넘는 경우, 가장 오래된 키 값을 **제거** 합니다.
+
+`get()` 과 `set()` 함수는 무조건 평균 `O(1)` 의 시간 복잡도 내에 실행되어야 합니다.
+
+## 구현
+
+### 버전 1: 더블 링크드 리스트 + 해시맵
+
+[LRUCache.js](./LRUCache.js) 에서 `LRUCache` 구현체 예시를 확인할 수 있습니다. 예시에서는 (평균적으로) 빠른 `O(1)` 캐시 아이템 접근을 위해 `HashMap` 을 사용했고, (평균적으로) 빠른 `O(1)` 캐시 아이템 수정과 제거를 위해 `DoublyLinkedList` 를 사용했습니다. (허용된 최대의 캐시 용량을 유지하기 위해)
+
+![Linked List](./images/lru-cache.jpg)
+
+_[okso.app](https://okso.app) 으로 만듦_
+
+LRU 캐시가 어떻게 작동하는지 더 많은 예시로 확인하고 싶다면 LRUCache.test.js](./**test**/LRUCache.test.js) 파일을 참고하세요.
+
+### 버전 2: 정렬된 맵
+
+더블 링크드 리스트로 구현한 첫번째 예시는 어떻게 평균 `O(1)` 시간 복잡도가 `set()` 과 `get()` 으로 나올 수 있는지 학습 목적과 이해를 돕기 위해 좋은 예시입니다.
+
+그러나, 더 쉬운 방법은 자바스크립트의 [Map](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Map) 객체를 사용하는 것입니다. 이 `Map` 객체는 키-값 쌍과 키를 **추가하는 순서 원본** 을 지닙니다. 우리는 이걸 아이템을 제거하거나 다시 추가하면서 맵의 "가장 마지막" 동작에서 최근에 사용된 아이템을 유지하기 위해 사용할 수 있습니다. `Map` 의 시작점에 있는 아이템은 캐시 용량이 넘칠 경우 가장 먼저 제거되는 대상입니다. 아이템의 순서는 `map.keys()` 와 같은 `IterableIterator` 을 사용해 확인할 수 있습니다.
+
+해당 구현체는 [LRUCacheOnMap.js](./LRUCacheOnMap.js) 의 `LRUCacheOnMap` 예시에서 확인할 수 있습니다.
+
+이 LRU 캐시 방식이 어떻게 작동하는지 더 많은 테스트 케이스를 확인하고 싶다면 [LRUCacheOnMap.test.js](./__test__/LRUCacheOnMap.test.js) 파일을 참고하세요.
+
+## 복잡도
+
+|                 | 평균   |
+| --------------- | ------ |
+| 공간            | `O(n)` |
+| 아이템 찾기     | `O(1)` |
+| 아이템 설정하기 | `O(1)` |
+
+## 참조
+
+- [LRU Cache on LeetCode](https://leetcode.com/problems/lru-cache/solutions/244744/lru-cache/)
+- [LRU Cache on InterviewCake](https://www.interviewcake.com/concept/java/lru-cache)
+- [LRU Cache on Wiki](https://en.wikipedia.org/wiki/Cache_replacement_policies)
diff --git a/src/data-structures/lru-cache/README.md b/src/data-structures/lru-cache/README.md
index 05bcc0a0f7..eaa075f809 100644
--- a/src/data-structures/lru-cache/README.md
+++ b/src/data-structures/lru-cache/README.md
@@ -1,5 +1,8 @@
 # Least Recently Used (LRU) Cache
 
+_Read this in other languages:_
+[한국어](README.ko-KR.md),
+
 A **Least Recently Used (LRU) Cache** organizes items in order of use, allowing you to quickly identify which item hasn't been used for the longest amount of time.
 
 Picture a clothes rack, where clothes are always hung up on one side. To find the least-recently used item, look at the item on the other end of the rack.
@@ -22,7 +25,7 @@ See the `LRUCache` implementation example in [LRUCache.js](./LRUCache.js). The s
 
 ![Linked List](./images/lru-cache.jpg)
 
-*Made with [okso.app](https://okso.app)*
+_Made with [okso.app](https://okso.app)_
 
 You may also find more test-case examples of how the LRU Cache works in [LRUCache.test.js](./__test__/LRUCache.test.js) file.
 
@@ -38,11 +41,11 @@ You may also find more test-case examples of how the LRU Cache works in [LRUCach
 
 ## Complexities
 
-|   | Average |
-|---|---|
-| Space |`O(n)`|
-| Get item | `O(1)` |
-| Set item | `O(1)` |
+|          | Average |
+| -------- | ------- |
+| Space    | `O(n)`  |
+| Get item | `O(1)`  |
+| Set item | `O(1)`  |
 
 ## References
 

From 0c054f782aa57f4dbc56975452406b73cba8dc09 Mon Sep 17 00:00:00 2001
From: Youssef Rabei <youssefrabei2003@gmail.com>
Date: Sat, 13 Jul 2024 22:22:10 +0300
Subject: [PATCH 254/264] Update README.ar-AR.md (#959)

Co-authored-by: Oleksii Trekhleb <3000285+trekhleb@users.noreply.github.com>
---
 README.ar-AR.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.ar-AR.md b/README.ar-AR.md
index fedd29c0e5..81c9c91a6f 100644
--- a/README.ar-AR.md
+++ b/README.ar-AR.md
@@ -3,7 +3,7 @@
 [![Build Status](https://travis-ci.org/trekhleb/javascript-algorithms.svg?branch=master)](https://travis-ci.org/trekhleb/javascript-algorithms)
 [![codecov](https://codecov.io/gh/trekhleb/javascript-algorithms/branch/master/graph/badge.svg)](https://codecov.io/gh/trekhleb/javascript-algorithms)
 
-تحتوي هذا مقالة على أمثلة عديدة تستند إلى الخوارزميات الشائعة وهياكل البيانات في الجافا سكريبت.
+تحتوي هذه المقالة على أمثلة عديدة تستند إلى الخوارزميات الشائعة وهياكل البيانات في الجافا سكريبت.
 
 كل خوارزمية وهياكل البيانات لها برنامج README منفصل خاص بها
 مع التفسيرات والروابط ذات الصلة لمزيد من القراءة (بما في ذلك تلك

From 0e2b2574f83d94adfe5822b1f09203ee60a34a31 Mon Sep 17 00:00:00 2001
From: Nikita Gurskiy <85452618+lilipops@users.noreply.github.com>
Date: Sat, 13 Jul 2024 21:23:02 +0200
Subject: [PATCH 255/264] update the ES README a lenguage correction (#952)

---
 README.es-ES.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.es-ES.md b/README.es-ES.md
index 24d1990a41..e6879a19cd 100644
--- a/README.es-ES.md
+++ b/README.es-ES.md
@@ -70,7 +70,7 @@ definen con precisión una secuencia de operaciones.
 * **Matemáticas**
   * `P` [Manipulación de bits](src/algorithms/math/bits) - asignar/obtener/actualizar/limpiar bits, multiplicación/división por dos, hacer negativo, etc.
   * `P` [Factorial](src/algorithms/math/factorial)
-  * `P` [Número de Fibonacci](src/algorithms/math/fibonacci)
+  * `P` [Sucesión de Fibonacci](src/algorithms/math/fibonacci)
   * `P` [Prueba de primalidad](src/algorithms/math/primality-test) (método de división de prueba)
   * `P` [Algoritmo de Euclides](src/algorithms/math/euclidean-algorithm) - calcular el Máximo común divisor (MCD)
   * `P` [Mínimo común múltiplo](src/algorithms/math/least-common-multiple) (MCM)

From 351a63a59fdea2e27eb69d50be897c7416a5951a Mon Sep 17 00:00:00 2001
From: Alaz Tetik <alaztetik@gmail.com>
Date: Sat, 13 Jul 2024 22:25:58 +0300
Subject: [PATCH 256/264] Update README.md by correcting Turkish lang name
 (#904)

Co-authored-by: Oleksii Trekhleb <3000285+trekhleb@users.noreply.github.com>

From 471e6d0791167756d0a7f35a2a197e235bca73f7 Mon Sep 17 00:00:00 2001
From: Enzo <enzovivallo05@hotmail.com>
Date: Sat, 13 Jul 2024 15:27:09 -0400
Subject: [PATCH 257/264] Add es-ES translation to search/binary-search (#893)

---
 .../search/binary-search/README.es-ES.md      | 27 +++++++++++++++++++
 src/algorithms/search/binary-search/README.md | 17 ++++++------
 .../search/binary-search/README.pt-BR.md      |  1 +
 3 files changed, 37 insertions(+), 8 deletions(-)
 create mode 100644 src/algorithms/search/binary-search/README.es-ES.md

diff --git a/src/algorithms/search/binary-search/README.es-ES.md b/src/algorithms/search/binary-search/README.es-ES.md
new file mode 100644
index 0000000000..f14aef985f
--- /dev/null
+++ b/src/algorithms/search/binary-search/README.es-ES.md
@@ -0,0 +1,27 @@
+# Búsqueda binaria
+
+_Lea esto en otros idiomas:_
+[English](README.md)
+[Português brasileiro](README.pt-BR.md).
+
+En informática, la búsqueda binaria, también conocida como búsqueda de medio intervalo
+búsqueda, búsqueda logarítmica, o corte binario, es un algoritmo de búsqueda
+que encuentra la posición de un valor objetivo dentro de una matriz
+ordenada. La búsqueda binaria compara el valor objetivo con el elemento central
+de la matriz; si son desiguales, se elimina la mitad en la que
+la mitad en la que no puede estar el objetivo se elimina y la búsqueda continúa
+en la mitad restante hasta que tenga éxito. Si la búsqueda
+termina con la mitad restante vacía, el objetivo no está
+en la matriz.
+
+![Búsqueda binaria](https://upload.wikimedia.org/wikipedia/commons/8/83/Binary_Search_Depiction.svg)
+
+## Complejidad
+
+**Complejidad de tiempo**: `O(log(n))` - ya que dividimos el área de búsqueda en dos para cada
+siguiente iteración.
+
+## Referencias
+
+- [Wikipedia](https://en.wikipedia.org/wiki/Binary_search_algorithm)
+- [YouTube](https://www.youtube.com/watch?v=P3YID7liBug&index=29&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
diff --git a/src/algorithms/search/binary-search/README.md b/src/algorithms/search/binary-search/README.md
index ebf3e123e0..34d1bd7a40 100644
--- a/src/algorithms/search/binary-search/README.md
+++ b/src/algorithms/search/binary-search/README.md
@@ -2,15 +2,16 @@
 
 _Read this in other languages:_
 [Português brasileiro](README.pt-BR.md).
+[Español](README.es-ES.md).
 
-In computer science, binary search, also known as half-interval 
-search, logarithmic search, or binary chop, is a search algorithm 
-that finds the position of a target value within a sorted 
-array. Binary search compares the target value to the middle 
-element of the array; if they are unequal, the half in which 
-the target cannot lie is eliminated and the search continues 
-on the remaining half until it is successful. If the search 
-ends with the remaining half being empty, the target is not 
+In computer science, binary search, also known as half-interval
+search, logarithmic search, or binary chop, is a search algorithm
+that finds the position of a target value within a sorted
+array. Binary search compares the target value to the middle
+element of the array; if they are unequal, the half in which
+the target cannot lie is eliminated and the search continues
+on the remaining half until it is successful. If the search
+ends with the remaining half being empty, the target is not
 in the array.
 
 ![Binary Search](https://upload.wikimedia.org/wikipedia/commons/8/83/Binary_Search_Depiction.svg)
diff --git a/src/algorithms/search/binary-search/README.pt-BR.md b/src/algorithms/search/binary-search/README.pt-BR.md
index 14445a048e..4f9de9f199 100644
--- a/src/algorithms/search/binary-search/README.pt-BR.md
+++ b/src/algorithms/search/binary-search/README.pt-BR.md
@@ -2,6 +2,7 @@
 
 _Leia isso em outras línguas:_
 [english](README.md).
+[Español](README.es-ES.md).
 
