From 3a9f3f59f8be95dd272e445a6338a246ecded95e Mon Sep 17 00:00:00 2001 From: punit1009 Date: Sun, 5 Oct 2025 18:31:19 +0530 Subject: [PATCH 1/4] chore: add .gitattributes to enforce LF line endings --- .gitattributes | Bin 0 -> 42 bytes 1 file changed, 0 insertions(+), 0 deletions(-) create mode 100644 .gitattributes diff --git a/.gitattributes b/.gitattributes new file mode 100644 index 0000000000000000000000000000000000000000..713f7330977dacbcf6fab1cd4a9fe8de2029cf45 GIT binary patch literal 42 rcmezWPm4i;p@boop#n(SG9)sT0_l99SSpar0gB`>q%rU^a4`S?;*to7 literal 0 HcmV?d00001 From e28d0d611ccd232646759816ea11f0179c152a19 Mon Sep 17 00:00:00 2001 From: punit1009 Date: Sun, 5 Oct 2025 18:32:40 +0530 Subject: [PATCH 2/4] chore: normalize all line endings to LF --- .babelrc | 3 - .editorconfig | 11 - .eslintrc | 21 - .gitattributes | Bin 42 -> 0 bytes .github/FUNDING.yml | 3 - .github/workflows/CI.yml | 35 - .gitignore | 5 - .husky/.gitignore | 1 - .husky/pre-commit | 5 - .npmrc | 1 - .nvmrc 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713f7330977dacbcf6fab1cd4a9fe8de2029cf45..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 42 rcmezWPm4i;p@boop#n(SG9)sT0_l99SSpar0gB`>q%rU^a4`S?;*to7 diff --git a/.github/FUNDING.yml b/.github/FUNDING.yml deleted file mode 100644 index deda41e7d6..0000000000 --- a/.github/FUNDING.yml +++ /dev/null @@ -1,3 +0,0 @@ -# @see: https://docs.github.com/en/github/administering-a-repository/displaying-a-sponsor-button-in-your-repository -github: trekhleb -patreon: trekhleb diff --git a/.github/workflows/CI.yml b/.github/workflows/CI.yml deleted file mode 100644 index e007b6c910..0000000000 --- a/.github/workflows/CI.yml +++ /dev/null @@ -1,35 +0,0 @@ -name: CI - -on: - push: - branches: [ master ] - pull_request: - branches: [ master ] - -jobs: - test: - runs-on: ubuntu-latest - strategy: - matrix: - node-version: [ 16.x ] - - steps: - - name: Checkout repository - uses: actions/checkout@v2 - - - name: Setup Node.js ${{ matrix.node-version }} - uses: actions/setup-node@v1 - with: - node-version: ${{ matrix.node-version }} - - - name: Install dependencies - run: npm i - - - name: Run linting - run: npm run lint - - - name: Run tests - run: npm run coverage - - - name: Upload coverage to Codecov - uses: codecov/codecov-action@v1 diff --git a/.gitignore b/.gitignore deleted file mode 100644 index e128b69788..0000000000 --- a/.gitignore +++ /dev/null @@ -1,5 +0,0 @@ -node_modules -.idea -coverage -.vscode -.DS_Store diff --git a/.husky/.gitignore b/.husky/.gitignore deleted file mode 100644 index 31354ec138..0000000000 --- a/.husky/.gitignore +++ /dev/null @@ -1 +0,0 @@ -_ diff --git a/.husky/pre-commit b/.husky/pre-commit deleted file mode 100755 index 598a5dceaa..0000000000 --- a/.husky/pre-commit +++ /dev/null @@ -1,5 +0,0 @@ -#!/bin/sh -. "$(dirname "$0")/_/husky.sh" - -npm run lint -# npm run test diff --git a/.npmrc b/.npmrc deleted file mode 100644 index b6f27f1359..0000000000 --- a/.npmrc +++ /dev/null @@ -1 +0,0 @@ -engine-strict=true diff --git a/.nvmrc b/.nvmrc deleted file mode 100644 index 7fd023741b..0000000000 --- a/.nvmrc +++ /dev/null @@ -1 +0,0 @@ -v16.15.0 diff --git a/BACKERS.md b/BACKERS.md deleted file mode 100644 index a244d3bed3..0000000000 --- a/BACKERS.md +++ /dev/null @@ -1,48 +0,0 @@ -# Project Backers - -> 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` - - - - diff --git a/CODE_OF_CONDUCT.md b/CODE_OF_CONDUCT.md deleted file mode 100644 index f809c8b0f5..0000000000 --- a/CODE_OF_CONDUCT.md +++ /dev/null @@ -1,40 +0,0 @@ -# Contributor Covenant Code of Conduct - -## Our Pledge - -In the interest of fostering an open and welcoming environment, we as contributors and maintainers pledge to making participation in our project and our community a harassment-free experience for everyone, regardless of age, body size, disability, ethnicity, gender identity and expression, level of experience, nationality, personal appearance, race, religion, or sexual identity and orientation. - -## Our Standards - -Examples of behavior that contributes to creating a positive environment include: - -* Using welcoming and inclusive language -* Being respectful of differing viewpoints and experiences -* Gracefully accepting constructive criticism -* Focusing on what is best for the community -* Showing empathy towards other community members - -Examples of unacceptable behavior by participants include: - -* The use of sexualized language or imagery and unwelcome sexual attention or advances -* Trolling, insulting/derogatory comments, and personal or political attacks -* Public or private harassment -* Publishing others' private information, such as a physical or electronic address, without explicit permission -* Other conduct which could reasonably be considered inappropriate in a professional setting - -## Our Responsibilities - -Project maintainers are responsible for clarifying the standards of acceptable behavior and are expected to take appropriate and fair corrective action in response to any instances of unacceptable behavior. - -Project maintainers have the right and responsibility to remove, edit, or reject comments, commits, code, wiki edits, issues, and other contributions that are not aligned to this Code of Conduct, or to ban temporarily or permanently any contributor for other behaviors that they deem inappropriate, threatening, offensive, or harmful. - -## Scope - -This Code of Conduct applies both within project spaces and in public spaces when an individual is representing the project or its community. Examples of representing a project or community include using an official project e-mail address, posting via an official social media account, or acting as an appointed representative at an online or offline event. Representation of a project may be further defined and clarified by project maintainers. - -## Attribution - -This Code of Conduct is adapted from the [Contributor Covenant][homepage], version 1.4, available at [http://contributor-covenant.org/version/1/4][version] - -[homepage]: http://contributor-covenant.org -[version]: http://contributor-covenant.org/version/1/4/ diff --git a/CONTRIBUTING.md b/CONTRIBUTING.md deleted file mode 100644 index 8f6bf07913..0000000000 --- a/CONTRIBUTING.md +++ /dev/null @@ -1,25 +0,0 @@ -## Contributing - -**General Rules** - -- As much as possible, try to follow the existing format of markdown and code. -- Don't forget to run `npm run lint` and `npm test` before submitting pull requests. -- Make sure that **100%** of your code is covered by tests. - -**Contributing New Translation** - -- Create new `README.xx-XX.md` file with translation alongside with -main `README.md` file where `xx-XX` is [locale and country/region codes](http://www.lingoes.net/en/translator/langcode.htm). -For example `en-US`, `zh-CN`, `zh-TW`, `ko-KR` etc. -- You may also translate all other sub-folders by creating -related `README.xx-XX.md` files in each of them. - -**Contributing New Algorithms** - -- Make your pull requests to be **specific** and **focused**. Instead of -contributing "several sorting algorithms" all at once contribute them all -one by one separately (i.e. one pull request for "Quick Sort", another one -for "Heap Sort" and so on). -- Provide **README.md** for each of the algorithms **with explanations** of -the algorithm and **with links** to further readings. -- Describe what you do in code using **comments**. diff --git a/LICENSE b/LICENSE deleted file mode 100644 index e7885bd74b..0000000000 --- a/LICENSE +++ /dev/null @@ -1,21 +0,0 @@ -The MIT License (MIT) - -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 -in the Software without restriction, including without limitation the rights -to use, copy, modify, merge, publish, distribute, sublicense, and/or sell -copies of the Software, and to permit persons to whom the Software is -furnished to do so, subject to the following conditions: - -The above copyright notice and this permission notice shall be included in all -copies or substantial portions of the Software. - -THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR -IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, -FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE -AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER -LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, -OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE -SOFTWARE. diff --git a/README.ar-AR.md b/README.ar-AR.md deleted file mode 100644 index 2ff0baddbd..0000000000 --- a/README.ar-AR.md +++ /dev/null @@ -1,328 +0,0 @@ -# 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 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 -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), -[_Tiếng Việt_](README.vi-VN.md), -[_Deutsch_](README.de-DE.md), -[_Uzbek_](README.uz-UZ.md) -[_עברית_](README.he-IL.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) - -### 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 | n2 | n2 | 1 | نعم | | -| **Insertion sort** | n | n2 | n2 | 1 | نعم | | -| **Selection sort** | n2 | n2 | n2 | 1 | لا | | -| **Heap sort** | n log(n) | n log(n) | n log(n) | 1 | لا | | -| **Merge sort** | n log(n) | n log(n) | n log(n) | n | نعم | | -| **Quick sort** | n log(n) | n log(n) | n2 | log(n) | No | عادةً ما يتم إجراء الفرز السريع في مكانه مع مساحة مكدس O (log (n))| -| **Shell sort** | n log(n) | depends on gap sequence | n (log(n))2 | 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) `∑ = 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) diff --git a/README.de-DE.md b/README.de-DE.md deleted file mode 100644 index 019e7d6b39..0000000000 --- a/README.de-DE.md +++ /dev/null @@ -1,338 +0,0 @@ -# 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), -[_Uzbek_](README.uz-UZ.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_ - -## 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 | n2 | n2 | 1 | JA | | -| **Insertion sort** | n | n2 | n2 | 1 | Ja | | -| **Selection sort** | n2 | n2 | n2 | 1 | Nein | | -| **Heap sort** | n log(n) | n log(n) | n log(n) | 1 | Nein | | -| **Merge sort** | n log(n) | n log(n) | n log(n) | n | Ja | | -| **Quick sort** | n log(n) | n log(n) | n2 | log(n) | Nein | Quicksort wird normalerweise in-place mit O(log(n)) Stapelplatz ausgeführt | -| **Shell sort** | n log(n) | abhängig von Spaltfolge | n (log(n))2 | 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` - -> 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 deleted file mode 100644 index 3a15ada4bd..0000000000 --- a/README.es-ES.md +++ /dev/null @@ -1,306 +0,0 @@ -# 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?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 -algoritmos y estructuras de datos populares. - -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:_ -[_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), -[_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), -[_Tiếng Việt_](README.vi-VN.md), -[_Deutsch_](README.de-DE.md), -[_Uzbek_](README.uz-UZ.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.* - -## Estructuras de Datos - -Una estructura de datos es una forma particular de organizar y almacenar datos en un ordenador para que puedan accederse -y modificarse de forma eficiente. Más concretamente, una estructura de datos es un conjunto de valores -de datos, las relaciones entre ellos y las funciones u operaciones que se pueden aplicar a -los datos. - -`P` - Principiante, `A` - Avanzado - -* `P` [Lista enlazada](src/data-structures/linked-list) -* `P` [Lista doblemente enlazada](src/data-structures/doubly-linked-list) -* `P` [Cola](src/data-structures/queue) -* `P` [Pila](src/data-structures/stack) -* `P` [Tabla hash](src/data-structures/hash-table) -* `P` [Heap](src/data-structures/heap) - versiones máx y mín -* `P` [Cola de prioridad](src/data-structures/priority-queue) -* `A` [Trie](src/data-structures/trie) -* `A` [Árbol](src/data-structures/tree) - * `A` [Árbol de búsqueda binaria](src/data-structures/tree/binary-search-tree) - * `A` [Árbol AVL](src/data-structures/tree/avl-tree) - * `A` [Árbol Rojo-Negro](src/data-structures/tree/red-black-tree) - * `A` [Árbol de segmentos](src/data-structures/tree/segment-tree) - con ejemplos de consultas de rango mín/máx/suma - * `A` [Árbol de Fenwick](src/data-structures/tree/fenwick-tree) (Árbol binario indexado) -* `A` [Grafo](src/data-structures/graph) (dirigido y no dirigido) -* `A` [Conjuntos disjuntos](src/data-structures/disjoint-set) -* `A` [Filtro de Bloom](src/data-structures/bloom-filter) - -## Algoritmos - -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 - -### Algoritmos por Tema - -* **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` [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) - * `P` [Criba de Eratóstenes](src/algorithms/math/sieve-of-eratosthenes) - encontrar todos los números primos hasta un límite dado - * `P` [Es una potencia de dos?](src/algorithms/math/is-power-of-two) - comprobar si el número es una potencia de dos (algoritmos ingenuos y de bits) - * `P` [Triángulo de Pascal](src/algorithms/math/pascal-triangle) - * `P` [Números complejos](src/algorithms/math/complex-number) - números complejos y operaciones con ellos - * `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` [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 - * `P` [Permutación de Fisher–Yates](src/algorithms/sets/fisher-yates) - permutación aleatoria de una secuencia finita - * `A` [Conjunto potencia](src/algorithms/sets/power-set) - todos los subconjuntos de un conjunto - * `A` [Permutaciones](src/algorithms/sets/permutations) (con y sin repeticiones) - * `A` [Combinaciones](src/algorithms/sets/combinations) (con y sin repeticiones) - * `A` [Subsecuencia común más larga](src/algorithms/sets/longest-common-subsequence) (LCS) - * `A` [Subsecuencia creciente más larga](src/algorithms/sets/longest-increasing-subsequence) - * `A` [Supersecuencia común más corta](src/algorithms/sets/shortest-common-supersequence) (SCS) - * `A` [Problema de la mochila](src/algorithms/sets/knapsack-problem) - "0/1" y "sin límite" - * `A` [Máximo subarreglo](src/algorithms/sets/maximum-subarray) - versiones de "fuerza bruta" y "programación dinámica" (de Kadane) - * `A` [Suma combinada](src/algorithms/sets/combination-sum) - encuentra todas las combinaciones que forman una suma específica -* **Cadenas de caracteres** - * `P` [Distancia de Hamming](src/algorithms/string/hamming-distance) - número de posiciones en las que los símbolos son diferentes - * `A` [Distancia de Levenshtein](src/algorithms/string/levenshtein-distance) - distancia mínima de edición entre dos secuencias - * `A` [Algoritmo Knuth-Morris-Pratt](src/algorithms/string/knuth-morris-pratt) (Algoritmo KMP) - búsqueda de subcadenas (coincidencia de patrones) - * `A` [Algoritmo Z](src/algorithms/string/z-algorithm) - búsqueda de subcadenas (coincidencia de patrones) - * `A` [Algoritmo de Rabin Karp](src/algorithms/string/rabin-karp) - búsqueda de subcadenas - * `A` [Subcadena común más larga](src/algorithms/string/longest-common-substring) - * `A` [Coincidencia por expresiones regulares](src/algorithms/string/regular-expression-matching) -* **Búsquedas** - * `P` [Búsqueda lineal](src/algorithms/search/linear-search) - * `P` [Búsqueda de salto](src/algorithms/search/jump-search) (o Búsqueda de bloque) - búsqueda en una lista ordenada - * `P` [Búsqueda binaria](src/algorithms/search/binary-search) - búsqueda en una lista ordenada - * `P` [Búsqueda por interpolación](src/algorithms/search/interpolation-search) - búsqueda en una lista ordenada uniformemente distribuida -* **Ordenamiento** - * `P` [Ordenamiento de burbuja](src/algorithms/sorting/bubble-sort) - * `P` [Ordenamiento por selección](src/algorithms/sorting/selection-sort) - * `P` [Ordenamiento por inserción](src/algorithms/sorting/insertion-sort) - * `P` [Ordenamiento por Heap](src/algorithms/sorting/heap-sort) - * `P` [Ordenamiento por mezcla](src/algorithms/sorting/merge-sort) - * `P` [Quicksort](src/algorithms/sorting/quick-sort) - implementaciones in situ y no in situ - * `P` [Shellsort](src/algorithms/sorting/shell-sort) - * `P` [Ordenamiento por cuentas](src/algorithms/sorting/counting-sort) - * `P` [Ordenamiento Radix](src/algorithms/sorting/radix-sort) -* **Listas enlazadas** - * `P` [Recorrido directo](src/algorithms/linked-list/traversal) - * `P` [Recorrido inverso](src/algorithms/linked-list/reverse-traversal) -* **Árboles** - * `P` [Búsqueda en profundidad](src/algorithms/tree/depth-first-search) (DFS) - * `P` [Búsqueda en anchura](src/algorithms/tree/breadth-first-search) (BFS) -* **Grafos** - * `P` [Búsqueda en profundidad](src/algorithms/graph/depth-first-search) (DFS) - * `P` [Búsqueda en anchura](src/algorithms/graph/breadth-first-search) (BFS) - * `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` [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 - * `A` [Puntos de articulación](src/algorithms/graph/articulation-points) - algoritmo de Tarjan (basado en DFS) - * `A` [Puentes](src/algorithms/graph/bridges) - algoritmo basado en DFS - * `A` [Camino euleriano y circuito euleriano](src/algorithms/graph/eulerian-path) - algoritmo de Fleury - visitar cada arista exactamente una vez - * `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 -* **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) - * `P` [Rotación de matriz cuadrada](src/algorithms/uncategorized/square-matrix-rotation) - algoritmo in situ - * `P` [Juego de los saltos](src/algorithms/uncategorized/jump-game) - ejemplos de backtracking, programación dinámica (de arriba hacia abajo + de abajo hacia arriba) y voraces - * `P` [Caminos únicos](src/algorithms/uncategorized/unique-paths) - ejemplos de backtracking, programación dinámica y basados en el Triángulo de Pascal - * `P` [Terrazas pluviales](src/algorithms/uncategorized/rain-terraces) - el problema de la retención del agua de lluvia (programación dinámica y fuerza bruta) - * `A` [Problema de las N Reinas](src/algorithms/uncategorized/n-queens) - * `A` [Problema del caballo (Knight tour)](src/algorithms/uncategorized/knight-tour) - -### Algoritmos por paradigma - -Un paradigma algorítmico es un método o enfoque genérico que subyace al diseño de una clase de algoritmos. -Es una abstracción superior a la noción de algoritmo, del mismo modo que un algoritmo es una abstracción superior a un programa de ordenador. - -* **Fuerza Bruta** - mira todas las posibilidades y selecciona la mejor solución - * `P` [Búsqueda lineal](src/algorithms/search/linear-search) - * `P` [Terrazas pluviales](src/algorithms/uncategorized/rain-terraces) - el problema de la retención del agua de lluvia - * `A` [Máximo subarreglo](src/algorithms/sets/maximum-subarray) - * `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 - * `A` [Transformada discreta de Fourier](src/algorithms/math/fourier-transform) - descomponer una función de tiempo (señal) en las frecuencias que la componen -* **Voraces** - escoge la mejor opción en el momento actual, sin ninguna consideración sobre el futuro - * `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` [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) - * `P` [Torre de Hanói](src/algorithms/uncategorized/hanoi-tower) - * `P` [Triángulo de Pascal](src/algorithms/math/pascal-triangle) - * `P` [Algoritmo de Euclides](src/algorithms/math/euclidean-algorithm) - calcular el Máximo Común Divisor (MCD) - * `P` [Ordenamiento por mezcla](src/algorithms/sorting/merge-sort) - * `P` [Quicksort](src/algorithms/sorting/quick-sort) - * `P` [Búsqueda en profundidad (árboles)](src/algorithms/tree/depth-first-search) - (DFS) - * `P` [Búsqueda en profundidad (grafos)](src/algorithms/graph/depth-first-search) - (DFS) - * `P` [Juego de los saltos](src/algorithms/uncategorized/jump-game) - * `P` [Exponenciación rápida](src/algorithms/math/fast-powering) - * `A` [Permutaciones](src/algorithms/sets/permutations) - (con y sin repeticiones) - * `A` [Combinaciones](src/algorithms/sets/combinations) - (con y sin repeticiones) -* **Programación Dinámica** - construye una solución usando sub-soluciones previamente encontradas - * `P` [Número de Fibonacci](src/algorithms/math/fibonacci) - * `P` [Juego de los saltos](src/algorithms/uncategorized/jump-game) - * `P` [Caminos únicos](src/algorithms/uncategorized/unique-paths) - * `P` [Terrazas pluviales](src/algorithms/uncategorized/rain-terraces) - el problema de la retención del agua de lluvia - * `A` [Distancia de Levenshtein](src/algorithms/string/levenshtein-distance) - distancia mínima de edición entre dos secuencias - * `A` [Subsecuencia común más larga](src/algorithms/sets/longest-common-subsequence) (LCS) - * `A` [Subcadena común más larga](src/algorithms/string/longest-common-substring) - * `A` [Subsecuencia creciente más larga](src/algorithms/sets/longest-increasing-subsequence) - * `A` [Supersecuencia común más corta](src/algorithms/sets/shortest-common-supersequence) - * `A` [Problema de la mochila 0/1](src/algorithms/sets/knapsack-problem) - * `A` [Partición entera](src/algorithms/math/integer-partition) - * `A` [Máximo subarreglo](src/algorithms/sets/maximum-subarray) - * `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` [Algoritmo de Floyd-Warshall](src/algorithms/graph/floyd-warshall) - encontrar los caminos más cortos entre todos los pares de vértices - * `A` [Coincidencia por expresiones regulares](src/algorithms/string/regular-expression-matching) -* **De Retorceso (Backtracking)** - De manera similar a la fuerza bruta, trata de generar todas las soluciones posibles, pero cada vez que genere la siguiente solución, comprueba si cumple con todas las condiciones, y sólo entonces continúa generando soluciones posteriores. De lo contrario, retrocede y sigue un camino diferente para encontrar una solución. Normalmente se utiliza un recorrido en profundidad (DFS) del espacio de estados. - * `P` [Juego de los saltos](src/algorithms/uncategorized/jump-game) - * `P` [Caminos únicos](src/algorithms/uncategorized/unique-paths) - * `P` [Conjunto potencia](src/algorithms/sets/power-set) - todos los subconjuntos de un conjunto - * `A` [Ciclo hamiltoniano](src/algorithms/graph/hamiltonian-cycle) - visitar cada vértice exactamente una vez - * `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 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 - -**Instalar las dependencias** - -``` -npm install -``` - -**Correr ESLint** - -Es posible que desee ejecutarlo para comprobar la calidad del código. - -``` -npm run lint -``` - -**Correr los tests** - -``` -npm test -``` - -**Correr tests por nombre** - -``` -npm test -- 'LinkedList' -``` - -**Campo de juegos** - -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: - -``` -npm test -- 'playground' -``` - -## Información útil - -### Referencias - -[▶ Estructuras de datos y algoritmos en YouTube](https://www.youtube.com/playlist?list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8) - -### Notación O Grande - -Orden de crecimiento de los algoritmos especificados en la notación O grande. - -![Gráficas de Notación O grande ](./assets/big-o-graph.png) - -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 -frente a diferentes tamaños de los datos de entrada. - -| Notación O grande | Cálculos para 10 elementos | Cálculos para 100 elementos | Cálculos para 1000 elementos | -| ----------------- | -------------------------- | --------------------------- | ---------------------------- | -| **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 | - -### Complejidad de las operaciones de estructuras de datos - -| Estructura de Datos | Accesso | Busqueda | Inserción | Borrado | Comentarios | -| ------------------------------ | :-----: | :------: | :-------: | :-----: | :-------------------------------------------------------------- | -| **Colección** | 1 | n | n | n | | -| **Stack** | n | n | 1 | 1 | | -| **Cola** | n | n | 1 | 1 | | -| **Lista enlazada** | n | n | 1 | 1 | | -| **Tabla hash** | - | n | n | n | En caso de función hash perfecta los costos serían O(1) | -| **Búsqueda por Árbol binario** | n | n | n | n | En el caso de un árbol equilibrado, los costos serían O(log(n)) | -| **Árbol B** | log(n) | log(n) | log(n) | log(n) | | -| **Árbol Rojo-Negro** | log(n) | log(n) | log(n) | log(n) | | -| **Árbol AVL** | log(n) | log(n) | log(n) | log(n) | | -| **Filtro de Bloom** | - | 1 | 1 | - | Falsos positivos son posibles durante la búsqueda | - -### Complejidad de algoritmos de ordenamiento de arreglos - -| Nombre | Mejor | Promedio | Pero | Memorya | Estable | Comentarios | -| -------------------------------- | :-----------: | :---------------------: | :-------------------------: | :-----: | :-----: | :------------------------------------------------------------ | -| **Ordenamiento de burbuja** | n | n2 | n2 | 1 | Si | | -| **Ordenamiento por inserción** | n | n2 | n2 | 1 | Si | | -| **Ordenamiento por selección** | n2 | n2 | n2 | 1 | No | | -| **Ordenamiento por Heap** | n log(n) | n log(n) | n log(n) | 1 | No | | -| **Ordenamiento por mezcla** | n log(n) | n log(n) | n log(n) | n | Si | | -| **Quicksort** | n log(n) | n log(n) | n2 | log(n) | No | Quicksort utiliza O(log(n)) de espacio en el stack | -| **Shellsort** | n log(n) | depende de la secuencia de huecos | n (log(n))2 | 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 Algunos otros [proyectos](https://trekhleb.dev/projects/) y [artículos](https://trekhleb.dev/blog/) sobre JavaScript y algoritmos en [trekhleb.dev](https://trekhleb.dev) diff --git a/README.fr-FR.md b/README.fr-FR.md deleted file mode 100644 index cb30d1833d..0000000000 --- a/README.fr-FR.md +++ /dev/null @@ -1,300 +0,0 @@ -# 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?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 -algorithmes et structures de données populaires. - -Chaque algorithme et structure de donnée possède son propre README contenant -les explications détaillées et liens (incluant aussi des vidéos Youtube) pour -complément d'informations. - -_Lisez ceci dans d'autres langues:_ -[_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), -[_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), -[_Tiếng Việt_](README.vi-VN.md), -[_Deutsch_](README.de-DE.md), -[_Uzbek_](README.uz-UZ.md) -[_עברית_](README.he-IL.md) - -## Data Structures - -Une structure de données est une manière spéciale d'organiser et de stocker -des données dans un ordinateur de manière à ce que l'on puisse accéder à -cette information et la modifier de manière efficiente. De manière plus -spécifique, une structure de données est un ensemble composé d'une collection -de valeurs, des relations entre ces valeurs ainsi que d'un ensemble de -fonctions ou d'opérations pouvant être appliquées sur ces données. - -`B` - Débutant, `A` - Avancé - -- `B` [Liste Chaînée](src/data-structures/linked-list) -- `B` [Liste Doublement Chaînée](src/data-structures/doubly-linked-list) -- `B` [Queue](src/data-structures/queue) -- `B` [Pile](src/data-structures/stack) -- `B` [Table de Hachage](src/data-structures/hash-table) -- `B` [Tas](src/data-structures/heap) -- `B` [Queue de Priorité](src/data-structures/priority-queue) -- `A` [Trie](src/data-structures/trie) -- `A` [Arbre](src/data-structures/tree) - - `A` [Arbre de recherche Binaire](src/data-structures/tree/binary-search-tree) - - `A` [Arbre AVL](src/data-structures/tree/avl-tree) - - `A` [Arbre Red-Black](src/data-structures/tree/red-black-tree) - - `A` [Arbre de Segments](src/data-structures/tree/segment-tree) - avec exemples de requêtes de type min/max/somme sur intervalles - - `A` [Arbre de Fenwick](src/data-structures/tree/fenwick-tree) (Arbre Binaire Indexé) -- `A` [Graphe](src/data-structures/graph) (orienté et non orienté) -- `A` [Ensembles Disjoints](src/data-structures/disjoint-set) -- `A` [Filtre de Bloom](src/data-structures/bloom-filter) - -## Algorithmes - -Un algorithme est une démarche non ambigüe expliquant comment résoudre une -classe de problèmes. C'est un ensemble de règles décrivant de manière précise -une séquence d'opérations. - -`B` - Débutant, `A` - Avancé - -### Algorithmes par topic - -- **Math** - - `B` [Manipulation de Bit](src/algorithms/math/bits/README.fr-FR.md) - définir/obtenir/mettre à jour/effacer les bits, multiplication/division par deux, négativiser etc. - - `B` [Factorielle](src/algorithms/math/factorial/README.fr-FR.md) - - `B` [Nombre de Fibonacci](src/algorithms/math/fibonacci/README.fr-FR.md) - - `B` [Test de Primalité](src/algorithms/math/primality-test) (méthode du test de division) - - `B` [Algorithme d'Euclide](src/algorithms/math/euclidean-algorithm/README.fr-FR.md) - calcule le Plus Grand Commun Diviseur (PGCD) - - `B` [Plus Petit Commun Multiple](src/algorithms/math/least-common-multiple) (PPCM) - - `B` [Crible d'Eratosthène](src/algorithms/math/sieve-of-eratosthenes) - trouve tous les nombres premiers inférieurs à une certaine limite - - `B` [Puissance de Deux](src/algorithms/math/is-power-of-two) - teste si un nombre donné est une puissance de deux (algorithmes naif et basé sur les opérations bit-à-bit) - - `B` [Triangle de Pascal](src/algorithms/math/pascal-triangle) - - `B` [Nombre complexe](src/algorithms/math/complex-number/README.fr-FR.md) - nombres complexes et opérations de bases - - `A` [Partition Entière](src/algorithms/math/integer-partition) - - `A` [Approximation de π par l'algorithme de Liu Hui](src/algorithms/math/liu-hui) - approximation du calcul de π basé sur les N-gons - - `B` [Exponentiation rapide](src/algorithms/math/fast-powering/README.fr-FR.md) - - `A` [Transformée de Fourier Discrète](src/algorithms/math/fourier-transform/README.fr-FR.md) - décomposer une fonction du temps (un signal) en fréquences qui la composent -- **Ensembles** - - `B` [Produit Cartésien](src/algorithms/sets/cartesian-product) - produit de plusieurs ensembles - - `B` [Mélange de Fisher–Yates](src/algorithms/sets/fisher-yates) - permulation aléatoire d'une séquence finie - - `A` [Ensemble des parties d'un ensemble](src/algorithms/sets/power-set) - tous les sous-ensembles d'un ensemble - - `A` [Permutations](src/algorithms/sets/permutations) (avec et sans répétitions) - - `A` [Combinaisons](src/algorithms/sets/combinations) (avec et sans répétitions) - - `A` [Plus Longue Sous-séquence Commune](src/algorithms/sets/longest-common-subsequence) - - `A` [Plus Longue Sous-suite strictement croissante](src/algorithms/sets/longest-increasing-subsequence) - - `A` [Plus Courte Super-séquence Commune](src/algorithms/sets/shortest-common-supersequence) - - `A` [Problème du Sac à Dos](src/algorithms/sets/knapsack-problem) - versions "0/1" et "Sans Contraintes" - - `A` [Sous-partie Maximum](src/algorithms/sets/maximum-subarray) - versions "Force Brute" et "Programmation Dynamique" (Kadane) - - `A` [Somme combinatoire](src/algorithms/sets/combination-sum) - trouve toutes les combinaisons qui forment une somme spécifique -- **Chaînes de Caractères** - - `B` [Distance de Hamming](src/algorithms/string/hamming-distance) - nombre de positions auxquelles les symboles sont différents - - `A` [Distance de Levenshtein](src/algorithms/string/levenshtein-distance) - distance minimale d'édition entre deux séquences - - `A` [Algorithme de Knuth–Morris–Pratt](src/algorithms/string/knuth-morris-pratt) (Algorithme KMP) - recherche de sous-chaîne (pattern matching) - - `A` [Algorithme Z](src/algorithms/string/z-algorithm) - recherche de sous-chaîne (pattern matching) - - `A` [Algorithme de Rabin Karp](src/algorithms/string/rabin-karp) - recherche de sous-chaîne - - `A` [Plus Longue Sous-chaîne Commune](src/algorithms/string/longest-common-substring) - - `A` [Expression Régulière](src/algorithms/string/regular-expression-matching) -- **Recherche** - - `B` [Recherche Linéaire](src/algorithms/search/linear-search) - - `B` [Jump Search](src/algorithms/search/jump-search) Recherche par saut (ou par bloc) - recherche dans une liste triée - - `B` [Recherche Binaire](src/algorithms/search/binary-search) - recherche dans une liste triée - - `B` [Recherche par Interpolation](src/algorithms/search/interpolation-search) - recherche dans une liste triée et uniformément distribuée -- **Tri** - - `B` [Tri Bullet](src/algorithms/sorting/bubble-sort) - - `B` [Tri Sélection](src/algorithms/sorting/selection-sort) - - `B` [Tri Insertion](src/algorithms/sorting/insertion-sort) - - `B` [Tri Par Tas](src/algorithms/sorting/heap-sort) - - `B` [Tri Fusion](src/algorithms/sorting/merge-sort) - - `B` [Tri Rapide](src/algorithms/sorting/quick-sort) - implémentations _in-place_ et _non in-place_ - - `B` [Tri Shell](src/algorithms/sorting/shell-sort) - - `B` [Tri Comptage](src/algorithms/sorting/counting-sort) - - `B` [Tri Radix](src/algorithms/sorting/radix-sort) -- **Arbres** - - `B` [Parcours en Profondeur](src/algorithms/tree/depth-first-search) (DFS) - - `B` [Parcours en Largeur](src/algorithms/tree/breadth-first-search) (BFS) -- **Graphes** - - `B` [Parcours en Profondeur](src/algorithms/graph/depth-first-search) (DFS) - - `B` [Parcours en Largeur](src/algorithms/graph/breadth-first-search) (BFS) - - `B` [Algorithme de Kruskal](src/algorithms/graph/kruskal) - trouver l'arbre couvrant de poids minimal sur un graphe pondéré non dirigé - - `A` [Algorithme de Dijkstra](src/algorithms/graph/dijkstra) - trouver tous les plus courts chemins partant d'un noeud vers tous les autres noeuds dans un graphe - - `A` [Algorithme de Bellman-Ford](src/algorithms/graph/bellman-ford) - trouver tous les plus courts chemins partant d'un noeud vers tous les autres noeuds dans un graphe - - `A` [Algorithme de Floyd-Warshall](src/algorithms/graph/floyd-warshall) - trouver tous les plus courts chemins entre toutes les paires de noeuds dans un graphe - - `A` [Détection de Cycle](src/algorithms/graph/detect-cycle) - pour les graphes dirigés et non dirigés (implémentations basées sur l'algorithme de Parcours en Profondeur et sur les Ensembles Disjoints) - - `A` [Algorithme de Prim](src/algorithms/graph/prim) - trouver l'arbre couvrant de poids minimal sur un graphe pondéré non dirigé - - `A` [Tri Topologique](src/algorithms/graph/topological-sorting) - méthode DFS - - `A` [Point d'Articulation](src/algorithms/graph/articulation-points) - algorithme de Tarjan (basé sur l'algorithme de Parcours en Profondeur) - - `A` [Bridges](src/algorithms/graph/bridges) - algorithme basé sur le Parcours en Profondeur - - `A` [Chemin Eulérien et Circuit Eulérien](src/algorithms/graph/eulerian-path) - algorithme de Fleury - visite chaque arc exactement une fois - - `A` [Cycle Hamiltonien](src/algorithms/graph/hamiltonian-cycle) - visite chaque noeud exactement une fois - - `A` [Composants Fortements Connexes](src/algorithms/graph/strongly-connected-components) - algorithme de Kosaraju - - `A` [Problème du Voyageur de Commerce](src/algorithms/graph/travelling-salesman) - chemin le plus court visitant chaque cité et retournant à la cité d'origine -- **Non catégorisé** - - `B` [Tours de Hanoi](src/algorithms/uncategorized/hanoi-tower) - - `B` [Rotation de Matrice Carrée](src/algorithms/uncategorized/square-matrix-rotation) - algorithme _in place_ - - `B` [Jump Game](src/algorithms/uncategorized/jump-game) - retour sur trace, programmation dynamique (haut-bas + bas-haut) et exemples gourmands - - `B` [Chemins Uniques](src/algorithms/uncategorized/unique-paths) - retour sur trace, programmation dynamique (haut-bas + bas-haut) et exemples basés sur le Triangle de Pascal - - `A` [Problème des N-Dames](src/algorithms/uncategorized/n-queens) - - `A` [Problème du Cavalier](src/algorithms/uncategorized/knight-tour) - -### Algorithmes par Paradigme - -Un paradigme algorithmique est une méthode générique ou une approche qui -sous-tend la conception d'une classe d'algorithmes. C'est une abstraction -au-dessus de la notion d'algorithme, tout comme l'algorithme est une abstraction -supérieure à un programme informatique. - -- **Force Brute** - cherche parmi toutes les possibilités et retient la meilleure - - `B` [Recherche Linéaire](src/algorithms/search/linear-search) - - `A` [Sous-partie Maximum](src/algorithms/sets/maximum-subarray) - - `A` [Problème du Voyageur de Commerce](src/algorithms/graph/travelling-salesman) - chemin le plus court visitant chaque cité et retournant à la cité d'origine -- **Gourmand** - choisit la meilleure option à l'instant courant, sans tenir compte de la situation future - - `B` [Jump Game](src/algorithms/uncategorized/jump-game) - - `A` [Problème du Sac à Dos Sans Contraintes](src/algorithms/sets/knapsack-problem) - - `A` [Algorithme de Dijkstra](src/algorithms/graph/dijkstra) - trouver tous les plus courts chemins partant d'un noeud vers tous les autres noeuds dans un graphe - - `A` [Algorithme de Prim](src/algorithms/graph/prim) - trouver l'arbre couvrant de poids minimal sur un graphe pondéré non dirigé - - `A` [Algorithme de Kruskal](src/algorithms/graph/kruskal) - trouver l'arbre couvrant de poids minimal sur un graphe pondéré non dirigé -- **Diviser et Régner** - divise le problème en sous problèmes (plus simples) et résoud ces sous problèmes - - `B` [Recherche Binaire](src/algorithms/search/binary-search) - - `B` [Tours de Hanoi](src/algorithms/uncategorized/hanoi-tower) - - `B` [Triangle de Pascal](src/algorithms/math/pascal-triangle) - - `B` [Algorithme d'Euclide](src/algorithms/math/euclidean-algorithm) - calcule le Plus Grand Commun Diviseur (PGCD) - - `B` [Tri Fusion](src/algorithms/sorting/merge-sort) - - `B` [Tri Rapide](src/algorithms/sorting/quick-sort) - - `B` [Arbre de Parcours en Profondeur](src/algorithms/tree/depth-first-search) (DFS) - - `B` [Graphe de Parcours en Profondeur](src/algorithms/graph/depth-first-search) (DFS) - - `B` [Jump Game](src/algorithms/uncategorized/jump-game) - - `A` [Permutations](src/algorithms/sets/permutations) (avec et sans répétitions) - - `A` [Combinations](src/algorithms/sets/combinations) (avec et sans répétitions) -- **Programmation Dynamique** - construit une solution en utilisant les solutions précédemment trouvées - - `B` [Nombre de Fibonacci](src/algorithms/math/fibonacci) - - `B` [Jump Game](src/algorithms/uncategorized/jump-game) - - `B` [Chemins Uniques](src/algorithms/uncategorized/unique-paths) - - `A` [Distance de Levenshtein](src/algorithms/string/levenshtein-distance) - distance minimale d'édition entre deux séquences - - `A` [Plus Longue Sous-séquence Commune](src/algorithms/sets/longest-common-subsequence) - - `A` [Plus Longue Sous-chaîne Commune](src/algorithms/string/longest-common-substring) - - `A` [Plus Longue Sous-suite strictement croissante](src/algorithms/sets/longest-increasing-subsequence) - - `A` [Plus Courte Super-séquence Commune](src/algorithms/sets/shortest-common-supersequence) - - `A` [Problème de Sac à Dos](src/algorithms/sets/knapsack-problem) - - `A` [Partition Entière](src/algorithms/math/integer-partition) - - `A` [Sous-partie Maximum](src/algorithms/sets/maximum-subarray) - - `A` [Algorithme de Bellman-Ford](src/algorithms/graph/bellman-ford) - trouver tous les plus courts chemins partant d'un noeud vers tous les autres noeuds dans un graphe - - `A` [Algorithme de Floyd-Warshall](src/algorithms/graph/floyd-warshall) - trouver tous les plus courts chemins entre toutes les paires de noeuds dans un graphe - - `A` [Expression Régulière](src/algorithms/string/regular-expression-matching) -- **Retour sur trace** - de même que la version "Force Brute", essaie de générer toutes les solutions possibles, mais pour chaque solution générée, on teste si elle satisfait toutes les conditions, et seulement ensuite continuer à générer des solutions ultérieures. Sinon, l'on revient en arrière, et l'on essaie un - chemin différent pour tester d'autres solutions. Normalement, la traversée en profondeur de l'espace d'états est utilisée. - - `B` [Jump Game](src/algorithms/uncategorized/jump-game) - - `B` [Unique Paths](src/algorithms/uncategorized/unique-paths) - - `A` [Hamiltonian Cycle](src/algorithms/graph/hamiltonian-cycle) - Visit every vertex exactly once - - `A` [Problème des N-Dames](src/algorithms/uncategorized/n-queens) - - `A` [Problème du Cavalier](src/algorithms/uncategorized/knight-tour) - - `A` [Somme combinatoire](src/algorithms/sets/combination-sum) - trouve toutes les combinaisons qui forment une somme spécifique -- **Séparation et Evaluation** - pemet de retenir une solution à moindre coût dans un ensemble. Pour chaque étape, l'on garde une trace de la solution la moins coûteuse trouvée jusqu'à présent en tant que borne inférieure du coût. Cela afin d'éliminer les solutions partielles dont les coûts sont plus élevés que celui de la solution actuelle retenue. Normalement, la traversée en largeur en combinaison avec la traversée en profondeur de l'espace d'états de l'arbre est utilisée. - -## Comment utiliser ce dépôt - -**Installer toutes les dépendances** - -``` -npm install -``` - -**Exécuter ESLint** - -Vous pouvez l'installer pour tester la qualité du code. - -``` -npm run lint -``` - -**Exécuter tous les tests** - -``` -npm test -``` - -**Exécuter les tests par nom** - -``` -npm test -- 'LinkedList' -``` - -**Tests personnalisés** - -Vous pouvez manipuler les structures de données et algorithmes présents dans ce -dépôt avec le fichier `./src/playground/playground.js` et écrire vos propres -tests dans file `./src/playground/__test__/playground.test.js`. - -Vous pourrez alors simplement exécuter la commande suivante afin de tester si -votre code fonctionne comme escompté - -``` -npm test -- 'playground' -``` - -## Informations Utiles - -### Références - -[▶ Structures de Données et Algorithmes sur YouTube](https://www.youtube.com/playlist?list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8) - -### Notation Grand O - -Comparaison de la performance d'algorithmes en notation Grand O. - -![Big O graphs](./assets/big-o-graph.png) - -Source: [Big O Cheat Sheet](http://bigocheatsheet.com/). - -Voici la liste de certaines des notations Grand O les plus utilisées et de leurs -comparaisons de performance suivant différentes tailles pour les données d'entrée. - -| Notation Grand O | Opérations pour 10 éléments | Opérations pour 100 éléments | Opérations pour 1000 éléments | -| ---------------- | --------------------------- | ---------------------------- | ----------------------------- | -| **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 | - -### Complexité des Opérations suivant les Structures de Données - -| Structure de donnée | Accès | Recherche | Insertion | Suppression | Commentaires | -| ------------------------------ | :----: | :-------: | :-------: | :---------: | :------------------------------------------------------------------------- | -| **Liste** | 1 | n | n | n | | -| **Pile** | n | n | 1 | 1 | | -| **Queue** | n | n | 1 | 1 | | -| **Liste Liée** | n | n | 1 | 1 | | -| **Table de Hachage** | - | n | n | n | Dans le cas des fonctions de hachage parfaites, les couts seraient de O(1) | -| **Arbre de Recherche Binaire** | n | n | n | n | Dans le cas des arbre équilibrés, les coûts seraient de O(log(n)) | -| **Arbre B** | log(n) | log(n) | log(n) | log(n) | | -| **Arbre Red-Black** | log(n) | log(n) | log(n) | log(n) | | -| **Arbre AVL** | log(n) | log(n) | log(n) | log(n) | | -| **Filtre de Bloom** | - | 1 | 1 | - | Les faux positifs sont possibles lors de la recherche | - -### Complexité des Algorithmes de Tri de Liste - -| Nom | Meilleur | Moyenne | Pire | Mémoire | Stable | Commentaires | -| ----------------- | :-----------: | :--------------------: | :-------------------------: | :-----: | :----: | :----------------------------------------------------------------------------------- | -| **Tri Bulle** | n | n2 | n2 | 1 | Oui | | -| **Tri Insertion** | n | n2 | n2 | 1 | Oui | | -| **Tri Sélection** | n2 | n2 | n2 | 1 | Non | | -| **Tri par Tas** | n log(n) | n log(n) | n log(n) | 1 | Non | | -| **Merge sort** | n log(n) | n log(n) | n log(n) | n | Oui | | -| **Tri Rapide** | n log(n) | n log(n) | n2 | log(n) | Non | le Tri Rapide est généralement effectué _in-place_ avec une pile de taille O(log(n)) | -| **Tri Shell** | n log(n) | dépend du gap séquence | n (log(n))2 | 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 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.he-IL.md b/README.he-IL.md deleted file mode 100644 index 43ef196e60..0000000000 --- a/README.he-IL.md +++ /dev/null @@ -1,370 +0,0 @@ -# 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 | n2 | n2 | 1 | כן | | -| **מיון הכנסה** | n | n2 | n2 | 1 | כן | | -| **מיון בחירה** | n2 | n2 | n2 | 1 | לא | | -| **מיון ערימה** | n log(n) | n log(n) | n log(n) | 1 | לא | | -| **מיון מיזוג** | n log(n) | n log(n) | n log(n) | n | כן | | -| **מיון מהיר** | n log(n) | n log(n) | n2 | log(n) | לא | מיון מהיר בדרך כלל מבוצע במקום עם O(log(n)) שטח מחסנית | -| **מיון צדפות** | n log(n) | תלוי ברצף הפער | n (log(n))2 | 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 deleted file mode 100644 index 9dd908c2e6..0000000000 --- a/README.id-ID.md +++ /dev/null @@ -1,311 +0,0 @@ -# Algoritme dan Struktur Data 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) - -Repositori ini berisi contoh-contoh algoritme dan struktur data yang populer menggunakan JavaScript. - -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/), -[_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), -[_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) -[_עברית_](README.he-IL.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) - -## Algoritma - -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 - -### Algoritma Berdasarkanan Topik - -- **Matematika** - - `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` [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 (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 - - `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` [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 - - `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` [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** - - `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` [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` [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) - 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) - 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 - - `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) - 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_) - - `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) - -### Algoritma Berdasarkan Paradigma - -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) - - `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` [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` [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) - - `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` [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) - - `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` [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_, 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 - - `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 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: - -``` -npm test -- 'playground' -``` - -## Informasi Bermanfaat - -### Referensi - -[▶ Algoritma dan Struktur Data di YouTube](https://www.youtube.com/playlist?list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8) - -### 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) - -Sumber: [Big O Cheat Sheet](http://bigocheatsheet.com/). - -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 | -| -------------- | ------------------------- | -------------------------- | --------------------------- | -| **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 Algoritma Sortir Larik - -| Nama | Terbaik | Rata-rata | Terburuk | Memori | Stabil | Keterangan | -| -------------------------------------- | :-----------: | :--------------------------: | :-------------------------: | :----: | :----: | :-------------------------------------------------------------------------------- | -| **Bubble sort (Sortir Gelembung)** | n | n2 | n2 | 1 | Ya | | -| **Insertion sort (Sortir Sisipan)** | n | n2 | n2 | 1 | Ya | | -| **Selection sort (Sortir Seleksi)** | n2 | n2 | n2 | 1 | Tidak | | -| **Heap sort (Sortir _Heap_)** | n log(n) | n log(n) | n log(n) | 1 | Tidak | | -| **Merge Sort (Sortir Gabungan)** | n log(n) | n log(n) | n log(n) | n | Ya | | -| **Quick sort (Sortir Cepat)** | n log(n) | n log(n) | n2 | log(n) | Tidak | Sortir Cepat biasanya dilakukan secara _in-place_ dengan O(log(n)) ruang tumpukan | -| **Shell sort (Sortir Shell)** | n log(n) | tergantung pada jarak urutan | n (log(n))2 | 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` - -> 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 deleted file mode 100644 index d749a6aa7f..0000000000 --- a/README.it-IT.md +++ /dev/null @@ -1,304 +0,0 @@ -# Algoritmi e Strutture Dati in 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) - -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), -[_Русский_](README.ru-RU.md), -[_Türk_](README.tr-TR.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) -[_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.* - -## 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 | n2 | n2 | 1 | Yes | | -| **Insertion sort** | n | n2 | n2 | 1 | Yes | | -| **Selection sort** | n2 | n2 | n2 | 1 | No | | -| **Heap sort** | n log(n) | n log(n) | n log(n) | 1 | No | | -| **Merge sort** | n log(n) | n log(n) | n log(n) | n | Yes | | -| **Quick sort** | n log(n) | n log(n) | n2 | log(n) | No | Quicksort viene eseguito in memoria solitamente con una pila di O(log(n)) | -| **Shell sort** | n log(n) | dipende dagli spazi vuoti nella sequenza | n (log(n))2 | 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 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 deleted file mode 100644 index acf9dee8f0..0000000000 --- a/README.ja-JP.md +++ /dev/null @@ -1,303 +0,0 @@ -# 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?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。 - - -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、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/), -[_简体中文_](README.zh-CN.md), -[_繁體中文_](README.zh-TW.md), -[_한국어_](README.ko-KR.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), -[_Tiếng Việt_](README.vi-VN.md), -[_Deutsch_](README.de-DE.md), -[_Uzbek_](README.uz-UZ.md) -[_עברית_](README.he-IL.md) - -## データ構造 - -データ構造は、データ値、データ値との間の関係、 -そして、データを扱うことができる関数と演算の集合で、 -データを特定の方法で構成して保存することで、より効率的に -アクセスして変更することができます。 - -`B` - 初心者, `A` - 上級 - -* `B` [リンクされたリスト](src/data-structures/linked-list) -* `B` [二重リンクリスト](src/data-structures/doubly-linked-list) -* `B` [キュー](src/data-structures/queue) -* `B` [スタック](src/data-structures/stack) -* `B` [ハッシュ表](src/data-structures/hash-table) -* `B` [ヒープ](src/data-structures/heap) - max and min heap versions -* `B` [優先度キュー](src/data-structures/priority-queue) -* `A` [トライ](src/data-structures/trie) -* `A` [ツリー](src/data-structures/tree) - * `A` [バイナリ検索ツリー](src/data-structures/tree/binary-search-tree) - * `A` [AVLツリー](src/data-structures/tree/avl-tree) - * `A` [赤黒のツリー](src/data-structures/tree/red-black-tree) - * `A` [セグメントツリー](src/data-structures/tree/segment-tree) - with min/max/sum range queries examples - * `A` [フェンウィック・ツリー](src/data-structures/tree/fenwick-tree) (Binary Indexed Tree) -* `A` [グラフ](src/data-structures/graph) (both directed and undirected) -* `A` [分離集合](src/data-structures/disjoint-set) -* `A` [ブルームフィルタ](src/data-structures/bloom-filter) - -## アルゴリズム - -アルゴリズムとは、問題のクラスをどのように解決するかの明確な仕様です。 -一連の操作を正確に定義する一連のルールです。 - -`B` - 初心者, `A` - 上級 - -### トピック別アルゴリズム - -* **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` [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) - * `B` [最小公倍数](src/algorithms/math/least-common-multiple) (LCM) - * `B` [エラトステネスのふるい](src/algorithms/math/sieve-of-eratosthenes) - 与えられた限度まですべての素数を見つける - * `B` [Is Power of Two](src/algorithms/math/is-power-of-two) - 数値が2の累乗であるかどうかを調べる（単純なアルゴリズムとビットごとのアルゴリズム） - * `B` [パスカルの三角形](src/algorithms/math/pascal-triangle) - * `B` [複素数](src/algorithms/math/complex-number) - 複素数とその基本演算 - * `B` [ラジアン＆度](src/algorithms/math/radian) - 度数と逆方向の変換に対するラジアン - * `B` [高速電力供給](src/algorithms/math/fast-powering) - * `A` [整数パーティション](src/algorithms/math/integer-partition) - * `A` [Liu Hui π アルゴリズム](src/algorithms/math/liu-hui) - N-gonsに基づく近似π計算 - * `A` [離散フーリエ変換](src/algorithms/math/fourier-transform) - 時間（信号）の関数をそれを構成する周波数に分解する -* **セット** - * `B` [デカルト積 ](src/algorithms/sets/cartesian-product) - 複数の積の積 - * `B` [Fisher–Yates Shuffle](src/algorithms/sets/fisher-yates) - 有限シーケンスのランダム置換 - * `A` [パワーセット](src/algorithms/sets/power-set) - セットのすべてのサブセット（ビットごとのソリューションとバックトラッキングソリューション） - * `A` [順列](src/algorithms/sets/permutations) （繰り返しの有無にかかわらず） - * `A` [組み合わせ](src/algorithms/sets/combinations) （繰返しあり、繰返しなし） - * `A` [最長共通部分列](src/algorithms/sets/longest-common-subsequence) (LCS) - * `A` [最長増加サブシーケンス](src/algorithms/sets/longest-increasing-subsequence) - * `A` [最短共通スーパーシーケンス](src/algorithms/sets/shortest-common-supersequence) (SCS) - * `A` [ナップザック問題 ](src/algorithms/sets/knapsack-problem) - 「0/1」と「非結合」問題 - * `A` [最大サブアレイ](src/algorithms/sets/maximum-subarray) - 「ブルートフォース」と「ダイナミックプログラミング」（Kadane's版） - * `A` [組み合わせ合計](src/algorithms/sets/combination-sum) - 特定の合計を構成するすべての組み合わせを見つける -* **文字列** - * `B` [ハミング距離](src/algorithms/string/hamming-distance) - シンボルが異なる位置の数 - * `A` [レーベンシュタイン距離](src/algorithms/string/levenshtein-distance) - 2つのシーケンス間の最小編集距離 - * `A` [Knuth-Morris-Prattアルゴリズム](src/algorithms/string/knuth-morris-pratt) (KMP Algorithm) - 部分文字列検索 (pattern matching) - * `A` [Z アルゴリズム](src/algorithms/string/z-algorithm) - 部分文字列検索 (pattern matching) - * `A` [Rabin Karpアルゴリズム](src/algorithms/string/rabin-karp) - 部分文字列検索 - * `A` [最長共通部分文字列](src/algorithms/string/longest-common-substring) - * `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) (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** - * `B` [バブルソート](src/algorithms/sorting/bubble-sort) - * `B` [選択ソート](src/algorithms/sorting/selection-sort) - * `B` [挿入ソート](src/algorithms/sorting/insertion-sort) - * `B` [ヒープソート](src/algorithms/sorting/heap-sort) - * `B` [マージソート](src/algorithms/sorting/merge-sort) - * `B` [クイックソート](src/algorithms/sorting/quick-sort) -インプレースおよび非インプレース・インプリメンテーション - * `B` [シェルソート](src/algorithms/sorting/shell-sort) - * `B` [並べ替えを数える](src/algorithms/sorting/counting-sort) - * `B` [基数ソート](src/algorithms/sorting/radix-sort) -* **リンクされたリスト** - * `B` [ストレートトラバーサル](src/algorithms/linked-list/traversal) - * `B` [逆方向のトラバーサル](src/algorithms/linked-list/reverse-traversal) -* **ツリー** - * `B` [深度優先検索](src/algorithms/tree/depth-first-search) (DFS) - * `B` [幅優先検索](src/algorithms/tree/breadth-first-search) (BFS) -* **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 - * `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 - * `A` [Detect Cycle](src/algorithms/graph/detect-cycle) - 有向グラフと無向グラフの両方（DFSおよびディスジョイントセットベースのバージョン） - * `A` [プリムのアルゴリズム](src/algorithms/graph/prim) - 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` [トポロジカルソート](src/algorithms/graph/topological-sorting) - DFSメソッド - * `A` [アーティキュレーションポイント](src/algorithms/graph/articulation-points) - Tarjanのアルゴリズム（DFSベース） - * `A` [ブリッジ ](src/algorithms/graph/bridges) - DFSベースのアルゴリズム - * `A` [オイラーパスとオイラー回路](src/algorithms/graph/eulerian-path) - フルリーアルゴリズム - すべてのエッジを正確に1回訪問する - * `A` [ハミルトニアンサイクル](src/algorithms/graph/hamiltonian-cycle) - すべての頂点を正確に1回訪問する - * `A` [強連結成分](src/algorithms/graph/strongly-connected-components) - コサラジュのアルゴリズム - * `A` [トラベリングセールスマン問題](src/algorithms/graph/travelling-salesman) - 各都市を訪問し、起点都市に戻る最短経路 -* **暗号** - * `B` [多項式ハッシュ](src/algorithms/cryptography/polynomial-hash) - 関数多項式に基づくハッシュ関数 -* **未分類** - * `B` [ハノイの塔](src/algorithms/uncategorized/hanoi-tower) - * `B` [正方行列回転](src/algorithms/uncategorized/square-matrix-rotation) - インプレイスアルゴリズム - * `B` [ジャンプゲーム](src/algorithms/uncategorized/jump-game) - バックトラック、ダイナミックプログラミング（トップダウン+ボトムアップ）、欲張りの例 - * `B` [ユニークなパス](src/algorithms/uncategorized/unique-paths) - バックトラック、動的プログラミング、PascalのTriangleベースの例 - * `B` [レインテラス](src/algorithms/uncategorized/rain-terraces) - トラップ雨水問題（ダイナミックプログラミングとブルートフォースバージョン） - * `B` [再帰的階段](src/algorithms/uncategorized/recursive-staircase) - 上に到達する方法の数を数える（4つのソリューション） - * `A` [N-クイーンズ問題](src/algorithms/uncategorized/n-queens) - * `A` [ナイトツアー](src/algorithms/uncategorized/knight-tour) - -### 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** - 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 - * `A` [最大サブアレイ](src/algorithms/sets/maximum-subarray) - * `A` [旅行セールスマン問題](src/algorithms/graph/travelling-salesman) - 各都市を訪れ、起点都市に戻る最短ルート - * `A` [離散フーリエ変換](src/algorithms/math/fourier-transform) - 時間（信号）の関数をそれを構成する周波数に分解する -* **欲張り** - 未来を考慮することなく、現時点で最適なオプションを選択する - * `B` [ジャンプゲーム](src/algorithms/uncategorized/jump-game) - * `A` [結合されていないナップザック問題](src/algorithms/sets/knapsack-problem) - * `A` [Dijkstra Algorithm](src/algorithms/graph/dijkstra) - すべてのグラフ頂点への最短経路を見つける - * `A` [Prim’s Algorithm](src/algorithms/graph/prim) - 重み付き無向グラフの最小スパニングツリー（MST）を見つける - * `A` [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）を見つける -* **分割と征服** - 問題をより小さな部分に分割し、それらの部分を解決する - * `B` [バイナリ検索](src/algorithms/search/binary-search) - * `B` [ハノイの塔](src/algorithms/uncategorized/hanoi-tower) - * `B` [パスカルの三角形](src/algorithms/math/pascal-triangle) - * `B` [ユークリッドアルゴリズム](src/algorithms/math/euclidean-algorithm) - GCD（Greatest Common Divisor）を計算する - * `B` [マージソート](src/algorithms/sorting/merge-sort) - * `B` [クイックソート](src/algorithms/sorting/quick-sort) - * `B` [ツリーの深さ優先検索](src/algorithms/tree/depth-first-search) (DFS) - * `B` [グラフの深さ優先検索](src/algorithms/graph/depth-first-search) (DFS) - * `B` [ジャンプゲーム](src/algorithms/uncategorized/jump-game) - * `B` [高速電力供給](src/algorithms/math/fast-powering) - * `A` [順列](src/algorithms/sets/permutations) （繰り返しの有無にかかわらず） - * `A` [組み合わせ](src/algorithms/sets/combinations)（繰返しあり、繰返しなし） -* **動的プログラミング** - 以前に発見されたサブソリューションを使用してソリューションを構築する - * `B` [フィボナッチ数](src/algorithms/math/fibonacci) - * `B` [ジャンプゲーム](src/algorithms/uncategorized/jump-game) - * `B` [ユニークなパス](src/algorithms/uncategorized/unique-paths) - * `B` [雨テラス](src/algorithms/uncategorized/rain-terraces) - トラップ雨水問題 - * `B` [再帰的階段](src/algorithms/uncategorized/recursive-staircase) - 上に到達する方法の数を数える - * `A` [Levenshtein Distance](src/algorithms/string/levenshtein-distance) - 2つのシーケンス間の最小編集距離 - * `A` [最長共通部分列](src/algorithms/sets/longest-common-subsequence) (LCS) - * `A` [最長共通部分文字列](src/algorithms/string/longest-common-substring) - * `A` [最長増加サブシーケンス](src/algorithms/sets/longest-increasing-subsequence) - * `A` [最短共通共通配列](src/algorithms/sets/shortest-common-supersequence) - * `A` [0/1ナップザック問題](src/algorithms/sets/knapsack-problem) - * `A` [整数パーティション](src/algorithms/math/integer-partition) - * `A` [最大サブアレイ](src/algorithms/sets/maximum-subarray) - * `A` [Bellman-Fordアルゴリズム](src/algorithms/graph/bellman-ford) - 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 - * `A` [正規表現マッチング](src/algorithms/string/regular-expression-matching) -* **バックトラッキング** - ブルートフォースと同様に、可能なすべてのソリューションを生成しようとしますが、 - 次のソリューションを生成するたびにすべての条件を満たすかどうかをテストし、それ以降は引き続きソリューションを生成します。 - それ以外の場合は、バックトラックして、解決策を見つける別の経路に進みます。 - 通常、状態空間のDFSトラバーサルが使用されています。 - * `B` [ジャンプゲーム](src/algorithms/uncategorized/jump-game) - * `B` [ユニークなパス](src/algorithms/uncategorized/unique-paths) - * `B` [パワーセット](src/algorithms/sets/power-set) - セットのすべてのサブセット - * `A` [ハミルトニアンサイクル](src/algorithms/graph/hamiltonian-cycle) - すべての頂点を正確に1回訪問する - * `A` [N-クイーンズ問題](src/algorithms/uncategorized/n-queens) - * `A` [ナイトツアー](src/algorithms/uncategorized/knight-tour) - * `A` [組み合わせ合計](src/algorithms/sets/combination-sum) - 特定の合計を構成するすべての組み合わせを見つける -* **ブランチ＆バウンド** - バックトラック検索の各段階で見つかった最もコストの低いソリューションを覚えておいて、最もコストの低いソリューションのコストを使用します。これまでに発見された最もコストの低いソリューションよりも大きなコストで部分ソリューションを破棄するように指示します。通常、状態空間ツリーのDFSトラバーサルと組み合わせたBFSトラバーサルが使用されています。 - -## このリポジトリの使い方 - -**すべての依存関係をインストールする** -``` -npm install -``` - -**ESLintを実行する** - -これを実行してコードの品質をチェックすることができます。 - -``` -npm run lint -``` - -**すべてのテストを実行する** -``` -npm test -``` - -**名前でテストを実行する** -``` -npm test -- 'LinkedList' -``` - -**playground** - -データ構造とアルゴリズムを `./src/playground/playground.js` ファイルで再生し、 -それに対するテストを書くことができ `./src/playground/__test__/playground.test.js`. - -次に、次のコマンドを実行して、遊び場コードが正常に動作するかどうかをテストします。 - -``` -npm test -- 'playground' -``` - -## 有用な情報 - -### 参考文献 - -[▶ データ構造とアルゴリズム on YouTube](https://www.youtube.com/playlist?list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8) - -### ビッグO表記 - -*Big O表記法は* 入力サイズが大きくなるにつれて実行時間やスペース要件がどのように増加するかに応じてアルゴリズムを分類するために使用されます。下のチャートでは、Big O表記で指定されたアルゴリズムの成長の最も一般的な順序を見つけることができます。 - -![Big Oグラフ](./assets/big-o-graph.png) - -出典: [Big Oチートシート](http://bigocheatsheet.com/). - -以下は、最も使用されているBig O表記のリストと、入力データのさまざまなサイズに対するパフォーマンス比較です。 - -| 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 | - -### データ構造操作の複雑さ - -| 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 | 1 | | -| **Hash Table** | - | n | n | n | In case of perfect hash function costs would be O(1) | -| **Binary Search Tree** | n | n | n | n | In case of balanced tree costs would be 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 | - | False positives are possible while searching | - -### 配列の並べ替えアルゴリズムの複雑さ - -| Name | Best | Average | Worst | Memory | Stable | Comments | -| --------------------- | :-------------: | :-----------------: | :-----------------: | :-------: | :-------: | :-------- | -| **Bubble sort** | n | n2 | n2 | 1 | Yes | | -| **Insertion sort** | n | n2 | n2 | 1 | Yes | | -| **Selection sort** | n2 | n2 | n2 | 1 | No | | -| **Heap sort** | n log(n) | n log(n) | n log(n) | 1 | No | | -| **Merge sort** | n log(n) | n log(n) | n log(n) | n | Yes | | -| **Quick sort** | n log(n) | n log(n) | n2 | log(n) | No | Quicksort is usually done in-place with O(log(n)) stack space | -| **Shell sort** | n log(n) | depends on gap sequence | n (log(n))2 | 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 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 deleted file mode 100644 index d4b0d4ef14..0000000000 --- a/README.ko-KR.md +++ /dev/null @@ -1,284 +0,0 @@ -# JavaScript 알고리즘 및 자료 구조 - -[![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. - -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:_ -[_English_](https://github.com/trekhleb/javascript-algorithms/), -[_简体中文_](README.zh-CN.md), -[_繁體中文_](README.zh-TW.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), -[_Tiếng Việt_](README.vi-VN.md), -[_Deutsch_](README.de-DE.md), -[_Uzbek_](README.uz-UZ.md) -[_עברית_](README.he-IL.md) - -## 자료 구조 - -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. - - -`B` - 입문자, `A` - 숙련자 - -* `B` [연결 리스트](src/data-structures/linked-list) -* `B` [이중 연결 리스트](src/data-structures/doubly-linked-list) -* `B` [큐](src/data-structures/queue) -* `B` [스택](src/data-structures/stack) -* `B` [해시 테이블](src/data-structures/hash-table) -* `B` [힙](src/data-structures/heap) -* `B` [우선순위 큐](src/data-structures/priority-queue) -* `A` [트라이](src/data-structures/trie) -* `A` [트리](src/data-structures/tree) - * `A` [이진 탐색 트리](src/data-structures/tree/binary-search-tree) - * `A` [AVL 트리](src/data-structures/tree/avl-tree) - * `A` [Red-Black 트리](src/data-structures/tree/red-black-tree) - * `A` [세그먼트 트리](src/data-structures/tree/segment-tree) - min/max/sum range 쿼리 예제. - * `A` [Fenwick 트리](src/data-structures/tree/fenwick-tree) (Binary Indexed Tree) -* `A` [그래프](src/data-structures/graph) (유방향, 무방향) -* `A` [서로소 집합](src/data-structures/disjoint-set) -* `A` [블룸 필터](src/data-structures/bloom-filter) - -## 알고리즘 - -알고리즘은 어떤 종류의 문제를 풀 수 있는 정확한 방법이며, -일련의 작업을 정확하게 정의해 놓은 규칙들입니다. - -`B` - 입문자, `A` - 숙련자 - -### 주제별 알고리즘 - -* **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` [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) - * `B` [최소 공배수](src/algorithms/math/least-common-multiple) - LCM - * `B` [에라토스테네스의 체](src/algorithms/math/sieve-of-eratosthenes) - 특정수 이하의 모든 소수 찾기 - * `B` [2의 거듭제곱 판별법](src/algorithms/math/is-power-of-two) - 어떤 수가 2의 거듭제곱인지 판별 (naive 와 bitwise 알고리즘) - * `B` [파스칼 삼각형](src/algorithms/math/pascal-triangle) - * `A` [자연수 분할](src/algorithms/math/integer-partition) - * `A` [리우 후이 π 알고리즘](src/algorithms/math/liu-hui) - N-각형을 기반으로 π 근사치 구하기 -* **Sets** - * `B` [카티지언 프로덕트](src/algorithms/sets/cartesian-product) - 곱집합 - * `B` [Fisher–Yates 셔플](src/algorithms/sets/fisher-yates) - 유한 시퀀스의 무작위 순열 - * `A` [멱집합](src/algorithms/sets/power-set) - 집합의 모든 부분집합 - * `A` [순열](src/algorithms/sets/permutations) (반복 유,무) - * `A` [조합](src/algorithms/sets/combinations) (반복 유,무) - * `A` [최장 공통 부분수열](src/algorithms/sets/longest-common-subsequence) (LCS) - * `A` [최장 증가 수열](src/algorithms/sets/longest-increasing-subsequence) - * `A` [Shortest Common Supersequence](src/algorithms/sets/shortest-common-supersequence) (SCS) - * `A` [배낭 문제](src/algorithms/sets/knapsack-problem) - "0/1" 과 "Unbound" - * `A` [최대 구간합](src/algorithms/sets/maximum-subarray) - "브루트 포스" 과 "동적 계획법" (Kadane's) 버전 - * `A` [조합 합](src/algorithms/sets/combination-sum) - 특정 합을 구성하는 모든 조합 찾기 -* **Strings** - * `B` [해밍 거리](src/algorithms/string/hamming-distance) - 심볼이 다른 위치의 갯수 - * `A` [편집 거리](src/algorithms/string/levenshtein-distance) - 두 시퀀스 간위 최소 편집거리 - * `A` [커누스-모리스-프랫 알고리즘](src/algorithms/string/knuth-morris-pratt) (KMP 알고리즘) - 부분 문자열 탐색 (패턴 매칭) - * `A` [Z 알고리즘](src/algorithms/string/z-algorithm) - 부분 문자열 탐색 (패턴 매칭) - * `A` [라빈 카프 알고리즘](src/algorithms/string/rabin-karp) - 부분 문자열 탐색 - * `A` [최장 공통 부분 문자열](src/algorithms/string/longest-common-substring) - * `A` [정규 표현식 매칭](src/algorithms/string/regular-expression-matching) -* **Searches** - * `B` [선형 탐색](src/algorithms/search/linear-search) - * `B` [점프 탐색](src/algorithms/search/jump-search) (or Block Search) - 정렬된 배열에서 탐색 - * `B` [이진 탐색](src/algorithms/search/binary-search) - 정렬된 배열에서 탐색 - * `B` [보간 탐색](src/algorithms/search/interpolation-search) - 균등한 분포를 이루는 정렬된 배열에서 탐색 -* **Sorting** - * `B` [거품 정렬](src/algorithms/sorting/bubble-sort) - * `B` [선택 정렬](src/algorithms/sorting/selection-sort) - * `B` [삽입 정렬](src/algorithms/sorting/insertion-sort) - * `B` [힙 정렬](src/algorithms/sorting/heap-sort) - * `B` [병합 정렬](src/algorithms/sorting/merge-sort) - * `B` [퀵 정렬](src/algorithms/sorting/quick-sort) - 제자리(in-place)와 제자리가 아닌(non-in-place) 구현 - * `B` [셸 정렬](src/algorithms/sorting/shell-sort) - * `B` [계수 정렬](src/algorithms/sorting/counting-sort) - * `B` [기수 정렬](src/algorithms/sorting/radix-sort) -* **Trees** - * `B` [깊이 우선 탐색](src/algorithms/tree/depth-first-search) (DFS) - * `B` [너비 우선 탐색](src/algorithms/tree/breadth-first-search) (BFS) -* **Graphs** - * `B` [깊이 우선 탐색](src/algorithms/graph/depth-first-search) (DFS) - * `B` [너비 우선 탐색](src/algorithms/graph/breadth-first-search) (BFS) - * `B` [크루스칼 알고리즘](src/algorithms/graph/kruskal) - 최소 신장 트리 찾기 (MST) 무방향 가중 그래프 - * `A` [다익스트라 알고리즘](src/algorithms/graph/dijkstra) - 한 점에서 다른 모든 점까지 최단 거리 찾기 - * `A` [벨만-포드 알고리즘](src/algorithms/graph/bellman-ford) - 한 점에서 다른 모든 점까지 최단 거리 찾기 - * `A` [플로이드-워셜 알고리즘](src/algorithms/graph/floyd-warshall) - 모든 종단 간의 최단거리 찾기 - * `A` [사이클 탐지](src/algorithms/graph/detect-cycle) - 유방향, 무방향 그래프 (DFS 와 Disjoint Set 에 기반한 버전) - * `A` [프림 알고리즘](src/algorithms/graph/prim) - 무방향 가중치 그래프에서 최소 신장 트리 (MST) 찾기 - * `A` [위상 정렬](src/algorithms/graph/topological-sorting) - DFS 방식 - * `A` [단절점](src/algorithms/graph/articulation-points) - 타잔의 알고리즘 (DFS 기반) - * `A` [단절선](src/algorithms/graph/bridges) - DFS 기반 알고리즘 - * `A` [오일러 경로 와 오일러 회로](src/algorithms/graph/eulerian-path) - Fleury의 알고리즘 - 모든 엣지를 한번만 방문 - * `A` [해밀턴 경로](src/algorithms/graph/hamiltonian-cycle) - 모든 꼭짓점을 한번만 방문 - * `A` [강결합 컴포넌트](src/algorithms/graph/strongly-connected-components) - Kosaraju의 알고리즘 - * `A` [외판원 문제](src/algorithms/graph/travelling-salesman) - 각 도시를 다 방문하고 다시 출발점으로 돌아오는 최단 경로 찾기 -* **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` [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) - * `A` [기사의 여행 문제](src/algorithms/uncategorized/knight-tour) - -### 패러다임별 알고리즘 - -알고리즘 패러다임 이란, 알고리즘이 주어진 문제를 해결하기 위해 채택한 기초가 되는 일반적인 방법 혹은 접근법입니다. 알고리즘이 해결하는 문제나 알고리즘의 동작 방식이 완전히 다르더라도,알고리즘의 동작 원칙이 같으면 같은 패러다음을 사용했다고 말할 수 있으며, 주로 알고리즘을 구분하는 기준으로 쓰인다. 알고리즘이 일반적인 컴퓨터의 프로그램에 대한 개념보다 보다 더 추상적인 개념인 것처럼 알고리즘의 패러다임은 명확히 정의된 수학적 실체가 있는 것이 아니기 때문에 그 어떤 알고리즘의 개념보다도 훨씬 추상적인 개념입니다. - -* **브루트 포스(Brute Force)** - 가능한 모든 경우를 탐색한 뒤 최적을 찾아내는 방식입니다. - * `B` [선형 탐색](src/algorithms/search/linear-search) - * `B` [빗물 담기 문제](src/algorithms/uncategorized/rain-terraces) - trapping rain water problem - * `A` [최대 구간합](src/algorithms/sets/maximum-subarray) - * `A` [외판원 문제](src/algorithms/graph/travelling-salesman) - 각 도시를 다 방문하고 다시 출발점으로 돌아오는 최단 경로 찾기 -* **탐욕 알고리즘(Greedy)** - 이후를 고려하지 않고 현재 시점에서 가장 최적인 선택을 하는 방식입니다. - * `B` [점프 게임](src/algorithms/uncategorized/jump-game) - * `A` [쪼갤수 있는 배낭 문제](src/algorithms/sets/knapsack-problem) - * `A` [다익스트라 알고리즘](src/algorithms/graph/dijkstra) - 모든 점 까지의 최단거리 찾기 - * `A` [프림 알고리즘](src/algorithms/graph/prim) - 무방향 가중치 그래프에서 최소 신창 트리 (MST) 찾기 - * `A` [크루스칼 알고리즘](src/algorithms/graph/kruskal) - 무방향 가중치 그래프에서 최소 신창 트리 (MST) 찾기 -* **분할 정복법(Divide and Conquer)** - 문제를 여러 작은 문제로 분할한 뒤 해결하는 방식입니다. - * `B` [이진 탐색](src/algorithms/search/binary-search) - * `B` [하노이 탑](src/algorithms/uncategorized/hanoi-tower) - * `B` [파스칼 삼각형](src/algorithms/math/pascal-triangle) - * `B` [유클리드 호제법](src/algorithms/math/euclidean-algorithm) - 최대공약수 계산 (GCD) - * `B` [병합 정렬](src/algorithms/sorting/merge-sort) - * `B` [퀵 정렬](src/algorithms/sorting/quick-sort) - * `B` [트리 깊이 우선 탐색](src/algorithms/tree/depth-first-search) (DFS) - * `B` [그래프 깊이 우선 탐색](src/algorithms/graph/depth-first-search) (DFS) - * `B` [점프 게임](src/algorithms/uncategorized/jump-game) - * `A` [순열](src/algorithms/sets/permutations) (반복 유,무) - * `A` [조합](src/algorithms/sets/combinations) (반복 유,무) -* **동적 계획법(Dynamic Programming)** - 이전에 찾은 결과를 이용하여 최종적으로 해결하는 방식입니다. - * `B` [피보나치 수](src/algorithms/math/fibonacci) - * `B` [점프 게임](src/algorithms/uncategorized/jump-game) - * `B` [Unique Paths](src/algorithms/uncategorized/unique-paths) - * `B` [빗물 담기 문제](src/algorithms/uncategorized/rain-terraces) - trapping rain water problem - * `A` [편집 거리](src/algorithms/string/levenshtein-distance) - 두 시퀀스 간의 최소 편집 거리 - * `A` [최장 공통 부분 수열](src/algorithms/sets/longest-common-subsequence) (LCS) - * `A` [최장 공통 부분 문자열](src/algorithms/string/longest-common-substring) - * `A` [최장 증가 수열](src/algorithms/sets/longest-increasing-subsequence) - * `A` [Shortest Common Supersequence](src/algorithms/sets/shortest-common-supersequence) - * `A` [0/1 배낭 문제](src/algorithms/sets/knapsack-problem) - * `A` [자연수 분할](src/algorithms/math/integer-partition) - * `A` [최대 구간합](src/algorithms/sets/maximum-subarray) - * `A` [벨만-포드 알고리즘](src/algorithms/graph/bellman-ford) - 모든 점 까지의 최단 거리 찾기 - * `A` [플로이드-워셜 알고리즘](src/algorithms/graph/floyd-warshall) - 모든 종단 간의 최단거리 찾기 - * `A` [정규 표현식 매칭](src/algorithms/string/regular-expression-matching) -* **백트래킹(Backtracking)** - 모든 가능한 경우를 고려한다는 점에서 브루트 포스와 유사합니다. 하지만 다음 단계로 넘어갈때 마다 모든 조건을 만족했는지 확인하고 진행합니다. 만약 조건을 만족하지 못했다면 뒤로 돌아갑니다 (백트래킹). 그리고 다른 경로를 선택합니다. 보통 상태를 유지한 DFS 탐색을 많이 사용합니다. - * `B` [점프 게임](src/algorithms/uncategorized/jump-game) - * `B` [Unique Paths](src/algorithms/uncategorized/unique-paths) - * `A` [해밀턴 경로](src/algorithms/graph/hamiltonian-cycle) - 모든 점을 한번씩 방문 - * `A` [N-Queens 문제](src/algorithms/uncategorized/n-queens) - * `A` [기사의 여행](src/algorithms/uncategorized/knight-tour) - * `A` [조합 합](src/algorithms/sets/combination-sum) - 특정 합을 구성하는 모든 조합 찾기 -* **분기 한정법** - 백트래킹으로 찾은 각 단계의 최소 비용이 드는 해를 기억해 두고 있다가, 이 비용을 이용해서 더 낮은 최적의 해를 찾습니다. 기억해둔 최소 비용들을 이용해 더 높은 비용이 드는 해결법을 탐색 안함으로써 불필요한 시간 소모를 줄입니다. 보통 상태 공간 트리의 DFS 탐색을 이용한 BFS 탐색 방식에서 사용됩니다. - -## 이 저장소의 사용법 - -**모든 종속 모듈들 설치** -``` -npm install -``` - -**ESLint 실행** - -코드의 품질을 확인 할 수 있습니다. - -``` -npm run lint -``` - -**모든 테스트 실행** -``` -npm test -``` - -**이름을 통해 특정 테스트 실행** -``` -npm test -- 'LinkedList' -``` - -**Playground** - - `./src/playground/playground.js` 파일을 통해 자료 구조와 알고리즘을 작성하고 `./src/playground/__test__/playground.test.js`에 테스트를 작성할 수 있습니다. - -그리고 간단하게 아래 명령어를 통해 의도한대로 동작하는지 확인 할 수 있습니다.: - -``` -npm test -- 'playground' -``` - -## 유용한 정보 - -### 참고 - -[▶ Data Structures and Algorithms on YouTube](https://www.youtube.com/playlist?list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8) - -### Big O 표기 - -Big O 표기로 표시한 알고리즘의 증가 양상입니다. - -![Big O graphs](./assets/big-o-graph.png) - -Source: [Big O Cheat Sheet](http://bigocheatsheet.com/). - -아래는 가장 많이 사용되는 Big O 표기와 입력 데이터 크기에 따른 성능을 비교한 표입니다. - -| Big O 표기 | 10 개 일때 | 100 개 일때 | 1000 개 일때 | -| -------------- | ---------------------------- | ----------------------------- | ------------------------------- | -| **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 | - -### 자료 구조 작업별 복잡도 - -| 자료 구조 | 접근 | 검색 | 삽입 | 삭제 | 비고 | -| ------------------------ | :-------: | :-------: | :-------: | :-------: | :-------- | -| **배열** | 1 | n | n | n | | -| **스택** | n | n | 1 | 1 | | -| **큐** | n | n | 1 | 1 | | -| **연결 리스트** | n | n | 1 | 1 | | -| **해시 테이블** | - | n | n | n | 완벽한 해시 함수의 경우 O(1) | -| **이진 탐색 트리** | n | n | n | n | 균형 트리의 경우 O(log(n)) | -| **B-트리** | log(n) | log(n) | log(n) | log(n) | | -| **Red-Black 트리** | log(n) | log(n) | log(n) | log(n) | | -| **AVL 트리** | log(n) | log(n) | log(n) | log(n) | | -| **Bloom Filter** | - | 1 | 1 | - | 거짓 양성이 탐색 중 발생 가능 | - -### 정렬 알고리즘 복잡도 - -| 이름 | 최적 | 평균 | 최악 | 메모리 | 동일값 순서유지 | 비고 | -| --------------------- | :-------------: | :-----------------: | :-----------------: | :-------: | :--------------: | :-------- | -| **거품 정렬** | n | n2 | n2 | 1 | Yes | | -| **삽입 정렬** | n | n2 | n2 | 1 | Yes | | -| **선택 정렬** | n2 | n2 | n2 | 1 | No | | -| **힙 정렬** | n log(n) | n log(n) | n log(n) | 1 | No | | -| **병합 정렬** | n log(n) | n log(n) | n log(n) | n | Yes | | -| **퀵 정렬** | n log(n) | n log(n) | n2 | log(n) | No | 퀵 정렬은 보통 제자리(in-place)로 O(log(n)) 스택공간으로 수행됩니다. | -| **셸 정렬** | n log(n) | 간격 순서에 영향을 받습니다. | n (log(n))2 | 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 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 deleted file mode 100644 index 3e5c5cc096..0000000000 --- a/README.md +++ /dev/null @@ -1,379 +0,0 @@ -# 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: -> - [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) - -
- -[![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. - -Each algorithm and data structure has its own separate README -with related explanations and links for further reading (including ones -to YouTube videos). - -_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), -[_Italiano_](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), -[_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.* - -## Data Structures - -A data structure is a particular way of organizing and storing data in a computer so that it can -be accessed and modified efficiently. More precisely, a data structure is a collection of data -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) -* `B` [Doubly Linked List](src/data-structures/doubly-linked-list) -* `B` [Queue](src/data-structures/queue) -* `B` [Stack](src/data-structures/stack) -* `B` [Hash Table](src/data-structures/hash-table) -* `B` [Heap](src/data-structures/heap) - max and min heap versions -* `B` [Priority Queue](src/data-structures/priority-queue) -* `A` [Trie](src/data-structures/trie) -* `A` [Tree](src/data-structures/tree) - * `A` [Binary Search Tree](src/data-structures/tree/binary-search-tree) - * `A` [AVL Tree](src/data-structures/tree/avl-tree) - * `A` [Red-Black Tree](src/data-structures/tree/red-black-tree) - * `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 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 - -## Algorithms - -An algorithm is an unambiguous specification of how to solve a class of problems. It is -a set of rules that precisely define a sequence of operations. - -`B` - Beginner, `A` - Advanced - -### Algorithms by Topic - -* **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 - * `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) - * `B` [Sieve of Eratosthenes](src/algorithms/math/sieve-of-eratosthenes) - finding all prime numbers up to any given limit - * `B` [Is Power of Two](src/algorithms/math/is-power-of-two) - check if the number is power of two (naive and bitwise algorithms) - * `B` [Pascal's Triangle](src/algorithms/math/pascal-triangle) - * `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 - * `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 - * `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 - * `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) - * `A` [Longest Increasing Subsequence](src/algorithms/sets/longest-increasing-subsequence) - * `A` [Shortest Common Supersequence](src/algorithms/sets/shortest-common-supersequence) (SCS) - * `A` [Knapsack Problem](src/algorithms/sets/knapsack-problem) - "0/1" and "Unbound" ones - * `A` [Maximum Subarray](src/algorithms/sets/maximum-subarray) - "Brute Force" and "Dynamic Programming" (Kadane's) versions - * `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](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) - * `A` [Rabin Karp Algorithm](src/algorithms/string/rabin-karp) - substring search - * `A` [Longest Common Substring](src/algorithms/string/longest-common-substring) - * `A` [Regular Expression Matching](src/algorithms/string/regular-expression-matching) -* **Searches** - * `B` [Linear Search](src/algorithms/search/linear-search) - * `B` [Jump Search](src/algorithms/search/jump-search) (or Block Search) - search in sorted array - * `B` [Binary Search](src/algorithms/search/binary-search) - search in sorted array - * `B` [Interpolation Search](src/algorithms/search/interpolation-search) - search in uniformly distributed sorted array -* **Sorting** - * `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) - in-place and non-in-place implementations - * `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) -* **Trees** - * `B` [Depth-First Search](src/algorithms/tree/depth-first-search) (DFS) - * `B` [Breadth-First Search](src/algorithms/tree/breadth-first-search) (BFS) -* **Graphs** - * `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 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 - * `A` [Articulation Points](src/algorithms/graph/articulation-points) - Tarjan's algorithm (DFS based) - * `A` [Bridges](src/algorithms/graph/bridges) - DFS based algorithm - * `A` [Eulerian Path and Eulerian Circuit](src/algorithms/graph/eulerian-path) - Fleury's algorithm - Visit every edge exactly once - * `A` [Hamiltonian Cycle](src/algorithms/graph/hamiltonian-cycle) - Visit every vertex exactly once - * `A` [Strongly Connected Components](src/algorithms/graph/strongly-connected-components) - Kosaraju's algorithm - * `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 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** - * `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 -* **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 - * `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) - * `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) - -### Algorithms by Paradigm - -An algorithmic paradigm is a generic method or approach which underlies the design of a class -of algorithms. It is an abstraction higher than the notion of an algorithm, just as an -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 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 -* **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 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 - * `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) - calculate the Greatest Common Divisor (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` [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) - * `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) - * `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 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) - * `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) - 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 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 - * `A` [Hamiltonian Cycle](src/algorithms/graph/hamiltonian-cycle) - Visit every vertex exactly once - * `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) - 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 -tree is being used. - -## How to use this repository - -**Install all dependencies** - -``` -npm install -``` - -**Run ESLint** - -You may want to run it to check code quality. - -``` -npm run lint -``` - -**Run all tests** - -``` -npm test -``` - -**Run tests by name** - -``` -npm test -- 'LinkedList' -``` - -**Troubleshooting** - -If linting or testing is failing, try to delete the `node_modules` folder and re-install npm packages: - -``` -rm -rf ./node_modules -npm i -``` - -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: - -``` -npm test -- 'playground' -``` - -## Useful Information - -### References - -- [▶ 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* 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 the most common orders of growth of algorithms specified in Big O notation. - -![Big O graphs](./assets/big-o-graph.png) - -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 | 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 - -| 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 | In case of perfect hash function costs would be O(1) | -| **Binary Search Tree** | n | n | n | n | In case of balanced tree costs would be 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 | - | False positives are possible while searching | - -### Array Sorting Algorithms Complexity - -| Name | Best | Average | Worst | Memory | Stable | Comments | -| --------------------- | :-------------: | :-----------------: | :-----------------: | :-------: | :-------: | :-------- | -| **Bubble sort** | n | n2 | n2 | 1 | Yes | | -| **Insertion sort** | n | n2 | n2 | 1 | Yes | | -| **Selection sort** | n2 | n2 | n2 | 1 | No | | -| **Heap sort** | n log(n) | n log(n) | n log(n) | 1 | No | | -| **Merge sort** | n log(n) | n log(n) | n log(n) | n | Yes | | -| **Quick sort** | n log(n) | n log(n) | n2 | log(n) | No | Quicksort is usually done in-place with O(log(n)) stack space | -| **Shell sort** | n log(n) | depends on gap sequence | n (log(n))2 | 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 | - -## Project Backers - -> 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` - -## Author - -[@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.pl-PL.md b/README.pl-PL.md deleted file mode 100644 index 56617030ab..0000000000 --- a/README.pl-PL.md +++ /dev/null @@ -1,296 +0,0 @@ -# JavaScript Algorytmy i Struktury Danych - -[![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 -znanych algorytmach i strukturach danych. - -Każdy algorytm i struktura danych zawiera osobny plik README -wraz z powiązanymi wyjaśnieniami i odnośnikami do dalszego czytania -(włącznie z tymi do YouTube videos). - -_Read this in other languages:_ -[_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), -[_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), -[_Tiếng Việt_](README.vi-VN.md), -[_Deutsch_](README.de-DE.md), -[_Uzbek_](README.uz-UZ.md) -[_עברית_](README.he-IL.md) - -## Struktury Danych - -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. - -`B` - Początkujący, `A` - Zaawansowany - -* `B` [Lista](src/data-structures/linked-list) -* `B` [Lista Dwukierunkowa](src/data-structures/doubly-linked-list) -* `B` [Kolejka](src/data-structures/queue) -* `B` [Stos](src/data-structures/stack) -* `B` [Tabela Skrótu](src/data-structures/hash-table) -* `B` [Sterta](src/data-structures/heap) -* `B` [Kolejka Priorytetowa](src/data-structures/priority-queue) -* `A` [Trie](src/data-structures/trie) -* `A` [Drzewo](src/data-structures/tree) - * `A` [Wyszukiwanie Binarne](src/data-structures/tree/binary-search-tree) - * `A` [AVL Drzewo](src/data-structures/tree/avl-tree) - * `A` [Drzewa czerwono-czarne](src/data-structures/tree/red-black-tree) - * `A` [Drzewo Segmentu](src/data-structures/tree/segment-tree) - z przykładami zapytań o min / max / sumie sum - * `A` [Drzewo Fenwicka](src/data-structures/tree/fenwick-tree) (Drzewo Indeksowane Binarnie) -* `A` [Graf](src/data-structures/graph) (zarówno skierowane i nieukierunkowane) -* `A` [Rozłączny Zestaw](src/data-structures/disjoint-set) -* `A` [Filtr Blooma](src/data-structures/bloom-filter) - -## Algorytmy - -Algorytm jest to skończony ciąg jasno zdefiniowanych czynności, koniecznych -do wykonania pewnego rodzaju zadań. Sposób postępowania prowadzący do -rozwiązania problemu. - -`B` - Początkujący, `A` - Zaawansowany - -### Algorytmy według tematu - -* **Matematyka** - * `B` [Manipulacja Bitami](src/algorithms/math/bits) - ustaw / uzyskaj / aktualizuj / usuwaj bity, mnożenie / dzielenie przez dwa, tworzenie negatywów itp. - * `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) - * `B` [Najmniejsza Wspólna Wielokrotność](src/algorithms/math/least-common-multiple) (LCM) - * `B` [Sito Eratosthenes-a](src/algorithms/math/sieve-of-eratosthenes) - znajdowanie wszystkich liczb pierwszych do określonego limitu - * `B` [Jest Potęgą Dwójki](src/algorithms/math/is-power-of-two) - sprawdź, czy liczba jest potęgą dwóch (algorytmy naiwne i bitowe) - * `B` [Trójkąt Pascala](src/algorithms/math/pascal-triangle) - * `A` [Partycja Całkowita](src/algorithms/math/integer-partition) - * `A` [Algorytm Liu Huia](src/algorithms/math/liu-hui) - przybliżone obliczenia na podstawie N-gonów -* **Zestawy** - * `B` [Produkt Kartezyjny](src/algorithms/sets/cartesian-product) - wynik wielu zestawów - * `B` [Przetasowanie Fisher Yates-a](src/algorithms/sets/fisher-yates) - losowa permutacja kończącej się serii - * `A` [Zestaw Zasilający](src/algorithms/sets/power-set) - podzbiór wszystkich serii - * `A` [Permutacje](src/algorithms/sets/permutations) (z albo bez powtórzeń) - * `A` [Kombinacje](src/algorithms/sets/combinations) (z albo bez powtórzeń) - * `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` [Maksymalna Podtablica](src/algorithms/sets/maximum-subarray) - "Metoda Siłowa" i "Dynamiczne Programowanie" (Kadane-a) wersje - * `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 - * `A` [Odległość Levenshteina](src/algorithms/string/levenshtein-distance) - minimalna odległość edycji między dwiema sekwencjami - * `A` [Algorytm Knuth–Morris–Pratta](src/algorithms/string/knuth-morris-pratt) (Algorytm KMP) - dopasowywanie wzorców (dopasowywanie wzorców) - * `A` [Algorytm Z](src/algorithms/string/z-algorithm) - szukanie podłańcucha(dopasowywanie wzorców) - * `A` [Algorytm Rabin Karpa](src/algorithms/string/rabin-karp) - szukanie podłańcucha - * `A` [Najdłuższa Wspólna Podłańcucha](src/algorithms/string/longest-common-substring) - * `A` [Dopasowanie Wyrażeń Regularnych](src/algorithms/string/regular-expression-matching) -* **Szukanie** - * `B` [Wyszukiwanie Liniowe](src/algorithms/search/linear-search) - * `B` [Jump Search](src/algorithms/search/jump-search) (lub Przeszukiwanie Bloku) - szukaj w posortowanej tablicy - * `B` [Wyszukiwanie Binarne](src/algorithms/search/binary-search) - szukaj w posortowanej tablicy - * `B` [Wyszukiwanie Interpolacyjne](src/algorithms/search/interpolation-search) - szukaj w równomiernie rozłożonej, posortowanej tablicy -* **Sortowanie** - * `B` [Sortowanie bąbelkowe](src/algorithms/sorting/bubble-sort) - * `B` [Sortowanie przez wymiane](src/algorithms/sorting/selection-sort) - * `B` [Sortowanie przez wstawianie](src/algorithms/sorting/insertion-sort) - * `B` [Sortowanie stogowe](src/algorithms/sorting/heap-sort) - * `B` [Sortowanie przez scalanie](src/algorithms/sorting/merge-sort) - * `B` [Sortowanie szybkie](src/algorithms/sorting/quick-sort) - wdrożenia w miejscu i nie na miejscu - * `B` [Sortowanie Shella](src/algorithms/sorting/shell-sort) - * `B` [Sortowanie przez zliczanie](src/algorithms/sorting/counting-sort) - * `B` [Sortowanie pozycyjne](src/algorithms/sorting/radix-sort) -* **Drzewa** - * `B` [Przeszukiwanie w głąb](src/algorithms/tree/depth-first-search) (DFS) - * `B` [Przeszukiwanie wszerz](src/algorithms/tree/breadth-first-search) (BFS) -* **Grafy** - * `B` [Przeszukiwanie w głąb](src/algorithms/graph/depth-first-search) (DFS) - * `B` [Przeszukiwanie wszerz](src/algorithms/graph/breadth-first-search) (BFS) - * `B` [Algorytm Kruskala](src/algorithms/graph/kruskal) - znalezienie Minimalnego Drzewa Opinającego (MST) dla ważonego nieukierunkowanego wykresu - * `A` [Algorytm Dijkstry](src/algorithms/graph/dijkstra) - znajdowanie najkrótszej ścieżki z pojedynczego źródła w grafie - * `A` [Algorytm Bellmana-Forda](src/algorithms/graph/bellman-ford) - znajdowanie najkrótszych ścieżek do wszystkich wierzchołków wykresu z jednego wierzchołka - * `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` [Punkty Artykulacji](src/algorithms/graph/articulation-points) - Algorytm Tarjana (oparty o 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` [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` [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 -program komputerowy. - -* **Metoda Siłowa** - Sprawdza wszystkie możliwosci i wybiera najlepsze rozwiązanie. - * `B` [Wyszukiwanie Liniowe](src/algorithms/search/linear-search) - * `A` [Maksymalna Podtablica](src/algorithms/sets/maximum-subarray) - * `A` [Problem z Podróżującym Sprzedawcą](src/algorithms/graph/travelling-salesman) - najkrótsza możliwa trasa, która odwiedza każde miasto i wraca do miasta początkowego -* **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) - -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 -* **Dziel i Zwyciężaj** - podziel problem na mniejsze części, a następnie rozwiąż te części - * `B` [Wyszukiwanie Binarne](src/algorithms/search/binary-search) - * `B` [Wieża Hanoi](src/algorithms/uncategorized/hanoi-tower) - * `B` [Trójkąt Pascala](src/algorithms/math/pascal-triangle) - * `B` [Algorytm Euclideana](src/algorithms/math/euclidean-algorithm) - obliczyć Największy Wspólny Dzielnik(GCD) - * `B` [Sortowanie przez scalanie](src/algorithms/sorting/merge-sort) - * `B` [Szybkie Sortowanie](src/algorithms/sorting/quick-sort) - * `B` [Drzewo Przeszukiwania W Głąb](src/algorithms/tree/depth-first-search) (DFS) - * `B` [Graf Przeszukiwania W Głąb](src/algorithms/graph/depth-first-search) (DFS) - * `B` [Jump Game](src/algorithms/uncategorized/jump-game) - * `A` [Permutacje](src/algorithms/sets/permutations) (z albo bez powtórzeń) - * `A` [Kombinacje](src/algorithms/sets/combinations) (z albo bez powtórzeń) -* **Programowanie Dynamiczne** - zbuduj rozwiązanie, korzystając z wcześniej znalezionych podrzędnych rozwiązań - * `B` [Ciąg Fibonacciego](src/algorithms/math/fibonacci) - * `B` [Jump Game](src/algorithms/uncategorized/jump-game) - * `B` [Unikatowe Scieżki](src/algorithms/uncategorized/unique-paths) - * `A` [Dystans Levenshteina](src/algorithms/string/levenshtein-distance) - minimalna odległość edycji między dwiema sekwencjami - * `A` [Najdłuższa Wspólna Podsekwencja](src/algorithms/sets/longest-common-subsequence) (LCS) - * `A` [Najdłuższa Wspólna Podłańcucha](src/algorithms/string/longest-common-substring) - * `A` [Najdłuższa Wzrostająca Podsekwencja](src/algorithms/sets/longest-increasing-subsequence) - * `A` [Najkrótsza Wspólna Supersekwencja](src/algorithms/sets/shortest-common-supersequence) - * `A` [0/1 Problem Knapsacka](src/algorithms/sets/knapsack-problem) - * `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) - -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 -jeżeli zaspokaja wszystkie warunki, tylko wtedy generuje kolejne rozwiązania. W innym wypadku, cofa sie, i podąża inna ścieżka znaleźenia rozwiązania. Zazwyczaj, używane jest przejście przez Przeszukiwania W Głąb(DFS) przestrzeni stanów. - * `B` [Jump Game](src/algorithms/uncategorized/jump-game) - * `B` [Unikatowe Scieżki](src/algorithms/uncategorized/unique-paths) - * `A` [Cykl Hamiltoniana](src/algorithms/graph/hamiltonian-cycle) - Odwiedź każdy wierzchołek dokładnie raz - * `A` [Problem N-Queens](src/algorithms/uncategorized/n-queens) - * `A` [Knight's Tour](src/algorithms/uncategorized/knight-tour) - * `A` [Zestaw Sumy](src/algorithms/sets/combination-sum) - znajduje wszystkie zestawy które tworzą określoną sumę -* **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. -Zazwyczan trajektoria BFS, w połączeniu z trajektorią Przeszukiwania W Głąb (DFS) drzewa przestrzeni stanów jest użyte. - -## Jak używać repozytorium - -**Zainstaluj wszystkie zależnosci** -``` -npm install -``` - -**Uruchom ESLint** - -Możesz to uruchomić aby sprawdzić jakość kodu. - -``` -npm run lint -``` - -**Uruchom wszystkie testy** -``` -npm test -``` - -**Uruchom testy używając określonej nazwy** -``` -npm test -- 'LinkedList' -``` - -**Playground** - -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: - -``` -npm test -- 'playground' -``` - -## Pomocne informacje - -### Źródła - -[â–¶ Struktury Danych i Algorytmy na YouTube](https://www.youtube.com/playlist?list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8) - -### Big O Notacja - -Kolejność wzrastania algorytmów według Big O notacji. - -![Big O grafy](./assets/big-o-graph.png) - -Źródło: [Big O Cheat Sheet](http://bigocheatsheet.com/). - -Poniżej umieszczamy listę najbardziej używanych Big O notacji i ich porównania wydajności do róznych rozmiarów z wprowadzonych danych. - -| Big O notacja | Obliczenia na 10 elementów | Obliczenia na 100 elementów | Obliczenia na 1000 elementów | -| -------------- | ---------------------------- | ----------------------------- | ------------------------------- | -| **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 | - -### Złożoność operacji struktury danych - -| Struktura Danych | Dostęp | Szukaj | Umieszczanie | Usuwanie | Komentarze | -| ------------------------------- | :-------: | :-------: | :----------: | :-------: | :----------- | -| **Szereg** | 1 | n | n | n | | -| **Sterta** | n | n | 1 | 1 | | -| **Kolejka** | n | n | 1 | 1 | | -| **Lista Powiązana** | n | n | 1 | 1 | | -| **Tablica funkcji mieszanej** | - | n | n | n | W wypadku idealnej funkcji skrótu koszt mógłby sie równać O(1) | -| **Binarne Drzewo Poszukiwań** | n | n | n | n | W przypadku zrównoważonych kosztów drzew byłoby O(log(n)) | -| **B-Drzewo** | log(n) | log(n) | log(n) | log(n) | | -| **Drzewa czerwono-czarne** | log(n) | log(n) | log(n) | log(n) | | -| **AVL Drzewo** | log(n) | log(n) | log(n) | log(n) | | -| **Filtr Blooma** | - | 1 | 1 | - | Fałszywe dotatnie są możliwe podczas wyszukiwania | - -### Sortowanie Tablic Złożoności Algorytmów - -| Nazwa | Najlepszy | Średni | Najgorszy | Pamięć | Stabilność | Komentarze | -| ----------------------------------- | :-------------: | :-----------------: | :-----------------: | :-------: | :---------: | :---------- | -| **Sortowanie bąbelkowe** | n | n2 | n2 | 1 | Yes | | -| **Sortowanie przez wstawianie** | n | n2 | n2 | 1 | Yes | | -| **Sortowanie przez wybieranie** | n2 | n2 | n2 | 1 | No | | -| **Sortowanie przez kopcowanie** | n log(n) | n log(n) | n log(n) | 1 | No | | -| **Sortowanie przez scalanie** | n log(n) | n log(n) | n log(n) | n | Yes | | -| **Szybkie sortowanie** | n log(n) | n log(n) | n2 | log(n) | No | Szybkie sortowanie jest zazwyczaj robione w miejsce O(log(n)) stosu przestrzeni | -| **Sortowanie Shella** | n log(n) | zależy od luki w układzie | n (log(n))2 | 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 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 deleted file mode 100644 index 5b16798bc9..0000000000 --- a/README.pt-BR.md +++ /dev/null @@ -1,304 +0,0 @@ -# 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?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 -algoritmos e estruturas de dados populares. - -Cada algoritmo e estrutura de dados possui seu próprio README -com explicações relacionadas e links para leitura adicional (incluindo -vídeos para YouTube) - -_Leia isto em outros idiomas:_ -[_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), -[_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), -[_Tiếng Việt_](README.vi-VN.md), -[_Deutsch_](README.de-DE.md), -[_Uzbek_](README.uz-UZ.md) -[_עברית_](README.he-IL.md) - -## 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 valores de dados, as relações entre eles e as funções ou operações que podem ser aplicadas aos dados. - -`B` - Iniciante, `A` - Avançado - -* `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` [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) - 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 (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 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 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 - -Um algoritmo é uma especificação inequívoca de como resolver uma classe de problemas. Isto é -um conjunto de regras que define precisamente uma sequência de operações. - -`B` - Iniciante, `A` - Avançado - -### Algoritmos por Tópico - -* **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` [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 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 - * `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` [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` [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` [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` [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` [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) - * `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` [Shellsort](src/algorithms/sorting/shell-sort) - * `B` [Counting Sort](src/algorithms/sorting/counting-sort) - * `B` [Radix Sort](src/algorithms/sorting/radix-sort) -* **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` [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` [Hash Polinomial](src/algorithms/cryptography/polynomial-hash) - Função de hash de rolagem baseada em polinômio -* **Sem categoria** - * `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 - -Um paradigma algorítmico é um método ou abordagem genérica subjacente ao design de uma classe -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** - Pense em todas as possibilidades e escolha a melhor solução - * `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` [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` [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` [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` [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 - -## Como usar este repositório - -**Instalar todas as dependências** -``` -npm install -``` - -**Executar o ESLint** - -Você pode querer executá-lo para verificar a qualidade do código. - -``` -npm run lint -``` - -**Execute todos os testes** -``` -npm test -``` - -**Executar testes por nome** -``` -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. - -**Playground** - -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: - -``` -npm test -- 'playground' -``` - -## Informação útil - -### Referências - -- [▶ 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 - -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/). - -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. - -| Notação Big-O | Cálculos para 10 elementos | Cálculos para 100 elementos | Cálculos para 1000 elementos | -| -------------- | ---------------------------- | ----------------------------- | ------------------------------- | -| **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 | - -### Complexidade de operações de estrutura de dados - -| Estrutura de dados | Acesso | Busca | Inserção | Eliminação | Comentários | -| ----------------------- | :-------: | :-------: | :-------: | :-------: | :-------- | -| **Array** | 1 | n | n | n | | -| **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)) -| **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 | - -### Complexidade dos Algoritmos de Ordenação de Matrizes - -| Nome | Melhor | Média | Pior | Mémoria | Estável | Comentários | -| --------------------- | :-------------: | :-----------------: | :-----------------: | :-------: | :-------: | :-------- | -| **Bubble sort** | n | n2 | n2 | 1 | Sim | | -| **Insertion sort** | n | n2 | n2 | 1 | Sim | | -| **Selection sort** | n2 | n2 | n2 | 1 | Não | | -| **Heap sort** | n log(n) | n log(n) | n log(n) | 1 | Não | | -| **Merge sort** | n log(n) | n log(n) | n log(n) | n | Sim | | -| **Quick sort** | n log(n) | n log(n) | n2 | log(n) | Não | O Quicksort geralmente é feito no local com espaço de pilha O(log(n)) | -| **Shell sort** | n log(n) | depende da sequência de lacunas | n (log(n))2 | 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 Outros [projetos](https://trekhleb.dev/projects/) e [artigos](https://trekhleb.dev/blog/) sobre JavaScript e algoritmos em [trekhleb.dev](https://trekhleb.dev) diff --git a/README.ru-RU.md b/README.ru-RU.md deleted file mode 100644 index 939ed46700..0000000000 --- a/README.ru-RU.md +++ /dev/null @@ -1,322 +0,0 @@ -# Алгоритмы и структуры данных на 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) - -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 YouTube). - -_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), -[_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), -[_Tiếng Việt_](README.vi-VN.md), -[_Deutsch_](README.de-DE.md), -[_Uzbek_](README.uz-UZ.md) -[_עברית_](README.he-IL.md) - -*☝ Замечание: этот репозиторий предназначен для учебно-исследовательских целей (**не** для использования в продакшн-системах).* - -## Структуры данных - -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` - Базовый уровень, `A` - Продвинутый уровень - -* `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-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) -* `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 — конечная совокупность точно заданных правил решения некоторого класса задач или набор инструкций, описывающих порядок действий исполнителя для решения некоторой задачи. - -`B` - Базовый уровень, `A` - Продвинутый уровень - -### 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. - * `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) - * `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) - * `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 - * `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 супер-последовательность](src/algorithms/sets/shortest-common-supersequence) - * `A` [Задача о рюкзаке](src/algorithms/sets/knapsack-problem) — "0/1" и "неограниченный" рюкзаки - * `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 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) - * `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. -* **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) - * `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 - * `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 - * `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) - * `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) - -### 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 программа". - -* **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` [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 - * `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 - * `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) - * `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. - -## Как использовать этот репозиторий - -**Установка всех зависимостей** -``` -npm install -``` - -**Запуск ESLint** - -Эта команда может потребоваться вам для проверки качества кода. - -``` -npm run lint -``` - -**Запуск всех тестов** - -``` -npm test -``` - -**Запуск определённого теста** - -``` -npm test -- 'LinkedList' -``` - -**Песочница** - -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: - -``` -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 ложно-положительного срабатывания | - -### Сложности алгоритмов сортировки - -| Наименование | Лучший случай | Средний случай | Худший случай | Память | Устойчивость | Комментарии | -| -------------------------- | :-----------: | :------------: | :-----------: | :----: | :----------: | :---------- | -| **Сортировка пузырьком** | n | n2 | n2 | 1 | Да | | -| **Сортировка вставками** | n | n2 | n2 | 1 | Да | | -| **Сортировка выбором** | n2 | n2 | n2 | 1 | Нет | | -| **Сортировка кучей** | n log(n) | n log(n) | n log(n) | 1 | Нет | | -| **Сортировка слиянием** | n log(n) | n log(n) | n log(n) | n | Да | | -| **Быстрая сортировка** | n log(n) | n log(n) | n2 | log(n) | Нет | Быстрая сортировка обычно выполняется с использованием O(log(n)) дополнительной памяти | -| **Сортировка Шелла** | n log(n) | зависит от выбранных шагов | n (log(n))2 | 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 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 deleted file mode 100644 index 53600480db..0000000000 --- a/README.tr-TR.md +++ /dev/null @@ -1,325 +0,0 @@ -# JavaScript Algoritmalar ve Veri Yapıları - -[![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 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. - -_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), -[_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) -[_עברית_](README.he-IL.md) - -*☝ Not, bu proje araştırma ve öğrenme amacı ile yapılmış -olup üretim için **yapılmamıştır**.