 Em ciência da computação, busca binária, também conhecida como busca de meio-intervalo, busca logarítmica ou corte binário, é um algoritmo de pesquisa
 que encontra a posição de um elemento alvo dentro de um

From e7f30a7bf76ffcbcd37a3163f2a5c8f346aea2e2 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Vicente=20Guti=C3=A9rrez?= <gtz.rvera@gmail.com>
Date: Sat, 13 Jul 2024 13:28:02 -0600
Subject: [PATCH 258/264] Fix typos README.es-ES for linked list (#850)

---
 src/data-structures/linked-list/README.es-ES.md | 12 ++++++------
 1 file changed, 6 insertions(+), 6 deletions(-)

diff --git a/src/data-structures/linked-list/README.es-ES.md b/src/data-structures/linked-list/README.es-ES.md
index c21c48cded..6c6ba7ee87 100644
--- a/src/data-structures/linked-list/README.es-ES.md
+++ b/src/data-structures/linked-list/README.es-ES.md
@@ -7,9 +7,9 @@ _Lee este artículo en otros idiomas:_
 [_Português_](README.pt-BR.md)
 [_English_](README.md)
 
-En ciencias de la computaciòn una **lista enlazada** es una  coleccion linear
-de elementos de datos, en los cuales el orden linear no es dado por
-su posciòn fisica en memoria. En cambio, cada
+En ciencias de la computación una **lista enlazada** es una  colección lineal 
+de elementos, en los cuales el orden lineal no es dado por
+su posición física en memoria. En cambio, cada 
 elemento señala al siguiente. Es una estructura de datos
 que consiste en un grupo de nodos los cuales juntos representan
 una secuencia. En su forma más sencilla, cada nodo está
@@ -19,10 +19,10 @@ permite la inserción o eliminación de elementos
 desde cualquier posición en la secuencia durante la iteración.
 Las variantes más complejas agregan enlaces adicionales, permitiendo
 una eficiente inserción o eliminación desde referencias arbitrarias
-del elemento. Una desventaja de las listas lazadas es que el tiempo de
+del elemento. Una desventaja de las listas enlazadas es que el tiempo de
 acceso es lineal (y difícil de canalizar). Un acceso
 más rápido, como un acceso aleatorio, no es factible. Los arreglos
-tienen una mejor locazion en caché comparados con las listas lazadas.
+tienen una mejor localización en caché comparados con las listas enlazadas.
 
 ![Linked List](./images/linked-list.jpeg)
 
@@ -112,7 +112,7 @@ Remove(head, value)
 end Remove
 ```
 
-### Atrevesar
+### Atravesar
 
 ```text
 Traverse(head)

From ca3d16dcce7a493ae12c03ca20ede4fd7801f7a2 Mon Sep 17 00:00:00 2001
From: Vlad Sosnov <vladsosnov2001@gmail.com>
Date: Sat, 13 Jul 2024 21:28:34 +0200
Subject: [PATCH 259/264] Update README.uk-UA.md (#991)

Co-authored-by: Oleksii Trekhleb <3000285+trekhleb@users.noreply.github.com>
---
 src/data-structures/stack/README.uk-UA.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/src/data-structures/stack/README.uk-UA.md b/src/data-structures/stack/README.uk-UA.md
index 9941114f5b..f71d2274eb 100644
--- a/src/data-structures/stack/README.uk-UA.md
+++ b/src/data-structures/stack/README.uk-UA.md
@@ -10,8 +10,8 @@
 Додаткова операція для читання головного елемента (peek) дає доступ
 до останнього елементу стека без зміни самого стека.
 
-Найчастіше принцип роботи стека порівнюють зі чаркою тарілок: щоб узяти другу
-зверху потрібно зняти верхню.
+Найчастіше принцип роботи стека порівнюють із стопкою тарілок: щоб узяти другу
+зверху потрібно спочатку зняти верхню.
 
 Ілюстрація роботи зі стеком.
 

From ae869ef3faf4f7547e6b047a1d48f45927dd76a4 Mon Sep 17 00:00:00 2001
From: Omotayo Obafemi <obafemitayor@gmail.com>
Date: Sun, 1 Oct 2023 13:21:29 +0100
Subject: [PATCH 260/264] Added algorithm problem that can be solved using
 stack data structure

---
 README.md                                     |  2 +
 .../stack/valid-parentheses/README.md         | 44 +++++++++++++++++++
 .../__test__/validParentheses.test.js         | 23 ++++++++++
 .../valid-parentheses/validParentheses.js     | 42 ++++++++++++++++++
 4 files changed, 111 insertions(+)
 create mode 100644 src/algorithms/stack/valid-parentheses/README.md
 create mode 100644 src/algorithms/stack/valid-parentheses/__test__/validParentheses.test.js
 create mode 100644 src/algorithms/stack/valid-parentheses/validParentheses.js

diff --git a/README.md b/README.md
index a20673989c..da1d9dda10 100644
--- a/README.md
+++ b/README.md
@@ -143,6 +143,8 @@ a set of rules that precisely define a sequence of operations.
 * **Linked Lists**
   * `B` [Straight Traversal](src/algorithms/linked-list/traversal)
   * `B` [Reverse Traversal](src/algorithms/linked-list/reverse-traversal)
+* **Stack**
+  * `B` [Valid Parentheses](src/algorithms/stack/valid-parentheses)  - check if a string has valid parentheses in the correct order
 * **Trees**
   * `B` [Depth-First Search](src/algorithms/tree/depth-first-search) (DFS)
   * `B` [Breadth-First Search](src/algorithms/tree/breadth-first-search) (BFS)
diff --git a/src/algorithms/stack/valid-parentheses/README.md b/src/algorithms/stack/valid-parentheses/README.md
new file mode 100644
index 0000000000..31d7fd60f3
--- /dev/null
+++ b/src/algorithms/stack/valid-parentheses/README.md
@@ -0,0 +1,44 @@
+# Valid Parentheses Problem
+
+Given a string s containing just the characters '(', ')', '{', '}', '[' and ']', determine if the input string is valid.
+
+An input string is valid if:
+
+Open brackets must be closed by the same type of brackets.
+Open brackets must be closed in the correct order.
+Every close bracket has a corresponding open bracket of the same type.
+ 
+
+Example 1:
+
+`Input: s = "()"`
+
+Output: true
+
+Example 2:
+
+`Input: s = "()[]{}"`
+
+Output: true
+
+Example 3:
+
+`Input: s = "(]"`
+
+Output: false
+
+This is actually a very common interview question and a very good example of how to use a stack data structure to solve problems. 
+
+## Solution
+The problem can be solved in two ways
+
+### Bruteforce Approach
+We can iterate through the string and then for each character in the string, we check for it's last closing character in the the string. Once we find the last closing character in the string, we remove both characters and then repeat the iteration, if we don't find a closing character for an opening character, then the string is invalid. The time complexity of this would be O(n^2) which is not so efficient.
+
+### Using a Stack
+We can use a hashtable to store all opening characters and the value would be the respective closing character. We can then iterate through the string and if we encounter an opening parantheses, we push it's closing character to the stack. If we ecounter a closing paraentheses, then we pop the stack and confirm that the popped element is equal to the current closing parentheses character. If it is not then the string is invalid. At the end of the iteration, we also need to check that the stack is empty. If it is not then the string is invalid. If it is, then the string is valid. This is a more efficient approach with a Time complexity and Space complexity of O(n).
+
+
+## References
+
+- [Leetcode](https://leetcode.com/problems/valid-parentheses/)
diff --git a/src/algorithms/stack/valid-parentheses/__test__/validParentheses.test.js b/src/algorithms/stack/valid-parentheses/__test__/validParentheses.test.js
new file mode 100644
index 0000000000..e286688dfd
--- /dev/null
+++ b/src/algorithms/stack/valid-parentheses/__test__/validParentheses.test.js
@@ -0,0 +1,23 @@
+import isValid from '../validParentheses';
+
+describe('validParentheses', () => {
+  it('should return false when string is empty', () => {
+    expect(isValid('')).toBe(false);
+  });
+
+  it('should return true when string contains valid parentheses in correct order', () => {
+    expect(isValid('()')).toBe(true);
+    expect(isValid('()[]{}')).toBe(true);
+    expect(isValid('((({[]})))')).toBe(true);
+  });
+
+  it('should return false when string contains invalid parentheses', () => {
+    expect(isValid('(]')).toBe(false);
+    expect(isValid('()[]{} }')).toBe(false);
+    expect(isValid('((({[(]})))')).toBe(false);
+  });
+
+  it('should return false when string contains valid parentheses in wrong order', () => {
+    expect(isValid('({)}')).toBe(false);
+  });
+});
diff --git a/src/algorithms/stack/valid-parentheses/validParentheses.js b/src/algorithms/stack/valid-parentheses/validParentheses.js
new file mode 100644
index 0000000000..a327780768
--- /dev/null
+++ b/src/algorithms/stack/valid-parentheses/validParentheses.js
@@ -0,0 +1,42 @@
+import Stack from '../../../data-structures/stack/Stack';
+import HashTable from '../../../data-structures/hash-table/HashTable';
+
+// Declare hashtable containg opening parentheses as key and it's closing parentheses as value.
+const hashTable = new HashTable(3);
+hashTable.set('{', '}');
+hashTable.set('(', ')');
+hashTable.set('[', ']');
+
+/**
+ * Check if string has valid parentheses.
+ *
+ * @param {string} parenthesesString
+ * @return {boolean}
+ */
+export default function isValid(parenthesesString) {
+  // If string is empty return false
+  if (parenthesesString.length === 0) {
+    return false;
+  }
+  // Create stack
+  const stack = new Stack();
+
+  // Loop through each character of string
+  for (let i = 0; i < parenthesesString.length; i += 1) {
+    const currentCharacter = parenthesesString[i];
+    // If character is opening parentheses push it's closing parentheses to stack
+    if (hashTable.has(currentCharacter)) {
+      stack.push(hashTable.get(currentCharacter));
+    } else {
+      /* If character is a closing parentheses then,:
+      check If stack is empty, if it is return false.
+      if stack is not empty, pop from stack and compare it with current character.
+      If they are not same return false. */
+      if (stack.isEmpty() || stack.pop() !== currentCharacter) {
+        return false;
+      }
+    }
+  }
+  // If stack is empty return true else return false
+  return stack.isEmpty();
+}

From 49e0814c434d52c66403a19f0c8c05bd2dfa6628 Mon Sep 17 00:00:00 2001
From: Gianfranco P <899175+gianpaj@users.noreply.github.com>
Date: Fri, 20 Dec 2024 19:35:01 +0000
Subject: [PATCH 261/264] "Italiano" is "italian" in italian :)

---
 README.md | 22 +++++++++++-----------
 1 file changed, 11 insertions(+), 11 deletions(-)

diff --git a/README.md b/README.md
index da1d9dda10..ace86b9c0b 100644
--- a/README.md
+++ b/README.md
@@ -31,7 +31,7 @@ _Read this in other languages:_
 [_Português_](README.pt-BR.md),
 [_Русский_](README.ru-RU.md),
 [_Türkçe_](README.tr-TR.md),
-[_Italiana_](README.it-IT.md),
+[_Italiano_](README.it-IT.md),
 [_Bahasa Indonesia_](README.id-ID.md),
 [_Українська_](README.uk-UA.md),
 [_Arabic_](README.ar-AR.md),
@@ -199,7 +199,7 @@ algorithm is an abstraction higher than a computer program.
 * **Brute Force** - look at all the possibilities and selects the best solution
   * `B` [Linear Search](src/algorithms/search/linear-search)
   * `B` [Rain Terraces](src/algorithms/uncategorized/rain-terraces) - trapping rain water problem
-  * `B` [Recursive Staircase](src/algorithms/uncategorized/recursive-staircase) - count the number of ways to reach to the top
+  * `B` [Recursive Staircase](src/algorithms/uncategorized/recursive-staircase) - count the number of ways to reach the top
   * `A` [Maximum Subarray](src/algorithms/sets/maximum-subarray)
   * `A` [Travelling Salesman Problem](src/algorithms/graph/travelling-salesman) - shortest possible route that visits each city and returns to the origin city
   * `A` [Discrete Fourier Transform](src/algorithms/math/fourier-transform) - decompose a function of time (a signal) into the frequencies that make it up
@@ -230,7 +230,7 @@ algorithm is an abstraction higher than a computer program.
   * `B` [Jump Game](src/algorithms/uncategorized/jump-game)
   * `B` [Unique Paths](src/algorithms/uncategorized/unique-paths)
   * `B` [Rain Terraces](src/algorithms/uncategorized/rain-terraces) - trapping rain water problem
-  * `B` [Recursive Staircase](src/algorithms/uncategorized/recursive-staircase) - count the number of ways to reach to the top
+  * `B` [Recursive Staircase](src/algorithms/uncategorized/recursive-staircase) - count the number of ways to reach the top
   * `B` [Seam Carving](src/algorithms/image-processing/seam-carving) - content-aware image resizing algorithm
   * `A` [Levenshtein Distance](src/algorithms/string/levenshtein-distance) - minimum edit distance between two sequences
   * `A` [Longest Common Subsequence](src/algorithms/sets/longest-common-subsequence) (LCS)
@@ -243,9 +243,9 @@ algorithm is an abstraction higher than a computer program.
   * `A` [Bellman-Ford Algorithm](src/algorithms/graph/bellman-ford) - finding the shortest path to all graph vertices
   * `A` [Floyd-Warshall Algorithm](src/algorithms/graph/floyd-warshall) - find the shortest paths between all pairs of vertices
   * `A` [Regular Expression Matching](src/algorithms/string/regular-expression-matching)
-* **Backtracking** - similarly to brute force, try to generate all possible solutions, but each time you generate next solution you test
-if it satisfies all conditions, and only then continue generating subsequent solutions. Otherwise, backtrack, and go on a
-different path of finding a solution. Normally the DFS traversal of state-space is being used.
+* **Backtracking** - similarly to brute force, try to generate all possible solutions, but each time you generate the next solution, you test
+if it satisfies all conditions and only then continue generating subsequent solutions. Otherwise, backtrack and go on a
+different path to finding a solution. Normally the DFS traversal of state-space is being used.
   * `B` [Jump Game](src/algorithms/uncategorized/jump-game)
   * `B` [Unique Paths](src/algorithms/uncategorized/unique-paths)
   * `B` [Power Set](src/algorithms/sets/power-set) - all subsets of a set
@@ -255,8 +255,8 @@ different path of finding a solution. Normally the DFS traversal of state-space
   * `A` [Combination Sum](src/algorithms/sets/combination-sum) - find all combinations that form specific sum
 * **Branch & Bound** - remember the lowest-cost solution found at each stage of the backtracking
 search, and use the cost of the lowest-cost solution found so far as a lower bound on the cost of
-a least-cost solution to the problem, in order to discard partial solutions with costs larger than the
-lowest-cost solution found so far. Normally BFS traversal in combination with DFS traversal of state-space
+a least-cost solution to the problem in order to discard partial solutions with costs larger than the
+lowest-cost solution found so far. Normally, BFS traversal in combination with DFS traversal of state-space
 tree is being used.
 
 ## How to use this repository
@@ -296,14 +296,14 @@ rm -rf ./node_modules
 npm i
 ```
 
-Also make sure that you're using a correct Node version (`>=16`). If you're using [nvm](https://github.com/nvm-sh/nvm) for Node version management you may run `nvm use` from the root folder of the project and the correct version will be picked up.
+Also, make sure that you're using the correct Node version (`>=16`). If you're using [nvm](https://github.com/nvm-sh/nvm) for Node version management you may run `nvm use` from the root folder of the project and the correct version will be picked up.
 
 **Playground**
 
 You may play with data-structures and algorithms in `./src/playground/playground.js` file and write
 tests for it in `./src/playground/__test__/playground.test.js`.
 
-Then just simply run the following command to test if your playground code works as expected:
+Then just, simply run the following command to test if your playground code works as expected:
 
 ```
 npm test -- 'playground'
@@ -319,7 +319,7 @@ npm test -- 'playground'
 ### Big O Notation
 
 *Big O notation* is used to classify algorithms according to how their running time or space requirements grow as the input size grows.
-On the chart below you may find most common orders of growth of algorithms specified in Big O notation.
+On the chart below, you may find the most common orders of growth of algorithms specified in Big O notation.
 
 ![Big O graphs](./assets/big-o-graph.png)
 

From bd4990955bdd4f06a37d3baa16b6a7910a8401dc Mon Sep 17 00:00:00 2001
From: Maxwell Knight <maxwell.knight98@gmail.com>
Date: Tue, 15 Oct 2024 11:04:00 +0300
Subject: [PATCH 262/264] feat: Added hebrew translation to README in all
 languages

---
 README.ar-AR.md |   1 +
 README.de-DE.md |   1 +
 README.es-ES.md |   1 +
 README.fr-FR.md |   1 +
 README.he-HE.md | 370 ++++++++++++++++++++++++++++++++++++++++++++++++
 README.id-ID.md |   1 +
 README.it-IT.md |   1 +
 README.ja-JP.md |   1 +
 README.ko-KR.md |   1 +
 README.md       |   3 +-
 README.pl-PL.md |   1 +
 README.pt-BR.md |   1 +
 README.ru-RU.md |   1 +
 README.tr-TR.md |   1 +
 README.uk-UA.md |   1 +
 README.uz-UZ.md |   1 +
 README.vi-VN.md |  41 +++---
 README.zh-CN.md |   1 +
 README.zh-TW.md |   1 +
 19 files changed, 409 insertions(+), 21 deletions(-)
 create mode 100644 README.he-HE.md

diff --git a/README.ar-AR.md b/README.ar-AR.md
index 81c9c91a6f..39997e24a5 100644
--- a/README.ar-AR.md
+++ b/README.ar-AR.md
@@ -25,6 +25,7 @@ _اقرأ هذا في لغات أخرى:_
 [_Tiếng Việt_](README.vi-VN.md),
 [_Deutsch_](README.de-DE.md),
 [_Uzbek_](README.uz-UZ.md)
+[_עברית_](README.he-HE.md)
 
  ☝ ملاحضة هذا المشروع مخصص للاستخدام لأغراض التعلم والبحث
 فقط ، و ** ليست ** معدة للاستخدام في **الإنتاج**
diff --git a/README.de-DE.md b/README.de-DE.md
index 9663f7b06b..e8f1b4b22b 100644
--- a/README.de-DE.md
+++ b/README.de-DE.md
@@ -26,6 +26,7 @@ _Lies dies in anderen Sprachen:_
 [_Українська_](README.uk-UA.md),
 [_Arabic_](README.ar-AR.md),
 [_Uzbek_](README.uz-UZ.md)
+[_עברית_](README.he-HE.md)
 
 _☝ Beachte, dass dieses Projekt nur für Lern- und Forschungszwecke gedacht ist und **nicht** für den produktiven Einsatz verwendet werden soll_
 
diff --git a/README.es-ES.md b/README.es-ES.md
index e6879a19cd..de4d6889f8 100644
--- a/README.es-ES.md
+++ b/README.es-ES.md
@@ -27,6 +27,7 @@ _Léelo en otros idiomas:_
 [_Tiếng Việt_](README.vi-VN.md),
 [_Deutsch_](README.de-DE.md),
 [_Uzbek_](README.uz-UZ.md)
+[_עברית_](README.he-HE.md)
 
 *☝ Nótese que este proyecto está pensado con fines de aprendizaje e investigación,
 y **no** para ser usado en producción.*
diff --git a/README.fr-FR.md b/README.fr-FR.md
index be8258befd..d24d5db915 100644
--- a/README.fr-FR.md
+++ b/README.fr-FR.md
@@ -28,6 +28,7 @@ _Lisez ceci dans d'autres langues:_
 [_Tiếng Việt_](README.vi-VN.md),
 [_Deutsch_](README.de-DE.md),
 [_Uzbek_](README.uz-UZ.md)
+[_עברית_](README.he-HE.md)
 