* - -## Veri Yapıları - -Bir veri yapısı, verileri bir bilgisayarda organize etmenin ve depolamanın belirli bir yoludur, böylece -verimli bir şekilde erişilebilir ve değiştirilebilir. Daha iyi ifadeyle, bir veri yapısı bir veri koleksiyonudur, -aralarındaki ilişkiler, ve işlevler veya işlemler -veriye uygulanabilir. - -`B` - Başlangıç, `A` - İleri Seviye - -* `B` [Bağlantılı Veri Yapısı](src/data-structures/linked-list) -* `B` [Çift Yönlü Bağlı Liste](src/data-structures/doubly-linked-list) -* `B` [Kuyruk](src/data-structures/queue) -* `B` [Yığın](src/data-structures/stack) -* `B` [Hash Table](src/data-structures/hash-table) -* `B` [Heap](src/data-structures/heap) - max and min heap versions -* `B` [Öncelikli Kuyruk](src/data-structures/priority-queue) -* `A` [Trie](src/data-structures/trie) -* `A` [Ağaç](src/data-structures/tree) - * `A` [İkili Arama Ağaçları](src/data-structures/tree/binary-search-tree) - * `A` [AVL Tree](src/data-structures/tree/avl-tree) - * `A` [Red-Black Tree](src/data-structures/tree/red-black-tree) - * `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` [Bloom Filter](src/data-structures/bloom-filter) - -## Algoritmalar - -Bir algoritma, bir problem sınıfının nasıl çözüleceğine dair kesin bir tanımlamadır. -Bir işlem dizisini açık olarak tanımlayan kurallar dizisidir. - - -`B` - Başlangıç, `A` - İleri Seviye - -### Konusuna göre Algoritma - -* **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) (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` [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 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 (sinyal) içerdiği frekanslara ayırın -* **Setler** - * `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 (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 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) - 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 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) - * `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) - in-place and non-in-place implementations - * `B` [Shellsort](src/algorithms/sorting/shell-sort) - * `B` [Counting Sort](src/algorithms/sorting/counting-sort) - * `B` [Radix Sort](src/algorithms/sorting/radix-sort) -* **Bağlantılı Liste** - * `B` [Straight Traversal](src/algorithms/linked-list/traversal) - * `B` [Reverse Traversal](src/algorithms/linked-list/reverse-traversal) -* **Ağaçlar** - * `B` [Depth-First Search](src/algorithms/tree/depth-first-search) (DFS) - * `B` [Breadth-First Search](src/algorithms/tree/breadth-first-search) (BFS) -* **Graphs** - * `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) - ağırlıklı yönlendirilmemiş grafik için Minimum Yayılma Ağacı'nı (MST) bulma - * `A` [Dijkstra Algorithm](src/algorithms/graph/dijkstra) - tek tepe noktasından tüm grafik köşelerine en kısa yolları bulmak - * `A` [Bellman-Ford Algorithm](src/algorithms/graph/bellman-ford) - tek tepe noktasından tüm grafik köşelerine en kısa yolları bulmak - * `A` [Floyd-Warshall Algorithm](src/algorithms/graph/floyd-warshall) - tüm köşe çiftleri arasındaki en kısa yolları bulun - * `A` [Detect Cycle](src/algorithms/graph/detect-cycle) - hem yönlendirilmiş hem de yönlendirilmemiş grafikler için (DFS ve Ayrık Küme tabanlı sürümler) - * `A` [Prim’s Algorithm](src/algorithms/graph/prim) - ağırlıklı yönlendirilmemiş grafik için Minimum Yayılma Ağacı'nı (MST) bulma - * `A` [Topological Sorting](src/algorithms/graph/topological-sorting) - DFS metodu - * `A` [Articulation Points](src/algorithms/graph/articulation-points) - Tarjan's algoritması (DFS based) - * `A` [Bridges](src/algorithms/graph/bridges) - DFS yöntemi ile algoritma - * `A` [Eulerian Path and Eulerian Circuit](src/algorithms/graph/eulerian-path) - Fleury'nin algoritması - Her kenara tam olarak bir kez ulaş - * `A` [Hamiltonian Cycle](src/algorithms/graph/hamiltonian-cycle) - Her köşeyi tam olarak bir kez ziyaret et - * `A` [Strongly Connected Components](src/algorithms/graph/strongly-connected-components) - Kosaraju's algorithm - * `A` [Travelling Salesman Problem](src/algorithms/graph/travelling-salesman) - her şehri ziyaret eden ve başlangıç ​​şehrine geri dönen mümkün olan en kısa rota -* **Kriptografi** - * `B` [Polynomial Hash](src/algorithms/cryptography/polynomial-hash) - polinom temelinde dönen hash işlevi - * `B` [Caesar Cipher](src/algorithms/cryptography/caesar-cipher) - simple substitution cipher -* **Makine Öğrenmesi** - * `B` [NanoNeuron](https://github.com/trekhleb/nano-neuron) - 7 simple JS functions that illustrate how machines can actually learn (forward/backward propagation) -* **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` [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) - * `A` [Knight's Tour](src/algorithms/uncategorized/knight-tour) - -### 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 -benzerlik gösteren problemlere uygulanabilir. - -* **Brute Force** - mümkün olan tüm çözümleri tara ve en iyisini seç - * `B` [Doğrusal Arama](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) - tepeye çıkmanın yollarını hesapla - * `A` [Maximum Subarray](src/algorithms/sets/maximum-subarray) - * `A` [Travelling Salesman Problem](src/algorithms/graph/travelling-salesman) - her şehri ziyaret eden ve başlangıç şehrine geri dönen mümkün olan en kısa rota - * `A` [Discrete Fourier Transform](src/algorithms/math/fourier-transform) - bir zaman fonksiyonunu (bir sinyal) onu oluşturan frekanslara ayırır -* **Açgözlü** - geleceği düşünmeden şu an için en iyi seçeneği seçin - * `B` [Jump Game](src/algorithms/uncategorized/jump-game) - * `A` [Unbound Knapsack Problem](src/algorithms/sets/knapsack-problem) - * `A` [Dijkstra Algorithm](src/algorithms/graph/dijkstra) - tüm grafik köşelerine giden en kısa yolu bulmak - * `A` [Prim’s Algorithm](src/algorithms/graph/prim) - ağırlıklı yönlendirilmemiş grafik için Minimum Yayılma Ağacı'nı (MST) bulma - * `A` [Kruskal’s Algorithm](src/algorithms/graph/kruskal) - ağırlıklı yönlendirilmemiş grafik için Minimum Yayılma Ağacı'nı (MST) bulma -* **Böl ve Fethet** - sorunu daha küçük parçalara bölün ve sonra bu parçaları çözün - * `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) - calculate the Greatest Common Divisor (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) (tekrarlı ve tekrarsız) - * `A` [Combinations](src/algorithms/sets/combinations) (tekrarlı ve tekrarsız) -* **Dinamik Programlama** - önceden bulunan alt çözümleri kullanarak bir çözüm oluşturmak - * `B` [Fibonacci Sayısı](src/algorithms/math/fibonacci) - * `B` [Jump Game](src/algorithms/uncategorized/jump-game) - * `B` [Eşsiz Yol](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) - zirveye ulaşmanın yollarının sayısını sayın - * `A` [Levenshtein Distance](src/algorithms/string/levenshtein-distance) - iki sekans arasındaki minimum düzenleme mesafesi - * `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) - 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) -* **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. - * `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 - * `A` [Hamiltonian Cycle](src/algorithms/graph/hamiltonian-cycle) - Her köşeyi tam olarak bir kez ziyaret edin - * `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) - belirli toplamı oluşturan tüm kombinasyonları bulun -* **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 -tree is being used. - -## Repository'in Kullanımı - -**Bütün dependencyleri kurun** -``` -npm install -``` - -**ESLint'i başlatın** - -Bunu kodun kalitesini kontrol etmek amacı ile çalıştırabilirsin. - -``` -npm run lint -``` - -**Bütün testleri çalıştır** -``` -npm test -``` - -**Testleri ismine göre çalıştır** -``` -npm test -- 'LinkedList' -``` - -**Deneme Alanı** - -data-structures ve algorithms içerisinde `./src/playground/playground.js` -yazarak `./src/playground/__test__/playground.test.js` için test edebilirsin. - - -Ardından basitçe alttaki komutu girerek kodunun beklendiği gibi çalışıp çalışmadığını test edebilirsin: - -``` -npm test -- 'playground' -``` - -## Yararlı Bilgiler - -### Referanslar - -[▶ Data Structures and Algorithms on YouTube](https://www.youtube.com/playlist?list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8) - -### Big O Notation - -* 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) - -Kaynak: [Big O Cheat Sheet](http://bigocheatsheet.com/). - -Altta Big O notations ve farklı input boyutlarına karşın yapılmış performans karşılaştırması listelenmektedir. - -| Big O Notation | 10 Element için hesaplama | 100 Element için hesaplama | 1000 Element için hesaplama | -| -------------- | ---------------------------- | ----------------------------- | ------------------------------- | -| **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 | - -### Veri Yapısı İşlem Karmaşıklığı - -| Veri Yapısı | Access | Search | Insertion | Deletion | Comments | -| ----------------------- | :-------: | :-------: | :-------: | :-------: | :-------- | -| **Dizi** | 1 | n | n | n | | -| **Yığın** | n | n | 1 | 1 | | -| **Sıralı** | n | n | 1 | 1 | | -| **Bağlantılı Liste** | n | n | 1 | n | | -| **Yığın Tablo** | - | n | n | n | Kusursuz hash fonksiyonu durumunda sonuç O(1) | -| **İkili Arama Ağacı** | n | n | n | n | In case of balanced tree costs would be 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 | - | Arama esnasında yanlış sonuçlar çıkabilir | - -### Dizi Sıralama Algoritmaları Karmaşıklığı - -| İsim | En İyi | Ortalama | En Kötü | Hafıza | Kararlı | Yorumlar | -| --------------------- | :-------------: | :-----------------: | :-----------------: | :-------: | :-------: | :-------- | -| **Bubble sort** | n | n2 | n2 | 1 | Evet | | -| **Insertion sort** | n | n2 | n2 | 1 | Evet | | -| **Selection sort** | n2 | n2 | n2 | 1 | Hayır | | -| **Heap sort** | n log(n) | n log(n) | n log(n) | 1 | Hayır | | -| **Merge sort** | n log(n) | n log(n) | n log(n) | n | Evet | | -| **Quick sort** | n log(n) | n log(n) | n2 | log(n) | Hayır | Hızlı sıralama genellikle O(log(n)) yığın alanıyla yapılır | -| **Shell sort** | n log(n) | depends on gap sequence | n (log(n))2 | 1 | Hayır | | -| **Counting sort** | n + r | n + r | n + r | n + r | Evet | r - dizideki en büyük sayı | -| **Radix sort** | n * k | n * k | n * k | n + k | Evet | k - en uzun key'in uzunluğu | - -## Projeyi Destekleme - -Bu projeyi buradan destekleyebilirsiniz ❤️️ [GitHub](https://github.com/sponsors/trekhleb) veya ❤️️ [Patreon](https://www.patreon.com/trekhleb). - -> 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 deleted file mode 100644 index 5ee5f7cbcc..0000000000 --- a/README.uk-UA.md +++ /dev/null @@ -1,312 +0,0 @@ -# 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), -[_Bahasa Indonesia_](README.id-ID.md), -[_Arabic_](README.ar-AR.md), -[_Tiếng Việt_](README.vi-VN.md), -[_Deutsch_](README.de-DE.md), -[_Uzbek_](README.uz-UZ.md) -[_עברית_](README.he-IL.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 | n2 | n2 | 1 | Так | | -| **Сортування включенням** | n | n2 | n2 | 1 | Так | | -| **Сортування вибором** | n2 | n2 | n2 | 1 | Ні | | -| **Пірамідальне сортування** | n log(n) | n log(n) | n log(n) | 1 | Ні | | -| **Сортування злиттям** | n log(n) | n log(n) | n log(n) | n | Так | | -| **Швидке сортування** | n log(n) | n log(n) | n2 | log(n) | Ні | Швидке сортування зазвичай виконується на місці з використанням O (log (n)) додаткової пам'яті | -| **Сортування Шелла** | n log(n) | залежить від послідовності проміжків | n (log(n))2 | 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` - -> 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.uz-UZ.md b/README.uz-UZ.md deleted file mode 100644 index 114a4de9cc..0000000000 --- a/README.uz-UZ.md +++ /dev/null @@ -1,359 +0,0 @@ -# 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) -[_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**. - -## 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 | n2 | n2 | 1 | Ha | | -| **Kiritish tartibi** | n | n2 | n2 | 1 | Ha | | -| **Tanlash tartibi** | n2 | n2 | n2 | 1 | Yo'q | | -| **Heap tartibi** | n log(n) | n log(n) | n log(n) | 1 | Yo'q | | -| **Birlashtirish tartibi** | n log(n) | n log(n) | n log(n) | n | Ha | | -| **Tezkor saralash** | n log(n) | n log(n) | n2 | log(n) | Yo'q | Tezkor saralash odatda O(log(n)) stek maydoni bilan joyida amalga oshiriladi | -| **Shell tartiblash** | n log(n) | depends on gap sequence | n (log(n))2 | 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.vi-VN.md b/README.vi-VN.md deleted file mode 100644 index 4c35f467f8..0000000000 --- a/README.vi-VN.md +++ /dev/null @@ -1,329 +0,0 @@ -# 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) -[_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.* - -## 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 | n2 | n2 | 1 | Có | | -| **Sắp xếp chèn** | n | n2 | n2 | 1 | Có | | -| **Sắp xếp chọn** | n2 | n2 | n2 | 1 | Không | | -| **Sắp xếp vun đống** | n log(n) | n log(n) | n log(n) | 1 | Không | | -| **Sắp xếp trộn** | n log(n) | n log(n) | n log(n) | n | Có | | -| **Sắp xếp nhanh** | n log(n) | n log(n) | n2 | log(n) | Không | Sắp xếp nhanh thường được thực hiện tại chỗ với không gian ngăn xếp O (log (n)) | -| **Shell sort** | n log(n) | phụ thuộc vào khoảng cách dãy | n (log(n))2 | 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 deleted file mode 100644 index 14e0f0e36c..0000000000 --- a/README.zh-CN.md +++ /dev/null @@ -1,299 +0,0 @@ -# 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?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。 - -每种算法和数据结构都有自己的 README，包含相关说明和链接，以便进一步阅读 (还有 YouTube 视频) 。 - -_Read this in other languages:_ -[_English_](https://github.com/trekhleb/javascript-algorithms/), -[_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), -[_Tiếng Việt_](README.vi-VN.md), -[_Deutsch_](README.de-DE.md), -[_Uzbek_](README.uz-UZ.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。* - -## 数据结构 - -数据结构是在计算机中组织和存储数据的一种特殊方式，使得数据可以高效地被访问和修改。更确切地说，数据结构是数据值的集合，表示数据之间的关系，也包括了作用在数据上的函数或操作。 - -`B` - 初学者， `A` - 进阶 - -* `B` [链表](src/data-structures/linked-list/README.zh-CN.md) -* `B` [双向链表](src/data-structures/doubly-linked-list/README.zh-CN.md) -* `B` [队列](src/data-structures/queue/README.zh-CN.md) -* `B` [栈](src/data-structures/stack/README.zh-CN.md) -* `B` [哈希表(散列)](src/data-structures/hash-table/README.zh-CN.md) -* `B` [堆](src/data-structures/heap/README.zh-CN.md) - 最大堆 & 最小堆 -* `B` [优先队列](src/data-structures/priority-queue/README.zh-CN.md) -* `A` [字典树](src/data-structures/trie/README.zh-CN.md) -* `A` [树](src/data-structures/tree/README.zh-CN.md) - * `A` [二叉查找树](src/data-structures/tree/binary-search-tree) - * `A` [AVL 树](src/data-structures/tree/avl-tree) - * `A` [红黑树](src/data-structures/tree/red-black-tree) - * `A` [线段树](src/data-structures/tree/segment-tree) - 使用 `最小/最大/总和` 范围查询示例 - * `A` [树状数组](src/data-structures/tree/fenwick-tree) (二叉索引树) -* `A` [图](src/data-structures/graph/README.zh-CN.md) (有向图与无向图) -* `A` [并查集](src/data-structures/disjoint-set) -* `A` [布隆过滤器](src/data-structures/bloom-filter) - -## 算法 - -算法是如何解决一类问题的明确规范。算法是一组精确定义操作序列的规则。 - -`B` - 初学者， `A` - 进阶 - -### 算法主题 - -* **数学** - * `B` [位运算](src/algorithms/math/bits) - set/get/update/clear 位、乘以/除以二进制位 、变负等 - * `B` [阶乘](src/algorithms/math/factorial/README.zh-CN.md) - * `B` [斐波那契数](src/algorithms/math/fibonacci) - `经典` 和 `闭式` 版本 - * `B` [素数检测](src/algorithms/math/primality-test) (排除法) - * `B` [欧几里得算法](src/algorithms/math/euclidean-algorithm) - 计算最大公约数 (GCD) - * `B` [最小公倍数](src/algorithms/math/least-common-multiple) (LCM) - * `B` [素数筛](src/algorithms/math/sieve-of-eratosthenes) - 查找任意给定范围内的所有素数 - * `B` [判断 2 次方数](src/algorithms/math/is-power-of-two) - 检查数字是否为 2 的幂 (原生和按位算法) - * `B` [杨辉三角形](src/algorithms/math/pascal-triangle) - * `B` [复数](src/algorithms/math/complex-number) - 复数及其基本运算 - * `B` [弧度和角](src/algorithms/math/radian) - 弧度与角的相互转换 - * `B` [快速算次方](src/algorithms/math/fast-powering) - * `A` [整数拆分](src/algorithms/math/integer-partition) - * `A` [割圆术](src/algorithms/math/liu-hui) - 基于 N-gons 的近似 π 计算 - * `A` [离散傅里叶变换](src/algorithms/math/fourier-transform) - 把时间信号解析成构成它的频率 -* **集合** - * `B` [笛卡尔积](src/algorithms/sets/cartesian-product) - 多集合结果 - * `A` [洗牌算法](src/algorithms/sets/fisher-yates) - 随机置换有限序列 - * `A` [幂集](src/algorithms/sets/power-set) - 该集合的所有子集 - * `A` [排列](src/algorithms/sets/permutations) (有/无重复) - * `A` [组合](src/algorithms/sets/combinations) (有/无重复) - * `A` [最长公共子序列](src/algorithms/sets/longest-common-subsequence) (LCS) - * `A` [最长递增子序列](src/algorithms/sets/longest-increasing-subsequence) - * `A` [最短公共父序列](src/algorithms/sets/shortest-common-supersequence) (SCS) - * `A` [背包问题](src/algorithms/sets/knapsack-problem) - `0/1` 和 `无边界` 问题 - * `A` [最大子数列问题](src/algorithms/sets/maximum-subarray) - `BF 算法` 和 `动态规划` - * `A` [组合求和](src/algorithms/sets/combination-sum) - 查找形成特定总和的所有组合 -* **字符串** - * `B` [汉明距离](src/algorithms/string/hamming-distance) - 符号不同的位置数 - * `A` [莱温斯坦距离](src/algorithms/string/levenshtein-distance) - 两个序列之间的最小编辑距离 - * `A` [Knuth–Morris–Pratt 算法](src/algorithms/string/knuth-morris-pratt) KMP 算法 - 子串搜索 (模式匹配) - * `A` [字符串快速查找](src/algorithms/string/z-algorithm) - 子串搜索 (模式匹配) - * `A` [Rabin Karp 算法](src/algorithms/string/rabin-karp) - 子串搜索 - * `A` [最长公共子串](src/algorithms/string/longest-common-substring) - * `A` [正则表达式匹配](src/algorithms/string/regular-expression-matching) -* **搜索** - * `B` [线性搜索](src/algorithms/search/linear-search) - * `B` [跳转搜索/块搜索](src/algorithms/search/jump-search) - 搜索有序数组 - * `B` [二分查找](src/algorithms/search/binary-search) - 搜索有序数组 - * `B` [插值搜索](src/algorithms/search/interpolation-search) - 搜索均匀分布的有序数组 -* **排序** - * `B` [冒泡排序](src/algorithms/sorting/bubble-sort) - * `B` [选择排序](src/algorithms/sorting/selection-sort) - * `B` [插入排序](src/algorithms/sorting/insertion-sort) - * `B` [堆排序](src/algorithms/sorting/heap-sort) - * `B` [归并排序](src/algorithms/sorting/merge-sort) - * `B` [快速排序](src/algorithms/sorting/quick-sort) - in-place (原地) 和 non-in-place 版本 - * `B` [希尔排序](src/algorithms/sorting/shell-sort) - * `B` [计数排序](src/algorithms/sorting/counting-sort) - * `B` [基数排序](src/algorithms/sorting/radix-sort) -* **链表** - - `B` [正向遍历](src/algorithms/linked-list/traversal) - - `B` [反向遍历](src/algorithms/linked-list/reverse-traversal) -* **树** - * `B` [深度优先搜索](src/algorithms/tree/depth-first-search) (DFS) - * `B` [广度优先搜索](src/algorithms/tree/breadth-first-search) (BFS) -* **图** - * `B` [深度优先搜索](src/algorithms/graph/depth-first-search) (DFS) - * `B` [广度优先搜索](src/algorithms/graph/breadth-first-search) (BFS) - * `B` [克鲁斯克尔演算法](src/algorithms/graph/kruskal) - 寻找加权无向图的最小生成树 (MST) - * `A` [戴克斯特拉算法](src/algorithms/graph/dijkstra) - 找到图中所有顶点的最短路径 - * `A` [贝尔曼-福特算法](src/algorithms/graph/bellman-ford) - 找到图中所有顶点的最短路径 - * `A` [弗洛伊德算法](src/algorithms/graph/floyd-warshall) - 找到所有顶点对 之间的最短路径 - * `A` [判圈算法](src/algorithms/graph/detect-cycle) - 对于有向图和无向图 (基于 DFS 和不相交集的版本) - * `A` [普林演算法](src/algorithms/graph/prim) - 寻找加权无向图的最小生成树 (MST) - * `A` [拓扑排序](src/algorithms/graph/topological-sorting) - DFS 方法 - * `A` [关节点](src/algorithms/graph/articulation-points) - Tarjan 算法 (基于 DFS) - * `A` [桥](src/algorithms/graph/bridges) - 基于 DFS 的算法 - * `A` [欧拉回径与一笔画问题](src/algorithms/graph/eulerian-path) - Fleury 的算法 - 一次访问每个边 - * `A` [哈密顿图](src/algorithms/graph/hamiltonian-cycle) - 恰好访问每个顶点一次 - * `A` [强连通分量](src/algorithms/graph/strongly-connected-components) - Kosaraju 算法 - * `A` [旅行推销员问题](src/algorithms/graph/travelling-salesman) - 尽可能以最短的路线访问每个城市并返回原始城市 -* **加密** - * `B` [多项式 hash](src/algorithms/cryptography/polynomial-hash) - 基于多项式的 rolling hash 函数 -* **机器学习** - * `B` [NanoNeuron](https://github.com/trekhleb/nano-neuron) -7个简单的JS函数，说明机器如何实际学习（向前/向后传播） -* **未分类** - * `B` [汉诺塔](src/algorithms/uncategorized/hanoi-tower) - * `B` [旋转矩阵](src/algorithms/uncategorized/square-matrix-rotation) - 原地算法 - * `B` [跳跃游戏](src/algorithms/uncategorized/jump-game) - 回溯,、动态编程 (自上而下+自下而上) 和贪婪的例子 - * `B` [独特(唯一) 路径](src/algorithms/uncategorized/unique-paths) - 回溯、动态编程和基于 Pascal 三角形的例子 - * `B` [雨水收集](src/algorithms/uncategorized/rain-terraces) - 诱捕雨水问题 (动态编程和暴力版本) - * `B` [递归楼梯](src/algorithms/uncategorized/recursive-staircase) - 计算有共有多少种方法可以到达顶层 (4 种解题方案) - * `A` [八皇后问题](src/algorithms/uncategorized/n-queens) - * `A` [骑士巡逻](src/algorithms/uncategorized/knight-tour) - -### 算法范式 - -算法范式是一种通用方法，基于一类算法的设计。这是比算法更高的抽象，就像算法是比计算机程序更高的抽象。 - -* **BF 算法** - `查找/搜索` 所有可能性并选择最佳解决方案 - * `B` [线性搜索](src/algorithms/search/linear-search) - * `B` [雨水收集](src/algorithms/uncategorized/rain-terraces) - 诱导雨水问题 - * `B` [递归楼梯](src/algorithms/uncategorized/recursive-staircase) - 计算有共有多少种方法可以到达顶层 (4 种解题方案) - * `A` [最大子数列](src/algorithms/sets/maximum-subarray) - * `A` [旅行推销员问题](src/algorithms/graph/travelling-salesman) - 尽可能以最短的路线访问每个城市并返回原始城市 - * `A` [离散傅里叶变换](src/algorithms/math/fourier-transform) - 把时间信号解析成构成它的频率 -* **贪心法** - 在当前选择最佳选项，不考虑以后情况 - * `B` [跳跃游戏](src/algorithms/uncategorized/jump-game) - * `A` [背包问题](src/algorithms/sets/knapsack-problem) - * `A` [戴克斯特拉算法](src/algorithms/graph/dijkstra) - 找到所有图顶点的最短路径 - * `A` [普里姆算法](src/algorithms/graph/prim) - 寻找加权无向图的最小生成树 (MST) - * `A` [克鲁斯卡尔算法](src/algorithms/graph/kruskal) - 寻找加权无向图的最小生成树 (MST) -* **分治法** - 将问题分成较小的部分，然后解决这些部分 - * `B` [二分查找](src/algorithms/search/binary-search) - * `B` [汉诺塔](src/algorithms/uncategorized/hanoi-tower) - * `B` [杨辉三角形](src/algorithms/math/pascal-triangle) - * `B` [欧几里得算法](src/algorithms/math/euclidean-algorithm) - 计算最大公约数 (GCD) - * `B` [归并排序](src/algorithms/sorting/merge-sort) - * `B` [快速排序](src/algorithms/sorting/quick-sort) - * `B` [树深度优先搜索](src/algorithms/tree/depth-first-search) (DFS) - * `B` [图深度优先搜索](src/algorithms/graph/depth-first-search) (DFS) - * `B` [跳跃游戏](src/algorithms/uncategorized/jump-game) - * `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) - * `B` [雨水收集](src/algorithms/uncategorized/rain-terraces) - 疏导雨水问题 - * `B` [递归楼梯](src/algorithms/uncategorized/recursive-staircase) - 计算有共有多少种方法可以到达顶层 (4 种解题方案) - * `A` [莱温斯坦距离](src/algorithms/string/levenshtein-distance) - 两个序列之间的最小编辑距离 - * `A` [最长公共子序列](src/algorithms/sets/longest-common-subsequence) (LCS) - * `A` [最长公共子串](src/algorithms/string/longest-common-substring) - * `A` [最长递增子序列](src/algorithms/sets/longest-increasing-subsequence) - * `A` [最短公共子序列](src/algorithms/sets/shortest-common-supersequence) - * `A` [0-1背包问题](src/algorithms/sets/knapsack-problem) - * `A` [整数拆分](src/algorithms/math/integer-partition) - * `A` [最大子数列](src/algorithms/sets/maximum-subarray) - * `A` [贝尔曼-福特算法](src/algorithms/graph/bellman-ford) - 找到所有图顶点的最短路径 - * `A` [弗洛伊德算法](src/algorithms/graph/floyd-warshall) - 找到所有顶点对之间的最短路径 - * `A` [正则表达式匹配](src/algorithms/string/regular-expression-matching) -* **回溯法** - 类似于 `BF 算法` 试图产生所有可能的解决方案，但每次生成解决方案测试如果它满足所有条件，那么只有继续生成后续解决方案。否则回溯并继续寻找不同路径的解决方案。 - * `B` [跳跃游戏](src/algorithms/uncategorized/jump-game) - * `B` [独特路径](src/algorithms/uncategorized/unique-paths) - * `A` [幂集](src/algorithms/sets/power-set) - 该集合的所有子集 - * `A` [哈密顿图](src/algorithms/graph/hamiltonian-cycle) - 恰好访问每个顶点一次 - * `A` [八皇后问题](src/algorithms/uncategorized/n-queens) - * `A` [骑士巡逻](src/algorithms/uncategorized/knight-tour) - * `A` [组合求和](src/algorithms/sets/combination-sum) - 从规定的总和中找出所有的组合 -* **Branch & Bound** - 记住在回溯搜索的每个阶段找到的成本最低的解决方案，并使用到目前为止找到的成本最小值作为下限。以便丢弃成本大于最小值的解决方案。通常，使用 BFS 遍历以及状态空间树的 DFS 遍历。 - -## 如何使用本仓库 - -**安装依赖** -``` -npm install -``` - -**运行 ESLint** - -检查代码质量 - -``` -npm run lint -``` - -**执行测试** - -``` -npm test -``` - -**按照名称执行测试** -``` -npm test -- 'LinkedList' -``` - -**Playground** - -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 是否无误: - -``` -npm test -- 'playground' -``` - -## 有用的信息 - -### 引用 - -[▶ YouTube](https://www.youtube.com/playlist?list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8) - -### 大O符号 - -大O符号中指定的算法的增长顺序。 - -![Big O graphs](./assets/big-o-graph.png) - -源: [Big O Cheat Sheet](http://bigocheatsheet.com/). - -以下是一些最常用的 大O标记法 列表以及它们与不同大小输入数据的性能比较。 - -| 大O标记法 | 计算10个元素 | 计算100个元素 | 计算1000个元素 | -| -------------- | ---------------------------- | ----------------------------- | ------------------------------- | -| **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 | - -### 数据结构操作的复杂性 - -| 数据结构 | 连接 | 查找 | 插入 | 删除 | 备注 | -| -------------- | :----: | :----: | :----: | :----: | ---- | -| **数组** | 1 | n | n | n | | -| **栈** | n | n | 1 | 1 | | -| **队列** | n | n | 1 | 1 | | -| **链表** | n | n | 1 | 1 | | -| **哈希表** | - | n | n | n | 在完全哈希函数情况下，复杂度是 O(1） | -| **二分查找树** | n | n | n | n | 在平衡树情况下，复杂度是 O(log(n)) | -| **B 树** | log(n) | log(n) | log(n) | log(n) | | -| **红黑树** | log(n) | log(n) | log(n) | log(n) | | -| **AVL 树** | log(n) | log(n) | log(n) | log(n) | | -| **布隆过滤器** | - | 1 | 1 | - | 存在一定概率的判断错误（误判成存在） | - -### 数组排序算法的复杂性 - -| 名称 | 最优 | 平均 | 最坏 | 内存 | 稳定 | 备注 | -| --------------------- | :-------: | :-------: | :-----------: | :-------: | :-------: | --------------------- | -| **冒泡排序** | n | n^2 | n^2 | 1 | Yes | | -| **插入排序** | n | n^2 | n^2 | 1 | Yes | | -| **选择排序** | n^2 | n^2 | n^2 | 1 | No | | -| **堆排序** | n log(n) | n log(n) | n log(n) | 1 | No | | -| **归并排序** | 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 | 在 in-place 版本下，内存复杂度通常是 O(log(n)) | -| **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 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 deleted file mode 100644 index aa48b40bd8..0000000000 --- a/README.zh-TW.md +++ /dev/null @@ -1,229 +0,0 @@ -# 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?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。 -每個演算法和資料結構都有其個別的文件，內有相關的解釋以及更多相關的文章或Youtube影片連結。 - -_Read this in other languages:_ -[_English_](https://github.com/trekhleb/javascript-algorithms/), -[_简体中文_](README.zh-CN.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), -[_Tiếng Việt_](README.vi-VN.md), -[_Deutsch_](README.de-DE.md), -[_Uzbek_](README.uz-UZ.md) -[_עברית_](README.he-IL.md) - -## 資料結構 - -資料結構是一個電腦用來組織和排序資料的特定方式，透過這樣的方式資料可以有效率地被讀取以及修改。更精確地說，一個資料結構是一個資料值的集合、彼此間的關係，函數或者運作可以應用於資料上。 - -* [鏈結串列](src/data-structures/linked-list) -* [貯列](src/data-structures/queue) -* [堆疊](src/data-structures/stack) -* [雜湊表](src/data-structures/hash-table) -* [堆](src/data-structures/heap) -* [優先貯列](src/data-structures/priority-queue) -* [字典樹](src/data-structures/trie) -* [樹](src/data-structures/tree) - * [二元搜尋樹](src/data-structures/tree/binary-search-tree) - * [AVL樹](src/data-structures/tree/avl-tree) - * [紅黑樹](src/data-structures/tree/red-black-tree) -* [圖](src/data-structures/graph) (有向跟無向皆包含) -* [互斥集](src/data-structures/disjoint-set) - -## 演算法 - -演算法是一個如何解決一類問題的非模糊規格。演算法是一個具有精確地定義了一系列運作的規則的集合 - -### 演算法議題分類 - -* **數學類** - * [階層](src/algorithms/math/factorial) - * [費伯納西數列](src/algorithms/math/fibonacci) - * [Primality Test](src/algorithms/math/primality-test) (排除法) - * [歐幾里得算法](src/algorithms/math/euclidean-algorithm) - 計算最大公因數 (GCD) - * [最小公倍數](src/algorithms/math/least-common-multiple) (LCM) - * [整數拆分](src/algorithms/math/integer-partition) -* **集合** - * [笛卡爾積](src/algorithms/sets/cartesian-product) - 多個集合的乘積 - * [冪集合](src/algorithms/sets/power-set) - 所有集合的子集合 - * [排列](src/algorithms/sets/permutations) (有/無重複) - * [组合](src/algorithms/sets/combinations) (有/無重複) - * [洗牌算法](src/algorithms/sets/fisher-yates) - 隨機置換一有限序列 - * [最長共同子序列](src/algorithms/sets/longest-common-subsequence) (LCS) - * [最長遞增子序列](src/algorithms/sets/longest-increasing-subsequence) - * [Shortest Common Supersequence](src/algorithms/sets/shortest-common-supersequence) (SCS) - * [背包問題](src/algorithms/sets/knapsack-problem) - "0/1" and "Unbound" ones - * [最大子序列問題](src/algorithms/sets/maximum-subarray) - 暴力法以及動態編程的(Kadane's)版本 -* **字串** - * [萊文斯坦距離](src/algorithms/string/levenshtein-distance) - 兩序列間的最小編輯距離 - * [漢明距離](src/algorithms/string/hamming-distance) - number of positions at which the symbols are different - * [KMP 演算法](src/algorithms/string/knuth-morris-pratt) - 子字串搜尋 - * [Rabin Karp 演算法](src/algorithms/string/rabin-karp) - 子字串搜尋 - * [最長共通子序列](src/algorithms/string/longest-common-substring) -* **搜尋** - * [二元搜尋](src/algorithms/search/binary-search) -* **排序** - * [氣泡排序](src/algorithms/sorting/bubble-sort) - * [選擇排序](src/algorithms/sorting/selection-sort) - * [插入排序](src/algorithms/sorting/insertion-sort) - * [堆排序](src/algorithms/sorting/heap-sort) - * [合併排序](src/algorithms/sorting/merge-sort) - * [快速排序](src/algorithms/sorting/quick-sort) - * [希爾排序](src/algorithms/sorting/shell-sort) -* **樹** - * [深度優先搜尋](src/algorithms/tree/depth-first-search) (DFS) - * [廣度優先搜尋](src/algorithms/tree/breadth-first-search) (BFS) -* **圖** - * [深度優先搜尋](src/algorithms/graph/depth-first-search) (DFS) - * [廣度優先搜尋](src/algorithms/graph/breadth-first-search) (BFS) - * [Dijkstra 演算法](src/algorithms/graph/dijkstra) - 找到所有圖頂點的最短路徑 - * [Bellman-Ford 演算法](src/algorithms/graph/bellman-ford) - 找到所有圖頂點的最短路徑 - * [Detect Cycle](src/algorithms/graph/detect-cycle) - for both directed and undirected graphs (DFS and Disjoint Set based versions) - * [Prim’s 演算法](src/algorithms/graph/prim) - finding Minimum Spanning Tree (MST) for weighted undirected graph - * [Kruskal’s 演算法](src/algorithms/graph/kruskal) - finding Minimum Spanning Tree (MST) for weighted undirected graph - * [拓撲排序](src/algorithms/graph/topological-sorting) - DFS method - * [關節點](src/algorithms/graph/articulation-points) - Tarjan's algorithm (DFS based) - * [橋](src/algorithms/graph/bridges) - DFS based algorithm - * [尤拉路徑及尤拉環](src/algorithms/graph/eulerian-path) - Fleury's algorithm - Visit every edge exactly once - * [漢彌爾頓環](src/algorithms/graph/hamiltonian-cycle) - Visit every vertex exactly once - * [強連通組件](src/algorithms/graph/strongly-connected-components) - Kosaraju's algorithm - * [旅行推銷員問題](src/algorithms/graph/travelling-salesman) - shortest possible route that visits each city and returns to the origin city - * [Floyd-Warshall algorithm](src/algorithms/graph/floyd-warshall) - 一次循环可以找出所有頂點之间的最短路徑 -* **未分類** - * [河內塔](src/algorithms/uncategorized/hanoi-tower) - * [N-皇后問題](src/algorithms/uncategorized/n-queens) - * [騎士走棋盤](src/algorithms/uncategorized/knight-tour) - -### 演算法範型 - -演算法的範型是一個泛用方法或設計一類底層演算法的方式。它是一個比演算法的概念更高階的抽象化，就像是演算法是比電腦程式更高階的抽象化。 - -* **暴力法** - 尋遍所有的可能解然後選取最好的解 - * [最大子序列](src/algorithms/sets/maximum-subarray) - * [旅行推銷員問題](src/algorithms/graph/travelling-salesman) - shortest possible route that visits each city and returns to the origin city -* **貪婪法** - choose the best option at the current time, without any consideration for the future - * [未定背包問題](src/algorithms/sets/knapsack-problem) - * [Dijkstra 演算法](src/algorithms/graph/dijkstra) - 找到所有圖頂點的最短路徑 - * [Prim’s 演算法](src/algorithms/graph/prim) - finding Minimum Spanning Tree (MST) for weighted undirected graph - * [Kruskal’s 演算法](src/algorithms/graph/kruskal) - finding Minimum Spanning Tree (MST) for weighted undirected graph -* **分治法** - divide the problem into smaller parts and then solve those parts - * [二元搜尋](src/algorithms/search/binary-search) - * [河內塔](src/algorithms/uncategorized/hanoi-tower) - * [歐幾里得演算法](src/algorithms/math/euclidean-algorithm) - calculate the Greatest Common Divisor (GCD) - * [排列](src/algorithms/sets/permutations) (有/無重複) - * [组合](src/algorithms/sets/combinations) (有/無重複) - * [合併排序](src/algorithms/sorting/merge-sort) - * [快速排序](src/algorithms/sorting/quick-sort) - * [樹深度優先搜尋](src/algorithms/tree/depth-first-search) (DFS) - * [圖深度優先搜尋](src/algorithms/graph/depth-first-search) (DFS) -* **動態編程** - build up to a solution using previously found sub-solutions - * [費伯納西數列](src/algorithms/math/fibonacci) - * [萊溫斯坦距離](src/algorithms/string/levenshtein-distance) - minimum edit distance between two sequences - * [最長共同子序列](src/algorithms/sets/longest-common-subsequence) (LCS) - * [最長共同子字串](src/algorithms/string/longest-common-substring) - * [最長遞增子序列](src/algorithms/sets/longest-increasing-subsequence) - * [最短共同子序列](src/algorithms/sets/shortest-common-supersequence) - * [0/1背包問題](src/algorithms/sets/knapsack-problem) - * [整數拆分](src/algorithms/math/integer-partition) - * [最大子序列](src/algorithms/sets/maximum-subarray) - * [Bellman-Ford 演算法](src/algorithms/graph/bellman-ford) - finding shortest path to all graph vertices -* **回溯法** - 用類似暴力法來嘗試產生所有可能解，但每次只在能滿足所有測試條件，且只有繼續產生子序列方案來產生的解決方案。否則回溯並尋找不同路徑的解決方案。 - * [漢彌爾頓迴路](src/algorithms/graph/hamiltonian-cycle) - Visit every vertex exactly once - * [N-皇后問題](src/algorithms/uncategorized/n-queens) - * [騎士走棋盤](src/algorithms/uncategorized/knight-tour) -* **Branch & Bound** - -## 如何使用本知識庫 - -**安裝所有必須套件** - -``` -npm install -``` - -**執行所有測試** -``` -npm test -``` - -**以名稱執行該測試** -``` -npm test -- 'LinkedList' -``` -**練習場** - -你可以透過在`./src/playground/playground.js`裡面的檔案練習資料結構以及演算法，並且撰寫在`./src/playground/__test__/playground.test.js`裡面的測試程式。 - -接著直接執行下列的指令來測試你練習的 code 是否如預期運作： - -``` -npm test -- 'playground' -``` - -## 有用的資訊 - -### 參考 - -[▶ Data Structures and Algorithms on YouTube](https://www.youtube.com/playlist?list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8) - -### 大 O 標記 - -特別用大 O 標記演算法增長度的排序。 - -![Big O 表](./assets/big-o-graph.png) - -資料來源: [Big O Cheat Sheet](http://bigocheatsheet.com/). - -下列列出幾個常用的 Big O 標記以及其不同大小資料量輸入後的運算效能比較。 - -| Big O 標記 | 10個資料量需花費的時間 | 100個資料量需花費的時間 | 1000個資料量需花費的時間 | -| -------------- | ---------------------------- | ----------------------------- | ------------------------------- | -| **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 | - -### 資料結構運作複雜度 - -| 資料結構 | 存取 | 搜尋 | 插入 | 刪除 | -| ----------------------- | :-------: | :-------: | :-------: | :-------: | -| **陣列** | 1 | n | n | n | -| **堆疊** | n | n | 1 | 1 | -| **貯列** | n | n | 1 | 1 | -| **鏈結串列** | n | n | 1 | 1 | -| **雜湊表** | - | n | n | n | -| **二元搜尋樹** | n | n | n | n | -| **B-Tree** | log(n) | log(n) | log(n) | log(n) | -| **紅黑樹** | log(n) | log(n) | log(n) | log(n) | -| **AVL Tree** | log(n) | log(n) | log(n) | log(n) | - -### 陣列排序演算法複雜度 - -| 名稱 | 最佳 | 平均 | 最差 | 記憶體 | 穩定 | -| ---------------------- | :-------: | :-------: | :-----------: | :-------: | :-------: | -| **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 | -| **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 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/assets/big-o-graph.png b/assets/big-o-graph.png deleted file mode 100644 index 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b/package.json deleted file mode 100644 index 95d6d28942..0000000000 --- a/package.json +++ /dev/null @@ -1,54 +0,0 @@ -{ - "name": "javascript-algorithms-and-data-structures", - "version": "0.0.4", - "description": "Algorithms and data-structures implemented on JavaScript", - "repository": { - "type": "git", - "url": "git+https://github.com/trekhleb/javascript-algorithms.git" - }, - "keywords": [ - "computer-science", - "cs", - "algorithms", - "data-structures", - "javascript", - "algorithm", - "javascript-algorithms", - "sorting-algorithms", - "graph", - "tree", - "interview", - "interview-preparation" - ], - "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": "7.20.7", - "@babel/preset-env": "7.20.2", - "@types/jest": "29.4.0", - "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", - "pngjs": "^7.0.0" - }, - "engines": { - "node": ">=16.15.0", - "npm": ">=8.5.5" - } -} diff --git a/src/algorithms/cryptography/caesar-cipher/README.md b/src/algorithms/cryptography/caesar-cipher/README.md deleted file mode 100644 index d648a62ee9..0000000000 --- a/src/algorithms/cryptography/caesar-cipher/README.md +++ /dev/null @@ -1,33 +0,0 @@ -# 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) - -## Example - -The transformation can be represented by aligning two alphabets; the cipher alphabet is the plain alphabet rotated left or right by some number of positions. For instance, here is a Caesar cipher using a left rotation of three places, equivalent to a right shift of 23 (the shift parameter is used as the key): - -```text -Plain: ABCDEFGHIJKLMNOPQRSTUVWXYZ -Cipher: XYZABCDEFGHIJKLMNOPQRSTUVW -``` - -When encrypting, a person looks up each letter of the message in the "plain" line and writes down the corresponding letter in the "cipher" line. - -```text -Plaintext: THE QUICK BROWN FOX JUMPS OVER THE LAZY DOG -Ciphertext: QEB NRFZH YOLTK CLU GRJMP LSBO QEB IXWV ALD -``` - -## Complexity - -- Time: `O(|n|)` -- Space: `O(|n|)` - -## References - -- [Caesar cipher on Wikipedia](https://en.wikipedia.org/wiki/Caesar_cipher) diff --git a/src/algorithms/cryptography/caesar-cipher/README.ru-RU.md b/src/algorithms/cryptography/caesar-cipher/README.ru-RU.md deleted file mode 100644 index dee4d14cd3..0000000000 --- a/src/algorithms/cryptography/caesar-cipher/README.ru-RU.md +++ /dev/null @@ -1,29 +0,0 @@ -# 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) diff --git a/src/algorithms/cryptography/caesar-cipher/__test__/caesarCipher.test.js b/src/algorithms/cryptography/caesar-cipher/__test__/caesarCipher.test.js deleted file mode 100644 index 90521cedf8..0000000000 --- a/src/algorithms/cryptography/caesar-cipher/__test__/caesarCipher.test.js +++ /dev/null @@ -1,40 +0,0 @@ -import { caesarCipherEncrypt, caesarCipherDecrypt } from '../caesarCipher'; - -describe('caesarCipher', () => { - it('should not change a string with zero shift', () => { - expect(caesarCipherEncrypt('abcd', 0)).toBe('abcd'); - expect(caesarCipherDecrypt('abcd', 0)).toBe('abcd'); - }); - - it('should cipher a string with different shifts', () => { - expect(caesarCipherEncrypt('abcde', 3)).toBe('defgh'); - expect(caesarCipherDecrypt('defgh', 3)).toBe('abcde'); - - expect(caesarCipherEncrypt('abcde', 1)).toBe('bcdef'); - expect(caesarCipherDecrypt('bcdef', 1)).toBe('abcde'); - - expect(caesarCipherEncrypt('xyz', 1)).toBe('yza'); - expect(caesarCipherDecrypt('yza', 1)).toBe('xyz'); - }); - - it('should be case insensitive', () => { - expect(caesarCipherEncrypt('ABCDE', 3)).toBe('defgh'); - }); - - it('should correctly handle an empty strings', () => { - expect(caesarCipherEncrypt('', 3)).toBe(''); - }); - - it('should not cipher unknown chars', () => { - expect(caesarCipherEncrypt('ab2cde', 3)).toBe('de2fgh'); - expect(caesarCipherDecrypt('de2fgh', 3)).toBe('ab2cde'); - }); - - it('should encrypt and decrypt full phrases', () => { - expect(caesarCipherEncrypt('THE QUICK BROWN FOX JUMPS OVER THE LAZY DOG', 23)) - .toBe('qeb nrfzh yoltk clu grjmp lsbo qeb ixwv ald'); - - expect(caesarCipherDecrypt('qeb nrfzh yoltk clu grjmp lsbo qeb ixwv ald', 23)) - .toBe('the quick brown fox jumps over the lazy dog'); - }); -}); diff --git a/src/algorithms/cryptography/caesar-cipher/caesarCipher.js b/src/algorithms/cryptography/caesar-cipher/caesarCipher.js deleted file mode 100644 index ba92299062..0000000000 --- a/src/algorithms/cryptography/caesar-cipher/caesarCipher.js +++ /dev/null @@ -1,58 +0,0 @@ -// Create alphabet array: ['a', 'b', 'c', ..., 'z']. -const englishAlphabet = 'abcdefghijklmnopqrstuvwxyz'.split(''); - -/** - * Generates a cipher map out of the alphabet. - * Example with a shift 3: {'a': 'd', 'b': 'e', 'c': 'f', ...} - * - * @param {string[]} alphabet - i.e. ['a', 'b', 'c', ... , 'z'] - * @param {number} shift - i.e. 3 - * @return {Object} - i.e. {'a': 'd', 'b': 'e', 'c': 'f', ..., 'z': 'c'} - */ -const getCipherMap = (alphabet, shift) => { - return alphabet - .reduce((charsMap, currentChar, charIndex) => { - const charsMapClone = { ...charsMap }; - // Making the shift to be cyclic (i.e. with a shift of 1 - 'z' would be mapped to 'a'). - let encryptedCharIndex = (charIndex + shift) % alphabet.length; - // Support negative shifts for creating a map for decryption - // (i.e. with shift -1 - 'a' would be mapped to 'z'). - if (encryptedCharIndex < 0) { - encryptedCharIndex += alphabet.length; - } - charsMapClone[currentChar] = alphabet[encryptedCharIndex]; - return charsMapClone; - }, {}); -}; - -/** - * @param {string} str - * @param {number} shift - * @param {string[]} alphabet - * @return {string} - */ -export const caesarCipherEncrypt = (str, shift, alphabet = englishAlphabet) => { - // Create a cipher map: - const cipherMap = getCipherMap(alphabet, shift); - return str - .toLowerCase() - .split('') - .map((char) => cipherMap[char] || char) - .join(''); -}; - -/** - * @param {string} str - * @param {number} shift - * @param {string[]} alphabet - * @return {string} - */ -export const caesarCipherDecrypt = (str, shift, alphabet = englishAlphabet) => { - // Create a cipher map: - const cipherMap = getCipherMap(alphabet, -shift); - return str - .toLowerCase() - .split('') - .map((char) => cipherMap[char] || char) - .join(''); -}; diff --git a/src/algorithms/cryptography/hill-cipher/README.md b/src/algorithms/cryptography/hill-cipher/README.md deleted file mode 100644 index bf496e2be9..0000000000 --- a/src/algorithms/cryptography/hill-cipher/README.md +++ /dev/null @@ -1,96 +0,0 @@ -# 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/hill-cipher/_test_/hillCipher.test.js b/src/algorithms/cryptography/hill-cipher/_test_/hillCipher.test.js deleted file mode 100644 index f540ae9ff1..0000000000 --- a/src/algorithms/cryptography/hill-cipher/_test_/hillCipher.test.js +++ /dev/null @@ -1,46 +0,0 @@ -import { hillCipherEncrypt, hillCipherDecrypt } from '../hillCipher'; - -describe('hillCipher', () => { - 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'); - }; - const invalidCharacterInKeyString = () => { - hillCipherEncrypt('hello', 'hel12world'); - }; - 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 deleted file mode 100644 index 1fe3033860..0000000000 --- a/src/algorithms/cryptography/hill-cipher/hillCipher.js +++ /dev/null @@ -1,87 +0,0 @@ -import * as mtrx from '../../math/matrix/Matrix'; - -// The code of an 'A' character (equals to 65). -const alphabetCodeShift = 'A'.codePointAt(0); -const englishAlphabetSize = 26; - -/** - * Generates key matrix from given keyString. - * - * @param {string} keyString - a string to build a key matrix (must be of matrixSize^2 length). - * @return {number[][]} keyMatrix - */ -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', - ); - } - let keyStringIndex = 0; - 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; - keyStringIndex += 1; - return charCodeShifted; - }, - ); -}; - -/** - * Generates a message vector from a given message. - * - * @param {string} message - the message to encrypt. - * @return {number[][]} messageVector - */ -const generateMessageVector = (message) => { - 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; - }, - ); -}; - -/** - * 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); - 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 cipherVector = mtrx.dot(keyMatrix, messageVector); - let cipherString = ''; - for (let row = 0; row < cipherVector.length; row += 1) { - const item = cipherVector[row]; - cipherString += String.fromCharCode((item % englishAlphabetSize) + alphabetCodeShift); - } - - return cipherString; -} - -// @TODO: Implement this method. -export const hillCipherDecrypt = () => { - throw new Error('This method is not implemented yet'); -}; diff --git a/src/algorithms/cryptography/polynomial-hash/PolynomialHash.js b/src/algorithms/cryptography/polynomial-hash/PolynomialHash.js deleted file mode 100644 index d6f774efd8..0000000000 --- a/src/algorithms/cryptography/polynomial-hash/PolynomialHash.js +++ /dev/null @@ -1,89 +0,0 @@ -const DEFAULT_BASE = 37; -const DEFAULT_MODULUS = 101; - -export default class PolynomialHash { - /** - * @param {number} [base] - Base number that is used to create the polynomial. - * @param {number} [modulus] - Modulus number that keeps the hash from overflowing. - */ - constructor({ base = DEFAULT_BASE, modulus = DEFAULT_MODULUS } = {}) { - this.base = base; - this.modulus = modulus; - } - - /** - * Function that creates hash representation of the word. - * - * Time complexity: O(word.length). - * - * @param {string} word - String that needs to be hashed. - * @return {number} - */ - hash(word) { - const charCodes = Array.from(word).map((char) => this.charToNumber(char)); - - let hash = 0; - for (let charIndex = 0; charIndex < charCodes.length; charIndex += 1) { - hash *= this.base; - hash += charCodes[charIndex]; - hash %= this.modulus; - } - - return hash; - } - - /** - * Function that creates hash representation of the word - * based on previous word (shifted by one character left) hash value. - * - * Recalculates the hash representation of a word so that it isn't - * necessary to traverse the whole word again. - * - * Time complexity: O(1). - * - * @param {number} prevHash - * @param {string} prevWord - * @param {string} newWord - * @return {number} - */ - roll(prevHash, prevWord, newWord) { - let hash = prevHash; - - const prevValue = this.charToNumber(prevWord[0]); - const newValue = this.charToNumber(newWord[newWord.length - 1]); - - let prevValueMultiplier = 1; - for (let i = 1; i < prevWord.length; i += 1) { - prevValueMultiplier *= this.base; - prevValueMultiplier %= this.modulus; - } - - hash += this.modulus; - hash -= (prevValue * prevValueMultiplier) % this.modulus; - - hash *= this.base; - hash += newValue; - hash %= this.modulus; - - return hash; - } - - /** - * Converts char to number. - * - * @param {string} char - * @return {number} - */ - charToNumber(char) { - let charCode = char.codePointAt(0); - - // Check if character has surrogate pair. - const surrogate = char.codePointAt(1); - if (surrogate !== undefined) { - const surrogateShift = 2 ** 16; - charCode += surrogate * surrogateShift; - } - - return charCode; - } -} diff --git a/src/algorithms/cryptography/polynomial-hash/README.md b/src/algorithms/cryptography/polynomial-hash/README.md deleted file mode 100644 index 7355d6649b..0000000000 --- a/src/algorithms/cryptography/polynomial-hash/README.md +++ /dev/null @@ -1,116 +0,0 @@ -# Polynomial Rolling Hash - -## Hash Function - -**Hash functions** are used to map large data sets of elements of an arbitrary -length (*the keys*) to smaller data sets of elements of a fixed length -(*the fingerprints*). - -The basic application of hashing is efficient testing of equality of keys by -comparing their fingerprints. - -A *collision* happens when two different keys have the same fingerprint. The way -in which collisions are handled is crucial in most applications of hashing. -Hashing is particularly useful in construction of efficient practical algorithms. - -## Rolling Hash - -A **rolling hash** (also known as recursive hashing or rolling checksum) is a hash -function where the input is hashed in a window that moves through the input. - -A few hash functions allow a rolling hash to be computed very quickly — the new -hash value is rapidly calculated given only the following data: - -- old hash value, -- the old value removed from the window, -- and the new value added to the window. - -## Polynomial String Hashing - -An ideal hash function for strings should obviously depend both on the *multiset* of -the symbols present in the key and on the *order* of the symbols. The most common -family of such hash functions treats the symbols of a string as coefficients of -a *polynomial* with an integer variable `p` and computes its value modulo an -integer constant `M`: - -The *Rabin–Karp string search algorithm* is often explained using a very simple -rolling hash function that only uses multiplications and -additions - **polynomial rolling hash**: - -> H(s0, s1, ..., sk) = s0 * pk-1 + s1 * pk-2 + ... + sk * p0 - -where `p` is a constant, and *(s1, ... , sk)* are the input -characters. - -For example we can convert short strings to key numbers by multiplying digit codes by -powers of a constant. The three letter word `ace` could turn into a number -by calculating: - -> key = 1 * 262 + 3 * 261 + 5 * 260 - -In order to avoid manipulating huge `H` values, all math is done modulo `M`. - -> H(s0, s1, ..., sk) = (s0 * pk-1 + s1 * pk-2 + ... + sk * p0) mod M - -A careful choice of the parameters `M`, `p` is important to obtain “good” -properties of the hash function, i.e., low collision rate. - -This approach has the desirable attribute of involving all the characters in the -input string. The calculated key value can then be hashed into an array index in -the usual way: - -```javascript -function hash(key, arraySize) { - const base = 13; - - let hash = 0; - for (let charIndex = 0; charIndex < key.length; charIndex += 1) { - const charCode = key.charCodeAt(charIndex); - hash += charCode * (base ** (key.length - charIndex - 1)); - } - - return hash % arraySize; -} -``` - -The `hash()` method is not as efficient as it might be. Other than the -character conversion, there are two multiplications and an addition inside -the loop. We can eliminate one multiplication by using **Horner's method*: - -> a4 * x4 + a3 * x3 + a2 * x2 + a1 * x1 + a0 = (((a4 * x + a3) * x + a2) * x + a1) * x + a0 - -In other words: - -> Hi = (P * Hi-1 + Si) mod M - -The `hash()` cannot handle long strings because the hashVal exceeds the size of -int. Notice that the key always ends up being less than the array size. -In Horner's method we can apply the modulo (%) operator at each step in the -calculation. This gives the same result as applying the modulo operator once at -the end, but avoids the overflow. - -```javascript -function hash(key, arraySize) { - const base = 13; - - let hash = 0; - for (let charIndex = 0; charIndex < key.length; charIndex += 1) { - const charCode = key.charCodeAt(charIndex); - hash = (hash * base + charCode) % arraySize; - } - - return hash; -} -``` - -Polynomial hashing has a rolling property: the fingerprints can be updated -efficiently when symbols are added or removed at the ends of the string -(provided that an array of powers of p modulo M of sufficient length is stored). -The popular Rabin–Karp pattern matching algorithm is based on this property - -## References - -- [Where to Use Polynomial String Hashing](https://www.mii.lt/olympiads_in_informatics/pdf/INFOL119.pdf) -- [Hashing on uTexas](https://www.cs.utexas.edu/~mitra/csSpring2017/cs313/lectures/hash.html) -- [Hash Function on Wikipedia](https://en.wikipedia.org/wiki/Hash_function) -- [Rolling Hash on Wikipedia](https://en.wikipedia.org/wiki/Rolling_hash) diff --git a/src/algorithms/cryptography/polynomial-hash/SimplePolynomialHash.js b/src/algorithms/cryptography/polynomial-hash/SimplePolynomialHash.js deleted file mode 100644 index 8e1d5123f4..0000000000 --- a/src/algorithms/cryptography/polynomial-hash/SimplePolynomialHash.js +++ /dev/null @@ -1,63 +0,0 @@ -const DEFAULT_BASE = 17; - -export default class SimplePolynomialHash { - /** - * @param {number} [base] - Base number that is used to create the polynomial. - */ - constructor(base = DEFAULT_BASE) { - this.base = base; - } - - /** - * Function that creates hash representation of the word. - * - * Time complexity: O(word.length). - * - * @assumption: This version of the function doesn't use modulo operator. - * Thus it may produce number overflows by generating numbers that are - * bigger than Number.MAX_SAFE_INTEGER. This function is mentioned here - * for simplicity and LEARNING reasons. - * - * @param {string} word - String that needs to be hashed. - * @return {number} - */ - hash(word) { - let hash = 0; - for (let charIndex = 0; charIndex < word.length; charIndex += 1) { - hash += word.charCodeAt(charIndex) * (this.base ** charIndex); - } - - return hash; - } - - /** - * Function that creates hash representation of the word - * based on previous word (shifted by one character left) hash value. - * - * Recalculates the hash representation of a word so that it isn't - * necessary to traverse the whole word again. - * - * Time complexity: O(1). - * - * @assumption: This function doesn't use modulo operator and thus is not safe since - * it may deal with numbers that are bigger than Number.MAX_SAFE_INTEGER. This - * function is mentioned here for simplicity and LEARNING reasons. - * - * @param {number} prevHash - * @param {string} prevWord - * @param {string} newWord - * @return {number} - */ - roll(prevHash, prevWord, newWord) { - let hash = prevHash; - - const prevValue = prevWord.charCodeAt(0); - const newValue = newWord.charCodeAt(newWord.length - 1); - - hash -= prevValue; - hash /= this.base; - hash += newValue * (this.base ** (newWord.length - 1)); - - return hash; - } -} diff --git a/src/algorithms/cryptography/polynomial-hash/__test__/PolynomialHash.test.js b/src/algorithms/cryptography/polynomial-hash/__test__/PolynomialHash.test.js deleted file mode 100644 index 0d487848dc..0000000000 --- a/src/algorithms/cryptography/polynomial-hash/__test__/PolynomialHash.test.js +++ /dev/null @@ -1,59 +0,0 @@ -import PolynomialHash from '../PolynomialHash'; - -describe('PolynomialHash', () => { - it('should calculate new hash based on previous one', () => { - const bases = [3, 79, 101, 3251, 13229, 122743, 3583213]; - const mods = [79, 101]; - const frameSizes = [5, 20]; - - // @TODO: Provide Unicode support. - const text = 'Lorem Ipsum is simply dummy text of the printing and ' - + 'typesetting industry. Lorem Ipsum has been the industry\'s standard ' - + 'galley of type and \u{ffff} scrambled it to make a type specimen book. It ' - + 'electronic 耀 typesetting, remaining essentially unchanged. It was ' - // + 'popularised in the \u{20005} \u{20000}1960s with the release of Letraset sheets ' - + 'publishing software like Aldus PageMaker 耀 including versions of Lorem.'; - - // Check hashing for different prime base. - bases.forEach((base) => { - mods.forEach((modulus) => { - const polynomialHash = new PolynomialHash({ base, modulus }); - - // Check hashing for different word lengths. - frameSizes.forEach((frameSize) => { - let previousWord = text.substr(0, frameSize); - let previousHash = polynomialHash.hash(previousWord); - - // Shift frame through the whole text. - for (let frameShift = 1; frameShift < (text.length - frameSize); frameShift += 1) { - const currentWord = text.substr(frameShift, frameSize); - const currentHash = polynomialHash.hash(currentWord); - const currentRollingHash = polynomialHash.roll(previousHash, previousWord, currentWord); - - // Check that rolling hash is the same as directly calculated hash. - expect(currentRollingHash).toBe(currentHash); - - previousWord = currentWord; - previousHash = currentHash; - } - }); - }); - }); - }); - - it('should generate numeric hashed less than 100', () => { - const polynomialHash = new PolynomialHash({ modulus: 100 }); - - expect(polynomialHash.hash('Some long text that is used as a key')).toBe(41); - expect(polynomialHash.hash('Test')).toBe(92); - expect(polynomialHash.hash('a')).toBe(97); - expect(polynomialHash.hash('b')).toBe(98); - expect(polynomialHash.hash('c')).toBe(99); - expect(polynomialHash.hash('d')).toBe(0); - expect(polynomialHash.hash('e')).toBe(1); - expect(polynomialHash.hash('ab')).toBe(87); - - // @TODO: Provide Unicode support. - expect(polynomialHash.hash('\u{20000}')).toBe(92); - }); -}); diff --git a/src/algorithms/cryptography/polynomial-hash/__test__/SimplePolynomialHash.test.js b/src/algorithms/cryptography/polynomial-hash/__test__/SimplePolynomialHash.test.js deleted file mode 100644 index 28c551966d..0000000000 --- a/src/algorithms/cryptography/polynomial-hash/__test__/SimplePolynomialHash.test.js +++ /dev/null @@ -1,52 +0,0 @@ -import SimplePolynomialHash from '../SimplePolynomialHash'; - -describe('PolynomialHash', () => { - it('should calculate new hash based on previous one', () => { - const bases = [3, 5]; - const frameSizes = [5, 10]; - - const text = 'Lorem Ipsum is simply dummy text of the printing and ' - + 'typesetting industry. Lorem Ipsum has been the industry\'s standard ' - + 'galley of type and \u{ffff} scrambled it to make a type specimen book. It ' - + 'electronic 耀 typesetting, remaining essentially unchanged. It was ' - + 'popularised in the 1960s with the release of Letraset sheets ' - + 'publishing software like Aldus 耀 PageMaker including versions of Lorem.'; - - // Check hashing for different prime base. - bases.forEach((base) => { - const polynomialHash = new SimplePolynomialHash(base); - - // Check hashing for different word lengths. - frameSizes.forEach((frameSize) => { - let previousWord = text.substr(0, frameSize); - let previousHash = polynomialHash.hash(previousWord); - - // Shift frame through the whole text. - for (let frameShift = 1; frameShift < (text.length - frameSize); frameShift += 1) { - const currentWord = text.substr(frameShift, frameSize); - const currentHash = polynomialHash.hash(currentWord); - const currentRollingHash = polynomialHash.roll(previousHash, previousWord, currentWord); - - // Check that rolling hash is the same as directly calculated hash. - expect(currentRollingHash).toBe(currentHash); - - previousWord = currentWord; - previousHash = currentHash; - } - }); - }); - }); - - it('should generate numeric hashed', () => { - const polynomialHash = new SimplePolynomialHash(); - - expect(polynomialHash.hash('Test')).toBe(604944); - expect(polynomialHash.hash('a')).toBe(97); - expect(polynomialHash.hash('b')).toBe(98); - expect(polynomialHash.hash('c')).toBe(99); - expect(polynomialHash.hash('d')).toBe(100); - expect(polynomialHash.hash('e')).toBe(101); - expect(polynomialHash.hash('ab')).toBe(1763); - expect(polynomialHash.hash('abc')).toBe(30374); - }); -}); diff --git a/src/algorithms/cryptography/rail-fence-cipher/README.md b/src/algorithms/cryptography/rail-fence-cipher/README.md deleted file mode 100644 index d01395f554..0000000000 --- a/src/algorithms/cryptography/rail-fence-cipher/README.md +++ /dev/null @@ -1,28 +0,0 @@ -# Rail Fence Cipher - -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: - -``` -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 . . -------------------------------------------------- - WECRLTEERDSOEEFEAOCAIVDEN -``` - -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 -. - . - . - . - . - . - . - . - . - . - . - . - . -. . - . . . - . . . - . . . - . . . - . . . - . . -``` - -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. - -## 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__/railFenceCipher.test.js b/src/algorithms/cryptography/rail-fence-cipher/__test__/railFenceCipher.test.js deleted file mode 100644 index db0c49eb6b..0000000000 --- a/src/algorithms/cryptography/rail-fence-cipher/__test__/railFenceCipher.test.js +++ /dev/null @@ -1,43 +0,0 @@ -import { encodeRailFenceCipher, decodeRailFenceCipher } from '../railFenceCipher'; - -describe('railFenceCipher', () => { - it('encodes a string correctly for base=3', () => { - expect(encodeRailFenceCipher('', 3)).toBe(''); - 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('15243', 3)).toBe( - '12345', - ); - }); - - 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/railFenceCipher.js b/src/algorithms/cryptography/rail-fence-cipher/railFenceCipher.js deleted file mode 100644 index 7b58037e22..0000000000 --- a/src/algorithms/cryptography/rail-fence-cipher/railFenceCipher.js +++ /dev/null @@ -1,242 +0,0 @@ -/** - * @typedef {string[]} Rail - * @typedef {Rail[]} Fence - * @typedef {number} Direction - */ - -/** - * @constant DIRECTIONS - * @type {object} - * @property {Direction} UP - * @property {Direction} DOWN - */ -const DIRECTIONS = { UP: -1, DOWN: 1 }; - -/** - * Builds a fence with a specific number of rows. - * - * @param {number} rowsNum - * @returns {Fence} - */ -const buildFence = (rowsNum) => Array(rowsNum) - .fill(null) - .map(() => []); - -/** - * Get next direction to move (based on the current one) while traversing the fence. - * - * @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 - */ -const getNextDirection = ({ railCount, currentRail, direction }) => { - switch (currentRail) { - 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; - } -}; - -/** - * @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; -}; - -/** - * Hangs the characters on the fence. - * - * @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} - */ -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: [], - }); -}; diff --git a/src/algorithms/graph/articulation-points/README.md b/src/algorithms/graph/articulation-points/README.md deleted file mode 100644 index aa6bede7a4..0000000000 --- a/src/algorithms/graph/articulation-points/README.md +++ /dev/null @@ -1,22 +0,0 @@ -# Articulation Points (or Cut Vertices) - -A vertex in an undirected connected graph is an articulation point -(or cut vertex) if removing it (and edges through it) disconnects -the graph. Articulation points represent vulnerabilities in a -connected network – single points whose failure would split the -network into 2 or more disconnected components. They are useful for -designing reliable networks. - -For a disconnected undirected graph, an articulation point is a -vertex removing which increases number of connected components. - -![Articulation Points](https://www.geeksforgeeks.org/wp-content/uploads/ArticulationPoints.png) - -![Articulation Points](https://www.geeksforgeeks.org/wp-content/uploads/ArticulationPoints1.png) - -![Articulation Points](https://www.geeksforgeeks.org/wp-content/uploads/ArticulationPoints21.png) - -## References - -- [GeeksForGeeks](https://www.geeksforgeeks.org/articulation-points-or-cut-vertices-in-a-graph/) -- [YouTube](https://www.youtube.com/watch?v=2kREIkF9UAs&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8) diff --git a/src/algorithms/graph/articulation-points/__test__/articulationPoints.test.js b/src/algorithms/graph/articulation-points/__test__/articulationPoints.test.js deleted file mode 100644 index b021305c5c..0000000000 --- a/src/algorithms/graph/articulation-points/__test__/articulationPoints.test.js +++ /dev/null @@ -1,232 +0,0 @@ -import GraphVertex from '../../../../data-structures/graph/GraphVertex'; -import GraphEdge from '../../../../data-structures/graph/GraphEdge'; -import Graph from '../../../../data-structures/graph/Graph'; -import articulationPoints from '../articulationPoints'; - -describe('articulationPoints', () => { - it('should find articulation points in simple graph', () => { - const vertexA = new GraphVertex('A'); - const vertexB = new GraphVertex('B'); - const vertexC = new GraphVertex('C'); - const vertexD = new GraphVertex('D'); - - const edgeAB = new GraphEdge(vertexA, vertexB); - const edgeBC = new GraphEdge(vertexB, vertexC); - const edgeCD = new GraphEdge(vertexC, vertexD); - - const graph = new Graph(); - - graph - .addEdge(edgeAB) - .addEdge(edgeBC) - .addEdge(edgeCD); - - const articulationPointsSet = Object.values(articulationPoints(graph)); - - expect(articulationPointsSet.length).toBe(2); - expect(articulationPointsSet[0].getKey()).toBe(vertexC.getKey()); - expect(articulationPointsSet[1].getKey()).toBe(vertexB.getKey()); - }); - - it('should find articulation points in simple graph with back edge', () => { - const vertexA = new GraphVertex('A'); - const vertexB = new GraphVertex('B'); - const vertexC = new GraphVertex('C'); - const vertexD = new GraphVertex('D'); - - const edgeAB = new GraphEdge(vertexA, vertexB); - const edgeBC = new GraphEdge(vertexB, vertexC); - const edgeCD = new GraphEdge(vertexC, vertexD); - const edgeAC = new GraphEdge(vertexA, vertexC); - - const graph = new Graph(); - - graph - .addEdge(edgeAB) - .addEdge(edgeAC) - .addEdge(edgeBC) - .addEdge(edgeCD); - - const articulationPointsSet = Object.values(articulationPoints(graph)); - - expect(articulationPointsSet.length).toBe(1); - expect(articulationPointsSet[0].getKey()).toBe(vertexC.getKey()); - }); - - it('should find articulation points in simple graph with back edge #2', () => { - const vertexA = new GraphVertex('A'); - const vertexB = new GraphVertex('B'); - const vertexC = new GraphVertex('C'); - const vertexD = new GraphVertex('D'); - const vertexE = new GraphVertex('E'); - - const edgeAB = new GraphEdge(vertexA, vertexB); - const edgeBC = new GraphEdge(vertexB, vertexC); - const edgeCD = new GraphEdge(vertexC, vertexD); - const edgeAE = new GraphEdge(vertexA, vertexE); - const edgeCE = new GraphEdge(vertexC, vertexE); - - const graph = new Graph(); - - graph - .addEdge(edgeAB) - .addEdge(edgeAE) - .addEdge(edgeCE) - .addEdge(edgeBC) - .addEdge(edgeCD); - - const articulationPointsSet = Object.values(articulationPoints(graph)); - - expect(articulationPointsSet.length).toBe(1); - expect(articulationPointsSet[0].getKey()).toBe(vertexC.getKey()); - }); - - it('should find articulation points in graph', () => { - const vertexA = new GraphVertex('A'); - const vertexB = new GraphVertex('B'); - const vertexC = new GraphVertex('C'); - const vertexD = new GraphVertex('D'); - const vertexE = new GraphVertex('E'); - const vertexF = new GraphVertex('F'); - const vertexG = new GraphVertex('G'); - const vertexH = new GraphVertex('H'); - - const edgeAB = new GraphEdge(vertexA, vertexB); - const edgeBC = new GraphEdge(vertexB, vertexC); - const edgeAC = new GraphEdge(vertexA, vertexC); - const edgeCD = new GraphEdge(vertexC, vertexD); - const edgeDE = new GraphEdge(vertexD, vertexE); - const edgeEG = new GraphEdge(vertexE, vertexG); - const edgeEF = new GraphEdge(vertexE, vertexF); - const edgeGF = new GraphEdge(vertexG, vertexF); - const edgeFH = new GraphEdge(vertexF, vertexH); - - const graph = new Graph(); - - graph - .addEdge(edgeAB) - .addEdge(edgeBC) - .addEdge(edgeAC) - .addEdge(edgeCD) - .addEdge(edgeDE) - .addEdge(edgeEG) - .addEdge(edgeEF) - .addEdge(edgeGF) - .addEdge(edgeFH); - - const articulationPointsSet = Object.values(articulationPoints(graph)); - - expect(articulationPointsSet.length).toBe(4); - expect(articulationPointsSet[0].getKey()).toBe(vertexF.getKey()); - expect(articulationPointsSet[1].getKey()).toBe(vertexE.getKey()); - expect(articulationPointsSet[2].getKey()).toBe(vertexD.getKey()); - expect(articulationPointsSet[3].getKey()).toBe(vertexC.getKey()); - }); - - it('should find articulation points in graph starting with articulation root vertex', () => { - const vertexA = new GraphVertex('A'); - const vertexB = new GraphVertex('B'); - const vertexC = new GraphVertex('C'); - const vertexD = new GraphVertex('D'); - const vertexE = new GraphVertex('E'); - const vertexF = new GraphVertex('F'); - const vertexG = new GraphVertex('G'); - const vertexH = new GraphVertex('H'); - - const edgeAB = new GraphEdge(vertexA, vertexB); - const edgeBC = new GraphEdge(vertexB, vertexC); - const edgeAC = new GraphEdge(vertexA, vertexC); - const edgeCD = new GraphEdge(vertexC, vertexD); - const edgeDE = new GraphEdge(vertexD, vertexE); - const edgeEG = new GraphEdge(vertexE, vertexG); - const edgeEF = new GraphEdge(vertexE, vertexF); - const edgeGF = new GraphEdge(vertexG, vertexF); - const edgeFH = new GraphEdge(vertexF, vertexH); - - const graph = new Graph(); - - graph - .addEdge(edgeDE) - .addEdge(edgeAB) - .addEdge(edgeBC) - .addEdge(edgeAC) - .addEdge(edgeCD) - .addEdge(edgeEG) - .addEdge(edgeEF) - .addEdge(edgeGF) - .addEdge(edgeFH); - - const articulationPointsSet = Object.values(articulationPoints(graph)); - - expect(articulationPointsSet.length).toBe(4); - expect(articulationPointsSet[0].getKey()).toBe(vertexF.getKey()); - expect(articulationPointsSet[1].getKey()).toBe(vertexE.getKey()); - expect(articulationPointsSet[2].getKey()).toBe(vertexC.getKey()); - expect(articulationPointsSet[3].getKey()).toBe(vertexD.getKey()); - }); - - it('should find articulation points in yet another graph #1', () => { - const vertexA = new GraphVertex('A'); - const vertexB = new GraphVertex('B'); - const vertexC = new GraphVertex('C'); - const vertexD = new GraphVertex('D'); - const vertexE = new GraphVertex('E'); - - const edgeAB = new GraphEdge(vertexA, vertexB); - const edgeAC = new GraphEdge(vertexA, vertexC); - const edgeBC = new GraphEdge(vertexB, vertexC); - const edgeCD = new GraphEdge(vertexC, vertexD); - const edgeDE = new GraphEdge(vertexD, vertexE); - - const graph = new Graph(); - - graph - .addEdge(edgeAB) - .addEdge(edgeAC) - .addEdge(edgeBC) - .addEdge(edgeCD) - .addEdge(edgeDE); - - const articulationPointsSet = Object.values(articulationPoints(graph)); - - expect(articulationPointsSet.length).toBe(2); - expect(articulationPointsSet[0].getKey()).toBe(vertexD.getKey()); - expect(articulationPointsSet[1].getKey()).toBe(vertexC.getKey()); - }); - - it('should find articulation points in yet another graph #2', () => { - const vertexA = new GraphVertex('A'); - const vertexB = new GraphVertex('B'); - const vertexC = new GraphVertex('C'); - const vertexD = new GraphVertex('D'); - const vertexE = new GraphVertex('E'); - const vertexF = new GraphVertex('F'); - const vertexG = new GraphVertex('G'); - - const edgeAB = new GraphEdge(vertexA, vertexB); - const edgeAC = new GraphEdge(vertexA, vertexC); - const edgeBC = new GraphEdge(vertexB, vertexC); - const edgeCD = new GraphEdge(vertexC, vertexD); - const edgeCE = new GraphEdge(vertexC, vertexE); - const edgeCF = new GraphEdge(vertexC, vertexF); - const edgeEG = new GraphEdge(vertexE, vertexG); - const edgeFG = new GraphEdge(vertexF, vertexG); - - const graph = new Graph(); - - graph - .addEdge(edgeAB) - .addEdge(edgeAC) - .addEdge(edgeBC) - .addEdge(edgeCD) - .addEdge(edgeCE) - .addEdge(edgeCF) - .addEdge(edgeEG) - .addEdge(edgeFG); - - const articulationPointsSet = Object.values(articulationPoints(graph)); - - expect(articulationPointsSet.length).toBe(1); - expect(articulationPointsSet[0].getKey()).toBe(vertexC.getKey()); - }); -}); diff --git a/src/algorithms/graph/articulation-points/articulationPoints.js b/src/algorithms/graph/articulation-points/articulationPoints.js deleted file mode 100644 index 0cc1db6e89..0000000000 --- a/src/algorithms/graph/articulation-points/articulationPoints.js +++ /dev/null @@ -1,113 +0,0 @@ -import depthFirstSearch from '../depth-first-search/depthFirstSearch'; - -/** - * Helper class for visited vertex metadata. - */ -class VisitMetadata { - constructor({ discoveryTime, lowDiscoveryTime }) { - this.discoveryTime = discoveryTime; - this.lowDiscoveryTime = lowDiscoveryTime; - // We need this in order to check graph root node, whether it has two - // disconnected children or not. - this.independentChildrenCount = 0; - } -} - -/** - * Tarjan's algorithm for finding articulation points in graph. - * - * @param {Graph} graph - * @return {Object} - */ -export default function articulationPoints(graph) { - // Set of vertices we've already visited during DFS. - const visitedSet = {}; - - // Set of articulation points. - const articulationPointsSet = {}; - - // Time needed to discover to the current vertex. - let discoveryTime = 0; - - // Peek the start vertex for DFS traversal. - const startVertex = graph.getAllVertices()[0]; - - const dfsCallbacks = { - /** - * @param {GraphVertex} currentVertex - * @param {GraphVertex} previousVertex - */ - enterVertex: ({ currentVertex, previousVertex }) => { - // Tick discovery time. - discoveryTime += 1; - - // Put current vertex to visited set. - visitedSet[currentVertex.getKey()] = new VisitMetadata({ - discoveryTime, - lowDiscoveryTime: discoveryTime, - }); - - if (previousVertex) { - // Update children counter for previous vertex. - visitedSet[previousVertex.getKey()].independentChildrenCount += 1; - } - }, - /** - * @param {GraphVertex} currentVertex - * @param {GraphVertex} previousVertex - */ - leaveVertex: ({ currentVertex, previousVertex }) => { - if (previousVertex === null) { - // Don't do anything for the root vertex if it is already current (not previous one) - return; - } - - // Update the low time with the smallest time of adjacent vertices. - // Get minimum low discovery time from all neighbors. - /** @param {GraphVertex} neighbor */ - visitedSet[currentVertex.getKey()].lowDiscoveryTime = currentVertex.getNeighbors() - .filter((earlyNeighbor) => earlyNeighbor.getKey() !== previousVertex.getKey()) - /** - * @param {number} lowestDiscoveryTime - * @param {GraphVertex} neighbor - */ - .reduce( - (lowestDiscoveryTime, neighbor) => { - const neighborLowTime = visitedSet[neighbor.getKey()].lowDiscoveryTime; - return neighborLowTime < lowestDiscoveryTime ? neighborLowTime : lowestDiscoveryTime; - }, - visitedSet[currentVertex.getKey()].lowDiscoveryTime, - ); - - // Detect whether previous vertex is articulation point or not. - // To do so we need to check two [OR] conditions: - // 1. Is it a root vertex with at least two independent children. - // 2. If its visited time is <= low time of adjacent vertex. - if (previousVertex === startVertex) { - // Check that root vertex has at least two independent children. - if (visitedSet[previousVertex.getKey()].independentChildrenCount >= 2) { - articulationPointsSet[previousVertex.getKey()] = previousVertex; - } - } else { - // Get current vertex low discovery time. - const currentLowDiscoveryTime = visitedSet[currentVertex.getKey()].lowDiscoveryTime; - - // Compare current vertex low discovery time with parent discovery time. Check if there - // are any short path (back edge) exists. If we can't get to current vertex other then - // via parent then the parent vertex is articulation point for current one. - const parentDiscoveryTime = visitedSet[previousVertex.getKey()].discoveryTime; - if (parentDiscoveryTime <= currentLowDiscoveryTime) { - articulationPointsSet[previousVertex.getKey()] = previousVertex; - } - } - }, - allowTraversal: ({ nextVertex }) => { - return !visitedSet[nextVertex.getKey()]; - }, - }; - - // Do Depth First Search traversal over submitted graph. - depthFirstSearch(graph, startVertex, dfsCallbacks); - - return articulationPointsSet; -} diff --git a/src/algorithms/graph/bellman-ford/README.md b/src/algorithms/graph/bellman-ford/README.md deleted file mode 100644 index 9c0922659e..0000000000 --- a/src/algorithms/graph/bellman-ford/README.md +++ /dev/null @@ -1,21 +0,0 @@ -# Bellman–Ford Algorithm - -The Bellman–Ford algorithm is an algorithm that computes shortest -paths from a single source vertex to all of the other vertices -in a weighted digraph. It is slower than Dijkstra's algorithm -for the same problem, but more versatile, as it is capable of -handling graphs in which some of the edge weights are negative -numbers. - -![Bellman-Ford](https://upload.wikimedia.org/wikipedia/commons/2/2e/Shortest_path_Dijkstra_vs_BellmanFord.gif) - -## Complexity - -Worst-case performance `O(|V||E|)` -Best-case performance `O(|E|)` -Worst-case space complexity `O(|V|)` - -## References - -- [Wikipedia](https://en.wikipedia.org/wiki/Bellman%E2%80%93Ford_algorithm) -- [On YouTube by Michael Sambol](https://www.youtube.com/watch?v=obWXjtg0L64&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8) diff --git a/src/algorithms/graph/bellman-ford/__test__/bellmanFord.test.js b/src/algorithms/graph/bellman-ford/__test__/bellmanFord.test.js deleted file mode 100644 index ffa30eba21..0000000000 --- a/src/algorithms/graph/bellman-ford/__test__/bellmanFord.test.js +++ /dev/null @@ -1,117 +0,0 @@ -import GraphVertex from '../../../../data-structures/graph/GraphVertex'; -import GraphEdge from '../../../../data-structures/graph/GraphEdge'; -import Graph from '../../../../data-structures/graph/Graph'; -import bellmanFord from '../bellmanFord'; - -describe('bellmanFord', () => { - it('should find minimum paths to all vertices for undirected graph', () => { - const vertexA = new GraphVertex('A'); - const vertexB = new GraphVertex('B'); - const vertexC = new GraphVertex('C'); - const vertexD = new GraphVertex('D'); - const vertexE = new GraphVertex('E'); - const vertexF = new GraphVertex('F'); - const vertexG = new GraphVertex('G'); - const vertexH = new GraphVertex('H'); - - const edgeAB = new GraphEdge(vertexA, vertexB, 4); - const edgeAE = new GraphEdge(vertexA, vertexE, 7); - const edgeAC = new GraphEdge(vertexA, vertexC, 3); - const edgeBC = new GraphEdge(vertexB, vertexC, 6); - const edgeBD = new GraphEdge(vertexB, vertexD, 5); - const edgeEC = new GraphEdge(vertexE, vertexC, 8); - const edgeED = new GraphEdge(vertexE, vertexD, 2); - const edgeDC = new GraphEdge(vertexD, vertexC, 11); - const edgeDG = new GraphEdge(vertexD, vertexG, 10); - const edgeDF = new GraphEdge(vertexD, vertexF, 2); - const edgeFG = new GraphEdge(vertexF, vertexG, 3); - const edgeEG = new GraphEdge(vertexE, vertexG, 5); - - const graph = new Graph(); - graph - .addVertex(vertexH) - .addEdge(edgeAB) - .addEdge(edgeAE) - .addEdge(edgeAC) - .addEdge(edgeBC) - .addEdge(edgeBD) - .addEdge(edgeEC) - .addEdge(edgeED) - .addEdge(edgeDC) - .addEdge(edgeDG) - .addEdge(edgeDF) - .addEdge(edgeFG) - .addEdge(edgeEG); - - const { distances, previousVertices } = bellmanFord(graph, vertexA); - - expect(distances).toEqual({ - H: Infinity, - A: 0, - B: 4, - E: 7, - C: 3, - D: 9, - G: 12, - F: 11, - }); - - expect(previousVertices.F.getKey()).toBe('D'); - expect(previousVertices.D.getKey()).toBe('B'); - expect(previousVertices.B.getKey()).toBe('A'); - expect(previousVertices.G.getKey()).toBe('E'); - expect(previousVertices.C.getKey()).toBe('A'); - expect(previousVertices.A).toBeNull(); - expect(previousVertices.H).toBeNull(); - }); - - it('should find minimum paths to all vertices for directed graph with negative edge weights', () => { - const vertexS = new GraphVertex('S'); - const vertexE = new GraphVertex('E'); - const vertexA = new GraphVertex('A'); - const vertexD = new GraphVertex('D'); - const vertexB = new GraphVertex('B'); - const vertexC = new GraphVertex('C'); - const vertexH = new GraphVertex('H'); - - const edgeSE = new GraphEdge(vertexS, vertexE, 8); - const edgeSA = new GraphEdge(vertexS, vertexA, 10); - const edgeED = new GraphEdge(vertexE, vertexD, 1); - const edgeDA = new GraphEdge(vertexD, vertexA, -4); - const edgeDC = new GraphEdge(vertexD, vertexC, -1); - const edgeAC = new GraphEdge(vertexA, vertexC, 2); - const edgeCB = new GraphEdge(vertexC, vertexB, -2); - const edgeBA = new GraphEdge(vertexB, vertexA, 1); - - const graph = new Graph(true); - graph - .addVertex(vertexH) - .addEdge(edgeSE) - .addEdge(edgeSA) - .addEdge(edgeED) - .addEdge(edgeDA) - .addEdge(edgeDC) - .addEdge(edgeAC) - .addEdge(edgeCB) - .addEdge(edgeBA); - - const { distances, previousVertices } = bellmanFord(graph, vertexS); - - expect(distances).toEqual({ - H: Infinity, - S: 0, - A: 5, - B: 5, - C: 7, - D: 9, - E: 8, - }); - - expect(previousVertices.H).toBeNull(); - expect(previousVertices.S).toBeNull(); - expect(previousVertices.B.getKey()).toBe('C'); - expect(previousVertices.C.getKey()).toBe('A'); - expect(previousVertices.A.getKey()).toBe('D'); - expect(previousVertices.D.getKey()).toBe('E'); - }); -}); diff --git a/src/algorithms/graph/bellman-ford/bellmanFord.js b/src/algorithms/graph/bellman-ford/bellmanFord.js deleted file mode 100644 index 70e811d992..0000000000 --- a/src/algorithms/graph/bellman-ford/bellmanFord.js +++ /dev/null @@ -1,45 +0,0 @@ -/** - * @param {Graph} graph - * @param {GraphVertex} startVertex - * @return {{distances, previousVertices}} - */ -export default function bellmanFord(graph, startVertex) { - const distances = {}; - const previousVertices = {}; - - // Init all distances with infinity assuming that currently we can't reach - // any of the vertices except start one. - distances[startVertex.getKey()] = 0; - graph.getAllVertices().forEach((vertex) => { - previousVertices[vertex.getKey()] = null; - if (vertex.getKey() !== startVertex.getKey()) { - distances[vertex.getKey()] = Infinity; - } - }); - - // We need (|V| - 1) iterations. - for (let iteration = 0; iteration < (graph.getAllVertices().length - 1); iteration += 1) { - // During each iteration go through all vertices. - Object.keys(distances).forEach((vertexKey) => { - const vertex = graph.getVertexByKey(vertexKey); - - // Go through all vertex edges. - graph.getNeighbors(vertex).forEach((neighbor) => { - const edge = graph.findEdge(vertex, neighbor); - // Find out if the distance to the neighbor is shorter in this iteration - // then in previous one. - const distanceToVertex = distances[vertex.getKey()]; - const distanceToNeighbor = distanceToVertex + edge.weight; - if (distanceToNeighbor < distances[neighbor.getKey()]) { - distances[neighbor.getKey()] = distanceToNeighbor; - previousVertices[neighbor.getKey()] = vertex; - } - }); - }); - } - - return { - distances, - previousVertices, - }; -} diff --git a/src/algorithms/graph/breadth-first-search/README.md b/src/algorithms/graph/breadth-first-search/README.md deleted file mode 100644 index 06073abd8b..0000000000 --- a/src/algorithms/graph/breadth-first-search/README.md +++ /dev/null @@ -1,16 +0,0 @@ -# Breadth-First Search (BFS) - -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. - -![Algorithm Visualization](https://upload.wikimedia.org/wikipedia/commons/5/5d/Breadth-First-Search-Algorithm.gif) - -## References - -- [Wikipedia](https://en.wikipedia.org/wiki/Breadth-first_search) -- [Tree Traversals (Inorder, Preorder and Postorder)](https://www.geeksforgeeks.org/tree-traversals-inorder-preorder-and-postorder/) -- [BFS vs DFS](https://www.geeksforgeeks.org/bfs-vs-dfs-binary-tree/) -- [BFS Visualization](https://www.cs.usfca.edu/~galles/visualization/BFS.html) diff --git a/src/algorithms/graph/breadth-first-search/__test__/breadthFirstSearch.test.js b/src/algorithms/graph/breadth-first-search/__test__/breadthFirstSearch.test.js deleted file mode 100644 index c9bff22fb0..0000000000 --- a/src/algorithms/graph/breadth-first-search/__test__/breadthFirstSearch.test.js +++ /dev/null @@ -1,174 +0,0 @@ -import Graph from '../../../../data-structures/graph/Graph'; -import GraphVertex from '../../../../data-structures/graph/GraphVertex'; -import GraphEdge from '../../../../data-structures/graph/GraphEdge'; -import breadthFirstSearch from '../breadthFirstSearch'; - -describe('breadthFirstSearch', () => { - it('should perform BFS operation on graph', () => { - const graph = new Graph(true); - - const vertexA = new GraphVertex('A'); - const vertexB = new GraphVertex('B'); - const vertexC = new GraphVertex('C'); - const vertexD = new GraphVertex('D'); - const vertexE = new GraphVertex('E'); - const vertexF = new GraphVertex('F'); - const vertexG = new GraphVertex('G'); - const vertexH = new GraphVertex('H'); - - const edgeAB = new GraphEdge(vertexA, vertexB); - const edgeBC = new GraphEdge(vertexB, vertexC); - const edgeCG = new GraphEdge(vertexC, vertexG); - const edgeAD = new GraphEdge(vertexA, vertexD); - const edgeAE = new GraphEdge(vertexA, vertexE); - const edgeEF = new GraphEdge(vertexE, vertexF); - const edgeFD = new GraphEdge(vertexF, vertexD); - const edgeDH = new GraphEdge(vertexD, vertexH); - const edgeGH = new GraphEdge(vertexG, vertexH); - - graph - .addEdge(edgeAB) - .addEdge(edgeBC) - .addEdge(edgeCG) - .addEdge(edgeAD) - .addEdge(edgeAE) - .addEdge(edgeEF) - .addEdge(edgeFD) - .addEdge(edgeDH) - .addEdge(edgeGH); - - expect(graph.toString()).toBe('A,B,C,G,D,E,F,H'); - - const enterVertexCallback = jest.fn(); - const leaveVertexCallback = jest.fn(); - - // Traverse graphs without callbacks first. - breadthFirstSearch(graph, vertexA); - - // Traverse graph with enterVertex and leaveVertex callbacks. - breadthFirstSearch(graph, vertexA, { - enterVertex: enterVertexCallback, - leaveVertex: leaveVertexCallback, - }); - - expect(enterVertexCallback).toHaveBeenCalledTimes(8); - expect(leaveVertexCallback).toHaveBeenCalledTimes(8); - - const enterVertexParamsMap = [ - { currentVertex: vertexA, previousVertex: null }, - { currentVertex: vertexB, previousVertex: vertexA }, - { currentVertex: vertexD, previousVertex: vertexB }, - { currentVertex: vertexE, previousVertex: vertexD }, - { currentVertex: vertexC, previousVertex: vertexE }, - { currentVertex: vertexH, previousVertex: vertexC }, - { currentVertex: vertexF, previousVertex: vertexH }, - { currentVertex: vertexG, previousVertex: vertexF }, - ]; - - for (let callIndex = 0; callIndex < graph.getAllVertices().length; callIndex += 1) { - const params = enterVertexCallback.mock.calls[callIndex][0]; - expect(params.currentVertex).toEqual(enterVertexParamsMap[callIndex].currentVertex); - expect(params.previousVertex).toEqual(enterVertexParamsMap[callIndex].previousVertex); - } - - const leaveVertexParamsMap = [ - { currentVertex: vertexA, previousVertex: null }, - { currentVertex: vertexB, previousVertex: vertexA }, - { currentVertex: vertexD, previousVertex: vertexB }, - { currentVertex: vertexE, previousVertex: vertexD }, - { currentVertex: vertexC, previousVertex: vertexE }, - { currentVertex: vertexH, previousVertex: vertexC }, - { currentVertex: vertexF, previousVertex: vertexH }, - { currentVertex: vertexG, previousVertex: vertexF }, - ]; - - for (let callIndex = 0; callIndex < graph.getAllVertices().length; callIndex += 1) { - const params = leaveVertexCallback.mock.calls[callIndex][0]; - expect(params.currentVertex).toEqual(leaveVertexParamsMap[callIndex].currentVertex); - expect(params.previousVertex).toEqual(leaveVertexParamsMap[callIndex].previousVertex); - } - }); - - it('should allow to create custom vertex visiting logic', () => { - const graph = new Graph(true); - - const vertexA = new GraphVertex('A'); - const vertexB = new GraphVertex('B'); - const vertexC = new GraphVertex('C'); - const vertexD = new GraphVertex('D'); - const vertexE = new GraphVertex('E'); - const vertexF = new GraphVertex('F'); - const vertexG = new GraphVertex('G'); - const vertexH = new GraphVertex('H'); - - const edgeAB = new GraphEdge(vertexA, vertexB); - const edgeBC = new GraphEdge(vertexB, vertexC); - const edgeCG = new GraphEdge(vertexC, vertexG); - const edgeAD = new GraphEdge(vertexA, vertexD); - const edgeAE = new GraphEdge(vertexA, vertexE); - const edgeEF = new GraphEdge(vertexE, vertexF); - const edgeFD = new GraphEdge(vertexF, vertexD); - const edgeDH = new GraphEdge(vertexD, vertexH); - const edgeGH = new GraphEdge(vertexG, vertexH); - - graph - .addEdge(edgeAB) - .addEdge(edgeBC) - .addEdge(edgeCG) - .addEdge(edgeAD) - .addEdge(edgeAE) - .addEdge(edgeEF) - .addEdge(edgeFD) - .addEdge(edgeDH) - .addEdge(edgeGH); - - expect(graph.toString()).toBe('A,B,C,G,D,E,F,H'); - - const enterVertexCallback = jest.fn(); - const leaveVertexCallback = jest.fn(); - - // Traverse graph with enterVertex and leaveVertex callbacks. - breadthFirstSearch(graph, vertexA, { - enterVertex: enterVertexCallback, - leaveVertex: leaveVertexCallback, - allowTraversal: ({ currentVertex, nextVertex }) => { - return !(currentVertex === vertexA && nextVertex === vertexB); - }, - }); - - expect(enterVertexCallback).toHaveBeenCalledTimes(7); - expect(leaveVertexCallback).toHaveBeenCalledTimes(7); - - const enterVertexParamsMap = [ - { currentVertex: vertexA, previousVertex: null }, - { currentVertex: vertexD, previousVertex: vertexA }, - { currentVertex: vertexE, previousVertex: vertexD }, - { currentVertex: vertexH, previousVertex: vertexE }, - { currentVertex: vertexF, previousVertex: vertexH }, - { currentVertex: vertexD, previousVertex: vertexF }, - { currentVertex: vertexH, previousVertex: vertexD }, - ]; - - for (let callIndex = 0; callIndex < 7; callIndex += 1) { - const params = enterVertexCallback.mock.calls[callIndex][0]; - expect(params.currentVertex).toEqual(enterVertexParamsMap[callIndex].currentVertex); - expect(params.previousVertex).toEqual(enterVertexParamsMap[callIndex].previousVertex); - } - - const leaveVertexParamsMap = [ - { currentVertex: vertexA, previousVertex: null }, - { currentVertex: vertexD, previousVertex: vertexA }, - { currentVertex: vertexE, previousVertex: vertexD }, - { currentVertex: vertexH, previousVertex: vertexE }, - { currentVertex: vertexF, previousVertex: vertexH }, - { currentVertex: vertexD, previousVertex: vertexF }, - { currentVertex: vertexH, previousVertex: vertexD }, - ]; - - for (let callIndex = 0; callIndex < 7; callIndex += 1) { - const params = leaveVertexCallback.mock.calls[callIndex][0]; - expect(params.currentVertex).toEqual(leaveVertexParamsMap[callIndex].currentVertex); - expect(params.previousVertex).toEqual(leaveVertexParamsMap[callIndex].previousVertex); - } - }); -}); diff --git a/src/algorithms/graph/breadth-first-search/breadthFirstSearch.js b/src/algorithms/graph/breadth-first-search/breadthFirstSearch.js deleted file mode 100644 index d4b955ece6..0000000000 --- a/src/algorithms/graph/breadth-first-search/breadthFirstSearch.js +++ /dev/null @@ -1,75 +0,0 @@ -import Queue from '../../../data-structures/queue/Queue'; - -/** - * @typedef {Object} Callbacks - * - * @property {function(vertices: Object): boolean} [allowTraversal] - - * Determines whether DFS should traverse from the vertex to its neighbor - * (along the edge). By default prohibits visiting the same vertex again. - * - * @property {function(vertices: Object)} [enterVertex] - Called when BFS enters the vertex. - * - * @property {function(vertices: Object)} [leaveVertex] - Called when BFS leaves the vertex. - */ - -/** - * @param {Callbacks} [callbacks] - * @returns {Callbacks} - */ -function initCallbacks(callbacks = {}) { - const initiatedCallback = callbacks; - - const stubCallback = () => {}; - - const allowTraversalCallback = ( - () => { - const seen = {}; - return ({ nextVertex }) => { - if (!seen[nextVertex.getKey()]) { - seen[nextVertex.getKey()] = true; - return true; - } - return false; - }; - } - )(); - - initiatedCallback.allowTraversal = callbacks.allowTraversal || allowTraversalCallback; - initiatedCallback.enterVertex = callbacks.enterVertex || stubCallback; - initiatedCallback.leaveVertex = callbacks.leaveVertex || stubCallback; - - return initiatedCallback; -} - -/** - * @param {Graph} graph - * @param {GraphVertex} startVertex - * @param {Callbacks} [originalCallbacks] - */ -export default function breadthFirstSearch(graph, startVertex, originalCallbacks) { - const callbacks = initCallbacks(originalCallbacks); - const vertexQueue = new Queue(); - - // Do initial queue setup. - vertexQueue.enqueue(startVertex); - - let previousVertex = null; - - // Traverse all vertices from the queue. - while (!vertexQueue.isEmpty()) { - const currentVertex = vertexQueue.dequeue(); - callbacks.enterVertex({ currentVertex, previousVertex }); - - // Add all neighbors to the queue for future traversals. - graph.getNeighbors(currentVertex).forEach((nextVertex) => { - if (callbacks.allowTraversal({ previousVertex, currentVertex, nextVertex })) { - vertexQueue.enqueue(nextVertex); - } - }); - - callbacks.leaveVertex({ currentVertex, previousVertex }); - - // Memorize current vertex before next loop. - previousVertex = currentVertex; - } -} diff --git a/src/algorithms/graph/bridges/README.md b/src/algorithms/graph/bridges/README.md deleted file mode 100644 index 08d919ff96..0000000000 --- a/src/algorithms/graph/bridges/README.md +++ /dev/null @@ -1,26 +0,0 @@ -# Bridges in Graph - -In graph theory, a **bridge**, **isthmus**, **cut-edge**, or **cut arc** is an edge -of a graph whose deletion increases its number of connected components. Equivalently, -an edge is a bridge if and only if it is not contained in any cycle. A graph is said -to be bridgeless or isthmus-free if it contains no bridges. - -![Bridges in graph](https://upload.wikimedia.org/wikipedia/commons/d/df/Graph_cut_edges.svg) - -A graph with 16 vertices and 6 bridges (highlighted in red) - -![Bridgeless](https://upload.wikimedia.org/wikipedia/commons/b/bf/Undirected.svg) - -An undirected connected graph with no cut edges - -![Bridges in graph](https://www.geeksforgeeks.org/wp-content/uploads/Bridge1.png) - -![Bridges in graph](https://www.geeksforgeeks.org/wp-content/uploads/Bridge2.png) - -![Bridges in graph](https://www.geeksforgeeks.org/wp-content/uploads/Bridge3.png) - -## References - -- [GeeksForGeeks on YouTube](https://www.youtube.com/watch?v=thLQYBlz2DM&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8) -- [Wikipedia](https://en.wikipedia.org/wiki/Bridge_%28graph_theory%29#Tarjan.27s_Bridge-finding_algorithm) -- [GeeksForGeeks](https://www.geeksforgeeks.org/bridge-in-a-graph/) diff --git a/src/algorithms/graph/bridges/__test__/graphBridges.test.js b/src/algorithms/graph/bridges/__test__/graphBridges.test.js deleted file mode 100644 index 01837528b0..0000000000 --- a/src/algorithms/graph/bridges/__test__/graphBridges.test.js +++ /dev/null @@ -1,203 +0,0 @@ -import GraphVertex from '../../../../data-structures/graph/GraphVertex'; -import GraphEdge from '../../../../data-structures/graph/GraphEdge'; -import Graph from '../../../../data-structures/graph/Graph'; -import graphBridges from '../graphBridges'; - -describe('graphBridges', () => { - it('should find bridges in simple graph', () => { - const vertexA = new GraphVertex('A'); - const vertexB = new GraphVertex('B'); - const vertexC = new GraphVertex('C'); - const vertexD = new GraphVertex('D'); - - const edgeAB = new GraphEdge(vertexA, vertexB); - const edgeBC = new GraphEdge(vertexB, vertexC); - const edgeCD = new GraphEdge(vertexC, vertexD); - - const graph = new Graph(); - - graph - .addEdge(edgeAB) - .addEdge(edgeBC) - .addEdge(edgeCD); - - const bridges = Object.values(graphBridges(graph)); - - expect(bridges.length).toBe(3); - expect(bridges[0].getKey()).toBe(edgeCD.getKey()); - expect(bridges[1].getKey()).toBe(edgeBC.getKey()); - expect(bridges[2].getKey()).toBe(edgeAB.getKey()); - }); - - it('should find bridges in simple graph with back edge', () => { - const vertexA = new GraphVertex('A'); - const vertexB = new GraphVertex('B'); - const vertexC = new GraphVertex('C'); - const vertexD = new GraphVertex('D'); - - const edgeAB = new GraphEdge(vertexA, vertexB); - const edgeBC = new GraphEdge(vertexB, vertexC); - const edgeCD = new GraphEdge(vertexC, vertexD); - const edgeAC = new GraphEdge(vertexA, vertexC); - - const graph = new Graph(); - - graph - .addEdge(edgeAB) - .addEdge(edgeAC) - .addEdge(edgeBC) - .addEdge(edgeCD); - - const bridges = Object.values(graphBridges(graph)); - - expect(bridges.length).toBe(1); - expect(bridges[0].getKey()).toBe(edgeCD.getKey()); - }); - - it('should find bridges in graph', () => { - const vertexA = new GraphVertex('A'); - const vertexB = new GraphVertex('B'); - const vertexC = new GraphVertex('C'); - const vertexD = new GraphVertex('D'); - const vertexE = new GraphVertex('E'); - const vertexF = new GraphVertex('F'); - const vertexG = new GraphVertex('G'); - const vertexH = new GraphVertex('H'); - - const edgeAB = new GraphEdge(vertexA, vertexB); - const edgeBC = new GraphEdge(vertexB, vertexC); - const edgeAC = new GraphEdge(vertexA, vertexC); - const edgeCD = new GraphEdge(vertexC, vertexD); - const edgeDE = new GraphEdge(vertexD, vertexE); - const edgeEG = new GraphEdge(vertexE, vertexG); - const edgeEF = new GraphEdge(vertexE, vertexF); - const edgeGF = new GraphEdge(vertexG, vertexF); - const edgeFH = new GraphEdge(vertexF, vertexH); - - const graph = new Graph(); - - graph - .addEdge(edgeAB) - .addEdge(edgeBC) - .addEdge(edgeAC) - .addEdge(edgeCD) - .addEdge(edgeDE) - .addEdge(edgeEG) - .addEdge(edgeEF) - .addEdge(edgeGF) - .addEdge(edgeFH); - - const bridges = Object.values(graphBridges(graph)); - - expect(bridges.length).toBe(3); - expect(bridges[0].getKey()).toBe(edgeFH.getKey()); - expect(bridges[1].getKey()).toBe(edgeDE.getKey()); - expect(bridges[2].getKey()).toBe(edgeCD.getKey()); - }); - - it('should find bridges in graph starting with different root vertex', () => { - const vertexA = new GraphVertex('A'); - const vertexB = new GraphVertex('B'); - const vertexC = new GraphVertex('C'); - const vertexD = new GraphVertex('D'); - const vertexE = new GraphVertex('E'); - const vertexF = new GraphVertex('F'); - const vertexG = new GraphVertex('G'); - const vertexH = new GraphVertex('H'); - - const edgeAB = new GraphEdge(vertexA, vertexB); - const edgeBC = new GraphEdge(vertexB, vertexC); - const edgeAC = new GraphEdge(vertexA, vertexC); - const edgeCD = new GraphEdge(vertexC, vertexD); - const edgeDE = new GraphEdge(vertexD, vertexE); - const edgeEG = new GraphEdge(vertexE, vertexG); - const edgeEF = new GraphEdge(vertexE, vertexF); - const edgeGF = new GraphEdge(vertexG, vertexF); - const edgeFH = new GraphEdge(vertexF, vertexH); - - const graph = new Graph(); - - graph - .addEdge(edgeDE) - .addEdge(edgeAB) - .addEdge(edgeBC) - .addEdge(edgeAC) - .addEdge(edgeCD) - .addEdge(edgeEG) - .addEdge(edgeEF) - .addEdge(edgeGF) - .addEdge(edgeFH); - - const bridges = Object.values(graphBridges(graph)); - - expect(bridges.length).toBe(3); - expect(bridges[0].getKey()).toBe(edgeFH.getKey()); - expect(bridges[1].getKey()).toBe(edgeDE.getKey()); - expect(bridges[2].getKey()).toBe(edgeCD.getKey()); - }); - - it('should find bridges in yet another graph #1', () => { - const vertexA = new GraphVertex('A'); - const vertexB = new GraphVertex('B'); - const vertexC = new GraphVertex('C'); - const vertexD = new GraphVertex('D'); - const vertexE = new GraphVertex('E'); - - const edgeAB = new GraphEdge(vertexA, vertexB); - const edgeAC = new GraphEdge(vertexA, vertexC); - const edgeBC = new GraphEdge(vertexB, vertexC); - const edgeCD = new GraphEdge(vertexC, vertexD); - const edgeDE = new GraphEdge(vertexD, vertexE); - - const graph = new Graph(); - - graph - .addEdge(edgeAB) - .addEdge(edgeAC) - .addEdge(edgeBC) - .addEdge(edgeCD) - .addEdge(edgeDE); - - const bridges = Object.values(graphBridges(graph)); - - expect(bridges.length).toBe(2); - expect(bridges[0].getKey()).toBe(edgeDE.getKey()); - expect(bridges[1].getKey()).toBe(edgeCD.getKey()); - }); - - it('should find bridges in yet another graph #2', () => { - const vertexA = new GraphVertex('A'); - const vertexB = new GraphVertex('B'); - const vertexC = new GraphVertex('C'); - const vertexD = new GraphVertex('D'); - const vertexE = new GraphVertex('E'); - const vertexF = new GraphVertex('F'); - const vertexG = new GraphVertex('G'); - - const edgeAB = new GraphEdge(vertexA, vertexB); - const edgeAC = new GraphEdge(vertexA, vertexC); - const edgeBC = new GraphEdge(vertexB, vertexC); - const edgeCD = new GraphEdge(vertexC, vertexD); - const edgeCE = new GraphEdge(vertexC, vertexE); - const edgeCF = new GraphEdge(vertexC, vertexF); - const edgeEG = new GraphEdge(vertexE, vertexG); - const edgeFG = new GraphEdge(vertexF, vertexG); - - const graph = new Graph(); - - graph - .addEdge(edgeAB) - .addEdge(edgeAC) - .addEdge(edgeBC) - .addEdge(edgeCD) - .addEdge(edgeCE) - .addEdge(edgeCF) - .addEdge(edgeEG) - .addEdge(edgeFG); - - const bridges = Object.values(graphBridges(graph)); - - expect(bridges.length).toBe(1); - expect(bridges[0].getKey()).toBe(edgeCD.getKey()); - }); -}); diff --git a/src/algorithms/graph/bridges/graphBridges.js b/src/algorithms/graph/bridges/graphBridges.js deleted file mode 100644 index 58a64004bc..0000000000 --- a/src/algorithms/graph/bridges/graphBridges.js +++ /dev/null @@ -1,95 +0,0 @@ -import depthFirstSearch from '../depth-first-search/depthFirstSearch'; - -/** - * Helper class for visited vertex metadata. - */ -class VisitMetadata { - constructor({ discoveryTime, lowDiscoveryTime }) { - this.discoveryTime = discoveryTime; - this.lowDiscoveryTime = lowDiscoveryTime; - } -} - -/** - * @param {Graph} graph - * @return {Object} - */ -export default function graphBridges(graph) { - // Set of vertices we've already visited during DFS. - const visitedSet = {}; - - // Set of bridges. - const bridges = {}; - - // Time needed to discover to the current vertex. - let discoveryTime = 0; - - // Peek the start vertex for DFS traversal. - const startVertex = graph.getAllVertices()[0]; - - const dfsCallbacks = { - /** - * @param {GraphVertex} currentVertex - */ - enterVertex: ({ currentVertex }) => { - // Tick discovery time. - discoveryTime += 1; - - // Put current vertex to visited set. - visitedSet[currentVertex.getKey()] = new VisitMetadata({ - discoveryTime, - lowDiscoveryTime: discoveryTime, - }); - }, - /** - * @param {GraphVertex} currentVertex - * @param {GraphVertex} previousVertex - */ - leaveVertex: ({ currentVertex, previousVertex }) => { - if (previousVertex === null) { - // Don't do anything for the root vertex if it is already current (not previous one). - return; - } - - // Check if current node is connected to any early node other then previous one. - visitedSet[currentVertex.getKey()].lowDiscoveryTime = currentVertex.getNeighbors() - .filter((earlyNeighbor) => earlyNeighbor.getKey() !== previousVertex.getKey()) - .reduce( - /** - * @param {number} lowestDiscoveryTime - * @param {GraphVertex} neighbor - */ - (lowestDiscoveryTime, neighbor) => { - const neighborLowTime = visitedSet[neighbor.getKey()].lowDiscoveryTime; - return neighborLowTime < lowestDiscoveryTime ? neighborLowTime : lowestDiscoveryTime; - }, - visitedSet[currentVertex.getKey()].lowDiscoveryTime, - ); - - // Compare low discovery times. In case if current low discovery time is less than the one - // in previous vertex then update previous vertex low time. - const currentLowDiscoveryTime = visitedSet[currentVertex.getKey()].lowDiscoveryTime; - const previousLowDiscoveryTime = visitedSet[previousVertex.getKey()].lowDiscoveryTime; - if (currentLowDiscoveryTime < previousLowDiscoveryTime) { - visitedSet[previousVertex.getKey()].lowDiscoveryTime = currentLowDiscoveryTime; - } - - // Compare current vertex low discovery time with parent discovery time. Check if there - // are any short path (back edge) exists. If we can't get to current vertex other then - // via parent then the parent vertex is articulation point for current one. - const parentDiscoveryTime = visitedSet[previousVertex.getKey()].discoveryTime; - if (parentDiscoveryTime < currentLowDiscoveryTime) { - const bridge = graph.findEdge(previousVertex, currentVertex); - bridges[bridge.getKey()] = bridge; - } - }, - allowTraversal: ({ nextVertex }) => { - return !visitedSet[nextVertex.getKey()]; - }, - }; - - // Do Depth First Search traversal over submitted graph. - depthFirstSearch(graph, startVertex, dfsCallbacks); - - return bridges; -} diff --git a/src/algorithms/graph/depth-first-search/README.md b/src/algorithms/graph/depth-first-search/README.md deleted file mode 100644 index b22a8aa9c8..0000000000 --- a/src/algorithms/graph/depth-first-search/README.md +++ /dev/null @@ -1,16 +0,0 @@ -# Depth-First Search (DFS) - -Depth-first search (DFS) is an algorithm for traversing or -searching tree or graph data structures. One starts at -the root (selecting some arbitrary node as the root in -the case of a graph) and explores as far as possible -along each branch before backtracking. - -![Algorithm Visualization](https://upload.wikimedia.org/wikipedia/commons/7/7f/Depth-First-Search.gif) - -## References - -- [Wikipedia](https://en.wikipedia.org/wiki/Depth-first_search) -- [Tree Traversals (Inorder, Preorder and Postorder)](https://www.geeksforgeeks.org/tree-traversals-inorder-preorder-and-postorder/) -- [BFS vs DFS](https://www.geeksforgeeks.org/bfs-vs-dfs-binary-tree/) -- [DFS Visualization](https://www.cs.usfca.edu/~galles/visualization/DFS.html) diff --git a/src/algorithms/graph/depth-first-search/__test__/depthFirstSearch.test.js b/src/algorithms/graph/depth-first-search/__test__/depthFirstSearch.test.js deleted file mode 100644 index 93ed61091a..0000000000 --- a/src/algorithms/graph/depth-first-search/__test__/depthFirstSearch.test.js +++ /dev/null @@ -1,165 +0,0 @@ -import Graph from '../../../../data-structures/graph/Graph'; -import GraphVertex from '../../../../data-structures/graph/GraphVertex'; -import GraphEdge from '../../../../data-structures/graph/GraphEdge'; -import depthFirstSearch from '../depthFirstSearch'; - -describe('depthFirstSearch', () => { - it('should perform DFS operation on graph', () => { - const graph = new Graph(true); - - const vertexA = new GraphVertex('A'); - const vertexB = new GraphVertex('B'); - const vertexC = new GraphVertex('C'); - const vertexD = new GraphVertex('D'); - const vertexE = new GraphVertex('E'); - const vertexF = new GraphVertex('F'); - const vertexG = new GraphVertex('G'); - - const edgeAB = new GraphEdge(vertexA, vertexB); - const edgeBC = new GraphEdge(vertexB, vertexC); - const edgeCG = new GraphEdge(vertexC, vertexG); - const edgeAD = new GraphEdge(vertexA, vertexD); - const edgeAE = new GraphEdge(vertexA, vertexE); - const edgeEF = new GraphEdge(vertexE, vertexF); - const edgeFD = new GraphEdge(vertexF, vertexD); - const edgeDG = new GraphEdge(vertexD, vertexG); - - graph - .addEdge(edgeAB) - .addEdge(edgeBC) - .addEdge(edgeCG) - .addEdge(edgeAD) - .addEdge(edgeAE) - .addEdge(edgeEF) - .addEdge(edgeFD) - .addEdge(edgeDG); - - expect(graph.toString()).toBe('A,B,C,G,D,E,F'); - - const enterVertexCallback = jest.fn(); - const leaveVertexCallback = jest.fn(); - - // Traverse graphs without callbacks first to check default ones. - depthFirstSearch(graph, vertexA); - - // Traverse graph with enterVertex and leaveVertex callbacks. - depthFirstSearch(graph, vertexA, { - enterVertex: enterVertexCallback, - leaveVertex: leaveVertexCallback, - }); - - expect(enterVertexCallback).toHaveBeenCalledTimes(graph.getAllVertices().length); - expect(leaveVertexCallback).toHaveBeenCalledTimes(graph.getAllVertices().length); - - const enterVertexParamsMap = [ - { currentVertex: vertexA, previousVertex: null }, - { currentVertex: vertexB, previousVertex: vertexA }, - { currentVertex: vertexC, previousVertex: vertexB }, - { currentVertex: vertexG, previousVertex: vertexC }, - { currentVertex: vertexD, previousVertex: vertexA }, - { currentVertex: vertexE, previousVertex: vertexA }, - { currentVertex: vertexF, previousVertex: vertexE }, - ]; - - for (let callIndex = 0; callIndex < graph.getAllVertices().length; callIndex += 1) { - const params = enterVertexCallback.mock.calls[callIndex][0]; - expect(params.currentVertex).toEqual(enterVertexParamsMap[callIndex].currentVertex); - expect(params.previousVertex).toEqual(enterVertexParamsMap[callIndex].previousVertex); - } - - const leaveVertexParamsMap = [ - { currentVertex: vertexG, previousVertex: vertexC }, - { currentVertex: vertexC, previousVertex: vertexB }, - { currentVertex: vertexB, previousVertex: vertexA }, - { currentVertex: vertexD, previousVertex: vertexA }, - { currentVertex: vertexF, previousVertex: vertexE }, - { currentVertex: vertexE, previousVertex: vertexA }, - { currentVertex: vertexA, previousVertex: null }, - ]; - - for (let callIndex = 0; callIndex < graph.getAllVertices().length; callIndex += 1) { - const params = leaveVertexCallback.mock.calls[callIndex][0]; - expect(params.currentVertex).toEqual(leaveVertexParamsMap[callIndex].currentVertex); - expect(params.previousVertex).toEqual(leaveVertexParamsMap[callIndex].previousVertex); - } - }); - - it('allow users to redefine vertex visiting logic', () => { - const graph = new Graph(true); - - const vertexA = new GraphVertex('A'); - const vertexB = new GraphVertex('B'); - const vertexC = new GraphVertex('C'); - const vertexD = new GraphVertex('D'); - const vertexE = new GraphVertex('E'); - const vertexF = new GraphVertex('F'); - const vertexG = new GraphVertex('G'); - - const edgeAB = new GraphEdge(vertexA, vertexB); - const edgeBC = new GraphEdge(vertexB, vertexC); - const edgeCG = new GraphEdge(vertexC, vertexG); - const edgeAD = new GraphEdge(vertexA, vertexD); - const edgeAE = new GraphEdge(vertexA, vertexE); - const edgeEF = new GraphEdge(vertexE, vertexF); - const edgeFD = new GraphEdge(vertexF, vertexD); - const edgeDG = new GraphEdge(vertexD, vertexG); - - graph - .addEdge(edgeAB) - .addEdge(edgeBC) - .addEdge(edgeCG) - .addEdge(edgeAD) - .addEdge(edgeAE) - .addEdge(edgeEF) - .addEdge(edgeFD) - .addEdge(edgeDG); - - expect(graph.toString()).toBe('A,B,C,G,D,E,F'); - - const enterVertexCallback = jest.fn(); - const leaveVertexCallback = jest.fn(); - - depthFirstSearch(graph, vertexA, { - enterVertex: enterVertexCallback, - leaveVertex: leaveVertexCallback, - allowTraversal: ({ currentVertex, nextVertex }) => { - return !(currentVertex === vertexA && nextVertex === vertexB); - }, - }); - - expect(enterVertexCallback).toHaveBeenCalledTimes(7); - expect(leaveVertexCallback).toHaveBeenCalledTimes(7); - - const enterVertexParamsMap = [ - { currentVertex: vertexA, previousVertex: null }, - { currentVertex: vertexD, previousVertex: vertexA }, - { currentVertex: vertexG, previousVertex: vertexD }, - { currentVertex: vertexE, previousVertex: vertexA }, - { currentVertex: vertexF, previousVertex: vertexE }, - { currentVertex: vertexD, previousVertex: vertexF }, - { currentVertex: vertexG, previousVertex: vertexD }, - ]; - - for (let callIndex = 0; callIndex < graph.getAllVertices().length; callIndex += 1) { - const params = enterVertexCallback.mock.calls[callIndex][0]; - expect(params.currentVertex).toEqual(enterVertexParamsMap[callIndex].currentVertex); - expect(params.previousVertex).toEqual(enterVertexParamsMap[callIndex].previousVertex); - } - - const leaveVertexParamsMap = [ - { currentVertex: vertexG, previousVertex: vertexD }, - { currentVertex: vertexD, previousVertex: vertexA }, - { currentVertex: vertexG, previousVertex: vertexD }, - { currentVertex: vertexD, previousVertex: vertexF }, - { currentVertex: vertexF, previousVertex: vertexE }, - { currentVertex: vertexE, previousVertex: vertexA }, - { currentVertex: vertexA, previousVertex: null }, - ]; - - for (let callIndex = 0; callIndex < graph.getAllVertices().length; callIndex += 1) { - const params = leaveVertexCallback.mock.calls[callIndex][0]; - expect(params.currentVertex).toEqual(leaveVertexParamsMap[callIndex].currentVertex); - expect(params.previousVertex).toEqual(leaveVertexParamsMap[callIndex].previousVertex); - } - }); -}); diff --git a/src/algorithms/graph/depth-first-search/depthFirstSearch.js b/src/algorithms/graph/depth-first-search/depthFirstSearch.js deleted file mode 100644 index a77c672f19..0000000000 --- a/src/algorithms/graph/depth-first-search/depthFirstSearch.js +++ /dev/null @@ -1,68 +0,0 @@ -/** - * @typedef {Object} Callbacks - * - * @property {function(vertices: Object): boolean} [allowTraversal] - - * Determines whether DFS should traverse from the vertex to its neighbor - * (along the edge). By default prohibits visiting the same vertex again. - * - * @property {function(vertices: Object)} [enterVertex] - Called when DFS enters the vertex. - * - * @property {function(vertices: Object)} [leaveVertex] - Called when DFS leaves the vertex. - */ - -/** - * @param {Callbacks} [callbacks] - * @returns {Callbacks} - */ -function initCallbacks(callbacks = {}) { - const initiatedCallback = callbacks; - - const stubCallback = () => {}; - - const allowTraversalCallback = ( - () => { - const seen = {}; - return ({ nextVertex }) => { - if (!seen[nextVertex.getKey()]) { - seen[nextVertex.getKey()] = true; - return true; - } - return false; - }; - } - )(); - - initiatedCallback.allowTraversal = callbacks.allowTraversal || allowTraversalCallback; - initiatedCallback.enterVertex = callbacks.enterVertex || stubCallback; - initiatedCallback.leaveVertex = callbacks.leaveVertex || stubCallback; - - return initiatedCallback; -} - -/** - * @param {Graph} graph - * @param {GraphVertex} currentVertex - * @param {GraphVertex} previousVertex - * @param {Callbacks} callbacks - */ -function depthFirstSearchRecursive(graph, currentVertex, previousVertex, callbacks) { - callbacks.enterVertex({ currentVertex, previousVertex }); - - graph.getNeighbors(currentVertex).forEach((nextVertex) => { - if (callbacks.allowTraversal({ previousVertex, currentVertex, nextVertex })) { - depthFirstSearchRecursive(graph, nextVertex, currentVertex, callbacks); - } - }); - - callbacks.leaveVertex({ currentVertex, previousVertex }); -} - -/** - * @param {Graph} graph - * @param {GraphVertex} startVertex - * @param {Callbacks} [callbacks] - */ -export default function depthFirstSearch(graph, startVertex, callbacks) { - const previousVertex = null; - depthFirstSearchRecursive(graph, startVertex, previousVertex, initCallbacks(callbacks)); -} diff --git a/src/algorithms/graph/detect-cycle/README.md b/src/algorithms/graph/detect-cycle/README.md deleted file mode 100644 index 82641c78a2..0000000000 --- a/src/algorithms/graph/detect-cycle/README.md +++ /dev/null @@ -1,60 +0,0 @@ -# Detect Cycle in Graphs - -In graph theory, a **cycle** is a path of edges and vertices -wherein a vertex is reachable from itself. There are several -different types of cycles, principally a **closed walk** and -a **simple cycle**. - -## Definitions - -A **closed walk** consists of a sequence of vertices starting -and ending at the same vertex, with each two consecutive vertices -in the sequence adjacent to each other in the graph. In a directed graph, -each edge must be traversed by the walk consistently with its direction: -the edge must be oriented from the earlier of two consecutive vertices -to the later of the two vertices in the sequence. -The choice of starting vertex is not important: traversing the same cyclic -sequence of edges from different starting vertices produces the same closed walk. - -A **simple cycle may** be defined either as a closed walk with no repetitions of -vertices and edges allowed, other than the repetition of the starting and ending -vertex, or as the set of edges in such a walk. The two definitions are equivalent -in directed graphs, where simple cycles are also called directed cycles: the cyclic -sequence of vertices and edges in a walk is completely determined by the set of -edges that it uses. In undirected graphs the set of edges of a cycle can be -traversed by a walk in either of two directions, giving two possible directed cycles -for every undirected cycle. A circuit can be a closed walk allowing repetitions of -vertices but not edges; however, it can also be a simple cycle, so explicit -definition is recommended when it is used. - -## Example - -![Cycles](https://upload.wikimedia.org/wikipedia/commons/e/e7/Graph_cycle.gif) - -A graph with edges colored to illustrate **path** `H-A-B` (green), closed path or -**walk with a repeated vertex** `B-D-E-F-D-C-B` (blue) and a **cycle with no repeated edge** or -vertex `H-D-G-H` (red) - -### Cycle in undirected graph - -![Undirected Cycle](https://www.geeksforgeeks.org/wp-content/uploads/cycleGraph.png) - -### Cycle in directed graph - -![Directed Cycle](https://cdncontribute.geeksforgeeks.org/wp-content/uploads/cycle.png) - -## References - -General information: - -- [Wikipedia](https://en.wikipedia.org/wiki/Cycle_(graph_theory)) - -Cycles in undirected graphs: - -- [Detect Cycle in Undirected Graph on GeeksForGeeks](https://www.geeksforgeeks.org/detect-cycle-undirected-graph/) -- [Detect Cycle in Undirected Graph Algorithm on YouTube](https://www.youtube.com/watch?v=n_t0a_8H8VY&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8) - -Cycles in directed graphs: - -- [Detect Cycle in Directed Graph on GeeksForGeeks](https://www.geeksforgeeks.org/detect-cycle-in-a-graph/) -- [Detect Cycle in Directed Graph Algorithm on YouTube](https://www.youtube.com/watch?v=rKQaZuoUR4M&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8) diff --git a/src/algorithms/graph/detect-cycle/__test__/detectDirectedCycle.test.js b/src/algorithms/graph/detect-cycle/__test__/detectDirectedCycle.test.js deleted file mode 100644 index 64a4149338..0000000000 --- a/src/algorithms/graph/detect-cycle/__test__/detectDirectedCycle.test.js +++ /dev/null @@ -1,42 +0,0 @@ -import GraphVertex from '../../../../data-structures/graph/GraphVertex'; -import GraphEdge from '../../../../data-structures/graph/GraphEdge'; -import Graph from '../../../../data-structures/graph/Graph'; -import detectDirectedCycle from '../detectDirectedCycle'; - -describe('detectDirectedCycle', () => { - it('should detect directed cycle', () => { - const vertexA = new GraphVertex('A'); - const vertexB = new GraphVertex('B'); - const vertexC = new GraphVertex('C'); - const vertexD = new GraphVertex('D'); - const vertexE = new GraphVertex('E'); - const vertexF = new GraphVertex('F'); - - const edgeAB = new GraphEdge(vertexA, vertexB); - const edgeBC = new GraphEdge(vertexB, vertexC); - const edgeAC = new GraphEdge(vertexA, vertexC); - const edgeDA = new GraphEdge(vertexD, vertexA); - const edgeDE = new GraphEdge(vertexD, vertexE); - const edgeEF = new GraphEdge(vertexE, vertexF); - const edgeFD = new GraphEdge(vertexF, vertexD); - - const graph = new Graph(true); - graph - .addEdge(edgeAB) - .addEdge(edgeBC) - .addEdge(edgeAC) - .addEdge(edgeDA) - .addEdge(edgeDE) - .addEdge(edgeEF); - - expect(detectDirectedCycle(graph)).toBeNull(); - - graph.addEdge(edgeFD); - - expect(detectDirectedCycle(graph)).toEqual({ - D: vertexF, - F: vertexE, - E: vertexD, - }); - }); -}); diff --git a/src/algorithms/graph/detect-cycle/__test__/detectUndirectedCycle.test.js b/src/algorithms/graph/detect-cycle/__test__/detectUndirectedCycle.test.js deleted file mode 100644 index c3f9903102..0000000000 --- a/src/algorithms/graph/detect-cycle/__test__/detectUndirectedCycle.test.js +++ /dev/null @@ -1,41 +0,0 @@ -import GraphVertex from '../../../../data-structures/graph/GraphVertex'; -import GraphEdge from '../../../../data-structures/graph/GraphEdge'; -import Graph from '../../../../data-structures/graph/Graph'; -import detectUndirectedCycle from '../detectUndirectedCycle'; - -describe('detectUndirectedCycle', () => { - it('should detect undirected cycle', () => { - const vertexA = new GraphVertex('A'); - const vertexB = new GraphVertex('B'); - const vertexC = new GraphVertex('C'); - const vertexD = new GraphVertex('D'); - const vertexE = new GraphVertex('E'); - const vertexF = new GraphVertex('F'); - - const edgeAF = new GraphEdge(vertexA, vertexF); - const edgeAB = new GraphEdge(vertexA, vertexB); - const edgeBE = new GraphEdge(vertexB, vertexE); - const edgeBC = new GraphEdge(vertexB, vertexC); - const edgeCD = new GraphEdge(vertexC, vertexD); - const edgeDE = new GraphEdge(vertexD, vertexE); - - const graph = new Graph(); - graph - .addEdge(edgeAF) - .addEdge(edgeAB) - .addEdge(edgeBE) - .addEdge(edgeBC) - .addEdge(edgeCD); - - expect(detectUndirectedCycle(graph)).toBeNull(); - - graph.addEdge(edgeDE); - - expect(detectUndirectedCycle(graph)).toEqual({ - B: vertexC, - C: vertexD, - D: vertexE, - E: vertexB, - }); - }); -}); diff --git a/src/algorithms/graph/detect-cycle/__test__/detectUndirectedCycleUsingDisjointSet.test.js b/src/algorithms/graph/detect-cycle/__test__/detectUndirectedCycleUsingDisjointSet.test.js deleted file mode 100644 index 15cb153471..0000000000 --- a/src/algorithms/graph/detect-cycle/__test__/detectUndirectedCycleUsingDisjointSet.test.js +++ /dev/null @@ -1,36 +0,0 @@ -import GraphVertex from '../../../../data-structures/graph/GraphVertex'; -import GraphEdge from '../../../../data-structures/graph/GraphEdge'; -import Graph from '../../../../data-structures/graph/Graph'; -import detectUndirectedCycleUsingDisjointSet from '../detectUndirectedCycleUsingDisjointSet'; - -describe('detectUndirectedCycleUsingDisjointSet', () => { - it('should detect undirected cycle', () => { - const vertexA = new GraphVertex('A'); - const vertexB = new GraphVertex('B'); - const vertexC = new GraphVertex('C'); - const vertexD = new GraphVertex('D'); - const vertexE = new GraphVertex('E'); - const vertexF = new GraphVertex('F'); - - const edgeAF = new GraphEdge(vertexA, vertexF); - const edgeAB = new GraphEdge(vertexA, vertexB); - const edgeBE = new GraphEdge(vertexB, vertexE); - const edgeBC = new GraphEdge(vertexB, vertexC); - const edgeCD = new GraphEdge(vertexC, vertexD); - const edgeDE = new GraphEdge(vertexD, vertexE); - - const graph = new Graph(); - graph - .addEdge(edgeAF) - .addEdge(edgeAB) - .addEdge(edgeBE) - .addEdge(edgeBC) - .addEdge(edgeCD); - - expect(detectUndirectedCycleUsingDisjointSet(graph)).toBe(false); - - graph.addEdge(edgeDE); - - expect(detectUndirectedCycleUsingDisjointSet(graph)).toBe(true); - }); -}); diff --git a/src/algorithms/graph/detect-cycle/detectDirectedCycle.js b/src/algorithms/graph/detect-cycle/detectDirectedCycle.js deleted file mode 100644 index 73b2b22419..0000000000 --- a/src/algorithms/graph/detect-cycle/detectDirectedCycle.js +++ /dev/null @@ -1,93 +0,0 @@ -import depthFirstSearch from '../depth-first-search/depthFirstSearch'; - -/** - * Detect cycle in directed graph using Depth First Search. - * - * @param {Graph} graph - */ -export default function detectDirectedCycle(graph) { - let cycle = null; - - // Will store parents (previous vertices) for all visited nodes. - // This will be needed in order to specify what path exactly is a cycle. - const dfsParentMap = {}; - - // White set (UNVISITED) contains all the vertices that haven't been visited at all. - const whiteSet = {}; - - // Gray set (VISITING) contains all the vertices that are being visited right now - // (in current path). - const graySet = {}; - - // Black set (VISITED) contains all the vertices that has been fully visited. - // Meaning that all children of the vertex has been visited. - const blackSet = {}; - - // If we encounter vertex in gray set it means that we've found a cycle. - // Because when vertex in gray set it means that its neighbors or its neighbors - // neighbors are still being explored. - - // Init white set and add all vertices to it. - /** @param {GraphVertex} vertex */ - graph.getAllVertices().forEach((vertex) => { - whiteSet[vertex.getKey()] = vertex; - }); - - // Describe BFS callbacks. - const callbacks = { - enterVertex: ({ currentVertex, previousVertex }) => { - if (graySet[currentVertex.getKey()]) { - // If current vertex already in grey set it means that cycle is detected. - // Let's detect cycle path. - cycle = {}; - - let currentCycleVertex = currentVertex; - let previousCycleVertex = previousVertex; - - while (previousCycleVertex.getKey() !