 ## Data Structures
 
diff --git a/README.he-HE.md b/README.he-HE.md
new file mode 100644
index 0000000000..43ef196e60
--- /dev/null
+++ b/README.he-HE.md
@@ -0,0 +1,370 @@
+# אלגוריתמים ומבני נתונים ב-JavaScript
+
+[![CI](https://github.com/trekhleb/javascript-algorithms/workflows/CI/badge.svg)](https://github.com/trekhleb/javascript-algorithms/actions?query=workflow%3ACI+branch%3Amaster)
+[![codecov](https://codecov.io/gh/trekhleb/javascript-algorithms/branch/master/graph/badge.svg)](https://codecov.io/gh/trekhleb/javascript-algorithms)
+![גודל המאגר](https://img.shields.io/github/repo-size/trekhleb/javascript-algorithms.svg)
+
+מאגר זה מכיל דוגמאות מבוססות JavaScript של אלגוריתמים ומבני נתונים פופולריים רבים.
+
+לכל אלגוריתם ומבנה נתונים יש README משלו עם הסברים קשורים וקישורים לקריאה נוספת (כולל קישורים לסרטוני YouTube).
+
+_קרא זאת בשפות אחרות:_
+[_简体中文_](README.zh-CN.md),
+[_繁體中文_](README.zh-TW.md),
+[_한국어_](README.ko-KR.md),
+[_日本語_](README.ja-JP.md),
+[_Polski_](README.pl-PL.md),
+[_Français_](README.fr-FR.md),
+[_Español_](README.es-ES.md),
+[_Português_](README.pt-BR.md),
+[_Русский_](README.ru-RU.md),
+[_Türkçe_](README.tr-TR.md),
+[_Italiana_](README.it-IT.md),
+[_Bahasa Indonesia_](README.id-ID.md),
+[_Українська_](README.uk-UA.md),
+[_Arabic_](README.ar-AR.md),
+[_Tiếng Việt_](README.vi-VN.md),
+[_Deutsch_](README.de-DE.md),
+[_Uzbek_](README.uz-UZ.md)
+
+*☝ שים לב שפרויקט זה מיועד למטרות לימוד ומחקר בלבד, ואינו מיועד לשימוש בייצור.*
+
+## מבני נתונים
+
+מבנה נתונים הוא דרך מסוימת לארגן ולאחסן נתונים במחשב כך שניתן לגשת אליהם ולשנות אותם ביעילות. ליתר דיוק, מבנה נתונים הוא אוסף של ערכי נתונים, היחסים ביניהם, והפונקציות או הפעולות שניתן ליישם על הנתונים.
+
+זכור שלכל מבנה נתונים יש את היתרונות והחסרונות שלו. חשוב לשים לב יותר לסיבה שבגללה אתה בוחר מבנה נתונים מסוים מאשר לאופן היישום שלו.
+
+`B` - מתחיל, `A` - מתקדם
+
+* `B` [רשימה מקושרת](src/data-structures/linked-list)
+* `B` [רשימה מקושרת כפולה](src/data-structures/doubly-linked-list)
+* `B` [תור](src/data-structures/queue)
+* `B` [מחסנית](src/data-structures/stack)
+* `B` [טבלת גיבוב](src/data-structures/hash-table)
+* `B` [ערימה](src/data-structures/heap) - גרסאות מקסימום ומינימום
+* `B` [תור עדיפויות](src/data-structures/priority-queue)
+* `A` [עץ תחיליות](src/data-structures/trie)
+* `A` [עץ](src/data-structures/tree)
+  * `A` [עץ חיפוש בינארי](src/data-structures/tree/binary-search-tree)
+  * `A` [עץ AVL](src/data-structures/tree/avl-tree)
+  * `A` [עץ אדום-שחור](src/data-structures/tree/red-black-tree)
+  * `A` [עץ מקטעים](src/data-structures/tree/segment-tree) - עם דוגמאות לשאילתות מינימום/מקסימום/סכום של טווח
+  * `A` [עץ פנוויק](src/data-structures/tree/fenwick-tree) (עץ בינארי מאונדקס)
+* `A` [גרף](src/data-structures/graph) (מכוון ולא מכוון)
+* `A` [קבוצה מופרדת](src/data-structures/disjoint-set) - מבנה נתונים של איחוד-מציאה או מיזוג-מציאה
+* `A` [מסנן בלום](src/data-structures/bloom-filter)
+* `A` [מטמון LRU](src/data-structures/lru-cache/) - מטמון פחות שימוש לאחרונה (LRU)
+
+## אלגוריתמים
+
+אלגוריתם הוא מפרט חד משמעי כיצד לפתור סוג של בעיות. זוהי קבוצה של כללים המגדירים במדויק רצף של פעולות.
+
+`B` - מתחיל, `A` - מתקדם
+
+### אלגוריתמים לפי נושא
+
+* **מתמטיקה**
+  * `B` [מניפולציה על ביטים](src/algorithms/math/bits) - קביעה/עדכון/ניקוי ביטים, הכפלה/חילוק ב-2, הפיכה לשלילי וכו'
+  * `B` [נקודה צפה בינארית](src/algorithms/math/binary-floating-point) - ייצוג בינארי של מספרים בנקודה צפה
+  * `B` [פקטוריאל](src/algorithms/math/factorial)
+  * `B` [מספר פיבונאצ'י](src/algorithms/math/fibonacci) - גרסאות קלאסיות וסגורות
+  * `B` [גורמים ראשוניים](src/algorithms/math/prime-factors) - מציאת גורמים ראשוניים וספירתם באמצעות משפט הארדי-רמנוג'אן
+  * `B` [בדיקת ראשוניות](src/algorithms/math/primality-test) (שיטת החלוקה הניסיונית)
+  * `B` [אלגוריתם אוקלידס](src/algorithms/math/euclidean-algorithm) - חישוב המחלק המשותף הגדול ביותר (GCD)
+  * `B` [המכפיל המשותף הקטן ביותר](src/algorithms/math/least-common-multiple) (LCM)
+  * `B` [נפה של ארטוסתנס](src/algorithms/math/sieve-of-eratosthenes) - מציאת כל המספרים הראשוניים עד לגבול כלשהו
+  * `B` [האם חזקה של שתיים](src/algorithms/math/is-power-of-two) - בדיקה אם מספר הוא חזקה של שתיים (אלגוריתמים נאיביים וביטיים)
+  * `B` [משולש פסקל](src/algorithms/math/pascal-triangle)
+  * `B` [מספר מרוכב](src/algorithms/math/complex-number) - מספרים מרוכבים ופעולות בסיסיות עליהם
+  * `B` [רדיאן ומעלות](src/algorithms/math/radian) - המרה מרדיאנים למעלות ובחזרה
+  * `B` [חזקה מהירה](src/algorithms/math/fast-powering)
+  * `B` [שיטת הורנר](src/algorithms/math/horner-method) - הערכת פולינום
+  * `B` [מטריצות](src/algorithms/math/matrix) - מטריצות ופעולות בסיסיות על מטריצות (כפל, טרנספוזיציה וכו')
+  * `B` [מרחק אוקלידי](src/algorithms/math/euclidean-distance) - מרחק בין שתי נקודות/וקטורים/מטריצות
+  * `A` [חלוקת מספר שלם](src/algorithms/math/integer-partition)
+  * `A` [שורש ריבועי](src/algorithms/math/square-root) - שיטת ניוטון
+  * `A` [אלגוריתם π של ליו הוי](src/algorithms/math/liu-hui) - חישובי π מקורבים על בסיס N-גונים
+  * `A` [התמרת פורייה הבדידה](src/algorithms/math/fourier-transform) - פירוק פונקציה של זמן (אות) לתדרים המרכיבים אותה
+
+* **קבוצות**
+  * `B` [מכפלה קרטזית](src/algorithms/sets/cartesian-product) - מכפלה של מספר קבוצות
+  * `B` [ערבוב פישר-ייטס](src/algorithms/sets/fisher-yates) - תמורה אקראית של רצף סופי
+  * `A` [קבוצת חזקה](src/algorithms/sets/power-set) - כל תתי הקבוצות של קבוצה (פתרונות ביטיים, מעקב לאחור וקסקדה)
+  * `A` [תמורות](src/algorithms/sets/permutations) (עם ובלי חזרות)
+  * `A` [צירופים](src/algorithms/sets/combinations) (עם ובלי חזרות)
+  * `A` [תת-רצף משותף ארוך ביותר](src/algorithms/sets/longest-common-subsequence) (LCS)
+  * `A` [תת-רצף עולה ארוך ביותר](src/algorithms/sets/longest-increasing-subsequence)
+  * `A` [על-רצף משותף קצר ביותר](src/algorithms/sets/shortest-common-supersequence) (SCS)
+  * `A` [בעיית התרמיל](src/algorithms/sets/knapsack-problem) - "0/1" ו"לא מוגבל"
+  * `A` [תת-מערך מקסימלי](src/algorithms/sets/maximum-subarray) - "כוח ברוטלי" ו"תכנות דינמי" (Kadane) גרסאות
+  * `A` [סכום צירוף](src/algorithms/sets/combination-sum) - מציאת כל הצירופים שיוצרים סכום ספציפי
+
+* **מחרוזות**
+  * `B` [מרחק המינג](src/algorithms/string/hamming-distance) - מספר העמדות שבהן הסמלים שונים
+  * `B` [פלינדרום](src/algorithms/string/palindrome) - בדיקה אם המחרוזת זהה בקריאה לאחור
+  * `A` [מרחק לוונשטיין](src/algorithms/string/levenshtein-distance) - מרחק העריכה המינימלי בין שתי רצפים
+  * `A` [אלגוריתם קנות'-מוריס-פראט](src/algorithms/string/knuth-morris-pratt) (אלגוריתם KMP) - חיפוש תת-מחרוזת (התאמת תבנית)
+  * `A` [אלגוריתם Z](src/algorithms/string/z-algorithm) - חיפוש תת-מחרוזת (התאמת תבנית)
+  * `A` [אלגוריתם רבין קארפ](src/algorithms/string/rabin-karp) - חיפוש תת-מחרוזת
+  * `A` [תת-מחרוזת משותפת ארוכה ביותר](src/algorithms/string/longest-common-substring)
+  * `A` [התאמת ביטוי רגולרי](src/algorithms/string/regular-expression-matching)
+
+* **חיפושים**
+  * `B` [חיפוש לינארי](src/algorithms/search/linear-search)
+  * `B` [חיפוש קפיצות](src/algorithms/search/jump-search) (או חיפוש בלוקים) - חיפוש במערך ממוין
+  * `B` [חיפוש בינארי](src/algorithms/search/binary-search) - חיפוש במערך ממוין
+  * `B` [חיפוש אינטרפולציה](src/algorithms/search/interpolation-search) - חיפוש במערך ממוין עם התפלגות אחידה
+
+* **מיון**
+  * `B` [מיון בועות](src/algorithms/sorting/bubble-sort)
+  * `B` [מיון בחירה](src/algorithms/sorting/selection-sort)
+  * `B` [מיון הכנסה](src/algorithms/sorting/insertion-sort)
+  * `B` [מיון ערימה](src/algorithms/sorting/heap-sort)
+  * `B` [מיון מיזוג](src/algorithms/sorting/merge-sort)
+  * `B` [מיון מהיר](src/algorithms/sorting/quick-sort) - יישומים במקום ולא במקום
+  * `B` [מיון צדפות](src/algorithms/sorting/shell-sort)
+  * `B` [מיון ספירה](src/algorithms/sorting/counting-sort)
+  * `B` [מיון בסיס](src/algorithms/sorting/radix-sort)
+  * `B` [מיון דלי](src/algorithms/sorting/bucket-sort)
+
+* **רשימות מקושרות**
+  * `B` [מעבר ישר](src/algorithms/linked-list/traversal)
+  * `B` [מעבר הפוך](src/algorithms/linked-list/reverse-traversal)
+
+* **עצים**
+  * `B` [חיפוש לעומק](src/algorithms/tree/depth-first-search) (DFS)
+  * `B` [חיפוש לרוחב](src/algorithms/tree/breadth-first-search) (BFS)
+
+* **גרפים**
+  * `B` [חיפוש לעומק](src/algorithms/graph/depth-first-search) (DFS)
+  * `B` [חיפוש לרוחב](src/algorithms/graph/breadth-first-search) (BFS)
+  * `B` [אלגוריתם קרוסקל](src/algorithms/graph/kruskal) - מציאת עץ פורש מינימלי (MST) עבור גרף לא מכוון משוקלל
+  * `A` [אלגוריתם דייקסטרה](src/algorithms/graph/dijkstra) - מציאת המסלולים הקצרים ביותר לכל קודקודי הגרף מקודקוד יחיד
+  * `A` [אלגוריתם בלמן-פורד](src/algorithms/graph/bellman-ford) - מציאת המסלולים הקצרים ביותר לכל קודקודי הגרף מקודקוד יחיד
+  * `A` [אלגוריתם פלויד-וורשל](src/algorithms/graph/floyd-warshall) - מציאת המסלולים הקצרים ביותר בין כל זוגות הקודקודים
+  * `A` [זיהוי מעגל](src/algorithms/graph/detect-cycle) - עבור גרפים מכוונים ולא מכוונים (גרסאות מבוססות DFS וקבוצה מופרדת)
+  * `A` [אלגוריתם פרים](src/algorithms/graph/prim) - מציאת עץ פורש מינימלי (MST) עבור גרף לא מכוון משוקלל
+  * `A` [מיון טופולוגי](src/algorithms/graph/topological-sorting) - שיטת DFS
+  * `A` [נקודות חיתוך](src/algorithms/graph/articulation-points) - אלגוריתם טרג'ן (מבוסס DFS)
+  * `A` [גשרים](src/algorithms/graph/bridges) - אלגוריתם מבוסס DFS
+  * `A` [מסלול ומעגל אוילר](src/algorithms/graph/eulerian-path) - אלגוריתם פלרי - ביקור בכל קשת בדיוק פעם אחת
+  * `A` [מעגל המילטון](src/algorithms/graph/hamiltonian-cycle) - ביקור בכל קודקוד בדיוק פעם אחת
+  * `A` [רכיבים קשירים חזק](src/algorithms/graph/strongly-connected-components) - אלגוריתם קוסרג'ו
+  * `A` [בעיית הסוכן הנוסע](src/algorithms/graph/travelling-salesman) - המסלול הקצר ביותר האפשרי שמבקר בכל עיר וחוזר לעיר המוצא
+
+* **הצפנה**
+  * `B` [גיבוב פולינומי](src/algorithms/cryptography/polynomial-hash) - פונקציית גיבוב מתגלגלת המבוססת על פולינום
+  * `B` [צופן גדר מסילה](src/algorithms/cryptography/rail-fence-cipher) - אלגוריתם הצפנת טרנספוזיציה להצפנת הודעות
+  * `B` [צופן קיסר](src/algorithms/cryptography/caesar-cipher) - צופן החלפה פשוט
+  * `B` [צופן היל](src/algorithms/cryptography/hill-cipher) - צופן החלפה המבוסס על אלגברה לינארית
+
+* **למידת מכונה**
+  * `B` [NanoNeuron](https://github.com/trekhleb/nano-neuron) - 7 פונקציות JS פשוטות שמדגימות כיצד מכונות יכולות ללמוד באמת (תפוצה קדימה/אחורה)
+  * `B` [k-NN](src/algorithms/ml/knn) - אלגוריתם סיווג k-השכנים הקרובים ביותר
+  * `B` [k-Means](src/algorithms/ml/k-means) - אלגוריתם אשכול k-Means
+
+* **עיבוד תמונה**
+  * `B` [Seam Carving](src/algorithms/image-processing/seam-carving) - אלגוריתם שינוי גודל תמונה מודע תוכן
+
+* **סטטיסטיקה**
+  * `B` [משקל אקראי](src/algorithms/statistics/weighted-random) - בחירת פריט אקראי מהרשימה על בסיס משקלי הפריטים
+
+* **אלגוריתמים אבולוציוניים**
+  * `A` [אלגוריתם גנטי](https://github.com/trekhleb/self-parking-car-evolution) - דוגמה לאופן שבו ניתן ליישם אלגוריתם גנטי לאימון מכוניות בחניה עצמית
+
+* **לא מסווג**
+  * `B` [מגדלי האנוי](src/algorithms/uncategorized/hanoi-tower)
+  * `B` [סיבוב מטריצה ריבועית](src/algorithms/uncategorized/square-matrix-rotation) - אלגוריתם במקום
+  * `B` [משחק הקפיצות](src/algorithms/uncategorized/jump-game) - דוגמאות למעקב לאחור, תכנות דינמי (מלמעלה למטה + מלמטה למעלה) וחמדני
+  * `B` [מסלולים ייחודיים](src/algorithms/uncategorized/unique-paths) - דוגמאות למעקב לאחור, תכנות דינמי ומבוססות על משולש פסקל
+  * `B` [מדרגות גשם](src/algorithms/uncategorized/rain-terraces) - בעיית לכידת מי גשם (גרסאות תכנות דינמי וכוח ברוטלי)