== currentVertex.getKey()) { - cycle[currentCycleVertex.getKey()] = previousCycleVertex; - currentCycleVertex = previousCycleVertex; - previousCycleVertex = dfsParentMap[previousCycleVertex.getKey()]; - } - - cycle[currentCycleVertex.getKey()] = previousCycleVertex; - } else { - // Otherwise let's add current vertex to gray set and remove it from white set. - graySet[currentVertex.getKey()] = currentVertex; - delete whiteSet[currentVertex.getKey()]; - - // Update DFS parents list. - dfsParentMap[currentVertex.getKey()] = previousVertex; - } - }, - leaveVertex: ({ currentVertex }) => { - // If all node's children has been visited let's remove it from gray set - // and move it to the black set meaning that all its neighbors are visited. - blackSet[currentVertex.getKey()] = currentVertex; - delete graySet[currentVertex.getKey()]; - }, - allowTraversal: ({ nextVertex }) => { - // If cycle was detected we must forbid all further traversing since it will - // cause infinite traversal loop. - if (cycle) { - return false; - } - - // Allow traversal only for the vertices that are not in black set - // since all black set vertices have been already visited. - return !blackSet[nextVertex.getKey()]; - }, - }; - - // Start exploring vertices. - while (Object.keys(whiteSet).length) { - // Pick fist vertex to start BFS from. - const firstWhiteKey = Object.keys(whiteSet)[0]; - const startVertex = whiteSet[firstWhiteKey]; - - // Do Depth First Search. - depthFirstSearch(graph, startVertex, callbacks); - } - - return cycle; -} diff --git a/src/algorithms/graph/detect-cycle/detectUndirectedCycle.js b/src/algorithms/graph/detect-cycle/detectUndirectedCycle.js deleted file mode 100644 index 5bcc9bb699..0000000000 --- a/src/algorithms/graph/detect-cycle/detectUndirectedCycle.js +++ /dev/null @@ -1,59 +0,0 @@ -import depthFirstSearch from '../depth-first-search/depthFirstSearch'; - -/** - * Detect cycle in undirected graph using Depth First Search. - * - * @param {Graph} graph - */ -export default function detectUndirectedCycle(graph) { - let cycle = null; - - // List of vertices that we have visited. - const visitedVertices = {}; - - // List of parents vertices for every visited vertex. - const parents = {}; - - // Callbacks for DFS traversing. - const callbacks = { - allowTraversal: ({ currentVertex, nextVertex }) => { - // Don't allow further traversal in case if cycle has been detected. - if (cycle) { - return false; - } - - // Don't allow traversal from child back to its parent. - const currentVertexParent = parents[currentVertex.getKey()]; - const currentVertexParentKey = currentVertexParent ? currentVertexParent.getKey() : null; - - return currentVertexParentKey !== nextVertex.getKey(); - }, - enterVertex: ({ currentVertex, previousVertex }) => { - if (visitedVertices[currentVertex.getKey()]) { - // Compile cycle path based on parents of previous vertices. - cycle = {}; - - let currentCycleVertex = currentVertex; - let previousCycleVertex = previousVertex; - - while (previousCycleVertex.getKey() !== currentVertex.getKey()) { - cycle[currentCycleVertex.getKey()] = previousCycleVertex; - currentCycleVertex = previousCycleVertex; - previousCycleVertex = parents[previousCycleVertex.getKey()]; - } - - cycle[currentCycleVertex.getKey()] = previousCycleVertex; - } else { - // Add next vertex to visited set. - visitedVertices[currentVertex.getKey()] = currentVertex; - parents[currentVertex.getKey()] = previousVertex; - } - }, - }; - - // Start DFS traversing. - const startVertex = graph.getAllVertices()[0]; - depthFirstSearch(graph, startVertex, callbacks); - - return cycle; -} diff --git a/src/algorithms/graph/detect-cycle/detectUndirectedCycleUsingDisjointSet.js b/src/algorithms/graph/detect-cycle/detectUndirectedCycleUsingDisjointSet.js deleted file mode 100644 index 7dec9c2890..0000000000 --- a/src/algorithms/graph/detect-cycle/detectUndirectedCycleUsingDisjointSet.js +++ /dev/null @@ -1,31 +0,0 @@ -import DisjointSet from '../../../data-structures/disjoint-set/DisjointSet'; - -/** - * Detect cycle in undirected graph using disjoint sets. - * - * @param {Graph} graph - */ -export default function detectUndirectedCycleUsingDisjointSet(graph) { - // Create initial singleton disjoint sets for each graph vertex. - /** @param {GraphVertex} graphVertex */ - const keyExtractor = (graphVertex) => graphVertex.getKey(); - const disjointSet = new DisjointSet(keyExtractor); - graph.getAllVertices().forEach((graphVertex) => disjointSet.makeSet(graphVertex)); - - // Go trough all graph edges one by one and check if edge vertices are from the - // different sets. In this case joint those sets together. Do this until you find - // an edge where to edge vertices are already in one set. This means that current - // edge will create a cycle. - let cycleFound = false; - /** @param {GraphEdge} graphEdge */ - graph.getAllEdges().forEach((graphEdge) => { - if (disjointSet.inSameSet(graphEdge.startVertex, graphEdge.endVertex)) { - // Cycle found. - cycleFound = true; - } else { - disjointSet.union(graphEdge.startVertex, graphEdge.endVertex); - } - }); - - return cycleFound; -} diff --git a/src/algorithms/graph/dijkstra/README.ko-KR.md b/src/algorithms/graph/dijkstra/README.ko-KR.md deleted file mode 100644 index e2595bbe23..0000000000 --- a/src/algorithms/graph/dijkstra/README.ko-KR.md +++ /dev/null @@ -1,16 +0,0 @@ -# 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 deleted file mode 100644 index d94e2a3cdf..0000000000 --- a/src/algorithms/graph/dijkstra/README.md +++ /dev/null @@ -1,28 +0,0 @@ -# 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. - -The algorithm exists in many variants; Dijkstra's original variant -found the shortest path between two nodes, but a more common -variant fixes a single node as the "source" node and finds -shortest paths from the source to all other nodes in the graph, -producing a shortest-path tree. - -![Dijkstra](https://upload.wikimedia.org/wikipedia/commons/5/57/Dijkstra_Animation.gif) - -Dijkstra's algorithm to find the shortest path between `a` and `b`. -It picks the unvisited vertex with the lowest distance, -calculates the distance through it to each unvisited neighbor, -and updates the neighbor's distance if smaller. Mark visited -(set to red) when done with neighbors. - -## References - -- [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/__test__/dijkstra.test.js b/src/algorithms/graph/dijkstra/__test__/dijkstra.test.js deleted file mode 100644 index f6c5a263f9..0000000000 --- a/src/algorithms/graph/dijkstra/__test__/dijkstra.test.js +++ /dev/null @@ -1,117 +0,0 @@ -import GraphVertex from '../../../../data-structures/graph/GraphVertex'; -import GraphEdge from '../../../../data-structures/graph/GraphEdge'; -import Graph from '../../../../data-structures/graph/Graph'; -import dijkstra from '../dijkstra'; - -describe('dijkstra', () => { - it('should find minimum paths to all vertices for undirected graph', () => { - const vertexA = new GraphVertex('A'); - const vertexB = new GraphVertex('B'); - const vertexC = new GraphVertex('C'); - const vertexD = new GraphVertex('D'); - const vertexE = new GraphVertex('E'); - const vertexF = new GraphVertex('F'); - const vertexG = new GraphVertex('G'); - const vertexH = new GraphVertex('H'); - - const edgeAB = new GraphEdge(vertexA, vertexB, 4); - const edgeAE = new GraphEdge(vertexA, vertexE, 7); - const edgeAC = new GraphEdge(vertexA, vertexC, 3); - const edgeBC = new GraphEdge(vertexB, vertexC, 6); - const edgeBD = new GraphEdge(vertexB, vertexD, 5); - const edgeEC = new GraphEdge(vertexE, vertexC, 8); - const edgeED = new GraphEdge(vertexE, vertexD, 2); - const edgeDC = new GraphEdge(vertexD, vertexC, 11); - const edgeDG = new GraphEdge(vertexD, vertexG, 10); - const edgeDF = new GraphEdge(vertexD, vertexF, 2); - const edgeFG = new GraphEdge(vertexF, vertexG, 3); - const edgeEG = new GraphEdge(vertexE, vertexG, 5); - - const graph = new Graph(); - graph - .addVertex(vertexH) - .addEdge(edgeAB) - .addEdge(edgeAE) - .addEdge(edgeAC) - .addEdge(edgeBC) - .addEdge(edgeBD) - .addEdge(edgeEC) - .addEdge(edgeED) - .addEdge(edgeDC) - .addEdge(edgeDG) - .addEdge(edgeDF) - .addEdge(edgeFG) - .addEdge(edgeEG); - - const { distances, previousVertices } = dijkstra(graph, vertexA); - - expect(distances).toEqual({ - H: Infinity, - A: 0, - B: 4, - E: 7, - C: 3, - D: 9, - G: 12, - F: 11, - }); - - expect(previousVertices.F.getKey()).toBe('D'); - expect(previousVertices.D.getKey()).toBe('B'); - expect(previousVertices.B.getKey()).toBe('A'); - expect(previousVertices.G.getKey()).toBe('E'); - expect(previousVertices.C.getKey()).toBe('A'); - expect(previousVertices.A).toBeNull(); - expect(previousVertices.H).toBeNull(); - }); - - it('should find minimum paths to all vertices for directed graph with negative edge weights', () => { - const vertexS = new GraphVertex('S'); - const vertexE = new GraphVertex('E'); - const vertexA = new GraphVertex('A'); - const vertexD = new GraphVertex('D'); - const vertexB = new GraphVertex('B'); - const vertexC = new GraphVertex('C'); - const vertexH = new GraphVertex('H'); - - const edgeSE = new GraphEdge(vertexS, vertexE, 8); - const edgeSA = new GraphEdge(vertexS, vertexA, 10); - const edgeED = new GraphEdge(vertexE, vertexD, 1); - const edgeDA = new GraphEdge(vertexD, vertexA, -4); - const edgeDC = new GraphEdge(vertexD, vertexC, -1); - const edgeAC = new GraphEdge(vertexA, vertexC, 2); - const edgeCB = new GraphEdge(vertexC, vertexB, -2); - const edgeBA = new GraphEdge(vertexB, vertexA, 1); - - const graph = new Graph(true); - graph - .addVertex(vertexH) - .addEdge(edgeSE) - .addEdge(edgeSA) - .addEdge(edgeED) - .addEdge(edgeDA) - .addEdge(edgeDC) - .addEdge(edgeAC) - .addEdge(edgeCB) - .addEdge(edgeBA); - - const { distances, previousVertices } = dijkstra(graph, vertexS); - - expect(distances).toEqual({ - H: Infinity, - S: 0, - A: 5, - B: 5, - C: 7, - D: 9, - E: 8, - }); - - expect(previousVertices.H).toBeNull(); - expect(previousVertices.S).toBeNull(); - expect(previousVertices.B.getKey()).toBe('C'); - expect(previousVertices.C.getKey()).toBe('A'); - expect(previousVertices.A.getKey()).toBe('D'); - expect(previousVertices.D.getKey()).toBe('E'); - }); -}); diff --git a/src/algorithms/graph/dijkstra/dijkstra.js b/src/algorithms/graph/dijkstra/dijkstra.js deleted file mode 100644 index c5b47b08d3..0000000000 --- a/src/algorithms/graph/dijkstra/dijkstra.js +++ /dev/null @@ -1,80 +0,0 @@ -import PriorityQueue from '../../../data-structures/priority-queue/PriorityQueue'; - -/** - * @typedef {Object} ShortestPaths - * @property {Object} distances - shortest distances to all vertices - * @property {Object} previousVertices - shortest paths to all vertices. - */ - -/** - * Implementation of Dijkstra algorithm of finding the shortest paths to graph nodes. - * @param {Graph} graph - graph we're going to traverse. - * @param {GraphVertex} startVertex - traversal start vertex. - * @return {ShortestPaths} - */ -export default function dijkstra(graph, startVertex) { - // Init helper variables that we will need for Dijkstra algorithm. - const distances = {}; - const visitedVertices = {}; - const previousVertices = {}; - const queue = new PriorityQueue(); - - // Init all distances with infinity assuming that currently we can't reach - // any of the vertices except the start one. - graph.getAllVertices().forEach((vertex) => { - distances[vertex.getKey()] = Infinity; - previousVertices[vertex.getKey()] = null; - }); - - // We are already at the startVertex so the distance to it is zero. - distances[startVertex.getKey()] = 0; - - // Init vertices queue. - queue.add(startVertex, distances[startVertex.getKey()]); - - // Iterate over the priority queue of vertices until it is empty. - while (!queue.isEmpty()) { - // Fetch next closest vertex. - const currentVertex = queue.poll(); - - // Iterate over every unvisited neighbor of the current vertex. - currentVertex.getNeighbors().forEach((neighbor) => { - // Don't visit already visited vertices. - if (!visitedVertices[neighbor.getKey()]) { - // Update distances to every neighbor from current vertex. - const edge = graph.findEdge(currentVertex, neighbor); - - const existingDistanceToNeighbor = distances[neighbor.getKey()]; - const distanceToNeighborFromCurrent = distances[currentVertex.getKey()] + edge.weight; - - // If we've found shorter path to the neighbor - update it. - if (distanceToNeighborFromCurrent < existingDistanceToNeighbor) { - distances[neighbor.getKey()] = distanceToNeighborFromCurrent; - - // Change priority of the neighbor in a queue since it might have became closer. - if (queue.hasValue(neighbor)) { - queue.changePriority(neighbor, distances[neighbor.getKey()]); - } - - // Remember previous closest vertex. - previousVertices[neighbor.getKey()] = currentVertex; - } - - // Add neighbor to the queue for further visiting. - if (!queue.hasValue(neighbor)) { - queue.add(neighbor, distances[neighbor.getKey()]); - } - } - }); - - // Add current vertex to visited ones to avoid visiting it again later. - visitedVertices[currentVertex.getKey()] = currentVertex; - } - - // Return the set of shortest distances to all vertices and the set of - // shortest paths to all vertices in a graph. - return { - distances, - previousVertices, - }; -} diff --git a/src/algorithms/graph/eulerian-path/README.md b/src/algorithms/graph/eulerian-path/README.md deleted file mode 100644 index 597a9ef32e..0000000000 --- a/src/algorithms/graph/eulerian-path/README.md +++ /dev/null @@ -1,35 +0,0 @@ -# Eulerian Path - -In graph theory, an **Eulerian trail** (or **Eulerian path**) is a -trail in a finite graph which visits every edge exactly once. -Similarly, an **Eulerian circuit** or **Eulerian cycle** is an -Eulerian trail which starts and ends on the same vertex. - -Euler proved that a necessary condition for the existence of Eulerian -circuits is that all vertices in the graph have an even degree, and -stated that connected graphs with all vertices of even degree have -an Eulerian circuit. - -![Eulerian Circuit](https://upload.wikimedia.org/wikipedia/commons/7/72/Labelled_Eulergraph.svg) - -Every vertex of this graph has an even degree. Therefore, this is -an Eulerian graph. Following the edges in alphabetical order gives -an Eulerian circuit/cycle. - -For the existence of Eulerian trails it is necessary that zero or -two vertices have an odd degree; this means the Königsberg graph -is not Eulerian. If there are no vertices of odd degree, -all Eulerian trails are circuits. If there are exactly two vertices -of odd degree, all Eulerian trails start at one of them and end at -the other. A graph that has an Eulerian trail but not an Eulerian -circuit is called semi-Eulerian. - -![Königsberg graph](https://upload.wikimedia.org/wikipedia/commons/9/96/K%C3%B6nigsberg_graph.svg) - -The Königsberg Bridges multigraph. This multigraph is not Eulerian, -therefore, a solution does not exist. - -## References - -- [Wikipedia](https://en.wikipedia.org/wiki/Eulerian_path) -- [YouTube](https://www.youtube.com/watch?v=vvP4Fg4r-Ns&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8) diff --git a/src/algorithms/graph/eulerian-path/__test__/eulerianPath.test.js b/src/algorithms/graph/eulerian-path/__test__/eulerianPath.test.js deleted file mode 100644 index d10d980806..0000000000 --- a/src/algorithms/graph/eulerian-path/__test__/eulerianPath.test.js +++ /dev/null @@ -1,139 +0,0 @@ -import GraphVertex from '../../../../data-structures/graph/GraphVertex'; -import GraphEdge from '../../../../data-structures/graph/GraphEdge'; -import Graph from '../../../../data-structures/graph/Graph'; -import eulerianPath from '../eulerianPath'; - -describe('eulerianPath', () => { - it('should throw an error when graph is not Eulerian', () => { - function findEulerianPathInNotEulerianGraph() { - const vertexA = new GraphVertex('A'); - const vertexB = new GraphVertex('B'); - const vertexC = new GraphVertex('C'); - const vertexD = new GraphVertex('D'); - const vertexE = new GraphVertex('E'); - - const edgeAB = new GraphEdge(vertexA, vertexB); - const edgeAC = new GraphEdge(vertexA, vertexC); - const edgeBC = new GraphEdge(vertexB, vertexC); - const edgeBD = new GraphEdge(vertexB, vertexD); - const edgeCE = new GraphEdge(vertexC, vertexE); - - const graph = new Graph(); - - graph - .addEdge(edgeAB) - .addEdge(edgeAC) - .addEdge(edgeBC) - .addEdge(edgeBD) - .addEdge(edgeCE); - - eulerianPath(graph); - } - - expect(findEulerianPathInNotEulerianGraph).toThrowError(); - }); - - it('should find Eulerian Circuit in graph', () => { - const vertexA = new GraphVertex('A'); - const vertexB = new GraphVertex('B'); - const vertexC = new GraphVertex('C'); - const vertexD = new GraphVertex('D'); - const vertexE = new GraphVertex('E'); - const vertexF = new GraphVertex('F'); - const vertexG = new GraphVertex('G'); - - const edgeAB = new GraphEdge(vertexA, vertexB); - const edgeAE = new GraphEdge(vertexA, vertexE); - const edgeAF = new GraphEdge(vertexA, vertexF); - const edgeAG = new GraphEdge(vertexA, vertexG); - const edgeGF = new GraphEdge(vertexG, vertexF); - const edgeBE = new GraphEdge(vertexB, vertexE); - const edgeEB = new GraphEdge(vertexE, vertexB); - const edgeBC = new GraphEdge(vertexB, vertexC); - const edgeED = new GraphEdge(vertexE, vertexD); - const edgeCD = new GraphEdge(vertexC, vertexD); - - const graph = new Graph(); - - graph - .addEdge(edgeAB) - .addEdge(edgeAE) - .addEdge(edgeAF) - .addEdge(edgeAG) - .addEdge(edgeGF) - .addEdge(edgeBE) - .addEdge(edgeEB) - .addEdge(edgeBC) - .addEdge(edgeED) - .addEdge(edgeCD); - - const graphEdgesCount = graph.getAllEdges().length; - - const eulerianPathSet = eulerianPath(graph); - - expect(eulerianPathSet.length).toBe(graphEdgesCount + 1); - - expect(eulerianPathSet[0].getKey()).toBe(vertexA.getKey()); - expect(eulerianPathSet[1].getKey()).toBe(vertexB.getKey()); - expect(eulerianPathSet[2].getKey()).toBe(vertexE.getKey()); - expect(eulerianPathSet[3].getKey()).toBe(vertexB.getKey()); - expect(eulerianPathSet[4].getKey()).toBe(vertexC.getKey()); - expect(eulerianPathSet[5].getKey()).toBe(vertexD.getKey()); - expect(eulerianPathSet[6].getKey()).toBe(vertexE.getKey()); - expect(eulerianPathSet[7].getKey()).toBe(vertexA.getKey()); - expect(eulerianPathSet[8].getKey()).toBe(vertexF.getKey()); - expect(eulerianPathSet[9].getKey()).toBe(vertexG.getKey()); - expect(eulerianPathSet[10].getKey()).toBe(vertexA.getKey()); - }); - - it('should find Eulerian Path in graph', () => { - const vertexA = new GraphVertex('A'); - const vertexB = new GraphVertex('B'); - const vertexC = new GraphVertex('C'); - const vertexD = new GraphVertex('D'); - const vertexE = new GraphVertex('E'); - const vertexF = new GraphVertex('F'); - const vertexG = new GraphVertex('G'); - const vertexH = new GraphVertex('H'); - - const edgeAB = new GraphEdge(vertexA, vertexB); - const edgeAC = new GraphEdge(vertexA, vertexC); - const edgeBD = new GraphEdge(vertexB, vertexD); - const edgeDC = new GraphEdge(vertexD, vertexC); - const edgeCE = new GraphEdge(vertexC, vertexE); - const edgeEF = new GraphEdge(vertexE, vertexF); - const edgeFH = new GraphEdge(vertexF, vertexH); - const edgeFG = new GraphEdge(vertexF, vertexG); - const edgeHG = new GraphEdge(vertexH, vertexG); - - const graph = new Graph(); - - graph - .addEdge(edgeAB) - .addEdge(edgeAC) - .addEdge(edgeBD) - .addEdge(edgeDC) - .addEdge(edgeCE) - .addEdge(edgeEF) - .addEdge(edgeFH) - .addEdge(edgeFG) - .addEdge(edgeHG); - - const graphEdgesCount = graph.getAllEdges().length; - - const eulerianPathSet = eulerianPath(graph); - - expect(eulerianPathSet.length).toBe(graphEdgesCount + 1); - - expect(eulerianPathSet[0].getKey()).toBe(vertexC.getKey()); - expect(eulerianPathSet[1].getKey()).toBe(vertexA.getKey()); - expect(eulerianPathSet[2].getKey()).toBe(vertexB.getKey()); - expect(eulerianPathSet[3].getKey()).toBe(vertexD.getKey()); - expect(eulerianPathSet[4].getKey()).toBe(vertexC.getKey()); - expect(eulerianPathSet[5].getKey()).toBe(vertexE.getKey()); - expect(eulerianPathSet[6].getKey()).toBe(vertexF.getKey()); - expect(eulerianPathSet[7].getKey()).toBe(vertexH.getKey()); - expect(eulerianPathSet[8].getKey()).toBe(vertexG.getKey()); - expect(eulerianPathSet[9].getKey()).toBe(vertexF.getKey()); - }); -}); diff --git a/src/algorithms/graph/eulerian-path/eulerianPath.js b/src/algorithms/graph/eulerian-path/eulerianPath.js deleted file mode 100644 index c82c6fd134..0000000000 --- a/src/algorithms/graph/eulerian-path/eulerianPath.js +++ /dev/null @@ -1,101 +0,0 @@ -import graphBridges from '../bridges/graphBridges'; - -/** - * Fleury's algorithm of finding Eulerian Path (visit all graph edges exactly once). - * - * @param {Graph} graph - * @return {GraphVertex[]} - */ -export default function eulerianPath(graph) { - const eulerianPathVertices = []; - - // Set that contains all vertices with even rank (number of neighbors). - const evenRankVertices = {}; - - // Set that contains all vertices with odd rank (number of neighbors). - const oddRankVertices = {}; - - // Set of all not visited edges. - const notVisitedEdges = {}; - graph.getAllEdges().forEach((vertex) => { - notVisitedEdges[vertex.getKey()] = vertex; - }); - - // Detect whether graph contains Eulerian Circuit or Eulerian Path or none of them. - /** @params {GraphVertex} vertex */ - graph.getAllVertices().forEach((vertex) => { - if (vertex.getDegree() % 2) { - oddRankVertices[vertex.getKey()] = vertex; - } else { - evenRankVertices[vertex.getKey()] = vertex; - } - }); - - // Check whether we're dealing with Eulerian Circuit or Eulerian Path only. - // Graph would be an Eulerian Circuit in case if all its vertices has even degree. - // If not all vertices have even degree then graph must contain only two odd-degree - // vertices in order to have Euler Path. - const isCircuit = !Object.values(oddRankVertices).length; - - if (!isCircuit && Object.values(oddRankVertices).length !== 2) { - throw new Error('Eulerian path must contain two odd-ranked vertices'); - } - - // Pick start vertex for traversal. - let startVertex = null; - - if (isCircuit) { - // For Eulerian Circuit it doesn't matter from what vertex to start thus we'll just - // peek a first node. - const evenVertexKey = Object.keys(evenRankVertices)[0]; - startVertex = evenRankVertices[evenVertexKey]; - } else { - // For Eulerian Path we need to start from one of two odd-degree vertices. - const oddVertexKey = Object.keys(oddRankVertices)[0]; - startVertex = oddRankVertices[oddVertexKey]; - } - - // Start traversing the graph. - let currentVertex = startVertex; - while (Object.values(notVisitedEdges).length) { - // Add current vertex to Eulerian path. - eulerianPathVertices.push(currentVertex); - - // Detect all bridges in graph. - // We need to do it in order to not delete bridges if there are other edges - // exists for deletion. - const bridges = graphBridges(graph); - - // Peek the next edge to delete from graph. - const currentEdges = currentVertex.getEdges(); - /** @var {GraphEdge} edgeToDelete */ - let edgeToDelete = null; - if (currentEdges.length === 1) { - // If there is only one edge left we need to peek it. - [edgeToDelete] = currentEdges; - } else { - // If there are many edges left then we need to peek any of those except bridges. - [edgeToDelete] = currentEdges.filter((edge) => !bridges[edge.getKey()]); - } - - // Detect next current vertex. - if (currentVertex.getKey() === edgeToDelete.startVertex.getKey()) { - currentVertex = edgeToDelete.endVertex; - } else { - currentVertex = edgeToDelete.startVertex; - } - - // Delete edge from not visited edges set. - delete notVisitedEdges[edgeToDelete.getKey()]; - - // If last edge were deleted then add finish vertex to Eulerian Path. - if (Object.values(notVisitedEdges).length === 0) { - eulerianPathVertices.push(currentVertex); - } - - // Delete the edge from graph. - graph.deleteEdge(edgeToDelete); - } - - return eulerianPathVertices; -} diff --git a/src/algorithms/graph/floyd-warshall/README.md b/src/algorithms/graph/floyd-warshall/README.md deleted file mode 100644 index f662861305..0000000000 --- a/src/algorithms/graph/floyd-warshall/README.md +++ /dev/null @@ -1,94 +0,0 @@ -# Floyd–Warshall Algorithm - -In computer science, the **Floyd–Warshall algorithm** is an algorithm for finding -shortest paths in a weighted graph with positive or negative edge weights (but -with no negative cycles). A single execution of the algorithm will find the -lengths (summed weights) of shortest paths between all pairs of vertices. Although -it does not return details of the paths themselves, it is possible to reconstruct -the paths with simple modifications to the algorithm. - -## Algorithm - -The Floyd–Warshall algorithm compares all possible paths through the graph between -each pair of vertices. It is able to do this with `O(|V|^3)` comparisons in a graph. -This is remarkable considering that there may be up to `|V|^2` edges in the graph, -and every combination of edges is tested. It does so by incrementally improving an -estimate on the shortest path between two vertices, until the estimate is optimal. - -Consider a graph `G` with vertices `V` numbered `1` through `N`. Further consider -a function `shortestPath(i, j, k)` that returns the shortest possible path -from `i` to `j` using vertices only from the set `{1, 2, ..., k}` as -intermediate points along the way. Now, given this function, our goal is to -find the shortest path from each `i` to each `j` using only vertices -in `{1, 2, ..., N}`. - -![Recursive Formula](https://wikimedia.org/api/rest_v1/media/math/render/svg/f9b75e25063384ccca499c56f9a279abf661ad3b) - -![Recursive Formula](https://wikimedia.org/api/rest_v1/media/math/render/svg/34ac7c89bbb18df3fd660225fd38997079e5e513) -![Recursive Formula](https://wikimedia.org/api/rest_v1/media/math/render/svg/0326d6c14def89269c029da59eba012d0f2edc9d) - -This formula is the heart of the Floyd–Warshall algorithm. - -## Example - -The algorithm above is executed on the graph on the left below: - -![Example](https://upload.wikimedia.org/wikipedia/commons/2/2e/Floyd-Warshall_example.svg) - -In the tables below `i` is row numbers and `j` is column numbers. - - -**k = 0** - -| | 1 | 2 | 3 | 4 | -|:-----:|:---:|:---:|:---:|:---:| -| **1** | 0 | ∞ | −2 | ∞ | -| **2** | 4 | 0 | 3 | ∞ | -| **3** | ∞ | ∞ | 0 | 2 | -| **4** | ∞ | −1 | ∞ | 0 | - - -**k = 1** - -| | 1 | 2 | 3 | 4 | -|:-----:|:---:|:---:|:---:|:---:| -| **1** | 0 | ∞ | −2 | ∞ | -| **2** | 4 | 0 | 2 | ∞ | -| **3** | ∞ | ∞ | 0 | 2 | -| **4** | ∞ | − | ∞ | 0 | - - -**k = 2** - -| | 1 | 2 | 3 | 4 | -|:-----:|:---:|:---:|:---:|:---:| -| **1** | 0 | ∞ | −2 | ∞ | -| **2** | 4 | 0 | 2 | ∞ | -| **3** | ∞ | ∞ | 0 | 2 | -| **4** | 3 | −1 | 1 | 0 | - - -**k = 3** - -| | 1 | 2 | 3 | 4 | -|:-----:|:---:|:---:|:---:|:---:| -| **1** | 0 | ∞ | −2 | 0 | -| **2** | 4 | 0 | 2 | 4 | -| **3** | ∞ | ∞ | 0 | 2 | -| **4** | 3 | −1 | 1 | 0 | - - -**k = 4** - -| | 1 | 2 | 3 | 4 | -|:-----:|:---:|:---:|:---:|:---:| -| **1** | 0 | −1 | −2 | 0 | -| **2** | 4 | 0 | 2 | 4 | -| **3** | 5 | 1 | 0 | 2 | -| **4** | 3 | −1 | 1 | 0 | - -## References - -- [Wikipedia](https://en.wikipedia.org/wiki/Floyd%E2%80%93Warshall_algorithm) -- [YouTube (by Abdul Bari)](https://www.youtube.com/watch?v=oNI0rf2P9gE&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8&index=74) -- [YouTube (by Tushar Roy)](https://www.youtube.com/watch?v=LwJdNfdLF9s&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8&index=75) diff --git a/src/algorithms/graph/floyd-warshall/__test__/floydWarshall.test.js b/src/algorithms/graph/floyd-warshall/__test__/floydWarshall.test.js deleted file mode 100644 index dea170c61a..0000000000 --- a/src/algorithms/graph/floyd-warshall/__test__/floydWarshall.test.js +++ /dev/null @@ -1,220 +0,0 @@ -import GraphVertex from '../../../../data-structures/graph/GraphVertex'; -import GraphEdge from '../../../../data-structures/graph/GraphEdge'; -import Graph from '../../../../data-structures/graph/Graph'; -import floydWarshall from '../floydWarshall'; - -describe('floydWarshall', () => { - it('should find minimum paths to all vertices for undirected graph', () => { - const vertexA = new GraphVertex('A'); - const vertexB = new GraphVertex('B'); - const vertexC = new GraphVertex('C'); - const vertexD = new GraphVertex('D'); - const vertexE = new GraphVertex('E'); - const vertexF = new GraphVertex('F'); - const vertexG = new GraphVertex('G'); - const vertexH = new GraphVertex('H'); - - const edgeAB = new GraphEdge(vertexA, vertexB, 4); - const edgeAE = new GraphEdge(vertexA, vertexE, 7); - const edgeAC = new GraphEdge(vertexA, vertexC, 3); - const edgeBC = new GraphEdge(vertexB, vertexC, 6); - const edgeBD = new GraphEdge(vertexB, vertexD, 5); - const edgeEC = new GraphEdge(vertexE, vertexC, 8); - const edgeED = new GraphEdge(vertexE, vertexD, 2); - const edgeDC = new GraphEdge(vertexD, vertexC, 11); - const edgeDG = new GraphEdge(vertexD, vertexG, 10); - const edgeDF = new GraphEdge(vertexD, vertexF, 2); - const edgeFG = new GraphEdge(vertexF, vertexG, 3); - const edgeEG = new GraphEdge(vertexE, vertexG, 5); - - const graph = new Graph(); - - // Add vertices first just to have them in desired order. - graph - .addVertex(vertexA) - .addVertex(vertexB) - .addVertex(vertexC) - .addVertex(vertexD) - .addVertex(vertexE) - .addVertex(vertexF) - .addVertex(vertexG) - .addVertex(vertexH); - - // Now, when vertices are in correct order let's add edges. - graph - .addEdge(edgeAB) - .addEdge(edgeAE) - .addEdge(edgeAC) - .addEdge(edgeBC) - .addEdge(edgeBD) - .addEdge(edgeEC) - .addEdge(edgeED) - .addEdge(edgeDC) - .addEdge(edgeDG) - .addEdge(edgeDF) - .addEdge(edgeFG) - .addEdge(edgeEG); - - const { distances, nextVertices } = floydWarshall(graph); - - const vertices = graph.getAllVertices(); - - const vertexAIndex = vertices.indexOf(vertexA); - const vertexBIndex = vertices.indexOf(vertexB); - const vertexCIndex = vertices.indexOf(vertexC); - const vertexDIndex = vertices.indexOf(vertexD); - const vertexEIndex = vertices.indexOf(vertexE); - const vertexFIndex = vertices.indexOf(vertexF); - const vertexGIndex = vertices.indexOf(vertexG); - const vertexHIndex = vertices.indexOf(vertexH); - - expect(distances[vertexAIndex][vertexHIndex]).toBe(Infinity); - expect(distances[vertexAIndex][vertexAIndex]).toBe(0); - expect(distances[vertexAIndex][vertexBIndex]).toBe(4); - expect(distances[vertexAIndex][vertexEIndex]).toBe(7); - expect(distances[vertexAIndex][vertexCIndex]).toBe(3); - expect(distances[vertexAIndex][vertexDIndex]).toBe(9); - expect(distances[vertexAIndex][vertexGIndex]).toBe(12); - expect(distances[vertexAIndex][vertexFIndex]).toBe(11); - - expect(nextVertices[vertexAIndex][vertexFIndex]).toBe(vertexD); - expect(nextVertices[vertexAIndex][vertexDIndex]).toBe(vertexB); - expect(nextVertices[vertexAIndex][vertexBIndex]).toBe(vertexA); - expect(nextVertices[vertexAIndex][vertexGIndex]).toBe(vertexE); - expect(nextVertices[vertexAIndex][vertexCIndex]).toBe(vertexA); - expect(nextVertices[vertexAIndex][vertexAIndex]).toBe(null); - expect(nextVertices[vertexAIndex][vertexHIndex]).toBe(null); - }); - - it('should find minimum paths to all vertices for directed graph', () => { - const vertexA = new GraphVertex('A'); - const vertexB = new GraphVertex('B'); - const vertexC = new GraphVertex('C'); - const vertexD = new GraphVertex('D'); - - const edgeAB = new GraphEdge(vertexA, vertexB, 3); - const edgeBA = new GraphEdge(vertexB, vertexA, 8); - const edgeAD = new GraphEdge(vertexA, vertexD, 7); - const edgeDA = new GraphEdge(vertexD, vertexA, 2); - const edgeBC = new GraphEdge(vertexB, vertexC, 2); - const edgeCA = new GraphEdge(vertexC, vertexA, 5); - const edgeCD = new GraphEdge(vertexC, vertexD, 1); - - const graph = new Graph(true); - - // Add vertices first just to have them in desired order. - graph - .addVertex(vertexA) - .addVertex(vertexB) - .addVertex(vertexC) - .addVertex(vertexD); - - // Now, when vertices are in correct order let's add edges. - graph - .addEdge(edgeAB) - .addEdge(edgeBA) - .addEdge(edgeAD) - .addEdge(edgeDA) - .addEdge(edgeBC) - .addEdge(edgeCA) - .addEdge(edgeCD); - - const { distances, nextVertices } = floydWarshall(graph); - - const vertices = graph.getAllVertices(); - - const vertexAIndex = vertices.indexOf(vertexA); - const vertexBIndex = vertices.indexOf(vertexB); - const vertexCIndex = vertices.indexOf(vertexC); - const vertexDIndex = vertices.indexOf(vertexD); - - expect(distances[vertexAIndex][vertexAIndex]).toBe(0); - expect(distances[vertexAIndex][vertexBIndex]).toBe(3); - expect(distances[vertexAIndex][vertexCIndex]).toBe(5); - expect(distances[vertexAIndex][vertexDIndex]).toBe(6); - - expect(distances).toEqual([ - [0, 3, 5, 6], - [5, 0, 2, 3], - [3, 6, 0, 1], - [2, 5, 7, 0], - ]); - - expect(nextVertices[vertexAIndex][vertexDIndex]).toBe(vertexC); - expect(nextVertices[vertexAIndex][vertexCIndex]).toBe(vertexB); - expect(nextVertices[vertexBIndex][vertexDIndex]).toBe(vertexC); - expect(nextVertices[vertexAIndex][vertexAIndex]).toBe(null); - expect(nextVertices[vertexAIndex][vertexBIndex]).toBe(vertexA); - }); - - it('should find minimum paths to all vertices for directed graph with negative edge weights', () => { - const vertexA = new GraphVertex('A'); - const vertexB = new GraphVertex('B'); - const vertexC = new GraphVertex('C'); - const vertexD = new GraphVertex('D'); - const vertexE = new GraphVertex('E'); - const vertexF = new GraphVertex('F'); - const vertexG = new GraphVertex('G'); - - const edgeFE = new GraphEdge(vertexF, vertexE, 8); - const edgeFA = new GraphEdge(vertexF, vertexA, 10); - const edgeED = new GraphEdge(vertexE, vertexD, 1); - const edgeDA = new GraphEdge(vertexD, vertexA, -4); - const edgeDC = new GraphEdge(vertexD, vertexC, -1); - const edgeAC = new GraphEdge(vertexA, vertexC, 2); - const edgeCB = new GraphEdge(vertexC, vertexB, -2); - const edgeBA = new GraphEdge(vertexB, vertexA, 1); - - const graph = new Graph(true); - - // Add vertices first just to have them in desired order. - graph - .addVertex(vertexA) - .addVertex(vertexB) - .addVertex(vertexC) - .addVertex(vertexD) - .addVertex(vertexE) - .addVertex(vertexF) - .addVertex(vertexG); - - // Now, when vertices are in correct order let's add edges. - graph - .addEdge(edgeFE) - .addEdge(edgeFA) - .addEdge(edgeED) - .addEdge(edgeDA) - .addEdge(edgeDC) - .addEdge(edgeAC) - .addEdge(edgeCB) - .addEdge(edgeBA); - - const { distances, nextVertices } = floydWarshall(graph); - - const vertices = graph.getAllVertices(); - - const vertexAIndex = vertices.indexOf(vertexA); - const vertexBIndex = vertices.indexOf(vertexB); - const vertexCIndex = vertices.indexOf(vertexC); - const vertexDIndex = vertices.indexOf(vertexD); - const vertexEIndex = vertices.indexOf(vertexE); - const vertexGIndex = vertices.indexOf(vertexG); - const vertexFIndex = vertices.indexOf(vertexF); - - expect(distances[vertexFIndex][vertexGIndex]).toBe(Infinity); - expect(distances[vertexFIndex][vertexFIndex]).toBe(0); - expect(distances[vertexFIndex][vertexAIndex]).toBe(5); - expect(distances[vertexFIndex][vertexBIndex]).toBe(5); - expect(distances[vertexFIndex][vertexCIndex]).toBe(7); - expect(distances[vertexFIndex][vertexDIndex]).toBe(9); - expect(distances[vertexFIndex][vertexEIndex]).toBe(8); - - expect(nextVertices[vertexFIndex][vertexGIndex]).toBe(null); - expect(nextVertices[vertexFIndex][vertexFIndex]).toBe(null); - expect(nextVertices[vertexAIndex][vertexBIndex]).toBe(vertexC); - expect(nextVertices[vertexAIndex][vertexCIndex]).toBe(vertexA); - expect(nextVertices[vertexFIndex][vertexBIndex]).toBe(vertexE); - expect(nextVertices[vertexEIndex][vertexBIndex]).toBe(vertexD); - expect(nextVertices[vertexDIndex][vertexBIndex]).toBe(vertexC); - expect(nextVertices[vertexCIndex][vertexBIndex]).toBe(vertexC); - }); -}); diff --git a/src/algorithms/graph/floyd-warshall/floydWarshall.js b/src/algorithms/graph/floyd-warshall/floydWarshall.js deleted file mode 100644 index 870d78a6e8..0000000000 --- a/src/algorithms/graph/floyd-warshall/floydWarshall.js +++ /dev/null @@ -1,72 +0,0 @@ -/** - * @param {Graph} graph - * @return {{distances: number[][], nextVertices: GraphVertex[][]}} - */ -export default function floydWarshall(graph) { - // Get all graph vertices. - const vertices = graph.getAllVertices(); - - // Init previous vertices matrix with nulls meaning that there are no - // previous vertices exist that will give us shortest path. - const nextVertices = Array(vertices.length).fill(null).map(() => { - return Array(vertices.length).fill(null); - }); - - // Init distances matrix with Infinities meaning there are no paths - // between vertices exist so far. - const distances = Array(vertices.length).fill(null).map(() => { - return Array(vertices.length).fill(Infinity); - }); - - // Init distance matrix with the distance we already now (from existing edges). - // And also init previous vertices from the edges. - vertices.forEach((startVertex, startIndex) => { - vertices.forEach((endVertex, endIndex) => { - if (startVertex === endVertex) { - // Distance to the vertex itself is 0. - distances[startIndex][endIndex] = 0; - } else { - // Find edge between the start and end vertices. - const edge = graph.findEdge(startVertex, endVertex); - - if (edge) { - // There is an edge from vertex with startIndex to vertex with endIndex. - // Save distance and previous vertex. - distances[startIndex][endIndex] = edge.weight; - nextVertices[startIndex][endIndex] = startVertex; - } else { - distances[startIndex][endIndex] = Infinity; - } - } - }); - }); - - // Now let's go to the core of the algorithm. - // Let's all pair of vertices (from start to end ones) and try to check if there - // is a shorter path exists between them via middle vertex. Middle vertex may also - // be one of the graph vertices. As you may see now we're going to have three - // loops over all graph vertices: for start, end and middle vertices. - vertices.forEach((middleVertex, middleIndex) => { - // Path starts from startVertex with startIndex. - vertices.forEach((startVertex, startIndex) => { - // Path ends to endVertex with endIndex. - vertices.forEach((endVertex, endIndex) => { - // Compare existing distance from startVertex to endVertex, with distance - // from startVertex to endVertex but via middleVertex. - // Save the shortest distance and previous vertex that allows - // us to have this shortest distance. - const distViaMiddle = distances[startIndex][middleIndex] + distances[middleIndex][endIndex]; - - if (distances[startIndex][endIndex] > distViaMiddle) { - // We've found a shortest pass via middle vertex. - distances[startIndex][endIndex] = distViaMiddle; - nextVertices[startIndex][endIndex] = middleVertex; - } - }); - }); - }); - - // Shortest distance from x to y: distance[x][y]. - // Next vertex after x one in path from x to y: nextVertices[x][y]. - return { distances, nextVertices }; -} diff --git a/src/algorithms/graph/hamiltonian-cycle/README.md b/src/algorithms/graph/hamiltonian-cycle/README.md deleted file mode 100644 index ccd15481ba..0000000000 --- a/src/algorithms/graph/hamiltonian-cycle/README.md +++ /dev/null @@ -1,48 +0,0 @@ -# Hamiltonian Path - -**Hamiltonian path** (or **traceable path**) is a path in an -undirected or directed graph that visits each vertex exactly once. -A **Hamiltonian cycle** (or **Hamiltonian circuit**) is a -Hamiltonian path that is a cycle. Determining whether such paths -and cycles exist in graphs is the **Hamiltonian path problem**. - -![Hamiltonian cycle](https://upload.wikimedia.org/wikipedia/commons/6/6c/Hamiltonian_path_3d.svg) - -One possible Hamiltonian cycle through every vertex of a -dodecahedron is shown in red – like all platonic solids, the -dodecahedron is Hamiltonian. - -## Naive Algorithm - -Generate all possible configurations of vertices and print a -configuration that satisfies the given constraints. There -will be `n!` (n factorial) configurations. - -``` -while there are untried configurations -{ - generate the next configuration - if ( there are edges between two consecutive vertices of this - configuration and there is an edge from the last vertex to - the first ). - { - print this configuration; - break; - } -} -``` - -## Backtracking Algorithm - -Create an empty path array and add vertex `0` to it. Add other -vertices, starting from the vertex `1`. Before adding a vertex, -check for whether it is adjacent to the previously added vertex -and not already added. If we find such a vertex, we add the -vertex as part of the solution. If we do not find a vertex -then we return false. - -## References - -- [Hamiltonian path on Wikipedia](https://en.wikipedia.org/wiki/Hamiltonian_path) -- [Hamiltonian path on YouTube](https://www.youtube.com/watch?v=dQr4wZCiJJ4&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8) -- [Hamiltonian cycle on GeeksForGeeks](https://www.geeksforgeeks.org/backtracking-set-7-hamiltonian-cycle/) diff --git a/src/algorithms/graph/hamiltonian-cycle/__test__/hamiltonianCycle.test.js b/src/algorithms/graph/hamiltonian-cycle/__test__/hamiltonianCycle.test.js deleted file mode 100644 index eab0d333dc..0000000000 --- a/src/algorithms/graph/hamiltonian-cycle/__test__/hamiltonianCycle.test.js +++ /dev/null @@ -1,90 +0,0 @@ -import GraphVertex from '../../../../data-structures/graph/GraphVertex'; -import GraphEdge from '../../../../data-structures/graph/GraphEdge'; -import Graph from '../../../../data-structures/graph/Graph'; -import hamiltonianCycle from '../hamiltonianCycle'; - -describe('hamiltonianCycle', () => { - it('should find hamiltonian paths in graph', () => { - const vertexA = new GraphVertex('A'); - const vertexB = new GraphVertex('B'); - const vertexC = new GraphVertex('C'); - const vertexD = new GraphVertex('D'); - const vertexE = new GraphVertex('E'); - - const edgeAB = new GraphEdge(vertexA, vertexB); - const edgeAE = new GraphEdge(vertexA, vertexE); - const edgeAC = new GraphEdge(vertexA, vertexC); - const edgeBE = new GraphEdge(vertexB, vertexE); - const edgeBC = new GraphEdge(vertexB, vertexC); - const edgeBD = new GraphEdge(vertexB, vertexD); - const edgeCD = new GraphEdge(vertexC, vertexD); - const edgeDE = new GraphEdge(vertexD, vertexE); - - const graph = new Graph(); - graph - .addEdge(edgeAB) - .addEdge(edgeAE) - .addEdge(edgeAC) - .addEdge(edgeBE) - .addEdge(edgeBC) - .addEdge(edgeBD) - .addEdge(edgeCD) - .addEdge(edgeDE); - - const hamiltonianCycleSet = hamiltonianCycle(graph); - - expect(hamiltonianCycleSet.length).toBe(8); - - expect(hamiltonianCycleSet[0][0].getKey()).toBe(vertexA.getKey()); - expect(hamiltonianCycleSet[0][1].getKey()).toBe(vertexB.getKey()); - expect(hamiltonianCycleSet[0][2].getKey()).toBe(vertexE.getKey()); - expect(hamiltonianCycleSet[0][3].getKey()).toBe(vertexD.getKey()); - expect(hamiltonianCycleSet[0][4].getKey()).toBe(vertexC.getKey()); - - expect(hamiltonianCycleSet[1][0].getKey()).toBe(vertexA.getKey()); - expect(hamiltonianCycleSet[1][1].getKey()).toBe(vertexB.getKey()); - expect(hamiltonianCycleSet[1][2].getKey()).toBe(vertexC.getKey()); - expect(hamiltonianCycleSet[1][3].getKey()).toBe(vertexD.getKey()); - expect(hamiltonianCycleSet[1][4].getKey()).toBe(vertexE.getKey()); - - expect(hamiltonianCycleSet[2][0].getKey()).toBe(vertexA.getKey()); - expect(hamiltonianCycleSet[2][1].getKey()).toBe(vertexE.getKey()); - expect(hamiltonianCycleSet[2][2].getKey()).toBe(vertexB.getKey()); - expect(hamiltonianCycleSet[2][3].getKey()).toBe(vertexD.getKey()); - expect(hamiltonianCycleSet[2][4].getKey()).toBe(vertexC.getKey()); - - expect(hamiltonianCycleSet[3][0].getKey()).toBe(vertexA.getKey()); - expect(hamiltonianCycleSet[3][1].getKey()).toBe(vertexE.getKey()); - expect(hamiltonianCycleSet[3][2].getKey()).toBe(vertexD.getKey()); - expect(hamiltonianCycleSet[3][3].getKey()).toBe(vertexB.getKey()); - expect(hamiltonianCycleSet[3][4].getKey()).toBe(vertexC.getKey()); - }); - - it('should return false for graph without Hamiltonian path', () => { - const vertexA = new GraphVertex('A'); - const vertexB = new GraphVertex('B'); - const vertexC = new GraphVertex('C'); - const vertexD = new GraphVertex('D'); - const vertexE = new GraphVertex('E'); - - const edgeAB = new GraphEdge(vertexA, vertexB); - const edgeAE = new GraphEdge(vertexA, vertexE); - const edgeBE = new GraphEdge(vertexB, vertexE); - const edgeBC = new GraphEdge(vertexB, vertexC); - const edgeBD = new GraphEdge(vertexB, vertexD); - const edgeCD = new GraphEdge(vertexC, vertexD); - - const graph = new Graph(); - graph - .addEdge(edgeAB) - .addEdge(edgeAE) - .addEdge(edgeBE) - .addEdge(edgeBC) - .addEdge(edgeBD) - .addEdge(edgeCD); - - const hamiltonianCycleSet = hamiltonianCycle(graph); - - expect(hamiltonianCycleSet.length).toBe(0); - }); -}); diff --git a/src/algorithms/graph/hamiltonian-cycle/hamiltonianCycle.js b/src/algorithms/graph/hamiltonian-cycle/hamiltonianCycle.js deleted file mode 100644 index 2a33bf7d69..0000000000 --- a/src/algorithms/graph/hamiltonian-cycle/hamiltonianCycle.js +++ /dev/null @@ -1,134 +0,0 @@ -import GraphVertex from '../../../data-structures/graph/GraphVertex'; - -/** - * @param {number[][]} adjacencyMatrix - * @param {object} verticesIndices - * @param {GraphVertex[]} cycle - * @param {GraphVertex} vertexCandidate - * @return {boolean} - */ -function isSafe(adjacencyMatrix, verticesIndices, cycle, vertexCandidate) { - const endVertex = cycle[cycle.length - 1]; - - // Get end and candidate vertices indices in adjacency matrix. - const candidateVertexAdjacencyIndex = verticesIndices[vertexCandidate.getKey()]; - const endVertexAdjacencyIndex = verticesIndices[endVertex.getKey()]; - - // Check if last vertex in the path and candidate vertex are adjacent. - if (adjacencyMatrix[endVertexAdjacencyIndex][candidateVertexAdjacencyIndex] === Infinity) { - return false; - } - - // Check if vertexCandidate is being added to the path for the first time. - const candidateDuplicate = cycle.find((vertex) => vertex.getKey() === vertexCandidate.getKey()); - - return !candidateDuplicate; -} - -/** - * @param {number[][]} adjacencyMatrix - * @param {object} verticesIndices - * @param {GraphVertex[]} cycle - * @return {boolean} - */ -function isCycle(adjacencyMatrix, verticesIndices, cycle) { - // Check if first and last vertices in hamiltonian path are adjacent. - - // Get start and end vertices from the path. - const startVertex = cycle[0]; - const endVertex = cycle[cycle.length - 1]; - - // Get start/end vertices indices in adjacency matrix. - const startVertexAdjacencyIndex = verticesIndices[startVertex.getKey()]; - const endVertexAdjacencyIndex = verticesIndices[endVertex.getKey()]; - - // Check if we can go from end vertex to the start one. - return adjacencyMatrix[endVertexAdjacencyIndex][startVertexAdjacencyIndex] !== Infinity; -} - -/** - * @param {number[][]} adjacencyMatrix - * @param {GraphVertex[]} vertices - * @param {object} verticesIndices - * @param {GraphVertex[][]} cycles - * @param {GraphVertex[]} cycle - */ -function hamiltonianCycleRecursive({ - adjacencyMatrix, - vertices, - verticesIndices, - cycles, - cycle, -}) { - // Clone cycle in order to prevent it from modification by other DFS branches. - const currentCycle = [...cycle].map((vertex) => new GraphVertex(vertex.value)); - - if (vertices.length === currentCycle.length) { - // Hamiltonian path is found. - // Now we need to check if it is cycle or not. - if (isCycle(adjacencyMatrix, verticesIndices, currentCycle)) { - // Another solution has been found. Save it. - cycles.push(currentCycle); - } - return; - } - - for (let vertexIndex = 0; vertexIndex < vertices.length; vertexIndex += 1) { - // Get vertex candidate that we will try to put into next path step and see if it fits. - const vertexCandidate = vertices[vertexIndex]; - - // Check if it is safe to put vertex candidate to cycle. - if (isSafe(adjacencyMatrix, verticesIndices, currentCycle, vertexCandidate)) { - // Add candidate vertex to cycle path. - currentCycle.push(vertexCandidate); - - // Try to find other vertices in cycle. - hamiltonianCycleRecursive({ - adjacencyMatrix, - vertices, - verticesIndices, - cycles, - cycle: currentCycle, - }); - - // BACKTRACKING. - // Remove candidate vertex from cycle path in order to try another one. - currentCycle.pop(); - } - } -} - -/** - * @param {Graph} graph - * @return {GraphVertex[][]} - */ -export default function hamiltonianCycle(graph) { - // Gather some information about the graph that we will need to during - // the problem solving. - const verticesIndices = graph.getVerticesIndices(); - const adjacencyMatrix = graph.getAdjacencyMatrix(); - const vertices = graph.getAllVertices(); - - // Define start vertex. We will always pick the first one - // this it doesn't matter which vertex to pick in a cycle. - // Every vertex is in a cycle so we can start from any of them. - const startVertex = vertices[0]; - - // Init cycles array that will hold all solutions. - const cycles = []; - - // Init cycle array that will hold current cycle path. - const cycle = [startVertex]; - - // Try to find cycles recursively in Depth First Search order. - hamiltonianCycleRecursive({ - adjacencyMatrix, - vertices, - verticesIndices, - cycles, - cycle, - }); - - // Return found cycles. - return cycles; -} diff --git a/src/algorithms/graph/kruskal/README.ko-KR.md b/src/algorithms/graph/kruskal/README.ko-KR.md deleted file mode 100644 index eefb6a6756..0000000000 --- a/src/algorithms/graph/kruskal/README.ko-KR.md +++ /dev/null @@ -1,29 +0,0 @@ -# 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 deleted file mode 100644 index 1a71390e2f..0000000000 --- a/src/algorithms/graph/kruskal/README.md +++ /dev/null @@ -1,52 +0,0 @@ -# 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 -as it finds a minimum spanning tree for a connected weighted -graph adding increasing cost arcs at each step. This means it -finds a subset of the edges that forms a tree that includes every -vertex, where the total weight of all the edges in the tree is -minimized. If the graph is not connected, then it finds a -minimum spanning forest (a minimum spanning tree for each -connected component). - -![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) - -A demo for Kruskal's algorithm based on Euclidean distance. - -## Minimum Spanning Tree - -A **minimum spanning tree** (MST) or minimum weight spanning tree -is a subset of the edges of a connected, edge-weighted -(un)directed graph that connects all the vertices together, -without any cycles and with the minimum possible total edge -weight. That is, it is a spanning tree whose sum of edge weights -is as small as possible. More generally, any edge-weighted -undirected graph (not necessarily connected) has a minimum -spanning forest, which is a union of the minimum spanning -trees for its connected components. - -![Minimum Spanning Tree](https://upload.wikimedia.org/wikipedia/commons/d/d2/Minimum_spanning_tree.svg) - -A planar graph and its minimum spanning tree. Each edge is -labeled with its weight, which here is roughly proportional -to its length. - -![Minimum Spanning Tree](https://upload.wikimedia.org/wikipedia/commons/c/c9/Multiple_minimum_spanning_trees.svg) - -This figure shows there may be more than one minimum spanning -tree in a graph. In the figure, the two trees below the graph -are two possibilities of minimum spanning tree of the given graph. - -## References - -- [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/__test__/kruskal.test.js b/src/algorithms/graph/kruskal/__test__/kruskal.test.js deleted file mode 100644 index da71d13740..0000000000 --- a/src/algorithms/graph/kruskal/__test__/kruskal.test.js +++ /dev/null @@ -1,91 +0,0 @@ -import GraphVertex from '../../../../data-structures/graph/GraphVertex'; -import GraphEdge from '../../../../data-structures/graph/GraphEdge'; -import Graph from '../../../../data-structures/graph/Graph'; -import kruskal from '../kruskal'; - -describe('kruskal', () => { - it('should fire an error for directed graph', () => { - function applyPrimToDirectedGraph() { - const graph = new Graph(true); - - kruskal(graph); - } - - expect(applyPrimToDirectedGraph).toThrowError(); - }); - - it('should find minimum spanning tree', () => { - const vertexA = new GraphVertex('A'); - const vertexB = new GraphVertex('B'); - const vertexC = new GraphVertex('C'); - const vertexD = new GraphVertex('D'); - const vertexE = new GraphVertex('E'); - const vertexF = new GraphVertex('F'); - const vertexG = new GraphVertex('G'); - - const edgeAB = new GraphEdge(vertexA, vertexB, 2); - const edgeAD = new GraphEdge(vertexA, vertexD, 3); - const edgeAC = new GraphEdge(vertexA, vertexC, 3); - const edgeBC = new GraphEdge(vertexB, vertexC, 4); - const edgeBE = new GraphEdge(vertexB, vertexE, 3); - const edgeDF = new GraphEdge(vertexD, vertexF, 7); - const edgeEC = new GraphEdge(vertexE, vertexC, 1); - const edgeEF = new GraphEdge(vertexE, vertexF, 8); - const edgeFG = new GraphEdge(vertexF, vertexG, 9); - const edgeFC = new GraphEdge(vertexF, vertexC, 6); - - const graph = new Graph(); - - graph - .addEdge(edgeAB) - .addEdge(edgeAD) - .addEdge(edgeAC) - .addEdge(edgeBC) - .addEdge(edgeBE) - .addEdge(edgeDF) - .addEdge(edgeEC) - .addEdge(edgeEF) - .addEdge(edgeFC) - .addEdge(edgeFG); - - expect(graph.getWeight()).toEqual(46); - - const minimumSpanningTree = kruskal(graph); - - expect(minimumSpanningTree.getWeight()).toBe(24); - expect(minimumSpanningTree.getAllVertices().length).toBe(graph.getAllVertices().length); - expect(minimumSpanningTree.getAllEdges().length).toBe(graph.getAllVertices().length - 1); - expect(minimumSpanningTree.toString()).toBe('E,C,A,B,D,F,G'); - }); - - it('should find minimum spanning tree for simple graph', () => { - const vertexA = new GraphVertex('A'); - const vertexB = new GraphVertex('B'); - const vertexC = new GraphVertex('C'); - const vertexD = new GraphVertex('D'); - - const edgeAB = new GraphEdge(vertexA, vertexB, 1); - const edgeAD = new GraphEdge(vertexA, vertexD, 3); - const edgeBC = new GraphEdge(vertexB, vertexC, 1); - const edgeBD = new GraphEdge(vertexB, vertexD, 3); - const edgeCD = new GraphEdge(vertexC, vertexD, 1); - - const graph = new Graph(); - - graph - .addEdge(edgeAB) - .addEdge(edgeAD) - .addEdge(edgeBC) - .addEdge(edgeBD) - .addEdge(edgeCD); - - expect(graph.getWeight()).toEqual(9); - - const minimumSpanningTree = kruskal(graph); - - expect(minimumSpanningTree.getWeight()).toBe(3); - expect(minimumSpanningTree.getAllVertices().length).toBe(graph.getAllVertices().length); - expect(minimumSpanningTree.getAllEdges().length).toBe(graph.getAllVertices().length - 1); - expect(minimumSpanningTree.toString()).toBe('A,B,C,D'); - }); -}); diff --git a/src/algorithms/graph/kruskal/kruskal.js b/src/algorithms/graph/kruskal/kruskal.js deleted file mode 100644 index 296616a142..0000000000 --- a/src/algorithms/graph/kruskal/kruskal.js +++ /dev/null @@ -1,62 +0,0 @@ -import Graph from '../../../data-structures/graph/Graph'; -import QuickSort from '../../sorting/quick-sort/QuickSort'; -import DisjointSet from '../../../data-structures/disjoint-set/DisjointSet'; - -/** - * @param {Graph} graph - * @return {Graph} - */ -export default function kruskal(graph) { - // It should fire error if graph is directed since the algorithm works only - // for undirected graphs. - if (graph.isDirected) { - throw new Error('Kruskal\'s algorithms works only for undirected graphs'); - } - - // Init new graph that will contain minimum spanning tree of original graph. - const minimumSpanningTree = new Graph(); - - // Sort all graph edges in increasing order. - const sortingCallbacks = { - /** - * @param {GraphEdge} graphEdgeA - * @param {GraphEdge} graphEdgeB - */ - compareCallback: (graphEdgeA, graphEdgeB) => { - if (graphEdgeA.weight === graphEdgeB.weight) { - return 1; - } - - return graphEdgeA.weight <= graphEdgeB.weight ? -1 : 1; - }, - }; - const sortedEdges = new QuickSort(sortingCallbacks).sort(graph.getAllEdges()); - - // Create disjoint sets for all graph vertices. - const keyCallback = (graphVertex) => graphVertex.getKey(); - const disjointSet = new DisjointSet(keyCallback); - - graph.getAllVertices().forEach((graphVertex) => { - disjointSet.makeSet(graphVertex); - }); - - // Go through all edges started from the minimum one and try to add them - // to minimum spanning tree. The criteria of adding the edge would be whether - // it is forms the cycle or not (if it connects two vertices from one disjoint - // set or not). - for (let edgeIndex = 0; edgeIndex < sortedEdges.length; edgeIndex += 1) { - /** @var {GraphEdge} currentEdge */ - const currentEdge = sortedEdges[edgeIndex]; - - // Check if edge forms the cycle. If it does then skip it. - if (!disjointSet.inSameSet(currentEdge.startVertex, currentEdge.endVertex)) { - // Unite two subsets into one. - disjointSet.union(currentEdge.startVertex, currentEdge.endVertex); - - // Add this edge to spanning tree. - minimumSpanningTree.addEdge(currentEdge); - } - } - - return minimumSpanningTree; -} diff --git a/src/algorithms/graph/prim/README.md b/src/algorithms/graph/prim/README.md deleted file mode 100644 index 49061a278e..0000000000 --- a/src/algorithms/graph/prim/README.md +++ /dev/null @@ -1,47 +0,0 @@ -# Prim's Algorithm - -In computer science, **Prim's algorithm** is a greedy algorithm that -finds a minimum spanning tree for a weighted undirected graph. - -The algorithm operates by building this tree one vertex at a -time, from an arbitrary starting vertex, at each step adding -the cheapest possible connection from the tree to another vertex. - -![Prim's Algorithm](https://upload.wikimedia.org/wikipedia/commons/f/f7/Prim%27s_algorithm.svg) - -Prim's algorithm starting at vertex `A`. In the third step, edges -`BD` and `AB` both have weight `2`, so `BD` is chosen arbitrarily. -After that step, `AB` is no longer a candidate for addition -to the tree because it links two nodes that are already -in the tree. - -## Minimum Spanning Tree - -A **minimum spanning tree** (MST) or minimum weight spanning tree -is a subset of the edges of a connected, edge-weighted -(un)directed graph that connects all the vertices together, -without any cycles and with the minimum possible total edge -weight. That is, it is a spanning tree whose sum of edge weights -is as small as possible. More generally, any edge-weighted -undirected graph (not necessarily connected) has a minimum -spanning forest, which is a union of the minimum spanning -trees for its connected components. - -![Minimum Spanning Tree](https://upload.wikimedia.org/wikipedia/commons/d/d2/Minimum_spanning_tree.svg) - -A planar graph and its minimum spanning tree. Each edge is -labeled with its weight, which here is roughly proportional -to its length. - -![Minimum Spanning Tree](https://upload.wikimedia.org/wikipedia/commons/c/c9/Multiple_minimum_spanning_trees.svg) - -This figure shows there may be more than one minimum spanning -tree in a graph. In the figure, the two trees below the graph -are two possibilities of minimum spanning tree of the given graph. - -## References - -- [Minimum Spanning Tree on Wikipedia](https://en.wikipedia.org/wiki/Minimum_spanning_tree) -- [Prim's Algorithm on Wikipedia](https://en.wikipedia.org/wiki/Prim%27s_algorithm) -- [Prim's Algorithm on YouTube by Tushar Roy](https://www.youtube.com/watch?v=oP2-8ysT3QQ&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8) -- [Prim's Algorithm on YouTube by Michael Sambol](https://www.youtube.com/watch?v=cplfcGZmX7I&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8) diff --git a/src/algorithms/graph/prim/__test__/prim.test.js b/src/algorithms/graph/prim/__test__/prim.test.js deleted file mode 100644 index ac608df875..0000000000 --- a/src/algorithms/graph/prim/__test__/prim.test.js +++ /dev/null @@ -1,91 +0,0 @@ -import GraphVertex from '../../../../data-structures/graph/GraphVertex'; -import GraphEdge from '../../../../data-structures/graph/GraphEdge'; -import Graph from '../../../../data-structures/graph/Graph'; -import prim from '../prim'; - -describe('prim', () => { - it('should fire an error for directed graph', () => { - function applyPrimToDirectedGraph() { - const graph = new Graph(true); - - prim(graph); - } - - expect(applyPrimToDirectedGraph).toThrowError(); - }); - - it('should find minimum spanning tree', () => { - const vertexA = new GraphVertex('A'); - const vertexB = new GraphVertex('B'); - const vertexC = new GraphVertex('C'); - const vertexD = new GraphVertex('D'); - const vertexE = new GraphVertex('E'); - const vertexF = new GraphVertex('F'); - const vertexG = new GraphVertex('G'); - - const edgeAB = new GraphEdge(vertexA, vertexB, 2); - const edgeAD = new GraphEdge(vertexA, vertexD, 3); - const edgeAC = new GraphEdge(vertexA, vertexC, 3); - const edgeBC = new GraphEdge(vertexB, vertexC, 4); - const edgeBE = new GraphEdge(vertexB, vertexE, 3); - const edgeDF = new GraphEdge(vertexD, vertexF, 7); - const edgeEC = new GraphEdge(vertexE, vertexC, 1); - const edgeEF = new GraphEdge(vertexE, vertexF, 8); - const edgeFG = new GraphEdge(vertexF, vertexG, 9); - const edgeFC = new GraphEdge(vertexF, vertexC, 6); - - const graph = new Graph(); - - graph - .addEdge(edgeAB) - .addEdge(edgeAD) - .addEdge(edgeAC) - .addEdge(edgeBC) - .addEdge(edgeBE) - .addEdge(edgeDF) - .addEdge(edgeEC) - .addEdge(edgeEF) - .addEdge(edgeFC) - .addEdge(edgeFG); - - expect(graph.getWeight()).toEqual(46); - - const minimumSpanningTree = prim(graph); - - expect(minimumSpanningTree.getWeight()).toBe(24); - expect(minimumSpanningTree.getAllVertices().length).toBe(graph.getAllVertices().length); - expect(minimumSpanningTree.getAllEdges().length).toBe(graph.getAllVertices().length - 1); - expect(minimumSpanningTree.toString()).toBe('A,B,C,E,D,F,G'); - }); - - it('should find minimum spanning tree for simple graph', () => { - const vertexA = new GraphVertex('A'); - const vertexB = new GraphVertex('B'); - const vertexC = new GraphVertex('C'); - const vertexD = new GraphVertex('D'); - - const edgeAB = new GraphEdge(vertexA, vertexB, 1); - const edgeAD = new GraphEdge(vertexA, vertexD, 3); - const edgeBC = new GraphEdge(vertexB, vertexC, 1); - const edgeBD = new GraphEdge(vertexB, vertexD, 3); - const edgeCD = new GraphEdge(vertexC, vertexD, 1); - - const graph = new Graph(); - - graph - .addEdge(edgeAB) - .addEdge(edgeAD) - .addEdge(edgeBC) - .addEdge(edgeBD) - .addEdge(edgeCD); - - expect(graph.getWeight()).toEqual(9); - - const minimumSpanningTree = prim(graph); - - expect(minimumSpanningTree.getWeight()).toBe(3); - expect(minimumSpanningTree.getAllVertices().length).toBe(graph.getAllVertices().length); - expect(minimumSpanningTree.getAllEdges().length).toBe(graph.getAllVertices().length - 1); - expect(minimumSpanningTree.toString()).toBe('A,B,C,D'); - }); -}); diff --git a/src/algorithms/graph/prim/prim.js b/src/algorithms/graph/prim/prim.js deleted file mode 100644 index 03b7a0b1b8..0000000000 --- a/src/algorithms/graph/prim/prim.js +++ /dev/null @@ -1,73 +0,0 @@ -import Graph from '../../../data-structures/graph/Graph'; -import PriorityQueue from '../../../data-structures/priority-queue/PriorityQueue'; - -/** - * @param {Graph} graph - * @return {Graph} - */ -export default function prim(graph) { - // It should fire error if graph is directed since the algorithm works only - // for undirected graphs. - if (graph.isDirected) { - throw new Error('Prim\'s algorithms works only for undirected graphs'); - } - - // Init new graph that will contain minimum spanning tree of original graph. - const minimumSpanningTree = new Graph(); - - // This priority queue will contain all the edges that are starting from - // visited nodes and they will be ranked by edge weight - so that on each step - // we would always pick the edge with minimal edge weight. - const edgesQueue = new PriorityQueue(); - - // Set of vertices that has been already visited. - const visitedVertices = {}; - - // Vertex from which we will start graph traversal. - const startVertex = graph.getAllVertices()[0]; - - // Add start vertex to the set of visited ones. - visitedVertices[startVertex.getKey()] = startVertex; - - // Add all edges of start vertex to the queue. - startVertex.getEdges().forEach((graphEdge) => { - edgesQueue.add(graphEdge, graphEdge.weight); - }); - - // Now let's explore all queued edges. - while (!edgesQueue.isEmpty()) { - // Fetch next queued edge with minimal weight. - /** @var {GraphEdge} currentEdge */ - const currentMinEdge = edgesQueue.poll(); - - // Find out the next unvisited minimal vertex to traverse. - let nextMinVertex = null; - if (!visitedVertices[currentMinEdge.startVertex.getKey()]) { - nextMinVertex = currentMinEdge.startVertex; - } else if (!visitedVertices[currentMinEdge.endVertex.getKey()]) { - nextMinVertex = currentMinEdge.endVertex; - } - - // If all vertices of current edge has been already visited then skip this round. - if (nextMinVertex) { - // Add current min edge to MST. - minimumSpanningTree.addEdge(currentMinEdge); - - // Add vertex to the set of visited ones. - visitedVertices[nextMinVertex.getKey()] = nextMinVertex; - - // Add all current vertex's edges to the queue. - nextMinVertex.getEdges().forEach((graphEdge) => { - // Add only vertices that link to unvisited nodes. - if ( - !visitedVertices[graphEdge.startVertex.getKey()] - || !visitedVertices[graphEdge.endVertex.getKey()] - ) { - edgesQueue.add(graphEdge, graphEdge.weight); - } - }); - } - } - - return minimumSpanningTree; -} diff --git a/src/algorithms/graph/strongly-connected-components/README.md b/src/algorithms/graph/strongly-connected-components/README.md deleted file mode 100644 index 74f23ce051..0000000000 --- a/src/algorithms/graph/strongly-connected-components/README.md +++ /dev/null @@ -1,16 +0,0 @@ -# Strongly Connected Component - -A directed graph is called **strongly connected** if there is a path -in each direction between each pair of vertices of the graph. -In a directed graph G that may not itself be strongly connected, -a pair of vertices `u` and `v` are said to be strongly connected -to each other if there is a path in each direction between them. - -![Strongly Connected](https://upload.wikimedia.org/wikipedia/commons/5/5c/Scc.png) - -Graph with strongly connected components marked - -## References - -- [Wikipedia](https://en.wikipedia.org/wiki/Strongly_connected_component) -- [YouTube](https://www.youtube.com/watch?v=RpgcYiky7uw&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8) diff --git a/src/algorithms/graph/strongly-connected-components/__test__/stronglyConnectedComponents.test.js b/src/algorithms/graph/strongly-connected-components/__test__/stronglyConnectedComponents.test.js deleted file mode 100644 index 3379ca75fb..0000000000 --- a/src/algorithms/graph/strongly-connected-components/__test__/stronglyConnectedComponents.test.js +++ /dev/null @@ -1,102 +0,0 @@ -import GraphVertex from '../../../../data-structures/graph/GraphVertex'; -import GraphEdge from '../../../../data-structures/graph/GraphEdge'; -import Graph from '../../../../data-structures/graph/Graph'; -import stronglyConnectedComponents from '../stronglyConnectedComponents'; - -describe('stronglyConnectedComponents', () => { - it('should detect strongly connected components in simple graph', () => { - const vertexA = new GraphVertex('A'); - const vertexB = new GraphVertex('B'); - const vertexC = new GraphVertex('C'); - const vertexD = new GraphVertex('D'); - - const edgeAB = new GraphEdge(vertexA, vertexB); - const edgeBC = new GraphEdge(vertexB, vertexC); - const edgeCA = new GraphEdge(vertexC, vertexA); - const edgeCD = new GraphEdge(vertexC, vertexD); - - const graph = new Graph(true); - - graph - .addEdge(edgeAB) - .addEdge(edgeBC) - .addEdge(edgeCA) - .addEdge(edgeCD); - - const components = stronglyConnectedComponents(graph); - - expect(components).toBeDefined(); - expect(components.length).toBe(2); - - expect(components[0][0].getKey()).toBe(vertexA.getKey()); - expect(components[0][1].getKey()).toBe(vertexC.getKey()); - expect(components[0][2].getKey()).toBe(vertexB.getKey()); - - expect(components[1][0].getKey()).toBe(vertexD.getKey()); - }); - - it('should detect strongly connected components in graph', () => { - const vertexA = new GraphVertex('A'); - const vertexB = new GraphVertex('B'); - const vertexC = new GraphVertex('C'); - const vertexD = new GraphVertex('D'); - const vertexE = new GraphVertex('E'); - const vertexF = new GraphVertex('F'); - const vertexG = new GraphVertex('G'); - const vertexH = new GraphVertex('H'); - const vertexI = new GraphVertex('I'); - const vertexJ = new GraphVertex('J'); - const vertexK = new GraphVertex('K'); - - const edgeAB = new GraphEdge(vertexA, vertexB); - const edgeBC = new GraphEdge(vertexB, vertexC); - const edgeCA = new GraphEdge(vertexC, vertexA); - const edgeBD = new GraphEdge(vertexB, vertexD); - const edgeDE = new GraphEdge(vertexD, vertexE); - const edgeEF = new GraphEdge(vertexE, vertexF); - const edgeFD = new GraphEdge(vertexF, vertexD); - const edgeGF = new GraphEdge(vertexG, vertexF); - const edgeGH = new GraphEdge(vertexG, vertexH); - const edgeHI = new GraphEdge(vertexH, vertexI); - const edgeIJ = new GraphEdge(vertexI, vertexJ); - const edgeJG = new GraphEdge(vertexJ, vertexG); - const edgeJK = new GraphEdge(vertexJ, vertexK); - - const graph = new Graph(true); - - graph - .addEdge(edgeAB) - .addEdge(edgeBC) - .addEdge(edgeCA) - .addEdge(edgeBD) - .addEdge(edgeDE) - .addEdge(edgeEF) - .addEdge(edgeFD) - .addEdge(edgeGF) - .addEdge(edgeGH) - .addEdge(edgeHI) - .addEdge(edgeIJ) - .addEdge(edgeJG) - .addEdge(edgeJK); - - const components = stronglyConnectedComponents(graph); - - expect(components).toBeDefined(); - expect(components.length).toBe(4); - - expect(components[0][0].getKey()).toBe(vertexG.getKey()); - expect(components[0][1].getKey()).toBe(vertexJ.getKey()); - expect(components[0][2].getKey()).toBe(vertexI.getKey()); - expect(components[0][3].getKey()).toBe(vertexH.getKey()); - - expect(components[1][0].getKey()).toBe(vertexK.getKey()); - - expect(components[2][0].getKey()).toBe(vertexA.getKey()); - expect(components[2][1].getKey()).toBe(vertexC.getKey()); - expect(components[2][2].getKey()).toBe(vertexB.getKey()); - - expect(components[3][0].getKey()).toBe(vertexD.getKey()); - expect(components[3][1].getKey()).toBe(vertexF.getKey()); - expect(components[3][2].getKey()).toBe(vertexE.getKey()); - }); -}); diff --git a/src/algorithms/graph/strongly-connected-components/stronglyConnectedComponents.js b/src/algorithms/graph/strongly-connected-components/stronglyConnectedComponents.js deleted file mode 100644 index 8096277356..0000000000 --- a/src/algorithms/graph/strongly-connected-components/stronglyConnectedComponents.js +++ /dev/null @@ -1,133 +0,0 @@ -import Stack from '../../../data-structures/stack/Stack'; -import depthFirstSearch from '../depth-first-search/depthFirstSearch'; - -/** - * @param {Graph} graph - * @return {Stack} - */ -function getVerticesSortedByDfsFinishTime(graph) { - // Set of all visited vertices during DFS pass. - const visitedVerticesSet = {}; - - // Stack of vertices by finish time. - // All vertices in this stack are ordered by finished time in decreasing order. - // Vertex that has been finished first will be at the bottom of the stack and - // vertex that has been finished last will be at the top of the stack. - const verticesByDfsFinishTime = new Stack(); - - // Set of all vertices we're going to visit. - const notVisitedVerticesSet = {}; - graph.getAllVertices().forEach((vertex) => { - notVisitedVerticesSet[vertex.getKey()] = vertex; - }); - - // Specify DFS traversal callbacks. - const dfsCallbacks = { - enterVertex: ({ currentVertex }) => { - // Add current vertex to visited set. - visitedVerticesSet[currentVertex.getKey()] = currentVertex; - - // Delete current vertex from not visited set. - delete notVisitedVerticesSet[currentVertex.getKey()]; - }, - leaveVertex: ({ currentVertex }) => { - // Push vertex to the stack when leaving it. - // This will make stack to be ordered by finish time in decreasing order. - verticesByDfsFinishTime.push(currentVertex); - }, - allowTraversal: ({ nextVertex }) => { - // Don't allow to traverse the nodes that have been already visited. - return !visitedVerticesSet[nextVertex.getKey()]; - }, - }; - - // Do FIRST DFS PASS traversal for all graph vertices to fill the verticesByFinishTime stack. - while (Object.values(notVisitedVerticesSet).length) { - // Peek any vertex to start DFS traversal from. - const startVertexKey = Object.keys(notVisitedVerticesSet)[0]; - const startVertex = notVisitedVerticesSet[startVertexKey]; - delete notVisitedVerticesSet[startVertexKey]; - - depthFirstSearch(graph, startVertex, dfsCallbacks); - } - - return verticesByDfsFinishTime; -} - -/** - * @param {Graph} graph - * @param {Stack} verticesByFinishTime - * @return {*[]} - */ -function getSCCSets(graph, verticesByFinishTime) { - // Array of arrays of strongly connected vertices. - const stronglyConnectedComponentsSets = []; - - // Array that will hold all vertices that are being visited during one DFS run. - let stronglyConnectedComponentsSet = []; - - // Visited vertices set. - const visitedVerticesSet = {}; - - // Callbacks for DFS traversal. - const dfsCallbacks = { - enterVertex: ({ currentVertex }) => { - // Add current vertex to SCC set of current DFS round. - stronglyConnectedComponentsSet.push(currentVertex); - - // Add current vertex to visited set. - visitedVerticesSet[currentVertex.getKey()] = currentVertex; - }, - leaveVertex: ({ previousVertex }) => { - // Once DFS traversal is finished push the set of found strongly connected - // components during current DFS round to overall strongly connected components set. - // The sign that traversal is about to be finished is that we came back to start vertex - // which doesn't have parent. - if (previousVertex === null) { - stronglyConnectedComponentsSets.push([...stronglyConnectedComponentsSet]); - } - }, - allowTraversal: ({ nextVertex }) => { - // Don't allow traversal of already visited vertices. - return !visitedVerticesSet[nextVertex.getKey()]; - }, - }; - - while (!verticesByFinishTime.isEmpty()) { - /** @var {GraphVertex} startVertex */ - const startVertex = verticesByFinishTime.pop(); - - // Reset the set of strongly connected vertices. - stronglyConnectedComponentsSet = []; - - // Don't do DFS on already visited vertices. - if (!visitedVerticesSet[startVertex.getKey()]) { - // Do DFS traversal. - depthFirstSearch(graph, startVertex, dfsCallbacks); - } - } - - return stronglyConnectedComponentsSets; -} - -/** - * Kosaraju's algorithm. - * - * @param {Graph} graph - * @return {*[]} - */ -export default function stronglyConnectedComponents(graph) { - // In this algorithm we will need to do TWO DFS PASSES overt the graph. - - // Get stack of vertices ordered by DFS finish time. - // All vertices in this stack are ordered by finished time in decreasing order: - // Vertex that has been finished first will be at the bottom of the stack and - // vertex that has been finished last will be at the top of the stack. - const verticesByFinishTime = getVerticesSortedByDfsFinishTime(graph); - - // Reverse the graph. - graph.reverse(); - - // Do DFS once again on reversed graph. - return getSCCSets(graph, verticesByFinishTime); -} diff --git a/src/algorithms/graph/topological-sorting/README.md b/src/algorithms/graph/topological-sorting/README.md deleted file mode 100644 index f4653a8b1e..0000000000 --- a/src/algorithms/graph/topological-sorting/README.md +++ /dev/null @@ -1,55 +0,0 @@ -# Topological Sorting - -In the field of computer science, a topological sort or -topological ordering of a directed graph is a linear ordering -of its vertices such that for every directed edge `uv` from -vertex `u` to vertex `v`, `u` comes before `v` in the ordering. - -For instance, the vertices of the graph may represent tasks to -be performed, and the edges may represent constraints that one -task must be performed before another; in this application, a -topological ordering is just a valid sequence for the tasks. - -A topological ordering is possible if and only if the graph has -no directed cycles, that is, if it is a [directed acyclic graph](https://en.wikipedia.org/wiki/Directed_acyclic_graph) -(DAG). Any DAG has at least one topological ordering, and algorithms are -known for constructing a topological ordering of any DAG in linear time. - -![Directed Acyclic Graph](https://upload.wikimedia.org/wikipedia/commons/c/c6/Topological_Ordering.svg) - -A topological ordering of a directed acyclic graph: every edge goes from -earlier in the ordering (upper left) to later in the ordering (lower right). -A directed graph is acyclic if and only if it has a topological ordering. - -## Example - -![Topologic Sorting](https://upload.wikimedia.org/wikipedia/commons/0/03/Directed_acyclic_graph_2.svg) - -The graph shown above has many valid topological sorts, including: - -- `5, 7, 3, 11, 8, 2, 9, 10` (visual left-to-right, top-to-bottom) -- `3, 5, 7, 8, 11, 2, 9, 10` (smallest-numbered available vertex first) -- `5, 7, 3, 8, 11, 10, 9, 2` (fewest edges first) -- `7, 5, 11, 3, 10, 8, 9, 2` (largest-numbered available vertex first) -- `5, 7, 11, 2, 3, 8, 9, 10` (attempting top-to-bottom, left-to-right) -- `3, 7, 8, 5, 11, 10, 2, 9` (arbitrary) - -## Application - -The canonical application of topological sorting is in -**scheduling a sequence of jobs** or tasks based on their dependencies. The jobs -are represented by vertices, and there is an edge from `x` to `y` if -job `x` must be completed before job `y` can be started (for -example, when washing clothes, the washing machine must finish -before we put the clothes in the dryer). Then, a topological sort -gives an order in which to perform the jobs. - -Other application is **dependency resolution**. Each vertex is a package -and each edge is a dependency of package `a` on package 'b'. Then topological -sorting will provide a sequence of installing dependencies in a way that every -next dependency has its dependent packages to be installed in prior. - -## References - -- [Wikipedia](https://en.wikipedia.org/wiki/Topological_sorting) -- [Topological Sorting on YouTube by Tushar Roy](https://www.youtube.com/watch?v=ddTC4Zovtbc&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8) diff --git a/src/algorithms/graph/topological-sorting/__test__/topologicalSort.test.js b/src/algorithms/graph/topological-sorting/__test__/topologicalSort.test.js deleted file mode 100644 index e2904cfb3d..0000000000 --- a/src/algorithms/graph/topological-sorting/__test__/topologicalSort.test.js +++ /dev/null @@ -1,53 +0,0 @@ -import GraphVertex from '../../../../data-structures/graph/GraphVertex'; -import GraphEdge from '../../../../data-structures/graph/GraphEdge'; -import Graph from '../../../../data-structures/graph/Graph'; -import topologicalSort from '../topologicalSort'; - -describe('topologicalSort', () => { - it('should do topological sorting on graph', () => { - const vertexA = new GraphVertex('A'); - const vertexB = new GraphVertex('B'); - const vertexC = new GraphVertex('C'); - const vertexD = new GraphVertex('D'); - const vertexE = new GraphVertex('E'); - const vertexF = new GraphVertex('F'); - const vertexG = new GraphVertex('G'); - const vertexH = new GraphVertex('H'); - - const edgeAC = new GraphEdge(vertexA, vertexC); - const edgeBC = new GraphEdge(vertexB, vertexC); - const edgeBD = new GraphEdge(vertexB, vertexD); - const edgeCE = new GraphEdge(vertexC, vertexE); - const edgeDF = new GraphEdge(vertexD, vertexF); - const edgeEF = new GraphEdge(vertexE, vertexF); - const edgeEH = new GraphEdge(vertexE, vertexH); - const edgeFG = new GraphEdge(vertexF, vertexG); - - const graph = new Graph(true); - - graph - .addEdge(edgeAC) - .addEdge(edgeBC) - .addEdge(edgeBD) - .addEdge(edgeCE) - .addEdge(edgeDF) - .addEdge(edgeEF) - .addEdge(edgeEH) - .addEdge(edgeFG); - - const sortedVertices = topologicalSort(graph); - - expect(sortedVertices).toBeDefined(); - expect(sortedVertices.length).toBe(graph.getAllVertices().length); - expect(sortedVertices).toEqual([ - vertexB, - vertexD, - vertexA, - vertexC, - vertexE, - vertexH, - vertexF, - vertexG, - ]); - }); -}); diff --git a/src/algorithms/graph/topological-sorting/topologicalSort.js b/src/algorithms/graph/topological-sorting/topologicalSort.js deleted file mode 100644 index cd7bdd3dde..0000000000 --- a/src/algorithms/graph/topological-sorting/topologicalSort.js +++ /dev/null @@ -1,47 +0,0 @@ -import Stack from '../../../data-structures/stack/Stack'; -import depthFirstSearch from '../depth-first-search/depthFirstSearch'; - -/** - * @param {Graph} graph - */ -export default function topologicalSort(graph) { - // Create a set of all vertices we want to visit. - const unvisitedSet = {}; - graph.getAllVertices().forEach((vertex) => { - unvisitedSet[vertex.getKey()] = vertex; - }); - - // Create a set for all vertices that we've already visited. - const visitedSet = {}; - - // Create a stack of already ordered vertices. - const sortedStack = new Stack(); - - const dfsCallbacks = { - enterVertex: ({ currentVertex }) => { - // Add vertex to visited set in case if all its children has been explored. - visitedSet[currentVertex.getKey()] = currentVertex; - - // Remove this vertex from unvisited set. - delete unvisitedSet[currentVertex.getKey()]; - }, - leaveVertex: ({ currentVertex }) => { - // If the vertex has been totally explored then we may push it to stack. - sortedStack.push(currentVertex); - }, - allowTraversal: ({ nextVertex }) => { - return !visitedSet[nextVertex.getKey()]; - }, - }; - - // Let's go and do DFS for all unvisited nodes. - while (Object.keys(unvisitedSet).length) { - const currentVertexKey = Object.keys(unvisitedSet)[0]; - const currentVertex = unvisitedSet[currentVertexKey]; - - // Do DFS for current node. - depthFirstSearch(graph, currentVertex, dfsCallbacks); - } - - return sortedStack.toArray(); -} diff --git a/src/algorithms/graph/travelling-salesman/README.md b/src/algorithms/graph/travelling-salesman/README.md deleted file mode 100644 index 6690cd47ad..0000000000 --- a/src/algorithms/graph/travelling-salesman/README.md +++ /dev/null @@ -1,26 +0,0 @@ -# Travelling Salesman Problem - -The travelling salesman problem (TSP) asks the following question: -"Given a list of cities and the distances between each pair of -cities, what is the shortest possible route that visits each city -and returns to the origin city?" - -![Travelling Salesman](https://upload.wikimedia.org/wikipedia/commons/1/11/GLPK_solution_of_a_travelling_salesman_problem.svg) - -Solution of a travelling salesman problem: the black line shows -the shortest possible loop that connects every red dot. - -![Travelling Salesman Graph](https://upload.wikimedia.org/wikipedia/commons/3/30/Weighted_K4.svg) - -TSP can be modelled as an undirected weighted graph, such that -cities are the graph's vertices, paths are the graph's edges, -and a path's distance is the edge's weight. It is a minimization -problem starting and finishing at a specified vertex after having -visited each other vertex exactly once. Often, the model is a -complete graph (i.e. each pair of vertices is connected by an -edge). If no path exists between two cities, adding an arbitrarily -long edge will complete the graph without affecting the optimal tour. - -## References - -- [Wikipedia](https://en.wikipedia.org/wiki/Travelling_salesman_problem) diff --git a/src/algorithms/graph/travelling-salesman/__test__/bfTravellingSalesman.test.js b/src/algorithms/graph/travelling-salesman/__test__/bfTravellingSalesman.test.js deleted file mode 100644 index 54eb07dcf0..0000000000 --- a/src/algorithms/graph/travelling-salesman/__test__/bfTravellingSalesman.test.js +++ /dev/null @@ -1,51 +0,0 @@ -import GraphVertex from '../../../../data-structures/graph/GraphVertex'; -import GraphEdge from '../../../../data-structures/graph/GraphEdge'; -import Graph from '../../../../data-structures/graph/Graph'; -import bfTravellingSalesman from '../bfTravellingSalesman'; - -describe('bfTravellingSalesman', () => { - it('should solve problem for simple graph', () => { - const vertexA = new GraphVertex('A'); - const vertexB = new GraphVertex('B'); - const vertexC = new GraphVertex('C'); - const vertexD = new GraphVertex('D'); - - const edgeAB = new GraphEdge(vertexA, vertexB, 1); - const edgeBD = new GraphEdge(vertexB, vertexD, 1); - const edgeDC = new GraphEdge(vertexD, vertexC, 1); - const edgeCA = new GraphEdge(vertexC, vertexA, 1); - - const edgeBA = new GraphEdge(vertexB, vertexA, 5); - const edgeDB = new GraphEdge(vertexD, vertexB, 8); - const edgeCD = new GraphEdge(vertexC, vertexD, 7); - const edgeAC = new GraphEdge(vertexA, vertexC, 4); - const edgeAD = new GraphEdge(vertexA, vertexD, 2); - const edgeDA = new GraphEdge(vertexD, vertexA, 3); - const edgeBC = new GraphEdge(vertexB, vertexC, 3); - const edgeCB = new GraphEdge(vertexC, vertexB, 9); - - const graph = new Graph(true); - graph - .addEdge(edgeAB) - .addEdge(edgeBD) - .addEdge(edgeDC) - .addEdge(edgeCA) - .addEdge(edgeBA) - .addEdge(edgeDB) - .addEdge(edgeCD) - .addEdge(edgeAC) - .addEdge(edgeAD) - .addEdge(edgeDA) - .addEdge(edgeBC) - .addEdge(edgeCB); - - const salesmanPath = bfTravellingSalesman(graph); - - expect(salesmanPath.length).toBe(4); - - expect(salesmanPath[0].getKey()).toEqual(vertexA.getKey()); - expect(salesmanPath[1].getKey()).toEqual(vertexB.getKey()); - expect(salesmanPath[2].getKey()).toEqual(vertexD.getKey()); - expect(salesmanPath[3].getKey()).toEqual(vertexC.getKey()); - }); -}); diff --git a/src/algorithms/graph/travelling-salesman/bfTravellingSalesman.js b/src/algorithms/graph/travelling-salesman/bfTravellingSalesman.js deleted file mode 100644 index a13fa241fc..0000000000 --- a/src/algorithms/graph/travelling-salesman/bfTravellingSalesman.js +++ /dev/null @@ -1,104 +0,0 @@ -/** - * Get all possible paths - * @param {GraphVertex} startVertex - * @param {GraphVertex[][]} [paths] - * @param {GraphVertex[]} [path] - */ -function findAllPaths(startVertex, paths = [], path = []) { - // Clone path. - const currentPath = [...path]; - - // Add startVertex to the path. - currentPath.push(startVertex); - - // Generate visited set from path. - const visitedSet = currentPath.reduce((accumulator, vertex) => { - const updatedAccumulator = { ...accumulator }; - updatedAccumulator[vertex.getKey()] = vertex; - - return updatedAccumulator; - }, {}); - - // Get all unvisited neighbors of startVertex. - const unvisitedNeighbors = startVertex.getNeighbors().filter((neighbor) => { - return !visitedSet[neighbor.getKey()]; - }); - - // If there no unvisited neighbors then treat current path as complete and save it. - if (!unvisitedNeighbors.length) { - paths.push(currentPath); - - return paths; - } - - // Go through all the neighbors. - for (let neighborIndex = 0; neighborIndex < unvisitedNeighbors.length; neighborIndex += 1) { - const currentUnvisitedNeighbor = unvisitedNeighbors[neighborIndex]; - findAllPaths(currentUnvisitedNeighbor, paths, currentPath); - } - - return paths; -} - -/** - * @param {number[][]} adjacencyMatrix - * @param {object} verticesIndices - * @param {GraphVertex[]} cycle - * @return {number} - */ -function getCycleWeight(adjacencyMatrix, verticesIndices, cycle) { - let weight = 0; - - for (let cycleIndex = 1; cycleIndex < cycle.length; cycleIndex += 1) { - const fromVertex = cycle[cycleIndex - 1]; - const toVertex = cycle[cycleIndex]; - const fromVertexIndex = verticesIndices[fromVertex.getKey()]; - const toVertexIndex = verticesIndices[toVertex.getKey()]; - weight += adjacencyMatrix[fromVertexIndex][toVertexIndex]; - } - - return weight; -} - -/** - * BRUTE FORCE approach to solve Traveling Salesman Problem. - * - * @param {Graph} graph - * @return {GraphVertex[]} - */ -export default function bfTravellingSalesman(graph) { - // Pick starting point from where we will traverse the graph. - const startVertex = graph.getAllVertices()[0]; - - // BRUTE FORCE. - // Generate all possible paths from startVertex. - const allPossiblePaths = findAllPaths(startVertex); - - // Filter out paths that are not cycles. - const allPossibleCycles = allPossiblePaths.filter((path) => { - /** @var {GraphVertex} */ - const lastVertex = path[path.length - 1]; - const lastVertexNeighbors = lastVertex.getNeighbors(); - - return lastVertexNeighbors.includes(startVertex); - }); - - // Go through all possible cycles and pick the one with minimum overall tour weight. - const adjacencyMatrix = graph.getAdjacencyMatrix(); - const verticesIndices = graph.getVerticesIndices(); - let salesmanPath = []; - let salesmanPathWeight = null; - for (let cycleIndex = 0; cycleIndex < allPossibleCycles.length; cycleIndex += 1) { - const currentCycle = allPossibleCycles[cycleIndex]; - const currentCycleWeight = getCycleWeight(adjacencyMatrix, verticesIndices, currentCycle); - - // If current cycle weight is smaller then previous ones treat current cycle as most optimal. - if (salesmanPathWeight === null || currentCycleWeight < salesmanPathWeight) { - salesmanPath = currentCycle; - salesmanPathWeight = currentCycleWeight; - } - } - - // Return the solution. - return salesmanPath; -} diff --git a/src/algorithms/image-processing/seam-carving/README.md b/src/algorithms/image-processing/seam-carving/README.md deleted file mode 100644 index 87004f7abe..0000000000 --- a/src/algorithms/image-processing/seam-carving/README.md +++ /dev/null @@ -1,509 +0,0 @@ -# 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 = (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(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(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 deleted file mode 100644 index 444ce6df61..0000000000 --- a/src/algorithms/image-processing/seam-carving/README.ru-RU.md +++ /dev/null @@ -1,509 +0,0 @@ -# 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 = (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(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(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.node.js b/src/algorithms/image-processing/seam-carving/__tests__/resizeImageWidth.node.js deleted file mode 100644 index e4f78b7a52..0000000000 --- a/src/algorithms/image-processing/seam-carving/__tests__/resizeImageWidth.node.js +++ /dev/null @@ -1,85 +0,0 @@ -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 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a/src/algorithms/image-processing/seam-carving/resizeImageWidth.js +++ /dev/null @@ -1,253 +0,0 @@ -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 deleted file mode 100644 index de397b8ead..0000000000 --- a/src/algorithms/image-processing/utils/imageData.js +++ /dev/null @@ -1,39 +0,0 @@ -/** - * @typedef {ArrayLike | 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); -}; diff --git a/src/algorithms/linked-list/reverse-traversal/README.md b/src/algorithms/linked-list/reverse-traversal/README.md deleted file mode 100644 index 7e3f3cd6bb..0000000000 --- a/src/algorithms/linked-list/reverse-traversal/README.md +++ /dev/null @@ -1,23 +0,0 @@ -# Reversed Linked List Traversal - -_Read this in other languages:_ -[_中文_](README.zh-CN.md), -[_Português_](README.pt-BR.md) - -The task is to traverse the given linked list in reversed order. - -For example for the following linked list: - -![](https://upload.wikimedia.org/wikipedia/commons/6/6d/Singly-linked-list.svg) - -The order of traversal should be: - -```text -37 → 99 → 12 -``` - -The time complexity is `O(n)` because we visit every node only once. - -## Reference - -- [Wikipedia](https://en.wikipedia.org/wiki/Linked_list) diff --git a/src/algorithms/linked-list/reverse-traversal/README.pt-BR.md b/src/algorithms/linked-list/reverse-traversal/README.pt-BR.md deleted file mode 100644 index b2761ad720..0000000000 --- a/src/algorithms/linked-list/reverse-traversal/README.pt-BR.md +++ /dev/null @@ -1,23 +0,0 @@ -# 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/reverse-traversal/README.zh-CN.md b/src/algorithms/linked-list/reverse-traversal/README.zh-CN.md deleted file mode 100644 index cf0217a5b1..0000000000 --- a/src/algorithms/linked-list/reverse-traversal/README.zh-CN.md +++ /dev/null @@ -1,19 +0,0 @@ -# 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/reverse-traversal/__test__/reverseTraversal.test.js b/src/algorithms/linked-list/reverse-traversal/__test__/reverseTraversal.test.js deleted file mode 100644 index 2fb5af9ae7..0000000000 --- a/src/algorithms/linked-list/reverse-traversal/__test__/reverseTraversal.test.js +++ /dev/null @@ -1,35 +0,0 @@ -import LinkedList from '../../../../data-structures/linked-list/LinkedList'; -import reverseTraversal from '../reverseTraversal'; - -describe('reverseTraversal', () => { - it('should traverse linked list in reverse order', () => { - const linkedList = new LinkedList(); - - linkedList - .append(1) - .append(2) - .append(3); - - const traversedNodeValues = []; - const traversalCallback = (nodeValue) => { - traversedNodeValues.push(nodeValue); - }; - - reverseTraversal(linkedList, traversalCallback); - - expect(traversedNodeValues).toEqual([3, 2, 1]); - }); -}); - -// it('should reverse traversal the linked list with callback', () => { -// const linkedList = new LinkedList(); -// -// linkedList -// .append(1) -// .append(2) -// .append(3); -// -// expect(linkedList.toString()).toBe('1,2,3'); -// expect(linkedList.reverseTraversal(linkedList.head, value => value * 2)).toEqual([6, 4, 2]); -// expect(() => linkedList.reverseTraversal(linkedList.head)).toThrow(); -// }); diff --git a/src/algorithms/linked-list/reverse-traversal/reverseTraversal.js b/src/algorithms/linked-list/reverse-traversal/reverseTraversal.js deleted file mode 100644 index d39260aab2..0000000000 --- a/src/algorithms/linked-list/reverse-traversal/reverseTraversal.js +++ /dev/null @@ -1,24 +0,0 @@ -/** - * Traversal callback function. - * @callback traversalCallback - * @param {*} nodeValue - */ - -/** - * @param {LinkedListNode} node - * @param {traversalCallback} callback - */ -function reverseTraversalRecursive(node, callback) { - if (node) { - reverseTraversalRecursive(node.next, callback); - callback(node.value); - } -} - -/** - * @param {LinkedList} linkedList - * @param {traversalCallback} callback - */ -export default function reverseTraversal(linkedList, callback) { - reverseTraversalRecursive(linkedList.head, callback); -} diff --git a/src/algorithms/linked-list/traversal/README.md b/src/algorithms/linked-list/traversal/README.md deleted file mode 100644 index 09b177494c..0000000000 --- a/src/algorithms/linked-list/traversal/README.md +++ /dev/null @@ -1,24 +0,0 @@ -# Linked List Traversal - -_Read this in other languages:_ -[_Русский_](README.ru-RU.md), -[_中文_](README.zh-CN.md), -[_Português_](README.pt-BR.md) - -The task is to traverse the given linked list in straight order. - -For example for the following linked list: - -![Singly linked list](https://upload.wikimedia.org/wikipedia/commons/6/6d/Singly-linked-list.svg) - -The order of traversal should be: - -```text -12 → 99 → 37 -``` - -The time complexity is `O(n)` because we visit every node only once. - -## Reference - -- [Wikipedia](https://en.wikipedia.org/wiki/Linked_list) diff --git a/src/algorithms/linked-list/traversal/README.pt-BR.md b/src/algorithms/linked-list/traversal/README.pt-BR.md deleted file mode 100644 index 0fae9ed01a..0000000000 --- a/src/algorithms/linked-list/traversal/README.pt-BR.md +++ /dev/null @@ -1,24 +0,0 @@ -# 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/linked-list/traversal/README.ru-RU.md b/src/algorithms/linked-list/traversal/README.ru-RU.md deleted file mode 100644 index fa3cfb2fb1..0000000000 --- a/src/algorithms/linked-list/traversal/README.ru-RU.md +++ /dev/null @@ -1,19 +0,0 @@ -# Обход связного списка - -Задача состоит в том, чтобы обойти связный список в прямом порядке. - -Например, для следующего связного списка: - -![Singly linked list](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) diff --git a/src/algorithms/linked-list/traversal/README.zh-CN.md b/src/algorithms/linked-list/traversal/README.zh-CN.md deleted file mode 100644 index 19a01502b5..0000000000 --- a/src/algorithms/linked-list/traversal/README.zh-CN.md +++ /dev/null @@ -1,19 +0,0 @@ -# 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 diff --git a/src/algorithms/linked-list/traversal/__test__/traversal.test.js b/src/algorithms/linked-list/traversal/__test__/traversal.test.js deleted file mode 100644 index 77ce79b69f..0000000000 --- a/src/algorithms/linked-list/traversal/__test__/traversal.test.js +++ /dev/null @@ -1,22 +0,0 @@ -import LinkedList from '../../../../data-structures/linked-list/LinkedList'; -import traversal from '../traversal'; - -describe('traversal', () => { - it('should traverse linked list', () => { - const linkedList = new LinkedList(); - - linkedList - .append(1) - .append(2) - .append(3); - - const traversedNodeValues = []; - const traversalCallback = (nodeValue) => { - traversedNodeValues.push(nodeValue); - }; - - traversal(linkedList, traversalCallback); - - expect(traversedNodeValues).toEqual([1, 2, 3]); - }); -}); diff --git a/src/algorithms/linked-list/traversal/traversal.js b/src/algorithms/linked-list/traversal/traversal.js deleted file mode 100644 index cfbfe4fb59..0000000000 --- a/src/algorithms/linked-list/traversal/traversal.js +++ /dev/null @@ -1,18 +0,0 @@ -/** - * Traversal callback function. - * @callback traversalCallback - * @param {*} nodeValue - */ - -/** - * @param {LinkedList} linkedList - * @param {traversalCallback} callback - */ -export default function traversal(linkedList, callback) { - let currentNode = linkedList.head; - - while (currentNode) { - callback(currentNode.value); - currentNode = currentNode.next; - } -} diff --git a/src/algorithms/math/binary-floating-point/README.md b/src/algorithms/math/binary-floating-point/README.md deleted file mode 100644 index d1ae72731e..0000000000 --- a/src/algorithms/math/binary-floating-point/README.md +++ /dev/null @@ -1,103 +0,0 @@ -# Binary representation of floating-point numbers - -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]`: - -```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 - -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 - -- 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: - -- [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/) diff --git a/src/algorithms/math/binary-floating-point/__tests__/bitsToFloat.test.js b/src/algorithms/math/binary-floating-point/__tests__/bitsToFloat.test.js deleted file mode 100644 index 53afe691a2..0000000000 --- a/src/algorithms/math/binary-floating-point/__tests__/bitsToFloat.test.js +++ /dev/null @@ -1,32 +0,0 @@ -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 deleted file mode 100644 index efb8a2ba5e..0000000000 --- a/src/algorithms/math/binary-floating-point/__tests__/floatAsBinaryString.test.js +++ /dev/null @@ -1,20 +0,0 @@ -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 deleted file mode 100644 index 6d1ef0d851..0000000000 --- a/src/algorithms/math/binary-floating-point/bitsToFloat.js +++ /dev/null @@ -1,119 +0,0 @@ -/** - * 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 deleted file mode 100644 index aa907ac049..0000000000 --- a/src/algorithms/math/binary-floating-point/floatAsBinaryString.js +++ /dev/null @@ -1,61 +0,0 @@ -// @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 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détails. - -#### Mettre un bit à 1(_set_) - -Cette méthode met un bit à `1` en fonction d'un rang (`bitPosition`), -créant ainsi une valeur qui ressemble à `00100`. -Ensuite, nous effectuons l'opération `OU` qui met un bit spécifique -en `1` sans affecter les autres bits du nombre. - -> Voir [setBit.js](setBit.js) pour plus de détails. - -#### Mettre un bit à 0 (_clear_) - -Cette méthode met un bit à `1` en fonction d'un rang (`bitPosition`), -créant ainsi une valeur qui ressemble à `00100`. -Puis on inverse ce masque de bits pour obtenir un nombre ressemblant à `11011`. -Enfin, l'opération `AND` est appliquée au nombre et au masque. -Cette opération annule le bit. - -> Voir [clearBit.js](clearBit.js) pour plus de détails. - -#### Mettre à jour un Bit (_update_) - -Cette méthode est une combinaison de l'"annulation de bit" -et du "forçage de bit". - -> Voir [updateBit.js](updateBit.js) pour plus de détails. - -#### Vérifier si un nombre est pair (_isEven_) - -Cette méthode détermine si un nombre donné est pair. -Elle s'appuie sur le fait que les nombres impairs ont leur dernier -bit droit à `1`. - -```text -Nombre: 5 = 0b0101 -isEven: false - -Nombre: 4 = 0b0100 -isEven: true -``` - -> Voir [isEven.js](isEven.js) pour plus de détails. - -#### Vérifier si un nombre est positif (_isPositive_) - -Cette méthode détermine un le nombre donné est positif. -Elle s'appuie sur le fait que tous les nombres positifs -ont leur bit le plus à gauche à `0`. -Cependant, si le nombre fourni est zéro -ou zéro négatif, il doit toujours renvoyer `false`. - -```text -Nombre: 1 = 0b0001 -isPositive: true - -Nombre: -1 = -0b0001 -isPositive: false -``` - -> Voir [isPositive.js](isPositive.js) pour plus de détails. - -#### Multiplier par deux - -Cette méthode décale un nombre donné d'un bit vers la gauche. -Ainsi, toutes les composantes du nombre binaire (en puissances de deux) sont -multipliées par deux et donc le nombre lui-même est -multiplié par deux. - -``` -Avant le décalage -Nombre: 0b0101 = 5 -Puissances de deux: 0 + 2^2 + 0 + 2^0 - -Après le décalage -Nombre: 0b1010 = 10 -Puissances de deux: 2^3 + 0 + 2^1 + 0 -``` - -> Voir [multiplyByTwo.js](multiplyByTwo.js) pour plus de détails. - -#### Diviser par deux - -Cette méthode décale un nombre donné d'un bit vers la droite. -Ainsi, toutes les composantes du nombre binaire (en puissances de deux) sont -divisées par deux et donc le nombre lui-même est -divisé par deux, sans reste. - -``` -Avant le décalage -Nombre: 0b0101 = 5 -Puissances de deux: 0 + 2^2 + 0 + 2^0 - -Après le décalage -Nombre: 0b0010 = 2 -Puissances de deux: 0 + 0 + 2^1 + 0 -``` - -> Voir [divideByTwo.js](divideByTwo.js) pour plus de détails. - -#### Inverser le signe (_Switch Sign_) - -Cette méthode rend positifs les nombres négatifs, et vice-versa. -Pour ce faire, elle s'appuie sur l'approche "Complément à deux", -qui inverse tous les bits du nombre et y ajoute 1. - -``` -1101 -3 -1110 -2 -1111 -1 -0000 0 -0001 1 -0010 2 -0011 3 -``` - -> Voir [switchSign.js](switchSign.js) pour plus de détails. - -#### Multiplier deux nombres signés - -Cette méthode multiplie deux nombres entiers signés -à l'aide d'opérateurs bit à bit. -Cette méthode est basée sur les faits suivants: - -```text -a * b peut être écrit sous les formes suivantes: - 0 si a est zero ou b est zero ou les deux sont zero - 2a * (b/2) si b est pair - 2a * (b - 1)/2 + a si b est impair et positif - 2a * (b + 1)/2 - a si b est impair et negatif -``` - -L'avantage de cette approche est qu'à chaque étape de la récursion -l'un des opérandes est réduit à la moitié de sa valeur d'origine. -Par conséquent, la complexité d'exécution est `O(log(b))` -où `b` est l'opérande qui se réduit de moitié à chaque récursion. - -> Voir [multiply.js](multiply.js) pour plus de détails. - -#### Multiplier deux nombres positifs - -Cette méthode multiplie deux nombres entiers à l'aide d'opérateurs bit à bit. -Cette méthode s'appuie sur le fait que "Chaque nombre peut être lu -comme une somme de puissances de 2". - -L'idée principale de la multiplication bit à bit -est que chaque nombre peut être divisé en somme des puissances de deux: - -Ainsi - -```text -19 = 2^4 + 2^1 + 2^0 -``` - -Donc multiplier `x` par `19` est equivalent à : - -```text -x * 19 = x * 2^4 + x * 2^1 + x * 2^0 -``` - -Nous devons maintenant nous rappeler que `x * 2 ^ 4` équivaut -à déplacer`x` vers la gauche par `4` bits (`x << 4`). - -> Voir [multiplyUnsigned.js](multiplyUnsigned.js) pour plus de détails. - -#### Compter les bits à 1 - -This method counts the number of set bits in a number using bitwise operators. -The main idea is that we shift the number right by one bit at a time and check -the result of `&` operation that is `1` if bit is set and `0` otherwise. - -Cette méthode décompte les bits à `1` d'un nombre -à l'aide d'opérateurs bit à bit. -L'idée principale est de décaler le nombre vers la droite, un bit à la fois, -et de vérifier le résultat de l'opération `&` : -`1` si le bit est défini et `0` dans le cas contraire. - -```text -Nombre: 5 = 0b0101 -Décompte des bits à 1 = 2 -``` - -> Voir [countSetBits.js](countSetBits.js) pour plus de détails. - -#### Compter les bits nécessaire pour remplacer un nombre - -This methods outputs the number of bits required to convert one number to another. -This makes use of property that when numbers are `XOR`-ed the result will be number -of different bits. - -Cette méthode retourne le nombre de bits requis -pour convertir un nombre en un autre. -Elle repose sur la propriété suivante: -lorsque les nombres sont évalués via `XOR`, le résultat est le nombre -de bits différents entre les deux. - -``` -5 = 0b0101 -1 = 0b0001 -Nombre de bits pour le remplacement: 1 -``` - -> Voir [bitsDiff.js](bitsDiff.js) pour plus de détails. - -#### Calculer les bits significatifs d'un nombre - -Pour connaître les bits significatifs d'un nombre, -on peut décaler `1` d'un bit à gauche plusieurs fois d'affilée -jusqu'à ce que ce nombre soit plus grand que le nombre à comparer. - -``` -5 = 0b0101 -Décompte des bits significatifs: 3 -On décale 1 quatre fois pour dépasser 5. -``` - -> Voir [bitLength.js](bitLength.js) pour plus de détails. - -#### Vérifier si un nombre est une puissance de 2 - -Cette méthode vérifie si un nombre donné est une puissance de deux. -Elle s'appuie sur la propriété suivante. -Disons que `powerNumber` est une puissance de deux (c'est-à-dire 2, 4, 8, 16 etc.). -Si nous faisons l'opération `&` entre `powerNumber` et `powerNumber - 1`, -elle retournera`0` (dans le cas où le nombre est une puissance de deux). - -``` -Nombre: 4 = 0b0100 -Nombre: 3 = (4 - 1) = 0b0011 -4 & 3 = 0b0100 & 0b0011 = 0b0000 <-- Égal à zéro, car c'est une puissance de 2. - -Nombre: 10 = 0b01010 -Nombre: 9 = (10 - 1) = 0b01001 -10 & 9 = 0b01010 & 0b01001 = 0b01000 <-- Différent de 0, donc n'est pas une puissance de 2. -``` - -> Voir [isPowerOfTwo.js](isPowerOfTwo.js) pour plus de détails. - -#### Additionneur complet - -Cette méthode ajoute deux nombres entiers à l'aide d'opérateurs bit à bit. - -Elle implémente un [additionneur](https://fr.wikipedia.org/wiki/Additionneur) -simulant un circuit électronique logique, -pour additionner deux entiers de 32 bits, -sous la forme « complément à deux ». -Elle utilise la logique booléenne pour couvrir tous les cas possibles -d'ajout de deux bits donnés: -avec et sans retenue de l'ajout de l'étape précédente la moins significative. - -Légende: - -- `A`: Nombre `A` -- `B`: Nombre `B` -- `ai`: ième bit du nombre `A` -- `bi`: ième bit du nombre `B` -- `carryIn`: un bit retenu de la précédente étape la moins significative -- `carryOut`: un bit retenu pour la prochaine étape la plus significative -- `bitSum`: La somme de `ai`, `bi`, et `carryIn` -- `resultBin`: Le résultat complet de l'ajout de l'étape actuelle avec toutes les étapes moins significatives (en binaire) -- `resultDec`: Le résultat complet de l'ajout de l'étape actuelle avec toutes les étapes moins significatives (en decimal) - -``` -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 │ -└──────┴────┴────┴─────────┴──────────┴─────────┴───────────┴───────────┘ -``` - -> Voir [fullAdder.js](fullAdder.js) pour plus de détails. -> Voir [Full Adder on YouTube](https://www.youtube.com/watch?v=wvJc9CZcvBc&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8). - -## Références - -- [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/bits/README.md b/src/algorithms/math/bits/README.md deleted file mode 100644 index 1218094287..0000000000 --- a/src/algorithms/math/bits/README.md +++ /dev/null @@ -1,274 +0,0 @@ -# Bit Manipulation - -_Read this in other languages:_ -[français](README.fr-FR.md), -[简体中文](README.zh-CN.md). - -#### Get Bit - -This method shifts the relevant bit to the zeroth position. -Then we perform `AND` operation with one which has bit -pattern like `0001`. This clears all bits from the original -number except the relevant one. If the relevant bit is one, -the result is `1`, otherwise the result is `0`. - -> See [getBit.js](getBit.js) for further details. - -#### Set Bit - -This method shifts `1` over by `bitPosition` bits, creating a -value that looks like `00100`. Then we perform `OR` operation -that sets specific bit into `1` but it does not affect on -other bits of the number. - -> See [setBit.js](setBit.js) for further details. - -#### Clear Bit - -This method shifts `1` over by `bitPosition` bits, creating a -value that looks like `00100`. Than it inverts this mask to get -the number that looks like `11011`. Then `AND` operation is -being applied to both the number and the mask. That operation -unsets the bit. - -> See [clearBit.js](clearBit.js) for further details. - -#### Update Bit - -This method is a combination of "Clear Bit" and "Set Bit" methods. - -> See [updateBit.js](updateBit.js) for further details. - -#### isEven - -This method determines if the number provided is even. -It is based on the fact that odd numbers have their last -right bit to be set to 1. - -```text -Number: 5 = 0b0101 -isEven: false - -Number: 4 = 0b0100 -isEven: true -``` - -> See [isEven.js](isEven.js) for further details. - -#### isPositive - -This method determines if the number is positive. It is based on the fact that all positive -numbers have their leftmost bit to be set to `0`. However, if the number provided is zero -or negative zero, it should still return `false`. - -```text -Number: 1 = 0b0001 -isPositive: true - -Number: -1 = -0b0001 -isPositive: false -``` - -> See [isPositive.js](isPositive.js) for further details. - -#### Multiply By Two - -This method shifts original number by one bit to the left. -Thus all binary number components (powers of two) are being -multiplying by two and thus the number itself is being -multiplied by two. - -``` -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 -``` - -> See [multiplyByTwo.js](multiplyByTwo.js) for further details. - -#### Divide By Two - -This method shifts original number by one bit to the right. -Thus all binary number components (powers of two) are being -divided by two and thus the number itself is being -divided by two without remainder. - -``` -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 -``` - -> See [divideByTwo.js](divideByTwo.js) for further details. - -#### Switch Sign - -This method make positive numbers to be negative and backwards. -To do so it uses "Twos Complement" approach which does it by -inverting all of the bits of the number and adding 1 to it. - -``` -1101 -3 -1110 -2 -1111 -1 -0000 0 -0001 1 -0010 2 -0011 3 -``` - -> See [switchSign.js](switchSign.js) for further details. - -#### Multiply Two Signed Numbers - -This method multiplies two signed integer numbers using bitwise operators. -This method is based on the following facts: - -```text -a * b can be written in the below formats: - 0 if a is zero or b is zero or both a and b are zeroes - 2a * (b/2) if b is even - 2a * (b - 1)/2 + a if b is odd and positive - 2a * (b + 1)/2 - a if b is odd and negative -``` - -The advantage of this approach is that in each recursive step one of the operands -reduces to half its original value. Hence, the run time complexity is `O(log(b))` where `b` is -the operand that reduces to half on each recursive step. - -> See [multiply.js](multiply.js) for further details. - -#### Multiply Two Unsigned Numbers - -This method multiplies two integer numbers using bitwise operators. -This method is based on that "Every number can be denoted as the sum of powers of 2". - -The main idea of bitwise multiplication is that every number may be split -to the sum of powers of two: - -I.e. - -```text -19 = 2^4 + 2^1 + 2^0 -``` - -Then multiplying number `x` by `19` is equivalent of: - -```text -x * 19 = x * 2^4 + x * 2^1 + x * 2^0 -``` - -Now we need to remember that `x * 2^4` is equivalent of shifting `x` left -by `4` bits (`x << 4`). - -> See [multiplyUnsigned.js](multiplyUnsigned.js) for further details. - -#### Count Set Bits - -This method counts the number of set bits in a number using bitwise operators. -The main idea is that we shift the number right by one bit at a time and check -the result of `&` operation that is `1` if bit is set and `0` otherwise. - -```text -Number: 5 = 0b0101 -Count of set bits = 2 -``` - -> See [countSetBits.js](countSetBits.js) for further details. - -#### Count Bits to Flip One Number to Another - -This methods outputs the number of bits required to convert one number to another. -This makes use of property that when numbers are `XOR`-ed the result will be number -of different bits. - -``` -5 = 0b0101 -1 = 0b0001 -Count of Bits to be Flipped: 1 -``` - -> See [bitsDiff.js](bitsDiff.js) for further details. - -#### Count Bits of a Number - -To calculate the number of valuable bits we need to shift `1` one bit left each -time and see if shifted number is bigger than the input number. - -``` -5 = 0b0101 -Count of valuable bits is: 3 -When we shift 1 four times it will become bigger than 5. -``` - -> See [bitLength.js](bitLength.js) for further details. - -#### Is Power of Two - -This method checks if a number provided is power of two. It uses the following -property. Let's say that `powerNumber` is a number that has been formed as a power -of two (i.e. 2, 4, 8, 16 etc.). Then if we'll do `&` operation between `powerNumber` -and `powerNumber - 1` it will return `0` (in case if number is power of two). - -``` -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. -``` - -> See [isPowerOfTwo.js](isPowerOfTwo.js) for further details. - -#### Full Adder - -This method adds up two integer numbers using bitwise operators. - -It implements [full adder]() -electronics circuit logic to sum two 32-bit integers in two's complement format. -It's using the boolean logic to cover all possible cases of adding two input bits: -with and without a "carry bit" from adding the previous less-significant stage. - -Legend: - -- `A`: Number `A` -- `B`: Number `B` -- `ai`: ith bit of number `A` -- `bi`: ith bit of number `B` -- `carryIn`: a bit carried in from the previous less-significant stage -- `carryOut`: a bit to carry to the next most-significant stage -- `bitSum`: The sum of `ai`, `bi`, and `carryIn` -- `resultBin`: The full result of adding current stage with all less-significant stages (in binary) -- `resultDec`: The full result of adding current stage with all less-significant stages (in decimal) - -``` -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 │ -└──────┴────┴────┴─────────┴──────────┴─────────┴───────────┴───────────┘ -``` - -> 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 - -- [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/bits/README.zh-CN.md b/src/algorithms/math/bits/README.zh-CN.md deleted file mode 100644 index 9ec75069c6..0000000000 --- a/src/algorithms/math/bits/README.zh-CN.md +++ /dev/null @@ -1,236 +0,0 @@ -# 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`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。 - -#### 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`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。 - -#### 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]()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/bits/__test__/bitLength.test.js b/src/algorithms/math/bits/__test__/bitLength.test.js deleted file mode 100644 index 1731b5685a..0000000000 --- a/src/algorithms/math/bits/__test__/bitLength.test.js +++ /dev/null @@ -1,14 +0,0 @@ -import bitLength from '../bitLength'; - -describe('bitLength', () => { - it('should calculate number of bits that the number is consists of', () => { - expect(bitLength(0b0)).toBe(0); - expect(bitLength(0b1)).toBe(1); - expect(bitLength(0b01)).toBe(1); - expect(bitLength(0b101)).toBe(3); - expect(bitLength(0b0101)).toBe(3); - expect(bitLength(0b10101)).toBe(5); - expect(bitLength(0b11110101)).toBe(8); - expect(bitLength(0b00011110101)).toBe(8); - }); -}); diff --git a/src/algorithms/math/bits/__test__/bitsDiff.test.js b/src/algorithms/math/bits/__test__/bitsDiff.test.js deleted file mode 100644 index e1fd641647..0000000000 --- a/src/algorithms/math/bits/__test__/bitsDiff.test.js +++ /dev/null @@ -1,13 +0,0 @@ -import bitsDiff from '../bitsDiff'; - -describe('bitsDiff', () => { - it('should calculate bits difference between two numbers', () => { - expect(bitsDiff(0, 0)).toBe(0); - expect(bitsDiff(1, 1)).toBe(0); - expect(bitsDiff(124, 124)).toBe(0); - expect(bitsDiff(0, 1)).toBe(1); - expect(bitsDiff(1, 0)).toBe(1); - expect(bitsDiff(1, 2)).toBe(2); - expect(bitsDiff(1, 3)).toBe(1); - }); -}); diff --git a/src/algorithms/math/bits/__test__/clearBit.test.js b/src/algorithms/math/bits/__test__/clearBit.test.js deleted file mode 100644 index 2d758779cd..0000000000 --- a/src/algorithms/math/bits/__test__/clearBit.test.js +++ /dev/null @@ -1,15 +0,0 @@ -import clearBit from '../clearBit'; - -describe('clearBit', () => { - it('should clear bit at specific position', () => { - // 1 = 0b0001 - expect(clearBit(1, 0)).toBe(0); - expect(clearBit(1, 1)).toBe(1); - expect(clearBit(1, 2)).toBe(1); - - // 10 = 0b1010 - expect(clearBit(10, 0)).toBe(10); - expect(clearBit(10, 1)).toBe(8); - expect(clearBit(10, 3)).toBe(2); - }); -}); diff --git a/src/algorithms/math/bits/__test__/countSetBits.test.js b/src/algorithms/math/bits/__test__/countSetBits.test.js deleted file mode 100644 index a6c0fb9989..0000000000 --- a/src/algorithms/math/bits/__test__/countSetBits.test.js +++ /dev/null @@ -1,20 +0,0 @@ -import countSetBits from '../countSetBits'; - -describe('countSetBits', () => { - it('should return number of set bits', () => { - expect(countSetBits(0)).toBe(0); - expect(countSetBits(1)).toBe(1); - expect(countSetBits(2)).toBe(1); - expect(countSetBits(3)).toBe(2); - expect(countSetBits(4)).toBe(1); - expect(countSetBits(5)).toBe(2); - expect(countSetBits(21)).toBe(3); - expect(countSetBits(255)).toBe(8); - expect(countSetBits(1023)).toBe(10); - expect(countSetBits(-1)).toBe(32); - expect(countSetBits(-21)).toBe(30); - expect(countSetBits(-255)).toBe(25); - expect(countSetBits(-1023)).toBe(23); - expect(countSetBits(-4294967296)).toBe(0); - }); -}); diff --git a/src/algorithms/math/bits/__test__/divideByTwo.test.js b/src/algorithms/math/bits/__test__/divideByTwo.test.js deleted file mode 100644 index ec829367ec..0000000000 --- a/src/algorithms/math/bits/__test__/divideByTwo.test.js +++ /dev/null @@ -1,12 +0,0 @@ -import divideByTwo from '../divideByTwo'; - -describe('divideByTwo', () => { - it('should divide numbers by two using bitwise operations', () => { - expect(divideByTwo(0)).toBe(0); - expect(divideByTwo(1)).toBe(0); - expect(divideByTwo(3)).toBe(1); - expect(divideByTwo(10)).toBe(5); - expect(divideByTwo(17)).toBe(8); - expect(divideByTwo(125)).toBe(62); - }); -}); diff --git a/src/algorithms/math/bits/__test__/fullAdder.test.js b/src/algorithms/math/bits/__test__/fullAdder.test.js deleted file mode 100644 index 529187dc4f..0000000000 --- a/src/algorithms/math/bits/__test__/fullAdder.test.js +++ /dev/null @@ -1,18 +0,0 @@ -import fullAdder from '../fullAdder'; - -describe('fullAdder', () => { - it('should add up two numbers', () => { - expect(fullAdder(0, 0)).toBe(0); - expect(fullAdder(2, 0)).toBe(2); - expect(fullAdder(0, 2)).toBe(2); - expect(fullAdder(1, 2)).toBe(3); - expect(fullAdder(2, 1)).toBe(3); - expect(fullAdder(6, 6)).toBe(12); - expect(fullAdder(-2, 4)).toBe(2); - expect(fullAdder(4, -2)).toBe(2); - expect(fullAdder(-4, -4)).toBe(-8); - expect(fullAdder(4, -5)).toBe(-1); - expect(fullAdder(2, 121)).toBe(123); - expect(fullAdder(121, 2)).toBe(123); - }); -}); diff --git a/src/algorithms/math/bits/__test__/getBit.test.js b/src/algorithms/math/bits/__test__/getBit.test.js deleted file mode 100644 index 3a7026f2d9..0000000000 --- a/src/algorithms/math/bits/__test__/getBit.test.js +++ /dev/null @@ -1,23 +0,0 @@ -import getBit from '../getBit'; - -describe('getBit', () => { - it('should get bit at specific position', () => { - // 1 = 0b0001 - expect(getBit(1, 0)).toBe(1); - expect(getBit(1, 1)).toBe(0); - - // 2 = 0b0010 - expect(getBit(2, 0)).toBe(0); - expect(getBit(2, 1)).toBe(1); - - // 3 = 0b0011 - expect(getBit(3, 0)).toBe(1); - expect(getBit(3, 1)).toBe(1); - - // 10 = 0b1010 - expect(getBit(10, 0)).toBe(0); - expect(getBit(10, 1)).toBe(1); - expect(getBit(10, 2)).toBe(0); - expect(getBit(10, 3)).toBe(1); - }); -}); diff --git a/src/algorithms/math/bits/__test__/isEven.test.js b/src/algorithms/math/bits/__test__/isEven.test.js deleted file mode 100644 index b21bbfb00c..0000000000 --- a/src/algorithms/math/bits/__test__/isEven.test.js +++ /dev/null @@ -1,19 +0,0 @@ -import isEven from '../isEven'; - -describe('isEven', () => { - it('should detect if a number is even', () => { - expect(isEven(0)).toBe(true); - expect(isEven(2)).toBe(true); - expect(isEven(-2)).toBe(true); - expect(isEven(1)).toBe(false); - expect(isEven(-1)).toBe(false); - expect(isEven(-3)).toBe(false); - expect(isEven(3)).toBe(false); - expect(isEven(8)).toBe(true); - expect(isEven(9)).toBe(false); - expect(isEven(121)).toBe(false); - expect(isEven(122)).toBe(true); - expect(isEven(1201)).toBe(false); - expect(isEven(1202)).toBe(true); - }); -}); diff --git a/src/algorithms/math/bits/__test__/isPositive.test.js b/src/algorithms/math/bits/__test__/isPositive.test.js deleted file mode 100644 index 45dcca0e4e..0000000000 --- a/src/algorithms/math/bits/__test__/isPositive.test.js +++ /dev/null @@ -1,19 +0,0 @@ -import isPositive from '../isPositive'; - -describe('isPositive', () => { - it('should detect if a number is positive', () => { - expect(isPositive(1)).toBe(true); - expect(isPositive(2)).toBe(true); - expect(isPositive(3)).toBe(true); - expect(isPositive(5665)).toBe(true); - expect(isPositive(56644325)).toBe(true); - - expect(isPositive(0)).toBe(false); - expect(isPositive(-0)).toBe(false); - expect(isPositive(-1)).toBe(false); - expect(isPositive(-2)).toBe(false); - expect(isPositive(-126)).toBe(false); - expect(isPositive(-5665)).toBe(false); - expect(isPositive(-56644325)).toBe(false); - }); -}); diff --git a/src/algorithms/math/bits/__test__/isPowerOfTwo.test.js b/src/algorithms/math/bits/__test__/isPowerOfTwo.test.js deleted file mode 100644 index 3408f2c137..0000000000 --- a/src/algorithms/math/bits/__test__/isPowerOfTwo.test.js +++ /dev/null @@ -1,20 +0,0 @@ -import isPowerOfTwo from '../isPowerOfTwo'; - -describe('isPowerOfTwo', () => { - it('should detect if the number is power of two', () => { - expect(isPowerOfTwo(1)).toBe(true); - expect(isPowerOfTwo(2)).toBe(true); - expect(isPowerOfTwo(3)).toBe(false); - expect(isPowerOfTwo(4)).toBe(true); - expect(isPowerOfTwo(5)).toBe(false); - expect(isPowerOfTwo(6)).toBe(false); - expect(isPowerOfTwo(7)).toBe(false); - expect(isPowerOfTwo(8)).toBe(true); - expect(isPowerOfTwo(9)).toBe(false); - expect(isPowerOfTwo(16)).toBe(true); - expect(isPowerOfTwo(23)).toBe(false); - expect(isPowerOfTwo(32)).toBe(true); - expect(isPowerOfTwo(127)).toBe(false); - expect(isPowerOfTwo(128)).toBe(true); - }); -}); diff --git a/src/algorithms/math/bits/__test__/multiply.test.js b/src/algorithms/math/bits/__test__/multiply.test.js deleted file mode 100644 index c21957041b..0000000000 --- a/src/algorithms/math/bits/__test__/multiply.test.js +++ /dev/null @@ -1,18 +0,0 @@ -import multiply from '../multiply'; - -describe('multiply', () => { - it('should multiply two numbers', () => { - expect(multiply(0, 0)).toBe(0); - expect(multiply(2, 0)).toBe(0); - expect(multiply(0, 2)).toBe(0); - expect(multiply(1, 2)).toBe(2); - expect(multiply(2, 1)).toBe(2); - expect(multiply(6, 6)).toBe(36); - expect(multiply(-2, 4)).toBe(-8); - expect(multiply(4, -2)).toBe(-8); - expect(multiply(-4, -4)).toBe(16); - expect(multiply(4, -5)).toBe(-20); - expect(multiply(2, 121)).toBe(242); - expect(multiply(121, 2)).toBe(242); - }); -}); diff --git a/src/algorithms/math/bits/__test__/multiplyByTwo.test.js b/src/algorithms/math/bits/__test__/multiplyByTwo.test.js deleted file mode 100644 index 07934c57ba..0000000000 --- a/src/algorithms/math/bits/__test__/multiplyByTwo.test.js +++ /dev/null @@ -1,12 +0,0 @@ -import multiplyByTwo from '../multiplyByTwo'; - -describe('multiplyByTwo', () => { - it('should multiply numbers by two using bitwise operations', () => { - expect(multiplyByTwo(0)).toBe(0); - expect(multiplyByTwo(1)).toBe(2); - expect(multiplyByTwo(3)).toBe(6); - expect(multiplyByTwo(10)).toBe(20); - expect(multiplyByTwo(17)).toBe(34); - expect(multiplyByTwo(125)).toBe(250); - }); -}); diff --git a/src/algorithms/math/bits/__test__/multiplyUnsigned.test.js b/src/algorithms/math/bits/__test__/multiplyUnsigned.test.js deleted file mode 100644 index d444dc1688..0000000000 --- a/src/algorithms/math/bits/__test__/multiplyUnsigned.test.js +++ /dev/null @@ -1,15 +0,0 @@ -import multiplyUnsigned from '../multiplyUnsigned'; - -describe('multiplyUnsigned', () => { - it('should multiply two unsigned numbers', () => { - expect(multiplyUnsigned(0, 2)).toBe(0); - expect(multiplyUnsigned(2, 0)).toBe(0); - expect(multiplyUnsigned(1, 1)).toBe(1); - expect(multiplyUnsigned(1, 2)).toBe(2); - expect(multiplyUnsigned(2, 7)).toBe(14); - expect(multiplyUnsigned(7, 2)).toBe(14); - expect(multiplyUnsigned(30, 2)).toBe(60); - expect(multiplyUnsigned(17, 34)).toBe(578); - expect(multiplyUnsigned(170, 2340)).toBe(397800); - }); -}); diff --git a/src/algorithms/math/bits/__test__/setBit.test.js b/src/algorithms/math/bits/__test__/setBit.test.js deleted file mode 100644 index d53d60c746..0000000000 --- a/src/algorithms/math/bits/__test__/setBit.test.js +++ /dev/null @@ -1,15 +0,0 @@ -import setBit from '../setBit'; - -describe('setBit', () => { - it('should set bit at specific position', () => { - // 1 = 0b0001 - expect(setBit(1, 0)).toBe(1); - expect(setBit(1, 1)).toBe(3); - expect(setBit(1, 2)).toBe(5); - - // 10 = 0b1010 - expect(setBit(10, 0)).toBe(11); - expect(setBit(10, 1)).toBe(10); - expect(setBit(10, 2)).toBe(14); - }); -}); diff --git a/src/algorithms/math/bits/__test__/switchSign.test.js b/src/algorithms/math/bits/__test__/switchSign.test.js deleted file mode 100644 index af3f36df5e..0000000000 --- a/src/algorithms/math/bits/__test__/switchSign.test.js +++ /dev/null @@ -1,13 +0,0 @@ -import switchSign from '../switchSign'; - -describe('switchSign', () => { - it('should switch the sign of the number using twos complement approach', () => { - expect(switchSign(0)).toBe(0); - expect(switchSign(1)).toBe(-1); - expect(switchSign(-1)).toBe(1); - expect(switchSign(32)).toBe(-32); - expect(switchSign(-32)).toBe(32); - expect(switchSign(23)).toBe(-23); - expect(switchSign(-23)).toBe(23); - }); -}); diff --git a/src/algorithms/math/bits/__test__/updateBit.test.js b/src/algorithms/math/bits/__test__/updateBit.test.js deleted file mode 100644 index e2ac2db005..0000000000 --- a/src/algorithms/math/bits/__test__/updateBit.test.js +++ /dev/null @@ -1,19 +0,0 @@ -import updateBit from '../updateBit'; - -describe('updateBit', () => { - it('should update bit at specific position', () => { - // 1 = 0b0001 - expect(updateBit(1, 0, 1)).toBe(1); - expect(updateBit(1, 0, 0)).toBe(0); - expect(updateBit(1, 1, 1)).toBe(3); - expect(updateBit(1, 2, 1)).toBe(5); - - // 10 = 0b1010 - expect(updateBit(10, 0, 1)).toBe(11); - expect(updateBit(10, 0, 0)).toBe(10); - expect(updateBit(10, 1, 1)).toBe(10); - expect(updateBit(10, 1, 0)).toBe(8); - expect(updateBit(10, 2, 1)).toBe(14); - expect(updateBit(10, 2, 0)).toBe(10); - }); -}); diff --git a/src/algorithms/math/bits/bitLength.js b/src/algorithms/math/bits/bitLength.js deleted file mode 100644 index 0fc2727d0e..0000000000 --- a/src/algorithms/math/bits/bitLength.js +++ /dev/null @@ -1,15 +0,0 @@ -/** - * Return the number of bits used in the binary representation of the number. - * - * @param {number} number - * @return {number} - */ -export default function bitLength(number) { - let bitsCounter = 0; - - while ((1 << bitsCounter) <= number) { - bitsCounter += 1; - } - - return bitsCounter; -} diff --git a/src/algorithms/math/bits/bitsDiff.js b/src/algorithms/math/bits/bitsDiff.js deleted file mode 100644 index dbb77b89ff..0000000000 --- a/src/algorithms/math/bits/bitsDiff.js +++ /dev/null @@ -1,13 +0,0 @@ -import countSetBits from './countSetBits'; - -/** - * Counts the number of bits that need to be change in order - * to convert numberA to numberB. - * - * @param {number} numberA - * @param {number} numberB - * @return {number} - */ -export default function bitsDiff(numberA, numberB) { - return countSetBits(numberA ^ numberB); -} diff --git a/src/algorithms/math/bits/clearBit.js b/src/algorithms/math/bits/clearBit.js deleted file mode 100644 index 0329a0476d..0000000000 --- a/src/algorithms/math/bits/clearBit.js +++ /dev/null @@ -1,10 +0,0 @@ -/** - * @param {number} number - * @param {number} bitPosition - zero based. - * @return {number} - */ -export default function clearBit(number, bitPosition) { - const mask = ~(1 << bitPosition); - - return number & mask; -} diff --git a/src/algorithms/math/bits/countSetBits.js b/src/algorithms/math/bits/countSetBits.js deleted file mode 100644 index 63839d4e68..0000000000 --- a/src/algorithms/math/bits/countSetBits.js +++ /dev/null @@ -1,18 +0,0 @@ -/** - * @param {number} originalNumber - * @return {number} - */ -export default function countSetBits(originalNumber) { - let setBitsCount = 0; - let number = originalNumber; - - while (number) { - // Add last bit of the number to the sum of set bits. - setBitsCount += number & 1; - - // Shift number right by one bit to investigate other bits. - number >>>= 1; - } - - return setBitsCount; -} diff --git a/src/algorithms/math/bits/divideByTwo.js b/src/algorithms/math/bits/divideByTwo.js deleted file mode 100644 index 359bef9d59..0000000000 --- a/src/algorithms/math/bits/divideByTwo.js +++ /dev/null @@ -1,7 +0,0 @@ -/** - * @param {number} number - * @return {number} - */ -export default function divideByTwo(number) { - return number >> 1; -} diff --git a/src/algorithms/math/bits/fullAdder.js b/src/algorithms/math/bits/fullAdder.js deleted file mode 100644 index 37d74bb911..0000000000 --- a/src/algorithms/math/bits/fullAdder.js +++ /dev/null @@ -1,70 +0,0 @@ -import getBit from './getBit'; - -/** - * Add two numbers using only binary operators. - * - * This is an implementation of full adders logic circuit. - * https://en.wikipedia.org/wiki/Adder_(electronics) - * Inspired by: https://www.youtube.com/watch?v=wvJc9CZcvBc - * - * Table(1) - * INPUT | OUT - * C Ai Bi | C Si | Row - * -------- | -----| --- - * 0 0 0 | 0 0 | 1 - * 0 0 1 | 0 1 | 2 - * 0 1 0 | 0 1 | 3 - * 0 1 1 | 1 0 | 4 - * -------- | ---- | -- - * 1 0 0 | 0 1 | 5 - * 1 0 1 | 1 0 | 6 - * 1 1 0 | 1 0 | 7 - * 1 1 1 | 1 1 | 8 - * --------------------- - * - * Legend: - * INPUT C = Carry in, from the previous less-significant stage - * INPUT Ai = ith bit of Number A - * INPUT Bi = ith bit of Number B - * OUT C = Carry out to the next most-significant stage - * OUT Si = Bit Sum, ith least significant bit of the result - * - * - * @param {number} a - * @param {number} b - * @return {number} - */ -export default function fullAdder(a, b) { - let result = 0; - let carry = 0; - - // The operands of all bitwise operators are converted to signed - // 32-bit integers in two's complement format. - // https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Operators/Bitwise_Operators#Signed_32-bit_integers - for (let i = 0; i < 32; i += 1) { - const ai = getBit(a, i); - const bi = getBit(b, i); - const carryIn = carry; - - // Calculate binary Ai + Bi without carry (half adder) - // See Table(1) rows 1 - 4: Si = Ai ^ Bi - const aiPlusBi = ai ^ bi; - - // Calculate ith bit of the result by adding the carry bit to Ai + Bi - // For Table(1) rows 5 - 8 carryIn = 1: Si = Ai ^ Bi ^ 1, flip the bit - // Fpr Table(1) rows 1 - 4 carryIn = 0: Si = Ai ^ Bi ^ 0, a no-op. - const bitSum = aiPlusBi ^ carryIn; - - // Carry out one to the next most-significant stage - // when at least one of these is true: - // 1) Table(1) rows 6, 7: one of Ai OR Bi is 1 AND carryIn = 1 - // 2) Table(1) rows 4, 8: Both Ai AND Bi are 1 - const carryOut = (aiPlusBi & carryIn) | (ai & bi); - carry = carryOut; - - // Set ith least significant bit of the result to bitSum. - result |= bitSum << i; - } - - return result; -} diff --git a/src/algorithms/math/bits/getBit.js b/src/algorithms/math/bits/getBit.js deleted file mode 100644 index 5ff2132691..0000000000 --- a/src/algorithms/math/bits/getBit.js +++ /dev/null @@ -1,8 +0,0 @@ -/** - * @param {number} number - * @param {number} bitPosition - zero based. - * @return {number} - */ -export default function getBit(number, bitPosition) { - return (number >> bitPosition) & 1; -} diff --git a/src/algorithms/math/bits/isEven.js b/src/algorithms/math/bits/isEven.js deleted file mode 100644 index 843b4d281e..0000000000 --- a/src/algorithms/math/bits/isEven.js +++ /dev/null @@ -1,7 +0,0 @@ -/** - * @param {number} number - * @return {boolean} - */ -export default function isEven(number) { - return (number & 1) === 0; -} diff --git a/src/algorithms/math/bits/isPositive.js b/src/algorithms/math/bits/isPositive.js deleted file mode 100644 index 0e64e8ae92..0000000000 --- a/src/algorithms/math/bits/isPositive.js +++ /dev/null @@ -1,13 +0,0 @@ -/** - * @param {number} number - 32-bit integer. - * @return {boolean} - */ -export default function isPositive(number) { - // Zero is neither a positive nor a negative number. - if (number === 0) { - return false; - } - - // The most significant 32nd bit can be used to determine whether the number is positive. - return ((number >> 31) & 1) === 0; -} diff --git a/src/algorithms/math/bits/isPowerOfTwo.js b/src/algorithms/math/bits/isPowerOfTwo.js deleted file mode 100644 index 28e3e673d8..0000000000 --- a/src/algorithms/math/bits/isPowerOfTwo.js +++ /dev/null @@ -1,7 +0,0 @@ -/** - * @param {number} number - * @return bool - */ -export default function isPowerOfTwo(number) { - return (number & (number - 1)) === 0; -} diff --git a/src/algorithms/math/bits/multiply.js b/src/algorithms/math/bits/multiply.js deleted file mode 100644 index da952f429e..0000000000 --- a/src/algorithms/math/bits/multiply.js +++ /dev/null @@ -1,41 +0,0 @@ -import multiplyByTwo from './multiplyByTwo'; -import divideByTwo from './divideByTwo'; -import isEven from './isEven'; -import isPositive from './isPositive'; - -/** - * Multiply two signed numbers using bitwise operations. - * - * If a is zero or b is zero or if both a and b are zeros: - * multiply(a, b) = 0 - * - * If b is even: - * multiply(a, b) = multiply(2a, b/2) - * - * If b is odd and b is positive: - * multiply(a, b) = multiply(2a, (b-1)/2) + a - * - * If b is odd and b is negative: - * multiply(a, b) = multiply(2a, (b+1)/2) - a - * - * Time complexity: O(log b) - * - * @param {number} a - * @param {number} b - * @return {number} - */ -export default function multiply(a, b) { - // If a is zero or b is zero or if both a and b are zeros then the production is also zero. - if (b === 0 || a === 0) { - return 0; - } - - // Otherwise we will have four different cases that are described above. - const multiplyByOddPositive = () => multiply(multiplyByTwo(a), divideByTwo(b - 1)) + a; - const multiplyByOddNegative = () => multiply(multiplyByTwo(a), divideByTwo(b + 1)) - a; - - const multiplyByEven = () => multiply(multiplyByTwo(a), divideByTwo(b)); - const multiplyByOdd = () => (isPositive(b) ? multiplyByOddPositive() : multiplyByOddNegative()); - - return isEven(b) ? multiplyByEven() : multiplyByOdd(); -} diff --git a/src/algorithms/math/bits/multiplyByTwo.js b/src/algorithms/math/bits/multiplyByTwo.js deleted file mode 100644 index 3e52544d29..0000000000 --- a/src/algorithms/math/bits/multiplyByTwo.js +++ /dev/null @@ -1,7 +0,0 @@ -/** - * @param {number} number - * @return {number} - */ -export default function multiplyByTwo(number) { - return number << 1; -} diff --git a/src/algorithms/math/bits/multiplyUnsigned.js b/src/algorithms/math/bits/multiplyUnsigned.js deleted file mode 100644 index 17a2c95a65..0000000000 --- a/src/algorithms/math/bits/multiplyUnsigned.js +++ /dev/null @@ -1,43 +0,0 @@ -/** - * Multiply to unsigned numbers using bitwise operator. - * - * The main idea of bitwise multiplication is that every number may be split - * to the sum of powers of two: - * - * I.e. 19 = 2^4 + 2^1 + 2^0 - * - * Then multiplying number x by 19 is equivalent of: - * - * x * 19 = x * 2^4 + x * 2^1 + x * 2^0 - * - * Now we need to remember that (x * 2^4) is equivalent of shifting x left by 4 bits (x << 4). - * - * @param {number} number1 - * @param {number} number2 - * @return {number} - */ -export default function multiplyUnsigned(number1, number2) { - let result = 0; - - // Let's treat number2 as a multiplier for the number1. - let multiplier = number2; - - // Multiplier current bit index. - let bitIndex = 0; - - // Go through all bits of number2. - while (multiplier !== 0) { - // Check if current multiplier bit is set. - if (multiplier & 1) { - // In case if multiplier's bit at position bitIndex is set - // it would mean that we need to multiply number1 by the power - // of bit with index bitIndex and then add it to the result. - result += (number1 << bitIndex); - } - - bitIndex += 1; - multiplier >>= 1; - } - - return result; -} diff --git a/src/algorithms/math/bits/setBit.js b/src/algorithms/math/bits/setBit.js deleted file mode 100644 index c574ac692e..0000000000 --- a/src/algorithms/math/bits/setBit.js +++ /dev/null @@ -1,8 +0,0 @@ -/** - * @param {number} number - * @param {number} bitPosition - zero based. - * @return {number} - */ -export default function setBit(number, bitPosition) { - return number | (1 << bitPosition); -} diff --git a/src/algorithms/math/bits/switchSign.js b/src/algorithms/math/bits/switchSign.js deleted file mode 100644 index e38ec487ef..0000000000 --- a/src/algorithms/math/bits/switchSign.js +++ /dev/null @@ -1,8 +0,0 @@ -/** - * Switch the sign of the number using "Twos Complement" approach. - * @param {number} number - * @return {number} - */ -export default function switchSign(number) { - return ~number + 1; -} diff --git a/src/algorithms/math/bits/updateBit.js b/src/algorithms/math/bits/updateBit.js deleted file mode 100644 index f56834a3ea..0000000000 --- a/src/algorithms/math/bits/updateBit.js +++ /dev/null @@ -1,16 +0,0 @@ -/** - * @param {number} number - * @param {number} bitPosition - zero based. - * @param {number} bitValue - 0 or 1. - * @return {number} - */ -export default function updateBit(number, bitPosition, bitValue) { - // Normalized bit value. - const bitValueNormalized = bitValue ? 1 : 0; - - // Init clear mask. - const clearMask = ~(1 << bitPosition); - - // Clear bit value and then set it up to required value. - return (number & clearMask) | (bitValueNormalized << bitPosition); -} diff --git a/src/algorithms/math/complex-number/ComplexNumber.js b/src/algorithms/math/complex-number/ComplexNumber.js deleted file mode 100644 index 9e8ffa566b..0000000000 --- a/src/algorithms/math/complex-number/ComplexNumber.js +++ /dev/null @@ -1,160 +0,0 @@ -import radianToDegree from '../radian/radianToDegree'; - -export default class ComplexNumber { - /** - * z = re + im * i - * z = radius * e^(i * phase) - * - * @param {number} [re] - * @param {number} [im] - */ - constructor({ re = 0, im = 0 } = {}) { - this.re = re; - this.im = im; - } - - /** - * @param {ComplexNumber|number} addend - * @return {ComplexNumber} - */ - add(addend) { - // Make sure we're dealing with complex number. - const complexAddend = this.toComplexNumber(addend); - - return new ComplexNumber({ - re: this.re + complexAddend.re, - im: this.im + complexAddend.im, - }); - } - - /** - * @param {ComplexNumber|number} subtrahend - * @return {ComplexNumber} - */ - subtract(subtrahend) { - // Make sure we're dealing with complex number. - const complexSubtrahend = this.toComplexNumber(subtrahend); - - return new ComplexNumber({ - re: this.re - complexSubtrahend.re, - im: this.im - complexSubtrahend.im, - }); - } - - /** - * @param {ComplexNumber|number} multiplicand - * @return {ComplexNumber} - */ - multiply(multiplicand) { - // Make sure we're dealing with complex number. - const complexMultiplicand = this.toComplexNumber(multiplicand); - - return new ComplexNumber({ - re: this.re * complexMultiplicand.re - this.im * complexMultiplicand.im, - im: this.re * complexMultiplicand.im + this.im * complexMultiplicand.re, - }); - } - - /** - * @param {ComplexNumber|number} divider - * @return {ComplexNumber} - */ - divide(divider) { - // Make sure we're dealing with complex number. - const complexDivider = this.toComplexNumber(divider); - - // Get divider conjugate. - const dividerConjugate = this.conjugate(complexDivider); - - // Multiply dividend by divider's conjugate. - const finalDivident = this.multiply(dividerConjugate); - - // Calculating final divider using formula (a + bi)(a − bi) = a^2 + b^2 - const finalDivider = (complexDivider.re ** 2) + (complexDivider.im ** 2); - - return new ComplexNumber({ - re: finalDivident.re / finalDivider, - im: finalDivident.im / finalDivider, - }); - } - - /** - * @param {ComplexNumber|number} number - */ - conjugate(number) { - // Make sure we're dealing with complex number. - const complexNumber = this.toComplexNumber(number); - - return new ComplexNumber({ - re: complexNumber.re, - im: -1 * complexNumber.im, - }); - } - - /** - * @return {number} - */ - getRadius() { - return Math.sqrt((this.re ** 2) + (this.im ** 2)); - } - - /** - * @param {boolean} [inRadians] - * @return {number} - */ - getPhase(inRadians = true) { - let phase = Math.atan(Math.abs(this.im) / Math.abs(this.re)); - - if (this.re < 0 && this.im > 0) { - phase = Math.PI - phase; - } else if (this.re < 0 && this.im < 0) { - phase = -(Math.PI - phase); - } else if (this.re > 0 && this.im < 0) { - phase = -phase; - } else if (this.re === 0 && this.im > 0) { - phase = Math.PI / 2; - } else if (this.re === 0 && this.im < 0) { - phase = -Math.PI / 2; - } else if (this.re < 0 && this.im === 0) { - phase = Math.PI; - } else if (this.re > 0 && this.im === 0) { - phase = 0; - } else if (this.re === 0 && this.im === 0) { - // More correctly would be to set 'indeterminate'. - // But just for simplicity reasons let's set zero. - phase = 0; - } - - if (!inRadians) { - phase = radianToDegree(phase); - } - - return phase; - } - - /** - * @param {boolean} [inRadians] - * @return {{radius: number, phase: number}} - */ - getPolarForm(inRadians = true) { - return { - radius: this.getRadius(), - phase: this.getPhase(inRadians), - }; - } - - /** - * Convert real numbers to complex number. - * In case if complex number is provided then lefts it as is. - * - * @param {ComplexNumber|number} number - * @return {ComplexNumber} - */ - toComplexNumber(number) { - if (number instanceof ComplexNumber) { - return number; - } - - return new ComplexNumber({ re: number }); - } -} diff --git a/src/algorithms/math/complex-number/README.fr-FR.md b/src/algorithms/math/complex-number/README.fr-FR.md deleted file mode 100644 index 0e42a484d4..0000000000 --- a/src/algorithms/math/complex-number/README.fr-FR.md +++ /dev/null @@ -1,237 +0,0 @@ -# Nombre complexe - -_Read this in other languages:_ -[english](README.md). - -Un **nombre complexe** est un nombre qui peut s'écrire sous la forme -`a + b * i`, tels que `a` et `b` sont des nombres réels, -et `i` est la solution de l'équation `x^2 = −1`. -Du fait qu'aucun _nombre réel_ ne statisfait l'équation, -`i` est appellé _nombre imaginaire_. Étant donné le nombre complexe `a + b * i`, -`a` est appellé _partie réelle_, et `b`, _partie imaginaire_. - -![Complex Number](https://www.mathsisfun.com/numbers/images/complex-example.svg) - -Un nombre complexe est donc la combinaison -d'un nombre réel et d'un nombre imaginaire : - -![Complex Number](https://www.mathsisfun.com/numbers/images/complex-number.svg) - -En géométrie, les nombres complexes étendent le concept -de ligne de nombres sur une dimension à un _plan complexe à deux dimensions_ -en utilisant l'axe horizontal pour lepartie réelle -et l'axe vertical pour la partie imaginaire. Le nombre complexe `a + b * i` -peut être identifié avec le point `(a, b)` dans le plan complexe. - -Un nombre complexe dont la partie réelle est zéro est dit _imaginaire pur_; -les points pour ces nombres se trouvent sur l'axe vertical du plan complexe. -Un nombre complexe dont la partie imaginaire est zéro -peut être considéré comme un _nombre réel_; son point -se trouve sur l'axe horizontal du plan complexe. - -| Nombre complexe | Partie réelle | partie imaginaire | | -| :-------------- | :-----------: | :---------------: | ---------------- | -| 3 + 2i | 3 | 2 | | -| 5 | 5 | **0** | Purely Real | -| −6i | **0** | -6 | Purely Imaginary | - -A complex number can be visually represented as a pair of numbers `(a, b)` forming -a vector on a diagram called an _Argand diagram_, representing the _complex plane_. -`Re` is the real axis, `Im` is the imaginary axis, and `i` satisfies `i^2 = −1`. - -Un nombre complexe peut être représenté visuellement comme une paire de nombres -`(a, b)` formant un vecteur sur un diagramme appelé _diagramme d'Argand_, -représentant le _plan complexe_. -_Re_ est l'axe réel, _Im_ est l'axe imaginaire et `i` satisfait `i^2 = −1`. - -![Complex Number](https://upload.wikimedia.org/wikipedia/commons/a/af/Complex_number_illustration.svg) - -> Complexe ne veut pas dire compliqué. Cela signifie simplement que -> les deux types de nombres, réels et imaginaires, forment ensemble un complexe -> comme on le dirait d'un complexe de bâtiments (bâtiments réunis). - -## Forme polaire - -Une manière de définir un point `P` dans le plan complexe, autre que d'utiliser -les coordonnées x et y, consiste à utiliser la distance entre le point `O`, le point -dont les coordonnées sont `(0, 0)` (l'origine), et l'angle sous-tendu -entre l'axe réel positif et le segment de droite `OP` dans le sens antihoraire. -Cette idée conduit à la forme polaire des nombres complexes. - -![Polar Form](https://upload.wikimedia.org/wikipedia/commons/7/7a/Complex_number_illustration_modarg.svg) - -The _valeur absolue_ (ou module) d'un nombre complexe `z = x + yi` est: - -![Radius](https://wikimedia.org/api/rest_v1/media/math/render/svg/b59629c801aa0ddcdf17ee489e028fb9f8d4ea75) - -L'argument de `z` (parfois appelé « phase » ou « amplitude ») est l'angle -du rayon `OP` avec l'axe des réels positifs, et s'écrit `arg(z)`. Comme -avec le module, l'argument peut être trouvé à partir de la forme rectangulaire `x + yi`: - -![Phase](https://wikimedia.org/api/rest_v1/media/math/render/svg/7cbbdd9bb1dd5df86dd2b820b20f82995023e566) - -Ensemble, `r` et`φ` donnent une autre façon de représenter les nombres complexes, la -forme polaire, car la combinaison du module et de l'argument suffit à indiquer la -position d'un point sur le plan. Obtenir les coordonnées du rectangle d'origine -à partir de la forme polaire se fait par la formule appelée forme trigonométrique : - -![Polar Form](https://wikimedia.org/api/rest_v1/media/math/render/svg/b03de1e1b7b049880b5e4870b68a57bc180ff6ce) - -En utilisant la formule d'Euler, cela peut être écrit comme suit: - -![Euler's Form](https://wikimedia.org/api/rest_v1/media/math/render/svg/0a087c772212e7375cb321d83fc1fcc715cd0ed2) - -## Opérations de base - -### Addition - -Pour ajouter deux nombres complexes, nous ajoutons chaque partie séparément : - -```text -(a + b * i) + (c + d * i) = (a + c) + (b + d) * i -``` - -**Exemple** - -```text -(3 + 5i) + (4 − 3i) = (3 + 4) + (5 − 3)i = 7 + 2i -``` - -Dans un plan complexe, l'addition ressemblera à ceci: - -![Complex Addition](https://www.mathsisfun.com/algebra/images/complex-plane-vector-add.svg) - -### Soustraction - -Pour soustraire deux nombres complexes, on soustrait chaque partie séparément : - -```text -(a + b * i) - (c + d * i) = (a - c) + (b - d) * i -``` - -**Exemple** - -```text -(3 + 5i) - (4 − 3i) = (3 - 4) + (5 + 3)i = -1 + 8i -``` - -### Multiplication - -Pour multiplier les nombres complexes, chaque partie du premier nombre complexe est multipliée -par chaque partie du deuxième nombre complexe: - -On peut utiliser le "FOIL" (parfois traduit PEID en français), acronyme de -**F**irsts (Premiers), **O**uters (Extérieurs), **I**nners (Intérieurs), **L**asts (Derniers)" ( -voir [Binomial Multiplication](ttps://www.mathsisfun.com/algebra/polynomials-multiplying.html) pour plus de détails): - -![Complex Multiplication](https://www.mathsisfun.com/algebra/images/foil-complex.svg) - -- Firsts: `a × c` -- Outers: `a × di` -- Inners: `bi × c` -- Lasts: `bi × di` - -En général, cela ressemble à: - -```text -(a + bi)(c + di) = ac + adi + bci + bdi^2 -``` - -Mais il existe aussi un moyen plus rapide ! - -Utiliser cette loi: - -```text -(a + bi)(c + di) = (ac − bd) + (ad + bc)i -``` - -**Exemple** - -```text -(3 + 2i)(1 + 7i) -= 3×1 + 3×7i + 2i×1+ 2i×7i -= 3 + 21i + 2i + 14i^2 -= 3 + 21i + 2i − 14 (because i^2 = −1) -= −11 + 23i -``` - -```text -(3 + 2i)(1 + 7i) = (3×1 − 2×7) + (3×7 + 2×1)i = −11 + 23i -``` - -### Conjugués - -En mathématiques, le conjugué d'un nombre complexe z -est le nombre complexe formé de la même partie réelle que z -mais de partie imaginaire opposée. - -Un conjugué vois son signe changer au milieu comme suit: - -![Complex Conjugate](https://www.mathsisfun.com/numbers/images/complex-conjugate.svg) - -Un conjugué est souvent écrit avec un trait suscrit (barre au-dessus): - -```text -______ -5 − 3i = 5 + 3i -``` - -Dans un plan complexe, le nombre conjugué sera mirroir par rapport aux axes réels. - -![Complex Conjugate](https://upload.wikimedia.org/wikipedia/commons/6/69/Complex_conjugate_picture.svg) - -### Division - -Le conjugué est utiliser pour aider à la division de nombres complexes - -L'astuce est de _multiplier le haut et le bas par le conjugué du bas_. - -**Exemple** - -```text -2 + 3i ------- -4 − 5i -``` - -Multiplier le haut et le bas par le conjugué de `4 − 5i`: - -```text - (2 + 3i) * (4 + 5i) 8 + 10i + 12i + 15i^2 -= ------------------- = ---------------------- - (4 − 5i) * (4 + 5i) 16 + 20i − 20i − 25i^2 -``` - -Et puisque `i^2 = −1`, il s'ensuit que: - -```text - 8 + 10i + 12i − 15 −7 + 22i −7 22 -= ------------------- = -------- = -- + -- * i - 16 + 20i − 20i + 25 41 41 41 - -``` - -Il existe cependant un moyen plus direct. - -Dans l'exemple précédent, ce qui s'est passé en bas était intéressant: - -```text -(4 − 5i)(4 + 5i) = 16 + 20i − 20i − 25i -``` - -Les termes du milieu `(20i − 20i)` s'annule! Et pusique `i^2 = −1` on retrouve: - -```text -(4 − 5i)(4 + 5i) = 4^2 + 5^2 -``` - -Ce qui est vraiment un résultat assez simple. La règle générale est: - -```text -(a + bi)(a − bi) = a^2 + b^2 -``` - -## Références - -- [Wikipedia](https://fr.wikipedia.org/wiki/Nombre_complexe) -- [Math is Fun](https://www.mathsisfun.com/numbers/complex-numbers.html) diff --git a/src/algorithms/math/complex-number/README.md b/src/algorithms/math/complex-number/README.md deleted file mode 100644 index 7629aad3f0..0000000000 --- a/src/algorithms/math/complex-number/README.md +++ /dev/null @@ -1,228 +0,0 @@ -# Complex Number - -_Read this in other languages:_ -[français](README.fr-FR.md). - -A **complex number** is a number that can be expressed in the -form `a + b * i`, where `a` and `b` are real numbers, and `i` is a solution of -the equation `x^2 = −1`. Because no _real number_ satisfies this -equation, `i` is called an _imaginary number_. For the complex -number `a + b * i`, `a` is called the _real part_, and `b` is called -the _imaginary part_. - -![Complex Number](https://www.mathsisfun.com/numbers/images/complex-example.svg) - -A Complex Number is a combination of a Real Number and an Imaginary Number: - -![Complex Number](https://www.mathsisfun.com/numbers/images/complex-number.svg) - -Geometrically, complex numbers extend the concept of the one-dimensional number -line to the _two-dimensional complex plane_ by using the horizontal axis for the -real part and the vertical axis for the imaginary part. The complex -number `a + b * i` can be identified with the point `(a, b)` in the complex plane. - -A complex number whose real part is zero is said to be _purely imaginary_; the -points for these numbers lie on the vertical axis of the complex plane. A complex -number whose imaginary part is zero can be viewed as a _real number_; its point -lies on the horizontal axis of the complex plane. - -| Complex Number | Real Part | Imaginary Part | | -| :------------- | :-------: | :------------: | ---------------- | -| 3 + 2i | 3 | 2 | | -| 5 | 5 | **0** | Purely Real | -| −6i | **0** | -6 | Purely Imaginary | - -A complex number can be visually represented as a pair of numbers `(a, b)` forming -a vector on a diagram called an _Argand diagram_, representing the _complex plane_. -`Re` is the real axis, `Im` is the imaginary axis, and `i` satisfies `i^2 = −1`. - -![Complex Number](https://upload.wikimedia.org/wikipedia/commons/a/af/Complex_number_illustration.svg) - -> Complex does not mean complicated. It means the two types of numbers, real and -> imaginary, together form a complex, just like a building complex (buildings -> joined together). - -## Polar Form - -An alternative way of defining a point `P` in the complex plane, other than using -the x- and y-coordinates, is to use the distance of the point from `O`, the point -whose coordinates are `(0, 0)` (the origin), together with the angle subtended -between the positive real axis and the line segment `OP` in a counterclockwise -direction. This idea leads to the polar form of complex numbers. - -![Polar Form](https://upload.wikimedia.org/wikipedia/commons/7/7a/Complex_number_illustration_modarg.svg) - -The _absolute value_ (or modulus or magnitude) of a complex number `z = x + yi` is: - -![Radius](https://wikimedia.org/api/rest_v1/media/math/render/svg/b59629c801aa0ddcdf17ee489e028fb9f8d4ea75) - -The argument of `z` (in many applications referred to as the "phase") is the angle -of the radius `OP` with the positive real axis, and is written as `arg(z)`. As -with the modulus, the argument can be found from the rectangular form `x+yi`: - -![Phase](https://wikimedia.org/api/rest_v1/media/math/render/svg/7cbbdd9bb1dd5df86dd2b820b20f82995023e566) - -Together, `r` and `φ` give another way of representing complex numbers, the -polar form, as the combination of modulus and argument fully specify the -position of a point on the plane. Recovering the original rectangular -co-ordinates from the polar form is done by the formula called trigonometric -form: - -![Polar Form](https://wikimedia.org/api/rest_v1/media/math/render/svg/b03de1e1b7b049880b5e4870b68a57bc180ff6ce) - -Using Euler's formula this can be written as: - -![Euler's Form](https://wikimedia.org/api/rest_v1/media/math/render/svg/0a087c772212e7375cb321d83fc1fcc715cd0ed2) - -## Basic Operations - -### Adding - -To add two complex numbers we add each part separately: - -```text -(a + b * i) + (c + d * i) = (a + c) + (b + d) * i -``` - -**Example** - -```text -(3 + 5i) + (4 − 3i) = (3 + 4) + (5 − 3)i = 7 + 2i -``` - -On complex plane the adding operation will look like the following: - -![Complex Addition](https://www.mathsisfun.com/algebra/images/complex-plane-vector-add.svg) - -### Subtracting - -To subtract two complex numbers we subtract each part separately: - -```text -(a + b * i) - (c + d * i) = (a - c) + (b - d) * i -``` - -**Example** - -```text -(3 + 5i) - (4 − 3i) = (3 - 4) + (5 + 3)i = -1 + 8i -``` - -### Multiplying - -To multiply complex numbers each part of the first complex number gets multiplied -by each part of the second complex number: - -Just use "FOIL", which stands for "**F**irsts, **O**uters, **I**nners, **L**asts" ( -see [Binomial Multiplication](ttps://www.mathsisfun.com/algebra/polynomials-multiplying.html) for -more details): - -![Complex Multiplication](https://www.mathsisfun.com/algebra/images/foil-complex.svg) - -- Firsts: `a × c` -- Outers: `a × di` -- Inners: `bi × c` -- Lasts: `bi × di` - -In general it looks like this: - -```text -(a + bi)(c + di) = ac + adi + bci + bdi^2 -``` - -But there is also a quicker way! - -Use this rule: - -```text -(a + bi)(c + di) = (ac − bd) + (ad + bc)i -``` - -**Example** - -```text -(3 + 2i)(1 + 7i) -= 3×1 + 3×7i + 2i×1+ 2i×7i -= 3 + 21i + 2i + 14i^2 -= 3 + 21i + 2i − 14 (because i^2 = −1) -= −11 + 23i -``` - -```text -(3 + 2i)(1 + 7i) = (3×1 − 2×7) + (3×7 + 2×1)i = −11 + 23i -``` - -### Conjugates - -We will need to know about conjugates in a minute! - -A conjugate is where we change the sign in the middle like this: - -![Complex Conjugate](https://www.mathsisfun.com/numbers/images/complex-conjugate.svg) - -A conjugate is often written with a bar over it: - -```text -______ -5 − 3i = 5 + 3i -``` - -On the complex plane the conjugate number will be mirrored against real axes. - -![Complex Conjugate](https://upload.wikimedia.org/wikipedia/commons/6/69/Complex_conjugate_picture.svg) - -### Dividing - -The conjugate is used to help complex division. - -The trick is to _multiply both top and bottom by the conjugate of the bottom_. - -**Example** - -```text -2 + 3i ------- -4 − 5i -``` - -Multiply top and bottom by the conjugate of `4 − 5i`: - -```text - (2 + 3i) * (4 + 5i) 8 + 10i + 12i + 15i^2 -= ------------------- = ---------------------- - (4 − 5i) * (4 + 5i) 16 + 20i − 20i − 25i^2 -``` - -Now remember that `i^2 = −1`, so: - -```text - 8 + 10i + 12i − 15 −7 + 22i −7 22 -= ------------------- = -------- = -- + -- * i - 16 + 20i − 20i + 25 41 41 41 - -``` - -There is a faster way though. - -In the previous example, what happened on the bottom was interesting: - -```text -(4 − 5i)(4 + 5i) = 16 + 20i − 20i − 25i -``` - -The middle terms `(20i − 20i)` cancel out! Also `i^2 = −1` so we end up with this: - -```text -(4 − 5i)(4 + 5i) = 4^2 + 5^2 -``` - -Which is really quite a simple result. The general rule is: - -```text -(a + bi)(a − bi) = a^2 + b^2 -``` - -## References - -- [Wikipedia](https://en.wikipedia.org/wiki/Complex_number) -- [Math is Fun](https://www.mathsisfun.com/numbers/complex-numbers.html) diff --git a/src/algorithms/math/complex-number/__test__/ComplexNumber.test.js b/src/algorithms/math/complex-number/__test__/ComplexNumber.test.js deleted file mode 100644 index 4392103d28..0000000000 --- a/src/algorithms/math/complex-number/__test__/ComplexNumber.test.js +++ /dev/null @@ -1,181 +0,0 @@ -import ComplexNumber from '../ComplexNumber'; - -describe('ComplexNumber', () => { - it('should create complex numbers', () => { - const complexNumber = new ComplexNumber({ re: 1, im: 2 }); - - expect(complexNumber).toBeDefined(); - expect(complexNumber.re).toBe(1); - expect(complexNumber.im).toBe(2); - - const defaultComplexNumber = new ComplexNumber(); - expect(defaultComplexNumber.re).toBe(0); - expect(defaultComplexNumber.im).toBe(0); - }); - - it('should add complex numbers', () => { - const complexNumber1 = new ComplexNumber({ re: 1, im: 2 }); - const complexNumber2 = new ComplexNumber({ re: 3, im: 8 }); - - const complexNumber3 = complexNumber1.add(complexNumber2); - const complexNumber4 = complexNumber2.add(complexNumber1); - - expect(complexNumber3.re).toBe(1 + 3); - expect(complexNumber3.im).toBe(2 + 8); - - expect(complexNumber4.re).toBe(1 + 3); - expect(complexNumber4.im).toBe(2 + 8); - }); - - it('should add complex and natural numbers', () => { - const complexNumber = new ComplexNumber({ re: 1, im: 2 }); - const realNumber = new ComplexNumber({ re: 3 }); - - const complexNumber3 = complexNumber.add(realNumber); - const complexNumber4 = realNumber.add(complexNumber); - const complexNumber5 = complexNumber.add(3); - - expect(complexNumber3.re).toBe(1 + 3); - expect(complexNumber3.im).toBe(2); - - expect(complexNumber4.re).toBe(1 + 3); - expect(complexNumber4.im).toBe(2); - - expect(complexNumber5.re).toBe(1 + 3); - expect(complexNumber5.im).toBe(2); - }); - - it('should subtract complex numbers', () => { - const complexNumber1 = new