+  * `B` [מדרגות רקורסיביות](src/algorithms/uncategorized/recursive-staircase) - ספירת מספר הדרכים להגיע לראש (4 פתרונות)
+  * `B` [הזמן הטוב ביותר לקנות ולמכור מניות](src/algorithms/uncategorized/best-time-to-buy-sell-stocks) - דוגמאות לחלוקה וכיבוש ומעבר אחד
+  * `A` [בעיית N-המלכות](src/algorithms/uncategorized/n-queens)
+  * `A` [סיור הפרש](src/algorithms/uncategorized/knight-tour)
+
+### אלגוריתמים לפי פרדיגמה
+
+פרדיגמה אלגוריתמית היא שיטה או גישה כללית המונחת בבסיס התכנון של מחלקת אלגוריתמים. זוהי הפשטה גבוהה יותר מהמושג של אלגוריתם, בדיוק כפי שאלגוריתם הוא הפשטה גבוהה יותר מתוכנית מחשב.
+
+* **כוח ברוטלי** - בודק את כל האפשרויות ובוחר את הפתרון הטוב ביותר
+  * `B` [חיפוש לינארי](src/algorithms/search/linear-search)
+  * `B` [מדרגות גשם](src/algorithms/uncategorized/rain-terraces) - בעיית לכידת מי גשם
+  * `B` [מדרגות רקורסיביות](src/algorithms/uncategorized/recursive-staircase) - ספירת מספר הדרכים להגיע לראש
+  * `A` [תת-מערך מקסימלי](src/algorithms/sets/maximum-subarray)
+  * `A` [בעיית הסוכן הנוסע](src/algorithms/graph/travelling-salesman) - המסלול הקצר ביותר האפשרי שמבקר בכל עיר וחוזר לעיר המוצא
+  * `A` [התמרת פורייה הבדידה](src/algorithms/math/fourier-transform) - פירוק פונקציה של זמן (אות) לתדרים המרכיבים אותה
+
+* **חמדני** - בוחר את האפשרות הטובה ביותר בזמן הנוכחי, ללא כל התחשבות בעתיד
+  * `B` [משחק הקפיצות](src/algorithms/uncategorized/jump-game)
+  * `A` [בעיית התרמיל הלא מוגבל](src/algorithms/sets/knapsack-problem)
+  * `A` [אלגוריתם דייקסטרה](src/algorithms/graph/dijkstra) - מציאת המסלולים הקצרים ביותר לכל קודקודי הגרף
+  * `A` [אלגוריתם פרים](src/algorithms/graph/prim) - מציאת עץ פורש מינימלי (MST) עבור גרף לא מכוון משוקלל
+  * `A` [אלגוריתם קרוסקל](src/algorithms/graph/kruskal) - מציאת עץ פורש מינימלי (MST) עבור גרף לא מכוון משוקלל
+
+* **חלוקה וכיבוש** - מחלק את הבעיה לחלקים קטנים יותר ואז פותר חלקים אלה
+  * `B` [חיפוש בינארי](src/algorithms/search/binary-search)
+  * `B` [מגדלי האנוי](src/algorithms/uncategorized/hanoi-tower)
+  * `B` [משולש פסקל](src/algorithms/math/pascal-triangle)
+  * `B` [אלגוריתם אוקלידס](src/algorithms/math/euclidean-algorithm) - חישוב המחלק המשותף הגדול ביותר (GCD)
+  * `B` [מיון מיזוג](src/algorithms/sorting/merge-sort)
+  * `B` [מיון מהיר](src/algorithms/sorting/quick-sort)
+  * `B` [חיפוש לעומק בעץ](src/algorithms/tree/depth-first-search) (DFS)
+  * `B` [חיפוש לעומק בגרף](src/algorithms/graph/depth-first-search) (DFS)
+  * `B` [מטריצות](src/algorithms/math/matrix) - יצירה ומעבר על מטריצות בצורות שונות
+  * `B` [משחק הקפיצות](src/algorithms/uncategorized/jump-game)
+  * `B` [חזקה מהירה](src/algorithms/math/fast-powering)
+  * `B` [הזמן הטוב ביותר לקנות ולמכור מניות](src/algorithms/uncategorized/best-time-to-buy-sell-stocks) - דוגמאות לחלוקה וכיבוש ומעבר אחד
+  * `A` [תמורות](src/algorithms/sets/permutations) (עם ובלי חזרות)
+  * `A` [צירופים](src/algorithms/sets/combinations) (עם ובלי חזרות)
+  * `A` [תת-מערך מקסימלי](src/algorithms/sets/maximum-subarray)
+
+* **תכנות דינמי** - בניית פתרון באמצעות תת-פתרונות שנמצאו קודם לכן
+  * `B` [מספר פיבונאצ'י](src/algorithms/math/fibonacci)
+  * `B` [משחק הקפיצות](src/algorithms/uncategorized/jump-game)
+  * `B` [מסלולים ייחודיים](src/algorithms/uncategorized/unique-paths)
+  * `B` [מדרגות גשם](src/algorithms/uncategorized/rain-terraces) - בעיית לכידת מי גשם
+  * `B` [מדרגות רקורסיביות](src/algorithms/uncategorized/recursive-staircase) - ספירת מספר הדרכים להגיע לראש
+  * `B` [Seam Carving](src/algorithms/image-processing/seam-carving) - אלגוריתם שינוי גודל תמונה מודע תוכן
+  * `A` [מרחק לוונשטיין](src/algorithms/string/levenshtein-distance) - מרחק העריכה המינימלי בין שתי רצפים
+  * `A` [תת-רצף משותף ארוך ביותר](src/algorithms/sets/longest-common-subsequence) (LCS)
+  * `A` [תת-מחרוזת משותפת ארוכה ביותר](src/algorithms/string/longest-common-substring)
+  * `A` [תת-רצף עולה ארוך ביותר](src/algorithms/sets/longest-increasing-subsequence)
+  * `A` [על-רצף משותף קצר ביותר](src/algorithms/sets/shortest-common-supersequence)
+  * `A` [בעיית התרמיל 0/1](src/algorithms/sets/knapsack-problem)
+  * `A` [חלוקת מספר שלם](src/algorithms/math/integer-partition)
+  * `A` [תת-מערך מקסימלי](src/algorithms/sets/maximum-subarray)
+  * `A` [אלגוריתם בלמן-פורד](src/algorithms/graph/bellman-ford) - מציאת המסלולים הקצרים ביותר לכל קודקודי הגרף
+  * `A` [אלגוריתם פלויד-וורשל](src/algorithms/graph/floyd-warshall) - מציאת המסלולים הקצרים ביותר בין כל זוגות הקודקודים
+  * `A` [התאמת ביטוי רגולרי](src/algorithms/string/regular-expression-matching)
+
+* **מעקב לאחור** - בדומה לכוח ברוטלי, מנסה לייצר את כל הפתרונות האפשריים, אך בכל פעם שאתה מייצר פתרון הבא אתה בודק אם הוא עומד בכל התנאים, ורק אז ממשיך לייצר פתרונות הבאים. אחרת, חוזר אחורה, והולך בנתיב אחר של מציאת פתרון. בדרך כלל מעבר DFS של מרחב המצבים משמש.
+  * `B` [משחק הקפיצות](src/algorithms/uncategorized/jump-game)
+  * `B` [מסלולים ייחודיים](src/algorithms/uncategorized/unique-paths)
+  * `B` [קבוצת חזקה](src/algorithms/sets/power-set) - כל תתי הקבוצות של קבוצה
+  * `A` [מעגל המילטון](src/algorithms/graph/hamiltonian-cycle) - ביקור בכל קודקוד בדיוק פעם אחת
+  * `A` [בעיית N-המלכות](src/algorithms/uncategorized/n-queens)
+  * `A` [סיור הפרש](src/algorithms/uncategorized/knight-tour)
+  * `A` [סכום צירוף](src/algorithms/sets/combination-sum) - מציאת כל הצירופים שיוצרים סכום ספציפי
+
+* **סניף וחסום** - זוכר את הפתרון בעלות הנמוכה ביותר שנמצא בכל שלב של החיפוש המעקב לאחור, ומשתמש בעלות של הפתרון בעלות הנמוכה ביותר שנמצא עד כה כגבול תחתון על העלות של פתרון בעלות מינימלית לבעיה, על מנת לפסול פתרונות חלקיים עם עלויות גדולות יותר מהפתרון בעלות הנמוכה ביותר שנמצא עד כה. בדרך כלל מעבר BFS בשילוב עם מעבר DFS של עץ מרחב המצבים משמש.
+
+## כיצד להשתמש במאגר זה
+
+**התקנת כל התלויות**
+
+```
+npm install
+```
+
+**הרצת ESLint**
+
+ייתכן שתרצה להריץ אותו כדי לבדוק את איכות הקוד.
+
+```
+npm run lint
+```
+
+**הרצת כל הבדיקות**
+
+```
+npm test
+```
+
+**הרצת בדיקות לפי שם**
+
+```
+npm test -- 'LinkedList'
+```
+
+**פתרון בעיות**
+
+אם הלינטינג או הבדיקות נכשלים, נסה למחוק את התיקייה `node_modules` ולהתקין מחדש את חבילות npm:
+
+```
+rm -rf ./node_modules
+npm i
+```
+
+בנוסף, ודא שאתה משתמש בגרסת Node נכונה (`>=16`). אם אתה משתמש ב-[nvm](https://github.com/nvm-sh/nvm) לניהול גרסאות Node, תוכל להריץ `nvm use` מתיקיית השורש של הפרויקט והגרסה הנכונה תיבחר.
+
+**שטח משחקים**
+
+אתה יכול לשחק עם מבני נתונים ואלגוריתמים בקובץ `./src/playground/playground.js` ולכתוב
+בדיקות עבורו ב-`./src/playground/__test__/playground.test.js`.
+
+לאחר מכן פשוט הרץ את הפקודה הבאה כדי לבדוק אם קוד שטח המשחקים שלך עובד כמצופה:
+
+```
+npm test -- 'playground'
+```
+
+## מידע שימושי
+
+### הפניות
+
+- [▶ מבני נתונים ואלגוריתמים ב-YouTube](https://www.youtube.com/playlist?list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
+- [✍🏻 סקיצות של מבני נתונים](https://okso.app/showcase/data-structures)
+
+### סימון ה-O הגדול
+
+סימון *ה-O הגדול* משמש לסיווג אלגוריתמים לפי כיצד זמן הריצה או דרישות המרחב שלהם גדלים ככל שגודל הקלט גדל.
+בתרשים שלהלן תוכל למצוא את הסדרים הנפוצים ביותר של צמיחת אלגוריתמים המצוינים בסימון ה-O הגדול.
+
+![גרפי ה-O הגדול](./assets/big-o-graph.png)
+
+מקור: [Big O Cheat Sheet](http://bigocheatsheet.com/).
+
+להלן רשימה של כמה מסימוני ה-O הגדול הנפוצים ביותר והשוואות הביצועים שלהם מול גדלים שונים של נתוני קלט.
+
+| סימון ה-O הגדול | חישובים ל-10 אלמנטים | חישובים ל-100 אלמנטים | חישובים ל-1000 אלמנטים |
+| ---------------- | --------------------- | ---------------------- | ----------------------- |
+| **O(1)**         | 1                     | 1                      | 1                       |
+| **O(log N)**     | 3                     | 6                      | 9                       |
+| **O(N)**         | 10                    | 100                    | 1000                    |
+| **O(N log N)**   | 30                    | 600                    | 9000                    |
+| **O(N^2)**       | 100                   | 10000                  | 1000000                 |
+| **O(2^N)**       | 1024                  | 1.26e+29               | 1.07e+301               |
+| **O(N!)**        | 3628800               | 9.3e+157               | 4.02e+2567              |
+
+### מורכבות פעולות מבני נתונים
+
+| מבנה נתונים          | גישה    | חיפוש   | הכנסה   | מחיקה   | הערות  |
+| --------------------- | :-----: | :-----: | :-----: | :-----: | :------ |
+| **מערך**              | 1       | n       | n       | n       |         |
+| **מחסנית**            | n       | n       | 1       | 1       |         |
+| **תור**               | n       | n       | 1       | 1       |         |
+| **רשימה מקושרת**      | n       | n       | 1       | n       |         |
+| **טבלת גיבוב**        | -       | n       | n       | n       | במקרה של פונקציית גיבוב מושלמת, העלויות יהיו O(1) |
+| **עץ חיפוש בינארי**   | n       | n       | n       | n       | במקרה של עץ מאוזן, העלויות יהיו O(log(n)) |
+| **עץ B**              | log(n)  | log(n)  | log(n)  | log(n)  |         |
+| **עץ אדום-שחור**      | log(n)  | log(n)  | log(n)  | log(n)  |         |
+| **עץ AVL**            | log(n)  | log(n)  | log(n)  | log(n)  |         |
+| **מסנן בלום**         | -       | 1       | 1       | -       | תוצאות חיוביות שגויות אפשריות בעת חיפוש |
+
+### מורכבות אלגוריתמי מיון מערכים
+
+| שם                  | הטוב ביותר        | ממוצע               | הגרוע ביותר         | זיכרון  | יציב    | הערות  |
+| ------------------- | :----------------: | :-----------------: | :------------------: | :-----: | :-----: | :------ |
+| **מיון בועות**      | n                  | n<sup>2</sup>       | n<sup>2</sup>        | 1       | כן      |         |
+| **מיון הכנסה**      | n                  | n<sup>2</sup>       | n<sup>2</sup>        | 1       | כן      |         |
+| **מיון בחירה**      | n<sup>2</sup>      | n<sup>2</sup>       | n<sup>2</sup>        | 1       | לא      |         |
+| **מיון ערימה**      | n&nbsp;log(n)      | n&nbsp;log(n)       | n&nbsp;log(n)        | 1       | לא      |         |
+| **מיון מיזוג**      | n&nbsp;log(n)      | n&nbsp;log(n)       | n&nbsp;log(n)        | n       | כן      |         |
+| **מיון מהיר**       | n&nbsp;log(n)      | n&nbsp;log(n)       | n<sup>2</sup>        | log(n)  | לא      | מיון מהיר בדרך כלל מבוצע במקום עם O(log(n)) שטח מחסנית |
+| **מיון צדפות**      | n&nbsp;log(n)      | תלוי ברצף הפער      | n&nbsp;(log(n))<sup>2</sup>  | 1         | לא      |         |
+| **מיון ספירה**      | n + r              | n + r               | n + r                | n + r   | כן      | r - המספר הגדול ביותר במערך |
+| **מיון בסיס**       | n * k              | n * k               | n * k                | n + k   | כן      | k - אורך המפתח הארוך ביותר |
+
+## תומכי הפרויקט
+
+> אתה יכול לתמוך בפרויקט זה דרך ❤️️ [GitHub](https://github.com/sponsors/trekhleb) או ❤️️ [Patreon](https://www.patreon.com/trekhleb).
+
+[אנשים שתומכים בפרויקט זה](https://github.com/trekhleb/javascript-algorithms/blob/master/BACKERS.md) `∑ = 1`
+
+## מחבר
+
+[@trekhleb](https://trekhleb.dev)
+
+כמה [פרויקטים](https://trekhleb.dev/projects/) ו[מאמרים](https://trekhleb.dev/blog/) נוספים על JavaScript ואלגוריתמים ב-[trekhleb.dev](https://trekhleb.dev)* `B` [משחק הקפיצות](src/algorithms/uncategor * `B` [חיפוש בינארי](src/algorithms
diff --git a/README.id-ID.md b/README.id-ID.md
index 2f4310fee3..527abb45f2 100644
--- a/README.id-ID.md
+++ b/README.id-ID.md
@@ -25,6 +25,7 @@ _Baca ini dalam bahasa yang lain:_
 [_Tiếng Việt_](README.vi-VN.md),
 [_Deutsch_](README.de-DE.md),
 [_Uzbek_](README.uz-UZ.md)
+[_עברית_](README.he-HE.md)
 
 _☝ Perhatikan bahwa proyek ini hanya dimaksudkan untuk tujuan pembelajaran dan riset, dan **tidak** dimaksudkan untuk digunakan sebagai produksi._
 
diff --git a/README.it-IT.md b/README.it-IT.md
index a86c52cfbb..63007d80d9 100644
--- a/README.it-IT.md
+++ b/README.it-IT.md
@@ -24,6 +24,7 @@ _Leggilo in altre lingue:_
 [_Tiếng Việt_](README.vi-VN.md),
 [_Deutsch_](README.de-DE.md),
 [_Uzbek_](README.uz-UZ.md)
+[_עברית_](README.he-HE.md)
 
 *☝ Si noti che questo progetto è destinato ad essere utilizzato solo per l'apprendimento e la ricerca e non è destinato ad essere utilizzato per il commercio.*
 
diff --git a/README.ja-JP.md b/README.ja-JP.md
index 6e3a8b8192..fc584780c2 100644
--- a/README.ja-JP.md
+++ b/README.ja-JP.md
@@ -27,6 +27,7 @@ _Read this in other languages:_
 [_Tiếng Việt_](README.vi-VN.md),
 [_Deutsch_](README.de-DE.md),
 [_Uzbek_](README.uz-UZ.md)
+[_עברית_](README.he-HE.md)
 
 ## データ構造
 
diff --git a/README.ko-KR.md b/README.ko-KR.md
index 9aac387e8d..20b6080eda 100644
--- a/README.ko-KR.md
+++ b/README.ko-KR.md
@@ -26,6 +26,7 @@ _Read this in other languages:_
 [_Tiếng Việt_](README.vi-VN.md),
 [_Deutsch_](README.de-DE.md),
 [_Uzbek_](README.uz-UZ.md)
+[_עברית_](README.he-HE.md)
 
 ## 자료 구조
 
diff --git a/README.md b/README.md
index ace86b9c0b..3201136c03 100644
--- a/README.md
+++ b/README.md
@@ -37,7 +37,8 @@ _Read this in other languages:_
 [_Arabic_](README.ar-AR.md),
 [_Tiếng Việt_](README.vi-VN.md),
 [_Deutsch_](README.de-DE.md),
-[_Uzbek_](README.uz-UZ.md)
+[_Uzbek_](README.uz-UZ.md),
+[_עברית_](README.he-HE.md)
 
 *☝ Note that this project is meant to be used for learning and researching purposes
 only, and it is **not** meant to be used for production.*
diff --git a/README.pl-PL.md b/README.pl-PL.md
index 9fac028aa3..f95cfaeb99 100644
--- a/README.pl-PL.md
+++ b/README.pl-PL.md
@@ -28,6 +28,7 @@ _Read this in other languages:_
 [_Tiếng Việt_](README.vi-VN.md),
 [_Deutsch_](README.de-DE.md),
 [_Uzbek_](README.uz-UZ.md)
+[_עברית_](README.he-HE.md)
 
 ## Struktury Danych
 
diff --git a/README.pt-BR.md b/README.pt-BR.md
index edb2bd4417..b451e5da5e 100644
--- a/README.pt-BR.md
+++ b/README.pt-BR.md
@@ -28,6 +28,7 @@ _Leia isto em outros idiomas:_
 [_Tiếng Việt_](README.vi-VN.md),
 [_Deutsch_](README.de-DE.md),
 [_Uzbek_](README.uz-UZ.md)
+[_עברית_](README.he-HE.md)
 
 ## Estrutura de Dados
 
diff --git a/README.ru-RU.md b/README.ru-RU.md
index b926b5eab3..a14171f260 100644
--- a/README.ru-RU.md
+++ b/README.ru-RU.md
@@ -25,6 +25,7 @@ _Читать на других языках:_
 [_Tiếng Việt_](README.vi-VN.md),
 [_Deutsch_](README.de-DE.md),
 [_Uzbek_](README.uz-UZ.md)
+[_עברית_](README.he-HE.md)
 
 *☝ Замечание: этот репозиторий предназначен для учебно-исследовательских целей (**не** для использования в продакшн-системах).*
 
diff --git a/README.tr-TR.md b/README.tr-TR.md
index fada4e0b48..2075132bda 100644
--- a/README.tr-TR.md
+++ b/README.tr-TR.md
@@ -25,6 +25,7 @@ _Read this in other languages:_
 [_Tiếng Việt_](README.vi-VN.md),
 [_Deutsch_](README.de-DE.md),
 [_Uzbek_](README.uz-UZ.md)
+[_עברית_](README.he-HE.md)
 
 *☝ Not, bu proje araştırma ve öğrenme amacı ile yapılmış
 olup üretim için **yapılmamıştır**.*
diff --git a/README.uk-UA.md b/README.uk-UA.md
index e79a8ae845..c636d21b09 100644
--- a/README.uk-UA.md
+++ b/README.uk-UA.md
@@ -25,6 +25,7 @@ _Вивчення матеріалу на інших мовах:_
 [_Tiếng Việt_](README.vi-VN.md),
 [_Deutsch_](README.de-DE.md),
 [_Uzbek_](README.uz-UZ.md)
+[_עברית_](README.he-HE.md)
 
 *☝ Зверніть увагу! Даний проект призначений лише для навчальних та дослідницьких цілей, і він **не** призначений для виробництва (продакшн).*
 
diff --git a/README.uz-UZ.md b/README.uz-UZ.md
index 130c1f99d3..32a8b509bd 100644
--- a/README.uz-UZ.md
+++ b/README.uz-UZ.md
@@ -29,6 +29,7 @@ _Read this in other languages:_
 [_Tiếng Việt_](README.vi-VN.md),
 [_Deutsch_](README.de-DE.md),
 [_Uzbek_](README.uz-UZ.md)
+[_עברית_](README.he-HE.md)
 
 Yodda tuting, bu loyiha faqat o'quv va tadqiqot maqsadida ishlatilishi
 uchun mo'ljallangan va ishlab chiqarishda ishlatilishi **mumkin emas**.
diff --git a/README.vi-VN.md b/README.vi-VN.md
index a5cbb72e07..6fd4deaaa4 100644
--- a/README.vi-VN.md
+++ b/README.vi-VN.md
@@ -25,6 +25,7 @@ _Đọc bằng ngôn ngữ khác:_
 [_Bahasa Indonesia_](README.id-ID.md),
 [_Українська_](README.uk-UA.md),
 [_Arabic_](README.ar-AR.md)
+[_עברית_](README.he-HE.md)
 
 *☝ Dự án này chỉ được sử dụng cho mục đích học tập và nghiên cứu, **không** được dùng
 cho mục đích thương mại.*
@@ -97,19 +98,19 @@ quy tắc xác định chính xác một chuỗi phép toán.
   * `A` [Dãy con chung ngắn nhất](src/algorithms/sets/shortest-common-supersequence) (SCS)
   * `A` [Bài toán xếp ba lô](src/algorithms/sets/knapsack-problem) - dạng 0-1 và không bị chặn
   * `A` [Mảng con lớn nhất](src/algorithms/sets/maximum-subarray) - phiên bản vét cạn và quy hoạch động (Kadane)
-  * `A` [Tổ hợp của tổng](src/algorithms/sets/combination-sum) - tìm tất cả các tổ hợp tạo thành tổng cụ thể 
+  * `A` [Tổ hợp của tổng](src/algorithms/sets/combination-sum) - tìm tất cả các tổ hợp tạo thành tổng cụ thể
 * **Chuỗi**
-  * `B` [Khoảng cách Hamming](src/algorithms/string/hamming-distance) - số các vị trí các ký hiệu khác nhau 
+  * `B` [Khoảng cách Hamming](src/algorithms/string/hamming-distance) - số các vị trí các ký hiệu khác nhau
   * `A` [Khoảng cách Levenshtein](src/algorithms/string/levenshtein-distance) - khoảng cách thay đổi nhỏ nhất giữa hai chuỗi ký tự
-  * `A` [Thuật toán Knuth–Morris–Pratt](src/algorithms/string/knuth-morris-pratt) (thuật toán KMP) - tìm chuỗi con (đối sánh mẫu) 
+  * `A` [Thuật toán Knuth–Morris–Pratt](src/algorithms/string/knuth-morris-pratt) (thuật toán KMP) - tìm chuỗi con (đối sánh mẫu)
   * `A` [Thuật toán Z](src/algorithms/string/z-algorithm) - tìm chuỗi con (đối sánh mẫu)
   * `A` [Thuật toán Rabin Karp](src/algorithms/string/rabin-karp) - tìm chuỗi con
   * `A` [Xâu con chung dài nhất](src/algorithms/string/longest-common-substring)
   * `A` [Phối biểu thức chính quy](src/algorithms/string/regular-expression-matching)
 * **Tìm kiếm**
   * `B` [Tìm kiếm tuyến tính](src/algorithms/search/linear-search)
-  * `B` [Tìm kiếm nhảy](src/algorithms/search/jump-search) (tìm khối) - tìm kiếm trong mảng đã sắp xếp 
-  * `B` [Tìm kiếm nhị phân](src/algorithms/search/binary-search) - tìm kiếm trong mảng đã sắp xếp 
+  * `B` [Tìm kiếm nhảy](src/algorithms/search/jump-search) (tìm khối) - tìm kiếm trong mảng đã sắp xếp
+  * `B` [Tìm kiếm nhị phân](src/algorithms/search/binary-search) - tìm kiếm trong mảng đã sắp xếp
   * `B` [Tìm kiếm nội suy ](src/algorithms/search/interpolation-search) - Tìm kiếm strong mảng có thứ tự được phân phối đồng nhất
 * **Sắp xếp**
   * `B` [Sắp xếp nổi bọt](src/algorithms/sorting/bubble-sort)
@@ -144,12 +145,12 @@ quy tắc xác định chính xác một chuỗi phép toán.
   * `A` [Các thành phần kết nối chặt](src/algorithms/graph/strongly-connected-components) - Thuật toán Kosaraju
   * `A` [Bài toán người bán hàng](src/algorithms/graph/travelling-salesman) - tuyến đường ngắn nhất có thể đến thăm từng thành phố và trở về thành phố gốc
 * **Mật mã học**
-  * `B` [Băm đa thức](src/algorithms/cryptography/polynomial-hash) - lăn hàm băm dựa trên đa thức 
-  * `B` [Mật mã hàng rào đường sắt](src/algorithms/cryptography/rail-fence-cipher) - một thuật toán mật mã chuyển vị để mã hóa thông điệp 
+  * `B` [Băm đa thức](src/algorithms/cryptography/polynomial-hash) - lăn hàm băm dựa trên đa thức
+  * `B` [Mật mã hàng rào đường sắt](src/algorithms/cryptography/rail-fence-cipher) - một thuật toán mật mã chuyển vị để mã hóa thông điệp
   * `B` [Mật mã Caesar](src/algorithms/cryptography/caesar-cipher) - mật mã chuyển vị đơn giản
   * `B` [Mật mã Hill](src/algorithms/cryptography/hill-cipher) - mật mã chuyển vị đơn giản dựa trên đại số tuyến tính
 * **Học máy**
-  * `B` [NanoNeuron](https://github.com/trekhleb/nano-neuron) - 7 hàm JS đơn giản minh họa cách máy tính thực sự có thể học (truyền thuận / truyền ngược) 
+  * `B` [NanoNeuron](https://github.com/trekhleb/nano-neuron) - 7 hàm JS đơn giản minh họa cách máy tính thực sự có thể học (truyền thuận / truyền ngược)
   * `B` [k-NN](src/algorithms/ml/knn) - thuật toán phân loại k láng giềng gần nhất
   * `B` [k-Means](src/algorithms/ml/k-means) - thuật toán phân cụm k-Means
 * **Khác**
@@ -167,22 +168,22 @@ quy tắc xác định chính xác một chuỗi phép toán.
 
 Mẫu hình thuật toán là một phương pháp hoặc cách tiếp cận chung làm cơ sở cho việc thiết kế một
 lớp thuật toán. Nó là một sự trừu tượng cao hơn khái niệm về một thuật toán, cũng giống như
-một thuật toán là một sự trừu tượng cao hơn một chương trình máy tính. 
+một thuật toán là một sự trừu tượng cao hơn một chương trình máy tính.
 
-* **Vét cạn** - xem xét tất cả các khả năng và chọn giải pháp tốt nhất 
+* **Vét cạn** - xem xét tất cả các khả năng và chọn giải pháp tốt nhất
   * `B` [Tìm kiếm tuyến tính](src/algorithms/search/linear-search)
   * `B` [Thu thập nước mưa](src/algorithms/uncategorized/rain-terraces) - bài toán bẫy nước mưa
   * `B` [Cầu thang đệ quy](src/algorithms/uncategorized/recursive-staircase) - đếm số cách lên đến đỉnh
   * `A` [Mảng con lớn nhất](src/algorithms/sets/maximum-subarray)
   * `A` [Bài toán người bán hàng](src/algorithms/graph/travelling-salesman) - tuyến đường ngắn nhất có thể đến thăm từng thành phố và trở về thành phố gốc
   * `A` [Biến đổi Fourier rời rạc](src/algorithms/math/fourier-transform) - phân giải tín hiệu thời gian thành các tần số tạo nên tín hiệu đó
-* **Tham lam** - chọn phương án tốt nhất vào thời điểm hiện tại mà không cần cân nhắc đến tương lai 
+* **Tham lam** - chọn phương án tốt nhất vào thời điểm hiện tại mà không cần cân nhắc đến tương lai
   * `B` [Trò chơi nhảy](src/algorithms/uncategorized/jump-game)
   * `A` [Bài xếp ba lô không bị chặn](src/algorithms/sets/knapsack-problem)
   * `A` [Thuật toán Dijkstra](src/algorithms/graph/dijkstra) - tìm những đường ngắn nhất từ một định tới tất cả các đỉnh
   * `A` [Thuật toán Prim](src/algorithms/graph/prim) - tìm cây bao trùm nhỏ nhất (MST) cho đồ thị vô hướng có trọng số
   * `A` [Thuật toán Kruskal](src/algorithms/graph/kruskal) - tìm cây bao trùm nhỏ nhất (MST) cho đồ thị vô hướng có trọng số
-* **Chia để trị** - chia vấn đề thành các phần nhỏ hơn rồi giải quyết các phần đó 
+* **Chia để trị** - chia vấn đề thành các phần nhỏ hơn rồi giải quyết các phần đó
   * `B` [Tìm kiếm nhị phân](src/algorithms/search/binary-search)
   * `B` [Tháp Hà Nội](src/algorithms/uncategorized/hanoi-tower)
   * `B` [Tam giác Pascal](src/algorithms/math/pascal-triangle)
@@ -191,7 +192,7 @@ một thuật toán là một sự trừu tượng cao hơn một chương trìn
   * `B` [Sắp xếp nhanh](src/algorithms/sorting/quick-sort)
   * `B` [Cây tìm kiếm theo chiều sâu](src/algorithms/tree/depth-first-search) (DFS)
   * `B` [Đồ thị tìm kiếm theo chiều sâu](src/algorithms/graph/depth-first-search) (DFS)
-  * `B` [Ma trận](src/algorithms/math/matrix) - tạo và duyệt các ma trận có kích thước khác nhau 
+  * `B` [Ma trận](src/algorithms/math/matrix) - tạo và duyệt các ma trận có kích thước khác nhau
   * `B` [Trò chơi nhảy](src/algorithms/uncategorized/jump-game)
   * `B` [Tính nhanh lũy thừa](src/algorithms/math/fast-powering)
   * `B` [Thời điểm tốt nhất để mua bán cổ phiếu](src/algorithms/uncategorized/best-time-to-buy-sell-stocks) - ví dụ chia để trị và một đường chuyền
@@ -216,18 +217,18 @@ một thuật toán là một sự trừu tượng cao hơn một chương trìn
   * `A` [Phối biểu thức chính quy](src/algorithms/string/regular-expression-matching)
 * **Quay lui** - tương tự như vét cạn, cố tạo ra tất cả các giải pháp có thể, nhưng mỗi lần bạn tạo ra giải pháp tiếp theo,
 bạn sẽ kiểm tra xem nó có thỏa mãn tất cả các điều kiện hay không và chỉ khi thỏa mãn mới tiếp tục tạo ra các giải pháp tiếp theo.
-Nếu không, hãy quay lại và đi trên một con đường khác để tìm ra giải pháp. Thông thường, truyền DFS của không gian trạng thái được sử dụng. 
+Nếu không, hãy quay lại và đi trên một con đường khác để tìm ra giải pháp. Thông thường, truyền DFS của không gian trạng thái được sử dụng.
   * `B` [Trò chơi nhảy](src/algorithms/uncategorized/jump-game)
   * `B` [Đường đi độc nhất](src/algorithms/uncategorized/unique-paths)
   * `B` [Tập lũy thừa](src/algorithms/sets/power-set) - tập hợp chứa tất cả các tập con
   * `A` [Chu trình Hamilton](src/algorithms/graph/hamiltonian-cycle) - đi qua các đỉnh một lần duy nhất
   * `A` [Bài toán n quân hậu](src/algorithms/uncategorized/n-queens)
   * `A` [Mã đi tuần](src/algorithms/uncategorized/knight-tour)
-  * `A` [Tổ hợp của tổng](src/algorithms/sets/combination-sum) - tìm tất cả các tổ hợp tạo thành tổng cụ thể 
+  * `A` [Tổ hợp của tổng](src/algorithms/sets/combination-sum) - tìm tất cả các tổ hợp tạo thành tổng cụ thể
 * **Branch & Bound** - ghi nhớ giải pháp chi với phí thấp nhất được tìm thấy ở mỗi giai đoạn của quá trình tìm kiếm quay lui,
 sử dụng chi phí của giải pháp có chi phí thấp nhất được tìm thấy cho đến nay như một giới hạn dưới về chi phí của
-một giải pháp ít chi phí nhân cho bài toán, để loại bỏ các giải pháp từng phần với chi phí lớn hơn giải pháp chi phí thấp nhất được tìm thấy cho đến nay. 
-Thông thường BFS duyệt kết hợp với duyệt DFS của cây không gian trạng thái đang được sử dụng. 
+một giải pháp ít chi phí nhân cho bài toán, để loại bỏ các giải pháp từng phần với chi phí lớn hơn giải pháp chi phí thấp nhất được tìm thấy cho đến nay.
+Thông thường BFS duyệt kết hợp với duyệt DFS của cây không gian trạng thái đang được sử dụng.
 
 ## Hướng dẫn sử dụng repository
 
@@ -238,7 +239,7 @@ npm install
 
 **Chạy ESLint**
 
-Bạn có thể muốn chạy nó để kiểm tra chất lượng code. 
+Bạn có thể muốn chạy nó để kiểm tra chất lượng code.
 
 ```
 npm run lint
@@ -259,7 +260,7 @@ npm test -- 'LinkedList'
 Bạn có thể chơi với các cấu trúc dữ liệu và thuật toán trong tệp `./src/playground/playground.js`
 và viết các bài kiểm thử cho nó ở `./src/playground/__test__/playground.test.js`.
 
-Sau đó, chỉ cần chạy lệnh sau để kiểm tra xem sân chơi của bạn có hoạt động như mong đợi hay không: 
+Sau đó, chỉ cần chạy lệnh sau để kiểm tra xem sân chơi của bạn có hoạt động như mong đợi hay không:
 
 ```
 npm test -- 'playground'
@@ -274,7 +275,7 @@ npm test -- 'playground'
 ### Kí hiệu O lớn
 
 *Kí hiệu O lớn* được dùng để phân loại thuật toán theo thời gian chạy hoặc yêu cầu không gian gia tăng khi kích thước đầu vào gia tăng.
-Trên biểu đồ bên dưới, bạn có thể tìm thấy hầu hết các thứ tự tăng trưởng phổ biến của các thuật toán được chỉ định trong ký hiệu O lớn. 
+Trên biểu đồ bên dưới, bạn có thể tìm thấy hầu hết các thứ tự tăng trưởng phổ biến của các thuật toán được chỉ định trong ký hiệu O lớn.
 
 ![Đồ thị O lớn](./assets/big-o-graph.png)
 
diff --git a/README.zh-CN.md b/README.zh-CN.md
index 27982c6553..59b3488142 100644
--- a/README.zh-CN.md
+++ b/README.zh-CN.md
@@ -25,6 +25,7 @@ _Read this in other languages:_
 [_Tiếng Việt_](README.vi-VN.md),
 [_Deutsch_](README.de-DE.md),
 [_Uzbek_](README.uz-UZ.md)
+[_עברית_](README.he-HE.md)
 
 *注意：这个项目仅用于学习和研究，**不是**用于生产环境。*
 
diff --git a/README.zh-TW.md b/README.zh-TW.md
index aeb0547d2e..2bfd9134b7 100644
--- a/README.zh-TW.md
+++ b/README.zh-TW.md
@@ -24,6 +24,7 @@ _Read this in other languages:_
 [_Tiếng Việt_](README.vi-VN.md),
 [_Deutsch_](README.de-DE.md),
 [_Uzbek_](README.uz-UZ.md)
+[_עברית_](README.he-HE.md)
 
 ## 資料結構
 

From c5dd0483bfd873e5f53c6d08f12f0b129caef339 Mon Sep 17 00:00:00 2001
From: trekhleb <3000285+trekhleb@users.noreply.github.com>
Date: Wed, 12 Feb 2025 17:17:52 +0100
Subject: [PATCH 263/264] Fix language code

---
 README.ar-AR.md                    | 2 +-
 README.de-DE.md                    | 2 +-
 README.es-ES.md                    | 2 +-
 README.fr-FR.md                    | 2 +-
 README.he-HE.md => README.he-IL.md | 0
 README.id-ID.md                    | 2 +-
 README.it-IT.md                    | 2 +-
 README.ja-JP.md                    | 2 +-
 README.ko-KR.md                    | 2 +-
 README.md                          | 2 +-
 README.pl-PL.md                    | 2 +-
 README.pt-BR.md                    | 2 +-
 README.ru-RU.md                    | 2 +-
 README.tr-TR.md                    | 2 +-
 README.uk-UA.md                    | 2 +-
 README.uz-UZ.md                    | 2 +-
 README.vi-VN.md                    | 2 +-
 README.zh-CN.md                    | 2 +-
 README.zh-TW.md                    | 2 +-
 19 files changed, 18 insertions(+), 18 deletions(-)
 rename README.he-HE.md => README.he-IL.md (100%)

diff --git a/README.ar-AR.md b/README.ar-AR.md
index 39997e24a5..2ff0baddbd 100644
--- a/README.ar-AR.md
+++ b/README.ar-AR.md
@@ -25,7 +25,7 @@ _اقرأ هذا في لغات أخرى:_
 [_Tiếng Việt_](README.vi-VN.md),
 [_Deutsch_](README.de-DE.md),
 [_Uzbek_](README.uz-UZ.md)
-[_עברית_](README.he-HE.md)
+[_עברית_](README.he-IL.md)
 
  ☝ ملاحضة هذا المشروع مخصص للاستخدام لأغراض التعلم والبحث
 فقط ، و ** ليست ** معدة للاستخدام في **الإنتاج**
diff --git a/README.de-DE.md b/README.de-DE.md
index e8f1b4b22b..019e7d6b39 100644
--- a/README.de-DE.md
+++ b/README.de-DE.md
@@ -26,7 +26,7 @@ _Lies dies in anderen Sprachen:_
 [_Українська_](README.uk-UA.md),
 [_Arabic_](README.ar-AR.md),
 [_Uzbek_](README.uz-UZ.md)
-[_עברית_](README.he-HE.md)
+[_עברית_](README.he-IL.md)
 
 _☝ Beachte, dass dieses Projekt nur für Lern- und Forschungszwecke gedacht ist und **nicht** für den produktiven Einsatz verwendet werden soll_
 
diff --git a/README.es-ES.md b/README.es-ES.md
index de4d6889f8..3a15ada4bd 100644
--- a/README.es-ES.md
+++ b/README.es-ES.md
@@ -27,7 +27,7 @@ _Léelo en otros idiomas:_
 [_Tiếng Việt_](README.vi-VN.md),
 [_Deutsch_](README.de-DE.md),
 [_Uzbek_](README.uz-UZ.md)
-[_עברית_](README.he-HE.md)
+[_עברית_](README.he-IL.md)
 
 *☝ Nótese que este proyecto está pensado con fines de aprendizaje e investigación,
 y **no** para ser usado en producción.*
diff --git a/README.fr-FR.md b/README.fr-FR.md
index d24d5db915..cb30d1833d 100644
--- a/README.fr-FR.md
+++ b/README.fr-FR.md
@@ -28,7 +28,7 @@ _Lisez ceci dans d'autres langues:_
 [_Tiếng Việt_](README.vi-VN.md),
 [_Deutsch_](README.de-DE.md),
 [_Uzbek_](README.uz-UZ.md)
-[_עברית_](README.he-HE.md)
+[_עברית_](README.he-IL.md)
 
 ## Data Structures
 
diff --git a/README.he-HE.md b/README.he-IL.md
similarity index 100%
rename from README.he-HE.md
rename to README.he-IL.md
diff --git a/README.id-ID.md b/README.id-ID.md
index 527abb45f2..9dd908c2e6 100644
--- a/README.id-ID.md
+++ b/README.id-ID.md
@@ -25,7 +25,7 @@ _Baca ini dalam bahasa yang lain:_
 [_Tiếng Việt_](README.vi-VN.md),
 [_Deutsch_](README.de-DE.md),
 [_Uzbek_](README.uz-UZ.md)
-[_עברית_](README.he-HE.md)
+[_עברית_](README.he-IL.md)
 
 _☝ Perhatikan bahwa proyek ini hanya dimaksudkan untuk tujuan pembelajaran dan riset, dan **tidak** dimaksudkan untuk digunakan sebagai produksi._
 
diff --git a/README.it-IT.md b/README.it-IT.md
index 63007d80d9..d749a6aa7f 100644
--- a/README.it-IT.md
+++ b/README.it-IT.md
@@ -24,7 +24,7 @@ _Leggilo in altre lingue:_
 [_Tiếng Việt_](README.vi-VN.md),
 [_Deutsch_](README.de-DE.md),
 [_Uzbek_](README.uz-UZ.md)
-[_עברית_](README.he-HE.md)
+[_עברית_](README.he-IL.md)
 
 *☝ Si noti che questo progetto è destinato ad essere utilizzato solo per l'apprendimento e la ricerca e non è destinato ad essere utilizzato per il commercio.*
 
diff --git a/README.ja-JP.md b/README.ja-JP.md
index fc584780c2..acf9dee8f0 100644
--- a/README.ja-JP.md
+++ b/README.ja-JP.md
@@ -27,7 +27,7 @@ _Read this in other languages:_
 [_Tiếng Việt_](README.vi-VN.md),
 [_Deutsch_](README.de-DE.md),
 [_Uzbek_](README.uz-UZ.md)
-[_עברית_](README.he-HE.md)
+[_עברית_](README.he-IL.md)
 
 ## データ構造
 
diff --git a/README.ko-KR.md b/README.ko-KR.md
index 20b6080eda..d4b0d4ef14 100644
--- a/README.ko-KR.md
+++ b/README.ko-KR.md
@@ -26,7 +26,7 @@ _Read this in other languages:_
 [_Tiếng Việt_](README.vi-VN.md),
 [_Deutsch_](README.de-DE.md),
 [_Uzbek_](README.uz-UZ.md)
-[_עברית_](README.he-HE.md)
+[_עברית_](README.he-IL.md)
 
 ## 자료 구조
 
diff --git a/README.md b/README.md
index 3201136c03..6a98a76fb0 100644
--- a/README.md
+++ b/README.md
@@ -38,7 +38,7 @@ _Read this in other languages:_
 [_Tiếng Việt_](README.vi-VN.md),
 [_Deutsch_](README.de-DE.md),
 [_Uzbek_](README.uz-UZ.md),
-[_עברית_](README.he-HE.md)
+[_עברית_](README.he-IL.md)
 
 *☝ Note that this project is meant to be used for learning and researching purposes
 only, and it is **not** meant to be used for production.*
diff --git a/README.pl-PL.md b/README.pl-PL.md
index f95cfaeb99..56617030ab 100644
--- a/README.pl-PL.md
+++ b/README.pl-PL.md
@@ -28,7 +28,7 @@ _Read this in other languages:_
 [_Tiếng Việt_](README.vi-VN.md),
 [_Deutsch_](README.de-DE.md),
 [_Uzbek_](README.uz-UZ.md)
-[_עברית_](README.he-HE.md)
+[_עברית_](README.he-IL.md)
 
 ## Struktury Danych
 
diff --git a/README.pt-BR.md b/README.pt-BR.md
index b451e5da5e..5b16798bc9 100644
--- a/README.pt-BR.md
+++ b/README.pt-BR.md
@@ -28,7 +28,7 @@ _Leia isto em outros idiomas:_
 [_Tiếng Việt_](README.vi-VN.md),
 [_Deutsch_](README.de-DE.md),
 [_Uzbek_](README.uz-UZ.md)
-[_עברית_](README.he-HE.md)
+[_עברית_](README.he-IL.md)
 
 ## Estrutura de Dados
 
diff --git a/README.ru-RU.md b/README.ru-RU.md
index a14171f260..939ed46700 100644
--- a/README.ru-RU.md
+++ b/README.ru-RU.md
@@ -25,7 +25,7 @@ _Читать на других языках:_
 [_Tiếng Việt_](README.vi-VN.md),
 [_Deutsch_](README.de-DE.md),
 [_Uzbek_](README.uz-UZ.md)
-[_עברית_](README.he-HE.md)
+[_עברית_](README.he-IL.md)
 
 *☝ Замечание: этот репозиторий предназначен для учебно-исследовательских целей (**не** для использования в продакшн-системах).*
 
diff --git a/README.tr-TR.md b/README.tr-TR.md
index 2075132bda..53600480db 100644
--- a/README.tr-TR.md
+++ b/README.tr-TR.md
@@ -25,7 +25,7 @@ _Read this in other languages:_
 [_Tiếng Việt_](README.vi-VN.md),
 [_Deutsch_](README.de-DE.md),
 [_Uzbek_](README.uz-UZ.md)
-[_עברית_](README.he-HE.md)
+[_עברית_](README.he-IL.md)
 
 *☝ Not, bu proje araştırma ve öğrenme amacı ile yapılmış
 olup üretim için **yapılmamıştır**.*
diff --git a/README.uk-UA.md b/README.uk-UA.md
index c636d21b09..5ee5f7cbcc 100644
--- a/README.uk-UA.md
+++ b/README.uk-UA.md
@@ -25,7 +25,7 @@ _Вивчення матеріалу на інших мовах:_
 [_Tiếng Việt_](README.vi-VN.md),
 [_Deutsch_](README.de-DE.md),
 [_Uzbek_](README.uz-UZ.md)
-[_עברית_](README.he-HE.md)
+[_עברית_](README.he-IL.md)
 
 *☝ Зверніть увагу! Даний проект призначений лише для навчальних та дослідницьких цілей, і він **не** призначений для виробництва (продакшн).*
 
diff --git a/README.uz-UZ.md b/README.uz-UZ.md
index 32a8b509bd..114a4de9cc 100644
--- a/README.uz-UZ.md
+++ b/README.uz-UZ.md
@@ -29,7 +29,7 @@ _Read this in other languages:_
 [_Tiếng Việt_](README.vi-VN.md),
 [_Deutsch_](README.de-DE.md),
 [_Uzbek_](README.uz-UZ.md)
-[_עברית_](README.he-HE.md)
+[_עברית_](README.he-IL.md)
 
 Yodda tuting, bu loyiha faqat o'quv va tadqiqot maqsadida ishlatilishi
 uchun mo'ljallangan va ishlab chiqarishda ishlatilishi **mumkin emas**.
diff --git a/README.vi-VN.md b/README.vi-VN.md
index 6fd4deaaa4..4c35f467f8 100644
--- a/README.vi-VN.md
+++ b/README.vi-VN.md
@@ -25,7 +25,7 @@ _Đọc bằng ngôn ngữ khác:_
 [_Bahasa Indonesia_](README.id-ID.md),
 [_Українська_](README.uk-UA.md),
 [_Arabic_](README.ar-AR.md)
-[_עברית_](README.he-HE.md)
+[_עברית_](README.he-IL.md)
 
 *☝ Dự án này chỉ được sử dụng cho mục đích học tập và nghiên cứu, **không** được dùng
 cho mục đích thương mại.*
diff --git a/README.zh-CN.md b/README.zh-CN.md
index 59b3488142..14e0f0e36c 100644
--- a/README.zh-CN.md
+++ b/README.zh-CN.md
@@ -25,7 +25,7 @@ _Read this in other languages:_
 [_Tiếng Việt_](README.vi-VN.md),
 [_Deutsch_](README.de-DE.md),
 [_Uzbek_](README.uz-UZ.md)
-[_עברית_](README.he-HE.md)
+[_עברית_](README.he-IL.md)
 
 *注意：这个项目仅用于学习和研究，**不是**用于生产环境。*
 
diff --git a/README.zh-TW.md b/README.zh-TW.md
index 2bfd9134b7..aa48b40bd8 100644
--- a/README.zh-TW.md
+++ b/README.zh-TW.md
@@ -24,7 +24,7 @@ _Read this in other languages:_
 [_Tiếng Việt_](README.vi-VN.md),
 [_Deutsch_](README.de-DE.md),
 [_Uzbek_](README.uz-UZ.md)
-[_עברית_](README.he-HE.md)
+[_עברית_](README.he-IL.md)
 
 ## 資料結構
 

From e40a67b5d1aaf006622a90e2bda60043f4f66679 Mon Sep 17 00:00:00 2001
From: trekhleb <3000285+trekhleb@users.noreply.github.com>
Date: Wed, 12 Feb 2025 17:19:46 +0100
Subject: [PATCH 264/264] Move "valid parentheses" to the "Uncategorized"
 section

---
 README.md | 3 +--
 1 file changed, 1 insertion(+), 2 deletions(-)

diff --git a/README.md b/README.md
index 6a98a76fb0..3e5c5cc096 100644
--- a/README.md
+++ b/README.md
@@ -144,8 +144,6 @@ a set of rules that precisely define a sequence of operations.
 * **Linked Lists**
   * `B` [Straight Traversal](src/algorithms/linked-list/traversal)
   * `B` [Reverse Traversal](src/algorithms/linked-list/reverse-traversal)
-* **Stack**
-  * `B` [Valid Parentheses](src/algorithms/stack/valid-parentheses)  - check if a string has valid parentheses in the correct order
 * **Trees**
   * `B` [Depth-First Search](src/algorithms/tree/depth-first-search) (DFS)
   * `B` [Breadth-First Search](src/algorithms/tree/breadth-first-search) (BFS)
@@ -188,6 +186,7 @@ a set of rules that precisely define a sequence of operations.
   * `B` [Rain Terraces](src/algorithms/uncategorized/rain-terraces) - trapping rain water problem (dynamic programming and brute force versions)
   * `B` [Recursive Staircase](src/algorithms/uncategorized/recursive-staircase) - count the number of ways to reach to the top (4 solutions)
   * `B` [Best Time To Buy Sell Stocks](src/algorithms/uncategorized/best-time-to-buy-sell-stocks) - divide and conquer and one-pass examples
+  * `B` [Valid Parentheses](src/algorithms/stack/valid-parentheses) - check if a string has valid parentheses (using stack)
   * `A` [N-Queens Problem](src/algorithms/uncategorized/n-queens)
   * `A` [Knight's Tour](src/algorithms/uncategorized/knight-tour)