ComplexNumber({ re: 1, im: 2 }); - const complexNumber2 = new ComplexNumber({ re: 3, im: 8 }); - - const complexNumber3 = complexNumber1.subtract(complexNumber2); - const complexNumber4 = complexNumber2.subtract(complexNumber1); - - expect(complexNumber3.re).toBe(1 - 3); - expect(complexNumber3.im).toBe(2 - 8); - - expect(complexNumber4.re).toBe(3 - 1); - expect(complexNumber4.im).toBe(8 - 2); - }); - - it('should subtract complex and natural numbers', () => { - const complexNumber = new ComplexNumber({ re: 1, im: 2 }); - const realNumber = new ComplexNumber({ re: 3 }); - - const complexNumber3 = complexNumber.subtract(realNumber); - const complexNumber4 = realNumber.subtract(complexNumber); - const complexNumber5 = complexNumber.subtract(3); - - expect(complexNumber3.re).toBe(1 - 3); - expect(complexNumber3.im).toBe(2); - - expect(complexNumber4.re).toBe(3 - 1); - expect(complexNumber4.im).toBe(-2); - - expect(complexNumber5.re).toBe(1 - 3); - expect(complexNumber5.im).toBe(2); - }); - - it('should multiply complex numbers', () => { - const complexNumber1 = new ComplexNumber({ re: 3, im: 2 }); - const complexNumber2 = new ComplexNumber({ re: 1, im: 7 }); - - const complexNumber3 = complexNumber1.multiply(complexNumber2); - const complexNumber4 = complexNumber2.multiply(complexNumber1); - const complexNumber5 = complexNumber1.multiply(5); - - expect(complexNumber3.re).toBe(-11); - expect(complexNumber3.im).toBe(23); - - expect(complexNumber4.re).toBe(-11); - expect(complexNumber4.im).toBe(23); - - expect(complexNumber5.re).toBe(15); - expect(complexNumber5.im).toBe(10); - }); - - it('should multiply complex numbers by themselves', () => { - const complexNumber = new ComplexNumber({ re: 1, im: 1 }); - - const result = complexNumber.multiply(complexNumber); - - expect(result.re).toBe(0); - expect(result.im).toBe(2); - }); - - it('should calculate i in power of two', () => { - const complexNumber = new ComplexNumber({ re: 0, im: 1 }); - - const result = complexNumber.multiply(complexNumber); - - expect(result.re).toBe(-1); - expect(result.im).toBe(0); - }); - - it('should divide complex numbers', () => { - const complexNumber1 = new ComplexNumber({ re: 2, im: 3 }); - const complexNumber2 = new ComplexNumber({ re: 4, im: -5 }); - - const complexNumber3 = complexNumber1.divide(complexNumber2); - const complexNumber4 = complexNumber1.divide(2); - - expect(complexNumber3.re).toBe(-7 / 41); - expect(complexNumber3.im).toBe(22 / 41); - - expect(complexNumber4.re).toBe(1); - expect(complexNumber4.im).toBe(1.5); - }); - - it('should return complex number in polar form', () => { - const complexNumber1 = new ComplexNumber({ re: 3, im: 3 }); - expect(complexNumber1.getPolarForm().radius).toBe(Math.sqrt((3 ** 2) + (3 ** 2))); - expect(complexNumber1.getPolarForm().phase).toBe(Math.PI / 4); - expect(complexNumber1.getPolarForm(false).phase).toBe(45); - - const complexNumber2 = new ComplexNumber({ re: -3, im: 3 }); - expect(complexNumber2.getPolarForm().radius).toBe(Math.sqrt((3 ** 2) + (3 ** 2))); - expect(complexNumber2.getPolarForm().phase).toBe(3 * (Math.PI / 4)); - expect(complexNumber2.getPolarForm(false).phase).toBe(135); - - const complexNumber3 = new ComplexNumber({ re: -3, im: -3 }); - expect(complexNumber3.getPolarForm().radius).toBe(Math.sqrt((3 ** 2) + (3 ** 2))); - expect(complexNumber3.getPolarForm().phase).toBe(-3 * (Math.PI / 4)); - expect(complexNumber3.getPolarForm(false).phase).toBe(-135); - - const complexNumber4 = new ComplexNumber({ re: 3, im: -3 }); - expect(complexNumber4.getPolarForm().radius).toBe(Math.sqrt((3 ** 2) + (3 ** 2))); - expect(complexNumber4.getPolarForm().phase).toBe(-1 * (Math.PI / 4)); - expect(complexNumber4.getPolarForm(false).phase).toBe(-45); - - const complexNumber5 = new ComplexNumber({ re: 5, im: 7 }); - expect(complexNumber5.getPolarForm().radius).toBeCloseTo(8.60); - expect(complexNumber5.getPolarForm().phase).toBeCloseTo(0.95); - expect(complexNumber5.getPolarForm(false).phase).toBeCloseTo(54.46); - - const complexNumber6 = new ComplexNumber({ re: 0, im: 0.25 }); - expect(complexNumber6.getPolarForm().radius).toBeCloseTo(0.25); - expect(complexNumber6.getPolarForm().phase).toBeCloseTo(1.57); - expect(complexNumber6.getPolarForm(false).phase).toBeCloseTo(90); - - const complexNumber7 = new ComplexNumber({ re: 0, im: -0.25 }); - expect(complexNumber7.getPolarForm().radius).toBeCloseTo(0.25); - expect(complexNumber7.getPolarForm().phase).toBeCloseTo(-1.57); - expect(complexNumber7.getPolarForm(false).phase).toBeCloseTo(-90); - - const complexNumber8 = new ComplexNumber(); - expect(complexNumber8.getPolarForm().radius).toBeCloseTo(0); - expect(complexNumber8.getPolarForm().phase).toBeCloseTo(0); - expect(complexNumber8.getPolarForm(false).phase).toBeCloseTo(0); - - const complexNumber9 = new ComplexNumber({ re: -0.25, im: 0 }); - expect(complexNumber9.getPolarForm().radius).toBeCloseTo(0.25); - expect(complexNumber9.getPolarForm().phase).toBeCloseTo(Math.PI); - expect(complexNumber9.getPolarForm(false).phase).toBeCloseTo(180); - - const complexNumber10 = new ComplexNumber({ re: 0.25, im: 0 }); - expect(complexNumber10.getPolarForm().radius).toBeCloseTo(0.25); - expect(complexNumber10.getPolarForm().phase).toBeCloseTo(0); - expect(complexNumber10.getPolarForm(false).phase).toBeCloseTo(0); - }); -}); diff --git a/src/algorithms/math/euclidean-algorithm/README.fr-FR.md b/src/algorithms/math/euclidean-algorithm/README.fr-FR.md deleted file mode 100644 index 75b6a90b88..0000000000 --- a/src/algorithms/math/euclidean-algorithm/README.fr-FR.md +++ /dev/null @@ -1,49 +0,0 @@ -# Algorithme d'Euclide - -_Read this in other languages:_ -[english](README.md). - -En mathématiques, l'algorithme d'Euclide est un algorithme qui calcule le plus grand commun diviseur (PGCD) de deux entiers, c'est-à-dire le plus grand entier qui divise les deux entiers, en laissant un reste nul. L'algorithme ne connaît pas la factorisation de ces deux nombres. - -Le PGCD de deux entiers relatifs est égal au PGCD de leurs valeurs absolues : de ce fait, on se restreint dans cette section aux entiers positifs. L'algorithme part du constat suivant : le PGCD de deux nombres n'est pas changé si on remplace le plus grand d'entre eux par leur différence. Autrement dit, `pgcd(a, b) = pgcd(b, a - b)`. Par exemple, le PGCD de `252` et `105` vaut `21` (en effet, `252 = 21 × 12` and `105 = 21 × 5`), mais c'est aussi le PGCD de `252 - 105 = 147` et `105`. Ainsi, comme le remplacement de ces nombres diminue strictement le plus grand d'entre eux, on peut continuer le processus, jusqu'à obtenir deux nombres égaux. - -En inversant les étapes, le PGCD peut être exprimé comme une somme de -les deux nombres originaux, chacun étant multiplié -par un entier positif ou négatif, par exemple `21 = 5 × 105 + (-2) × 252`. -Le fait que le PGCD puisse toujours être exprimé de cette manière est -connue sous le nom de Théorème de Bachet-Bézout. - -![GCD](https://upload.wikimedia.org/wikipedia/commons/3/37/Euclid%27s_algorithm_Book_VII_Proposition_2_3.png) - -La Méthode d'Euclide pour trouver le plus grand diviseur commun (PGCD) -de deux longueurs de départ`BA` et `DC`, toutes deux définies comme étant -multiples d'une longueur commune. La longueur `DC` étant -plus courte, elle est utilisée pour « mesurer » `BA`, mais une seule fois car -le reste `EA` est inférieur à `DC`. `EA` mesure maintenant (deux fois) -la longueur la plus courte `DC`, le reste `FC` étant plus court que `EA`. -Alors `FC` mesure (trois fois) la longueur `EA`. Parce qu'il y a -pas de reste, le processus se termine par `FC` étant le « PGCD ». -À droite, l'exemple de Nicomaque de Gérase avec les nombres `49` et `21` -ayan un PGCD de `7` (dérivé de Heath 1908: 300). - -![GCD](https://upload.wikimedia.org/wikipedia/commons/7/74/24x60.svg) - -Un de rectangle de dimensions `24 par 60` peux se carreler en carrés de `12 par 12`, -puisque `12` est le PGCD ed `24` et `60`. De façon générale, -un rectangle de dimension `a par b` peut se carreler en carrés -de côté `c`, seulement si `c` est un diviseur commun de `a` et `b`. - -![GCD](https://upload.wikimedia.org/wikipedia/commons/1/1c/Euclidean_algorithm_1071_462.gif) - -Animation basée sur la soustraction via l'algorithme euclidien. -Le rectangle initial a les dimensions `a = 1071` et `b = 462`. -Des carrés de taille `462 × 462` y sont placés en laissant un -rectangle de `462 × 147`. Ce rectangle est carrelé avec des -carrés de `147 × 147` jusqu'à ce qu'un rectangle de `21 × 147` soit laissé, -qui à son tour estcarrelé avec des carrés `21 × 21`, -ne laissant aucune zone non couverte. -La plus petite taille carrée, `21`, est le PGCD de `1071` et `462`. - -## References - -[Wikipedia](https://fr.wikipedia.org/wiki/Algorithme_d%27Euclide) diff --git a/src/algorithms/math/euclidean-algorithm/README.md b/src/algorithms/math/euclidean-algorithm/README.md deleted file mode 100644 index 89af03b15e..0000000000 --- a/src/algorithms/math/euclidean-algorithm/README.md +++ /dev/null @@ -1,60 +0,0 @@ -# Euclidean algorithm - -_Read this in other languages:_ -[français](README.fr-FR.md). - -In mathematics, the Euclidean algorithm, or Euclid's algorithm, -is an efficient method for computing the greatest common divisor -(GCD) of two numbers, the largest number that divides both of -them without leaving a remainder. - -The Euclidean algorithm is based on the principle that the -greatest common divisor of two numbers does not change if -the larger number is replaced by its difference with the -smaller number. For example, `21` is the GCD of `252` and -`105` (as `252 = 21 × 12` and `105 = 21 × 5`), and the same -number `21` is also the GCD of `105` and `252 − 105 = 147`. -Since this replacement reduces the larger of the two numbers, -repeating this process gives successively smaller pairs of -numbers until the two numbers become equal. -When that occurs, they are the GCD of the original two numbers. - -By reversing the steps, the GCD can be expressed as a sum of -the two original numbers each multiplied by a positive or -negative integer, e.g., `21 = 5 × 105 + (−2) × 252`. -The fact that the GCD can always be expressed in this way is -known as Bézout's identity. - -![GCD](https://upload.wikimedia.org/wikipedia/commons/3/37/Euclid%27s_algorithm_Book_VII_Proposition_2_3.png) - -Euclid's method for finding the greatest common divisor (GCD) -of two starting lengths `BA` and `DC`, both defined to be -multiples of a common "unit" length. The length `DC` being -shorter, it is used to "measure" `BA`, but only once because -remainder `EA` is less than `DC`. EA now measures (twice) -the shorter length `DC`, with remainder `FC` shorter than `EA`. -Then `FC` measures (three times) length `EA`. Because there is -no remainder, the process ends with `FC` being the `GCD`. -On the right Nicomachus' example with numbers `49` and `21` -resulting in their GCD of `7` (derived from Heath 1908:300). - -![GCD](https://upload.wikimedia.org/wikipedia/commons/7/74/24x60.svg) - -A `24-by-60` rectangle is covered with ten `12-by-12` square -tiles, where `12` is the GCD of `24` and `60`. More generally, -an `a-by-b` rectangle can be covered with square tiles of -side-length `c` only if `c` is a common divisor of `a` and `b`. - -![GCD](https://upload.wikimedia.org/wikipedia/commons/1/1c/Euclidean_algorithm_1071_462.gif) - -Subtraction-based animation of the Euclidean algorithm. -The initial rectangle has dimensions `a = 1071` and `b = 462`. -Squares of size `462×462` are placed within it leaving a -`462×147` rectangle. This rectangle is tiled with `147×147` -squares until a `21×147` rectangle is left, which in turn is -tiled with `21×21` squares, leaving no uncovered area. -The smallest square size, `21`, is the GCD of `1071` and `462`. - -## References - -[Wikipedia](https://en.wikipedia.org/wiki/Euclidean_algorithm) diff --git a/src/algorithms/math/euclidean-algorithm/__test__/euclideanAlgorithm.test.js b/src/algorithms/math/euclidean-algorithm/__test__/euclideanAlgorithm.test.js deleted file mode 100644 index bbf92b26a5..0000000000 --- a/src/algorithms/math/euclidean-algorithm/__test__/euclideanAlgorithm.test.js +++ /dev/null @@ -1,26 +0,0 @@ -import euclideanAlgorithm from '../euclideanAlgorithm'; - -describe('euclideanAlgorithm', () => { - it('should calculate GCD recursively', () => { - expect(euclideanAlgorithm(0, 0)).toBe(0); - expect(euclideanAlgorithm(2, 0)).toBe(2); - expect(euclideanAlgorithm(0, 2)).toBe(2); - expect(euclideanAlgorithm(1, 2)).toBe(1); - expect(euclideanAlgorithm(2, 1)).toBe(1); - expect(euclideanAlgorithm(6, 6)).toBe(6); - expect(euclideanAlgorithm(2, 4)).toBe(2); - expect(euclideanAlgorithm(4, 2)).toBe(2); - expect(euclideanAlgorithm(12, 4)).toBe(4); - expect(euclideanAlgorithm(4, 12)).toBe(4); - expect(euclideanAlgorithm(5, 13)).toBe(1); - expect(euclideanAlgorithm(27, 13)).toBe(1); - expect(euclideanAlgorithm(24, 60)).toBe(12); - expect(euclideanAlgorithm(60, 24)).toBe(12); - expect(euclideanAlgorithm(252, 105)).toBe(21); - expect(euclideanAlgorithm(105, 252)).toBe(21); - expect(euclideanAlgorithm(1071, 462)).toBe(21); - expect(euclideanAlgorithm(462, 1071)).toBe(21); - expect(euclideanAlgorithm(462, -1071)).toBe(21); - expect(euclideanAlgorithm(-462, -1071)).toBe(21); - }); -}); diff --git a/src/algorithms/math/euclidean-algorithm/__test__/euclideanAlgorithmIterative.test.js b/src/algorithms/math/euclidean-algorithm/__test__/euclideanAlgorithmIterative.test.js deleted file mode 100644 index 5fd0f846ea..0000000000 --- a/src/algorithms/math/euclidean-algorithm/__test__/euclideanAlgorithmIterative.test.js +++ /dev/null @@ -1,26 +0,0 @@ -import euclideanAlgorithmIterative from '../euclideanAlgorithmIterative'; - -describe('euclideanAlgorithmIterative', () => { - it('should calculate GCD iteratively', () => { - expect(euclideanAlgorithmIterative(0, 0)).toBe(0); - expect(euclideanAlgorithmIterative(2, 0)).toBe(2); - expect(euclideanAlgorithmIterative(0, 2)).toBe(2); - expect(euclideanAlgorithmIterative(1, 2)).toBe(1); - expect(euclideanAlgorithmIterative(2, 1)).toBe(1); - expect(euclideanAlgorithmIterative(6, 6)).toBe(6); - expect(euclideanAlgorithmIterative(2, 4)).toBe(2); - expect(euclideanAlgorithmIterative(4, 2)).toBe(2); - expect(euclideanAlgorithmIterative(12, 4)).toBe(4); - expect(euclideanAlgorithmIterative(4, 12)).toBe(4); - expect(euclideanAlgorithmIterative(5, 13)).toBe(1); - expect(euclideanAlgorithmIterative(27, 13)).toBe(1); - expect(euclideanAlgorithmIterative(24, 60)).toBe(12); - expect(euclideanAlgorithmIterative(60, 24)).toBe(12); - expect(euclideanAlgorithmIterative(252, 105)).toBe(21); - expect(euclideanAlgorithmIterative(105, 252)).toBe(21); - expect(euclideanAlgorithmIterative(1071, 462)).toBe(21); - expect(euclideanAlgorithmIterative(462, 1071)).toBe(21); - expect(euclideanAlgorithmIterative(462, -1071)).toBe(21); - expect(euclideanAlgorithmIterative(-462, -1071)).toBe(21); - }); -}); diff --git a/src/algorithms/math/euclidean-algorithm/euclideanAlgorithm.js b/src/algorithms/math/euclidean-algorithm/euclideanAlgorithm.js deleted file mode 100644 index b9cec97c19..0000000000 --- a/src/algorithms/math/euclidean-algorithm/euclideanAlgorithm.js +++ /dev/null @@ -1,15 +0,0 @@ -/** - * Recursive version of Euclidean Algorithm of finding greatest common divisor (GCD). - * @param {number} originalA - * @param {number} originalB - * @return {number} - */ -export default function euclideanAlgorithm(originalA, originalB) { - // Make input numbers positive. - const a = Math.abs(originalA); - const b = Math.abs(originalB); - - // To make algorithm work faster instead of subtracting one number from the other - // we may use modulo operation. - return (b === 0) ? a : euclideanAlgorithm(b, a % b); -} diff --git a/src/algorithms/math/euclidean-algorithm/euclideanAlgorithmIterative.js b/src/algorithms/math/euclidean-algorithm/euclideanAlgorithmIterative.js deleted file mode 100644 index 302b5bffe9..0000000000 --- a/src/algorithms/math/euclidean-algorithm/euclideanAlgorithmIterative.js +++ /dev/null @@ -1,20 +0,0 @@ -/** - * Iterative version of Euclidean Algorithm of finding greatest common divisor (GCD). - * @param {number} originalA - * @param {number} originalB - * @return {number} - */ -export default function euclideanAlgorithmIterative(originalA, originalB) { - // Make input numbers positive. - let a = Math.abs(originalA); - let b = Math.abs(originalB); - - // Subtract one number from another until both numbers would become the same. - // This will be out GCD. Also quit the loop if one of the numbers is zero. - while (a && b && a !== b) { - [a, b] = a > b ? [a - b, b] : [a, b - a]; - } - - // Return the number that is not equal to zero since the last subtraction (it will be a GCD). - return a || b; -} diff --git a/src/algorithms/math/euclidean-distance/README.md b/src/algorithms/math/euclidean-distance/README.md deleted file mode 100644 index d67c217efe..0000000000 --- a/src/algorithms/math/euclidean-distance/README.md +++ /dev/null @@ -1,36 +0,0 @@ -# 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 deleted file mode 100644 index 78d7d8dc86..0000000000 --- a/src/algorithms/math/euclidean-distance/__tests__/euclideanDistance.test.js +++ /dev/null @@ -1,23 +0,0 @@ -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 deleted file mode 100644 index afa5c2fece..0000000000 --- a/src/algorithms/math/euclidean-distance/euclideanDistance.js +++ /dev/null @@ -1,28 +0,0 @@ -/** - * @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/factorial/README.fr-FR.md b/src/algorithms/math/factorial/README.fr-FR.md deleted file mode 100644 index aa092c1b78..0000000000 --- a/src/algorithms/math/factorial/README.fr-FR.md +++ /dev/null @@ -1,35 +0,0 @@ -# Factorielle - -_Lisez ceci dans d'autres langues:_ -[english](README.md), [_简体中文_](README.zh-CN.md). - -En mathématiques, la factorielle d'un entier naturel `n`, -notée avec un point d'exclamation `n!`, est le produit des nombres entiers -strictement positifs inférieurs ou égaux à n. Par exemple: - -``` -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 | - -## References - -[Wikipedia](https://fr.wikipedia.org/wiki/Factorielle) diff --git a/src/algorithms/math/factorial/README.ka-GE.md b/src/algorithms/math/factorial/README.ka-GE.md deleted file mode 100644 index 1d02b9f7d3..0000000000 --- a/src/algorithms/math/factorial/README.ka-GE.md +++ /dev/null @@ -1,32 +0,0 @@ -# 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 deleted file mode 100644 index 9c75b41aae..0000000000 --- a/src/algorithms/math/factorial/README.md +++ /dev/null @@ -1,35 +0,0 @@ -# Factorial - -_Read this in other languages:_ -[_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 -than or equal to `n`. For example: - -``` -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 | - -## References - -[Wikipedia](https://en.wikipedia.org/wiki/Factorial) diff --git a/src/algorithms/math/factorial/README.tr-TR.md b/src/algorithms/math/factorial/README.tr-TR.md deleted file mode 100644 index 68ce21a299..0000000000 --- a/src/algorithms/math/factorial/README.tr-TR.md +++ /dev/null @@ -1,38 +0,0 @@ -# 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) diff --git a/src/algorithms/math/factorial/README.uk-UA.md b/src/algorithms/math/factorial/README.uk-UA.md deleted file mode 100644 index bf75963113..0000000000 --- a/src/algorithms/math/factorial/README.uk-UA.md +++ /dev/null @@ -1,33 +0,0 @@ -# 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/algorithms/math/factorial/README.zh-CN.md b/src/algorithms/math/factorial/README.zh-CN.md deleted file mode 100644 index 89bcff1ff2..0000000000 --- a/src/algorithms/math/factorial/README.zh-CN.md +++ /dev/null @@ -1,27 +0,0 @@ -# 阶乘 - -在数学上, 一个正整数 `n` 的阶乘 (写作 `n!`), 就是所有小于等于 `n` 的正整数的乘积. 比如: - -``` -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 | - diff --git a/src/algorithms/math/factorial/__test__/factorial.test.js b/src/algorithms/math/factorial/__test__/factorial.test.js deleted file mode 100644 index bf6aa0ecbd..0000000000 --- a/src/algorithms/math/factorial/__test__/factorial.test.js +++ /dev/null @@ -1,11 +0,0 @@ -import factorial from '../factorial'; - -describe('factorial', () => { - it('should calculate factorial', () => { - expect(factorial(0)).toBe(1); - expect(factorial(1)).toBe(1); - expect(factorial(5)).toBe(120); - expect(factorial(8)).toBe(40320); - expect(factorial(10)).toBe(3628800); - }); -}); diff --git a/src/algorithms/math/factorial/__test__/factorialRecursive.test.js b/src/algorithms/math/factorial/__test__/factorialRecursive.test.js deleted file mode 100644 index 9029faee0a..0000000000 --- a/src/algorithms/math/factorial/__test__/factorialRecursive.test.js +++ /dev/null @@ -1,11 +0,0 @@ -import factorialRecursive from '../factorialRecursive'; - -describe('factorialRecursive', () => { - it('should calculate factorial', () => { - expect(factorialRecursive(0)).toBe(1); - expect(factorialRecursive(1)).toBe(1); - expect(factorialRecursive(5)).toBe(120); - expect(factorialRecursive(8)).toBe(40320); - expect(factorialRecursive(10)).toBe(3628800); - }); -}); diff --git a/src/algorithms/math/factorial/factorial.js b/src/algorithms/math/factorial/factorial.js deleted file mode 100644 index 6c717d051f..0000000000 --- a/src/algorithms/math/factorial/factorial.js +++ /dev/null @@ -1,13 +0,0 @@ -/** - * @param {number} number - * @return {number} - */ -export default function factorial(number) { - let result = 1; - - for (let i = 2; i <= number; i += 1) { - result *= i; - } - - return result; -} diff --git a/src/algorithms/math/factorial/factorialRecursive.js b/src/algorithms/math/factorial/factorialRecursive.js deleted file mode 100644 index e2b4aec6c9..0000000000 --- a/src/algorithms/math/factorial/factorialRecursive.js +++ /dev/null @@ -1,7 +0,0 @@ -/** - * @param {number} number - * @return {number} - */ -export default function factorialRecursive(number) { - return number > 1 ? number * factorialRecursive(number - 1) : 1; -} diff --git a/src/algorithms/math/fast-powering/README.fr-FR.md b/src/algorithms/math/fast-powering/README.fr-FR.md deleted file mode 100644 index ba44244cc8..0000000000 --- a/src/algorithms/math/fast-powering/README.fr-FR.md +++ /dev/null @@ -1,73 +0,0 @@ -# Algorithme d'exponentiation rapide - -_Read this in other languages:_ -[english](README.md). - -En algèbre, une **puissance** d'un nombre est le résultat de la multiplication répétée de ce nombre avec lui-même. - -Elle est souvent notée en assortissant le nombre d'un entier, typographié en exposant, qui indique le nombre de fois qu'apparaît le nombre comme facteur dans cette multiplication. - -![Power](https://www.mathsisfun.com/algebra/images/exponent-8-2.svg) - -## Implémentation « naïve » - -Comment trouver `a` élevé à la puissance `b` ? - -On multiplie `a` avec lui-même, `b` nombre de fois. -Ainsi, `a^b = a * a * a * ... * a` (`b` occurrences de `a`). - -Cette opération aura un complexité linéaire, notée `O(n)`, -car la multiplication aura lieu exactement `n` fois. - -## Algorithme d'exponentiation rapide - -Peut-on faire mieux que cette implémentation naïve? -Oui, on peut réduire le nombre de puissance à un complexité de `O(log(n))`. - -Cet algorithme utilise l'approche « diviser pour mieux régner » -pour calculer cette puissance. -En l'état, cet algorithme fonctionne pour deux entiers positifs `X` et `Y`. - -L'idée derrière cet algorithme est basée sur l'observation suivante. - -Lorsque `Y` est **pair**: - -```text -X^Y = X^(Y/2) * X^(Y/2) -``` - -Lorsque `Y` est **impair**: - -```text -X^Y = X^(Y//2) * X^(Y//2) * X -où Y//2 est le résultat de la division entière de Y par 2. -``` - -**Par exemple** - -```text -2^4 = (2 * 2) * (2 * 2) = (2^2) * (2^2) -``` - -```text -2^5 = (2 * 2) * (2 * 2) * 2 = (2^2) * (2^2) * (2) -``` - -Ainsi, puisqu'à chaque étape on doits calculer -deux fois la même puissance `X ^ (Y / 2)`, -on peut optimiser en l'enregistrant dans une variable intermédiaire -pour éviter son calcul en double. - -**Complexité en temps** - -Comme à chaque itération nous réduisons la puissance de moitié, -nous appelons récursivement la fonction `log(n)` fois. Le complexité de temps de cet algorithme est donc réduite à: - -```text -O(log(n)) -``` - -## Références - -- [YouTube](https://www.youtube.com/watch?v=LUWavfN9zEo&index=80&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8&t=0s) -- [Wikipedia](https://fr.wikipedia.org/wiki/Exponentiation_rapide) diff --git a/src/algorithms/math/fast-powering/README.md b/src/algorithms/math/fast-powering/README.md deleted file mode 100644 index 2c2619d2ef..0000000000 --- a/src/algorithms/math/fast-powering/README.md +++ /dev/null @@ -1,71 +0,0 @@ -# Fast Powering Algorithm - -_Read this in other languages:_ -[français](README.fr-FR.md). - -**The power of a number** says how many times to use the number in a -multiplication. - -It is written as a small number to the right and above the base number. - -![Power](https://www.mathsisfun.com/algebra/images/exponent-8-2.svg) - -## Naive Algorithm Complexity - -How to find `a` raised to the power `b`? - -We multiply `a` to itself, `b` times. That -is, `a^b = a * a * a * ... * a` (`b` occurrences of `a`). - -This operation will take `O(n)` time since we need to do multiplication operation -exactly `n` times. - -## Fast Power Algorithm - -Can we do better than naive algorithm does? Yes we may solve the task of -powering in `O(log(n))` time. - -The algorithm uses divide and conquer approach to compute power. Currently the -algorithm work for two positive integers `X` and `Y`. - -The idea behind the algorithm is based on the fact that: - -For **even** `Y`: - -```text -X^Y = X^(Y/2) * X^(Y/2) -``` - -For **odd** `Y`: - -```text -X^Y = X^(Y//2) * X^(Y//2) * X -where Y//2 is result of division of Y by 2 without reminder. -``` - -**For example** - -```text -2^4 = (2 * 2) * (2 * 2) = (2^2) * (2^2) -``` - -```text -2^5 = (2 * 2) * (2 * 2) * 2 = (2^2) * (2^2) * (2) -``` - -Now, since on each step we need to compute the same `X^(Y/2)` power twice we may optimise -it by saving it to some intermediate variable to avoid its duplicate calculation. - -**Time Complexity** - -Since each iteration we split the power by half then we will call function -recursively `log(n)` times. This the time complexity of the algorithm is reduced to: - -```text -O(log(n)) -``` - -## References - -- [YouTube](https://www.youtube.com/watch?v=LUWavfN9zEo&index=80&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8&t=0s) -- [Wikipedia](https://en.wikipedia.org/wiki/Exponentiation_by_squaring) diff --git a/src/algorithms/math/fast-powering/__test__/fastPowering.test.js b/src/algorithms/math/fast-powering/__test__/fastPowering.test.js deleted file mode 100644 index 0a5da7561a..0000000000 --- a/src/algorithms/math/fast-powering/__test__/fastPowering.test.js +++ /dev/null @@ -1,23 +0,0 @@ -import fastPowering from '../fastPowering'; - -describe('fastPowering', () => { - it('should compute power in log(n) time', () => { - expect(fastPowering(1, 1)).toBe(1); - expect(fastPowering(2, 0)).toBe(1); - expect(fastPowering(2, 2)).toBe(4); - expect(fastPowering(2, 3)).toBe(8); - expect(fastPowering(2, 4)).toBe(16); - expect(fastPowering(2, 5)).toBe(32); - expect(fastPowering(2, 6)).toBe(64); - expect(fastPowering(2, 7)).toBe(128); - expect(fastPowering(2, 8)).toBe(256); - expect(fastPowering(3, 4)).toBe(81); - expect(fastPowering(190, 2)).toBe(36100); - expect(fastPowering(11, 5)).toBe(161051); - expect(fastPowering(13, 11)).toBe(1792160394037); - expect(fastPowering(9, 16)).toBe(1853020188851841); - expect(fastPowering(16, 16)).toBe(18446744073709552000); - expect(fastPowering(7, 21)).toBe(558545864083284000); - expect(fastPowering(100, 9)).toBe(1000000000000000000); - }); -}); diff --git a/src/algorithms/math/fast-powering/fastPowering.js b/src/algorithms/math/fast-powering/fastPowering.js deleted file mode 100644 index 4f4a6b3571..0000000000 --- a/src/algorithms/math/fast-powering/fastPowering.js +++ /dev/null @@ -1,30 +0,0 @@ -/** - * Fast Powering Algorithm. - * Recursive implementation to compute power. - * - * Complexity: log(n) - * - * @param {number} base - Number that will be raised to the power. - * @param {number} power - The power that number will be raised to. - * @return {number} - */ -export default function fastPowering(base, power) { - if (power === 0) { - // Anything that is raised to the power of zero is 1. - return 1; - } - - if (power % 2 === 0) { - // If the power is even... - // we may recursively redefine the result via twice smaller powers: - // x^8 = x^4 * x^4. - const multiplier = fastPowering(base, power / 2); - return multiplier * multiplier; - } - - // If the power is odd... - // we may recursively redefine the result via twice smaller powers: - // x^9 = x^4 * x^4 * x. - const multiplier = fastPowering(base, Math.floor(power / 2)); - return multiplier * multiplier * base; -} diff --git a/src/algorithms/math/fibonacci/README.fr-FR.md b/src/algorithms/math/fibonacci/README.fr-FR.md deleted file mode 100644 index 81e3549b0d..0000000000 --- a/src/algorithms/math/fibonacci/README.fr-FR.md +++ /dev/null @@ -1,24 +0,0 @@ -# Nombre de Fibonacci - -_Read this in other languages:_ -[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) -est la somme des deux termes qui le précèdent. -Les termes de cette suite sont appelés nombres de Fibonacci: - -`0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ...` - -Les carrés de Fibonacci en spirale s'ajustent ensemble pour former une spirale d'or. - -![Fibonacci](https://upload.wikimedia.org/wikipedia/commons/d/db/34%2A21-FibonacciBlocks.png) - -La spirale de Fibonacci: approximation d'une spirale d'or créée en dessinant des arcs de cercle reliant les coins opposés de carrés dans un pavage Fibonacci[4] . Celui-ci utilise des carrés de tailles 1, 1, 2, 3, 5, 8, 13, 21, et 34. - -![Fibonacci Spiral](https://upload.wikimedia.org/wikipedia/commons/2/2e/FibonacciSpiral.svg) - -## References - -- [Wikipedia](https://fr.wikipedia.org/wiki/Suite_de_Fibonacci) diff --git a/src/algorithms/math/fibonacci/README.ka-GE.md b/src/algorithms/math/fibonacci/README.ka-GE.md deleted file mode 100644 index ae7e11218b..0000000000 --- a/src/algorithms/math/fibonacci/README.ka-GE.md +++ /dev/null @@ -1,20 +0,0 @@ -# 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 deleted file mode 100644 index 3d476c5020..0000000000 --- a/src/algorithms/math/fibonacci/README.md +++ /dev/null @@ -1,25 +0,0 @@ -# Fibonacci Number - -_Read this in other languages:_ -[français](README.fr-FR.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 -the fact that every number after the first two is the sum of the two -preceding ones: - -`0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ...` - -A tiling with squares whose side lengths are successive Fibonacci numbers - -![Fibonacci](https://upload.wikimedia.org/wikipedia/commons/d/db/34%2A21-FibonacciBlocks.png) - -The Fibonacci spiral: an approximation of the golden spiral created by drawing circular arcs connecting the opposite corners of squares in the Fibonacci tiling;[4] this one uses squares of sizes 1, 1, 2, 3, 5, 8, 13 and 21. - -![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/fibonacci/README.zh-CN.md b/src/algorithms/math/fibonacci/README.zh-CN.md deleted file mode 100644 index 20378000d4..0000000000 --- a/src/algorithms/math/fibonacci/README.zh-CN.md +++ /dev/null @@ -1,23 +0,0 @@ -# 斐波那契数 - -_Read this in other languages:_ -[français](README.fr-FR.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： - -`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/fibonacci/__test__/fibonacci.test.js b/src/algorithms/math/fibonacci/__test__/fibonacci.test.js deleted file mode 100644 index ffbee8d9ea..0000000000 --- a/src/algorithms/math/fibonacci/__test__/fibonacci.test.js +++ /dev/null @@ -1,16 +0,0 @@ -import fibonacci from '../fibonacci'; - -describe('fibonacci', () => { - it('should calculate fibonacci correctly', () => { - expect(fibonacci(1)).toEqual([1]); - expect(fibonacci(2)).toEqual([1, 1]); - expect(fibonacci(3)).toEqual([1, 1, 2]); - expect(fibonacci(4)).toEqual([1, 1, 2, 3]); - expect(fibonacci(5)).toEqual([1, 1, 2, 3, 5]); - expect(fibonacci(6)).toEqual([1, 1, 2, 3, 5, 8]); - expect(fibonacci(7)).toEqual([1, 1, 2, 3, 5, 8, 13]); - expect(fibonacci(8)).toEqual([1, 1, 2, 3, 5, 8, 13, 21]); - expect(fibonacci(9)).toEqual([1, 1, 2, 3, 5, 8, 13, 21, 34]); - expect(fibonacci(10)).toEqual([1, 1, 2, 3, 5, 8, 13, 21, 34, 55]); - }); -}); diff --git a/src/algorithms/math/fibonacci/__test__/fibonacciNth.test.js b/src/algorithms/math/fibonacci/__test__/fibonacciNth.test.js deleted file mode 100644 index 4a098eba70..0000000000 --- a/src/algorithms/math/fibonacci/__test__/fibonacciNth.test.js +++ /dev/null @@ -1,23 +0,0 @@ -import fibonacciNth from '../fibonacciNth'; - -describe('fibonacciNth', () => { - it('should calculate fibonacci correctly', () => { - expect(fibonacciNth(1)).toBe(1); - expect(fibonacciNth(2)).toBe(1); - expect(fibonacciNth(3)).toBe(2); - expect(fibonacciNth(4)).toBe(3); - expect(fibonacciNth(5)).toBe(5); - expect(fibonacciNth(6)).toBe(8); - expect(fibonacciNth(7)).toBe(13); - expect(fibonacciNth(8)).toBe(21); - expect(fibonacciNth(20)).toBe(6765); - expect(fibonacciNth(30)).toBe(832040); - expect(fibonacciNth(50)).toBe(12586269025); - expect(fibonacciNth(70)).toBe(190392490709135); - expect(fibonacciNth(71)).toBe(308061521170129); - expect(fibonacciNth(72)).toBe(498454011879264); - expect(fibonacciNth(73)).toBe(806515533049393); - expect(fibonacciNth(74)).toBe(1304969544928657); - expect(fibonacciNth(75)).toBe(2111485077978050); - }); -}); diff --git a/src/algorithms/math/fibonacci/__test__/fibonacciNthClosedForm.test.js b/src/algorithms/math/fibonacci/__test__/fibonacciNthClosedForm.test.js deleted file mode 100644 index 4828ef5827..0000000000 --- a/src/algorithms/math/fibonacci/__test__/fibonacciNthClosedForm.test.js +++ /dev/null @@ -1,26 +0,0 @@ -import fibonacciNthClosedForm from '../fibonacciNthClosedForm'; - -describe('fibonacciClosedForm', () => { - it('should throw an error when trying to calculate fibonacci for not allowed positions', () => { - const calculateFibonacciForNotAllowedPosition = () => { - fibonacciNthClosedForm(76); - }; - - expect(calculateFibonacciForNotAllowedPosition).toThrow(); - }); - - it('should calculate fibonacci correctly', () => { - expect(fibonacciNthClosedForm(1)).toBe(1); - expect(fibonacciNthClosedForm(2)).toBe(1); - expect(fibonacciNthClosedForm(3)).toBe(2); - expect(fibonacciNthClosedForm(4)).toBe(3); - expect(fibonacciNthClosedForm(5)).toBe(5); - expect(fibonacciNthClosedForm(6)).toBe(8); - expect(fibonacciNthClosedForm(7)).toBe(13); - expect(fibonacciNthClosedForm(8)).toBe(21); - expect(fibonacciNthClosedForm(20)).toBe(6765); - expect(fibonacciNthClosedForm(30)).toBe(832040); - expect(fibonacciNthClosedForm(50)).toBe(12586269025); - expect(fibonacciNthClosedForm(70)).toBe(190392490709135); - }); -}); diff --git a/src/algorithms/math/fibonacci/fibonacci.js b/src/algorithms/math/fibonacci/fibonacci.js deleted file mode 100644 index 4caa1d9bd6..0000000000 --- a/src/algorithms/math/fibonacci/fibonacci.js +++ /dev/null @@ -1,29 +0,0 @@ -/** - * Return a fibonacci sequence as an array. - * - * @param n - * @return {number[]} - */ -export default function fibonacci(n) { - const fibSequence = [1]; - - let currentValue = 1; - let previousValue = 0; - - if (n === 1) { - return fibSequence; - } - - let iterationsCounter = n - 1; - - while (iterationsCounter) { - currentValue += previousValue; - previousValue = currentValue - previousValue; - - fibSequence.push(currentValue); - - iterationsCounter -= 1; - } - - return fibSequence; -} diff --git a/src/algorithms/math/fibonacci/fibonacciNth.js b/src/algorithms/math/fibonacci/fibonacciNth.js deleted file mode 100644 index 729224470a..0000000000 --- a/src/algorithms/math/fibonacci/fibonacciNth.js +++ /dev/null @@ -1,25 +0,0 @@ -/** - * Calculate fibonacci number at specific position using Dynamic Programming approach. - * - * @param n - * @return {number} - */ -export default function fibonacciNth(n) { - let currentValue = 1; - let previousValue = 0; - - if (n === 1) { - return 1; - } - - let iterationsCounter = n - 1; - - while (iterationsCounter) { - currentValue += previousValue; - previousValue = currentValue - previousValue; - - iterationsCounter -= 1; - } - - return currentValue; -} diff --git a/src/algorithms/math/fibonacci/fibonacciNthClosedForm.js b/src/algorithms/math/fibonacci/fibonacciNthClosedForm.js deleted file mode 100644 index e2a2a367cb..0000000000 --- a/src/algorithms/math/fibonacci/fibonacciNthClosedForm.js +++ /dev/null @@ -1,23 +0,0 @@ -/** - * Calculate fibonacci number at specific position using closed form function (Binet's formula). - * @see: https://en.wikipedia.org/wiki/Fibonacci_number#Closed-form_expression - * - * @param {number} position - Position number of fibonacci sequence (must be number from 1 to 75). - * @return {number} - */ -export default function fibonacciClosedForm(position) { - const topMaxValidPosition = 70; - - // Check that position is valid. - if (position < 1 || position > topMaxValidPosition) { - throw new Error(`Can't handle position smaller than 1 or greater than ${topMaxValidPosition}`); - } - - // Calculate √5 to re-use it in further formulas. - const sqrt5 = Math.sqrt(5); - // Calculate φ constant (≈ 1.61803). - const phi = (1 + sqrt5) / 2; - - // Calculate fibonacci number using Binet's formula. - return Math.floor((phi ** position) / sqrt5 + 0.5); -} diff --git a/src/algorithms/math/fourier-transform/README.fr-FR.md b/src/algorithms/math/fourier-transform/README.fr-FR.md deleted file mode 100644 index 0d345164c7..0000000000 --- a/src/algorithms/math/fourier-transform/README.fr-FR.md +++ /dev/null @@ -1,135 +0,0 @@ -# Transformation de Fourier - -_Read this in other languages:_ -[english](README.md). - -## Définitions - -La transformation de Fourier (**ℱ**) est une opération qui transforme -une fonction intégrable sur ℝ en une autre fonction, -décrivant le spectre fréquentiel de cette dernière - -La **Transformée de Fourier Discrète** (**TFD**) convertit une séquence finie d'échantillons également espacés d'une fonction, dans une séquence de même longueur d'échantillons, également espacés de la Transformée de Fourier à temps discret (TFtd), qui est une fonction complexe de la fréquence. -L'intervalle auquel le TFtd est échantillonné est l'inverse de la durée de la séquence d'entrée. -Une TFD inverse est une série de Fourier, utilisant les échantillons TFtd comme coefficients de sinusoïdes complexes aux fréquences TFtd correspondantes. Elle a les mêmes valeurs d'échantillonnage que la -séquence d'entrée originale. On dit donc que la TFD est une représentation du domaine fréquentiel -de la séquence d'entrée d'origine. Si la séquence d'origine couvre toutes les -valeurs non nulles d'une fonction, sa TFtd est continue (et périodique), et la TFD fournit -les échantillons discrets d'une fenêtre. Si la séquence d'origine est un cycle d'une fonction périodique, la TFD fournit toutes les valeurs non nulles d'une fenêtre TFtd. - -Transformée de Fourier Discrète converti une séquence de `N` nombres complexes: - -{xn} = x0, x1, x2 ..., xN-1 - -en une atre séquence de nombres complexes:: - -{Xk} = X0, X1, X2 ..., XN-1 - -décrite par: - -![DFT](https://wikimedia.org/api/rest_v1/media/math/render/svg/1af0a78dc50bbf118ab6bd4c4dcc3c4ff8502223) - -The **Transformée de Fourier à temps discret** (**TFtd**) est une forme d'analyse de Fourier -qui s'applique aux échantillons uniformément espacés d'une fonction continue. Le terme "temps discret" fait référence au fait que la transformée fonctionne sur des données discrètes -(échantillons) dont l'intervalle a souvent des unités de temps. -À partir des seuls échantillons, elle produit une fonction de fréquence qui est une somme périodique de la -Transformée de Fourier continue de la fonction continue d'origine. - -A **Transformation de Fourier rapide** (**FFT** pour Fast Fourier Transform) est un algorithme de calcul de la transformation de Fourier discrète (TFD). Il est couramment utilisé en traitement numérique du signal pour transformer des données discrètes du domaine temporel dans le domaine fréquentiel, en particulier dans les oscilloscopes numériques (les analyseurs de spectre utilisant plutôt des filtres analogiques, plus précis). Son efficacité permet de réaliser des filtrages en modifiant le spectre et en utilisant la transformation inverse (filtre à réponse impulsionnelle finie). - -Cette transformation peut être illustée par la formule suivante. Sur la période de temps mesurée -dans le diagramme, le signal contient 3 fréquences dominantes distinctes. - -Vue d'un signal dans le domaine temporel et fréquentiel: - -![FFT](https://upload.wikimedia.org/wikipedia/commons/6/61/FFT-Time-Frequency-View.png) - -An FFT algorithm computes the discrete Fourier transform (DFT) of a sequence, or -its inverse (IFFT). Fourier analysis converts a signal from its original domain -to a representation in the frequency domain and vice versa. An FFT rapidly -computes such transformations by factorizing the DFT matrix into a product of -sparse (mostly zero) factors. As a result, it manages to reduce the complexity of -computing the DFT from O(n2), which arises if one simply applies the -definition of DFT, to O(n log n), where n is the data size. - -Un algorithme FFT calcule la Transformée de Fourier discrète (TFD) d'une séquence, ou -son inverse (IFFT). L'analyse de Fourier convertit un signal de son domaine d'origine -en une représentation dans le domaine fréquentiel et vice versa. Une FFT -calcule rapidement ces transformations en factorisant la matrice TFD en un produit de -facteurs dispersés (généralement nuls). En conséquence, il parvient à réduire la complexité de -calcul de la TFD de O (n 2 ), qui survient si l'on applique simplement la -définition de TFD, à O (n log n), où n est la taille des données. - -Voici une analyse de Fourier discrète d'une somme d'ondes cosinus à 10, 20, 30, 40, -et 50 Hz: - -![FFT](https://upload.wikimedia.org/wikipedia/commons/6/64/FFT_of_Cosine_Summation_Function.png) - -## Explanation - -La Transformée de Fourier est l'une des connaissances les plus importante jamais découverte. Malheureusement, le -son sens est enfoui dans des équations denses:: - -![](https://betterexplained.com/wp-content/plugins/wp-latexrender/pictures/45c088dbb767150fc0bacfeb49dd49e5.png) - -et - -![](https://betterexplained.com/wp-content/plugins/wp-latexrender/pictures/faeb9c5bf2e60add63ae4a70b293c7b4.png) - -Plutôt que se noyer dans les symboles, faisons en premier lieu l'expérience de l'idée principale. Voici une métaphore en français simple: - -- _Que fait la transformée de Fourier ?_ A partir d'un smoothie, elle trouve sa recette. -- _Comment ?_ Elle passe le smoothie dans un filtre pour en extraire chaque ingrédient. -- _Pourquoi ?_ Les recettes sont plus faciles à analyser, comparer et modifier que le smoothie lui-même. -- _Comment récupérer le smoothie ?_ Re-mélanger les ingrédients. - -**Pensez en cercles, pas seulement en sinusoïdes** - -La transformée de Fourier concerne des trajectoires circulaires (pas les sinusoïdes 1-d) -et la formuled'Euler est une manière intelligente d'en générer une: - -![](https://betterexplained.com/wp-content/uploads/euler/equal_paths.png) - -Doit-on utiliser des exposants imaginaires pour se déplacer en cercle ? Non. Mais c'est pratique -et compact. Et bien sûr, nous pouvons décrire notre chemin comme un mouvement coordonné en deux -dimensions (réelle et imaginaire), mais n'oubliez pas la vue d'ensemble: nous sommes juste -en déplacement dans un cercle. - -**À la découverte de la transformation complète** - -L'idée générale: notre signal n'est qu'un tas de pics de temps, d'instant T ! Si nous combinons les -recettes pour chaque pic de temps, nous devrions obtenir la recette du signal complet. - -La transformée de Fourier construit cette recette fréquence par fréquence: - -![](https://betterexplained.com/wp-content/uploads/images/fourier-explained-20121219-224649.png) - -Quelques notes - -- N = nombre d'échantillons de temps dont nous disposons -- n = échantillon actuellement étudié (0 ... N-1) -- xn = valeur du signal au temps n -- k = fréquence actuellement étudiée (0 Hertz up to N-1 Hertz) -- Xk = quantité de fréquence k dans le signal (amplitude et phase, un nombre complexe) -- Le facteur 1 / N est généralement déplacé vers la transformée inverse (passant des fréquences au temps). Ceci est autorisé, bien que je préfère 1 / N dans la transformation directe car cela donne les tailles réelles des pics de temps. Vous pouvez être plus ambitieux et utiliser 1 / racine carrée de (N) sur les deux transformations (aller en avant et en arrière crée le facteur 1 / N). -- n/N est le pourcentage du temps que nous avons passé. 2 _ pi _ k est notre vitesse en radians/s. e ^ -ix est notre chemin circulaire vers l'arrière. La combinaison est la distance parcourue, pour cette vitesse et ce temps. -- Les équations brutes de la transformée de Fourier consiste simplement à "ajouter les nombres complexes". De nombreux langages de programmation ne peuvent pas gérer directement les nombres complexes, on converti donc tout en coordonnées rectangulaires, pour les ajouter. - -Stuart Riffle a une excellente interprétation de la transformée de Fourier: - -![](https://betterexplained.com/wp-content/uploads/images/DerivedDFT.png) - -## Références - -- Wikipedia - - - [TF](https://fr.wikipedia.org/wiki/Transformation_de_Fourier) - - [TFD](https://fr.wikipedia.org/wiki/Transformation_de_Fourier_discr%C3%A8te) - - [FFT](https://fr.wikipedia.org/wiki/Transformation_de_Fourier_rapide) - - [TFtd (en anglais)](https://en.wikipedia.org/wiki/Discrete-time_Fourier_transform) - -- en Anglais - - [An Interactive Guide To The Fourier Transform](https://betterexplained.com/articles/an-interactive-guide-to-the-fourier-transform/) - - [DFT on YouTube by Better Explained](https://www.youtube.com/watch?v=iN0VG9N2q0U&t=0s&index=77&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8) - - [FT on YouTube by 3Blue1Brown](https://www.youtube.com/watch?v=spUNpyF58BY&t=0s&index=76&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8) - - [FFT on YouTube by Simon Xu](https://www.youtube.com/watch?v=htCj9exbGo0&index=78&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8&t=0s) diff --git a/src/algorithms/math/fourier-transform/README.md b/src/algorithms/math/fourier-transform/README.md deleted file mode 100644 index f7969ddd5c..0000000000 --- a/src/algorithms/math/fourier-transform/README.md +++ /dev/null @@ -1,133 +0,0 @@ -# Fourier Transform - -_Read this in other languages:_ -[français](README.fr-FR.md). - -## Definitions - -The **Fourier Transform** (**FT**) decomposes a function of time (a signal) into -the frequencies that make it up, in a way similar to how a musical chord can be -expressed as the frequencies (or pitches) of its constituent notes. - -The **Discrete Fourier Transform** (**DFT**) converts a finite sequence of -equally-spaced samples of a function into a same-length sequence of -equally-spaced samples of the discrete-time Fourier transform (DTFT), which is a -complex-valued function of frequency. The interval at which the DTFT is sampled -is the reciprocal of the duration of the input sequence. An inverse DFT is a -Fourier series, using the DTFT samples as coefficients of complex sinusoids at -the corresponding DTFT frequencies. It has the same sample-values as the original -input sequence. The DFT is therefore said to be a frequency domain representation -of the original input sequence. If the original sequence spans all the non-zero -values of a function, its DTFT is continuous (and periodic), and the DFT provides -discrete samples of one cycle. If the original sequence is one cycle of a periodic -function, the DFT provides all the non-zero values of one DTFT cycle. - -The Discrete Fourier transform transforms a sequence of `N` complex numbers: - -{xn} = x0, x1, x2 ..., xN-1 - -into another sequence of complex numbers: - -{Xk} = X0, X1, X2 ..., XN-1 - -which is defined by: - -![DFT](https://wikimedia.org/api/rest_v1/media/math/render/svg/1af0a78dc50bbf118ab6bd4c4dcc3c4ff8502223) - -The **Discrete-Time Fourier Transform** (**DTFT**) is a form of Fourier analysis -that is applicable to the uniformly-spaced samples of a continuous function. The -term discrete-time refers to the fact that the transform operates on discrete data -(samples) whose interval often has units of time. From only the samples, it -produces a function of frequency that is a periodic summation of the continuous -Fourier transform of the original continuous function. - -A **Fast Fourier Transform** (**FFT**) is an algorithm that samples a signal over -a period of time (or space) and divides it into its frequency components. These -components are single sinusoidal oscillations at distinct frequencies each with -their own amplitude and phase. - -This transformation is illustrated in Diagram below. Over the time period measured -in the diagram, the signal contains 3 distinct dominant frequencies. - -View of a signal in the time and frequency domain: - -![FFT](https://upload.wikimedia.org/wikipedia/commons/6/61/FFT-Time-Frequency-View.png) - -An FFT algorithm computes the discrete Fourier transform (DFT) of a sequence, or -its inverse (IFFT). Fourier analysis converts a signal from its original domain -to a representation in the frequency domain and vice versa. An FFT rapidly -computes such transformations by factorizing the DFT matrix into a product of -sparse (mostly zero) factors. As a result, it manages to reduce the complexity of -computing the DFT from O(n2), which arises if one simply applies the -definition of DFT, to O(n log n), where n is the data size. - -Here a discrete Fourier analysis of a sum of cosine waves at 10, 20, 30, 40, -and 50 Hz: - -![FFT](https://upload.wikimedia.org/wikipedia/commons/6/64/FFT_of_Cosine_Summation_Function.png) - -## Explanation - -The Fourier Transform is one of deepest insights ever made. Unfortunately, the -meaning is buried within dense equations: - -![](https://betterexplained.com/wp-content/plugins/wp-latexrender/pictures/45c088dbb767150fc0bacfeb49dd49e5.png) - -and - -![](https://betterexplained.com/wp-content/plugins/wp-latexrender/pictures/faeb9c5bf2e60add63ae4a70b293c7b4.png) - -Rather than jumping into the symbols, let's experience the key idea firsthand. Here's a plain-English metaphor: - -- _What does the Fourier Transform do?_ Given a smoothie, it finds the recipe. -- _How?_ Run the smoothie through filters to extract each ingredient. -- _Why?_ Recipes are easier to analyze, compare, and modify than the smoothie itself. -- _How do we get the smoothie back?_ Blend the ingredients. - -**Think With Circles, Not Just Sinusoids** - -The Fourier Transform is about circular paths (not 1-d sinusoids) and Euler's -formula is a clever way to generate one: - -![](https://betterexplained.com/wp-content/uploads/euler/equal_paths.png) - -Must we use imaginary exponents to move in a circle? Nope. But it's convenient -and compact. And sure, we can describe our path as coordinated motion in two -dimensions (real and imaginary), but don't forget the big picture: we're just -moving in a circle. - -**Discovering The Full Transform** - -The big insight: our signal is just a bunch of time spikes! If we merge the -recipes for each time spike, we should get the recipe for the full signal. - -The Fourier Transform builds the recipe frequency-by-frequency: - -![](https://betterexplained.com/wp-content/uploads/images/fourier-explained-20121219-224649.png) - -A few notes: - -- N = number of time samples we have -- n = current sample we're considering (0 ... N-1) -- xn = value of the signal at time n -- k = current frequency we're considering (0 Hertz up to N-1 Hertz) -- Xk = amount of frequency k in the signal (amplitude and phase, a complex number) -- The 1/N factor is usually moved to the reverse transform (going from frequencies back to time). This is allowed, though I prefer 1/N in the forward transform since it gives the actual sizes for the time spikes. You can get wild and even use 1/sqrt(N) on both transforms (going forward and back creates the 1/N factor). -- n/N is the percent of the time we've gone through. 2 _ pi _ k is our speed in radians / sec. e^-ix is our backwards-moving circular path. The combination is how far we've moved, for this speed and time. -- The raw equations for the Fourier Transform just say "add the complex numbers". Many programming languages cannot handle complex numbers directly, so you convert everything to rectangular coordinates and add those. - -Stuart Riffle has a great interpretation of the Fourier Transform: - -![](https://betterexplained.com/wp-content/uploads/images/DerivedDFT.png) - -## References - -- [An Interactive Guide To The Fourier Transform](https://betterexplained.com/articles/an-interactive-guide-to-the-fourier-transform/) -- [DFT on YouTube by Better Explained](https://www.youtube.com/watch?v=iN0VG9N2q0U&t=0s&index=77&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8) -- [FT on YouTube by 3Blue1Brown](https://www.youtube.com/watch?v=spUNpyF58BY&t=0s&index=76&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8) -- [FFT on YouTube by Simon Xu](https://www.youtube.com/watch?v=htCj9exbGo0&index=78&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8&t=0s) -- Wikipedia - - [FT](https://en.wikipedia.org/wiki/Fourier_transform) - - [DFT](https://www.wikiwand.com/en/Discrete_Fourier_transform) - - [DTFT](https://en.wikipedia.org/wiki/Discrete-time_Fourier_transform) - - [FFT](https://www.wikiwand.com/en/Fast_Fourier_transform) diff --git a/src/algorithms/math/fourier-transform/__test__/FourierTester.js b/src/algorithms/math/fourier-transform/__test__/FourierTester.js deleted file mode 100644 index d2a2787d38..0000000000 --- a/src/algorithms/math/fourier-transform/__test__/FourierTester.js +++ /dev/null @@ -1,295 +0,0 @@ -import ComplexNumber from '../../complex-number/ComplexNumber'; - -export const fourierTestCases = [ - { - input: [ - { amplitude: 1 }, - ], - output: [ - { - frequency: 0, amplitude: 1, phase: 0, re: 1, im: 0, - }, - ], - }, - { - input: [ - { amplitude: 1 }, - { amplitude: 0 }, - ], - output: [ - { - frequency: 0, amplitude: 0.5, phase: 0, re: 0.5, im: 0, - }, - { - frequency: 1, amplitude: 0.5, phase: 0, re: 0.5, im: 0, - }, - ], - }, - { - input: [ - { amplitude: 2 }, - { amplitude: 0 }, - ], - output: [ - { - frequency: 0, amplitude: 1, phase: 0, re: 1, im: 0, - }, - { - frequency: 1, amplitude: 1, phase: 0, re: 1, im: 0, - }, - ], - }, - { - input: [ - { amplitude: 1 }, - { amplitude: 0 }, - { amplitude: 0 }, - ], - output: [ - { - frequency: 0, amplitude: 0.33333, phase: 0, re: 0.33333, im: 0, - }, - { - frequency: 1, amplitude: 0.33333, phase: 0, re: 0.33333, im: 0, - }, - { - frequency: 2, amplitude: 0.33333, phase: 0, re: 0.33333, im: 0, - }, - ], - }, - { - input: [ - { amplitude: 1 }, - { amplitude: 0 }, - { amplitude: 0 }, - { amplitude: 0 }, - ], - output: [ - { - frequency: 0, amplitude: 0.25, phase: 0, re: 0.25, im: 0, - }, - { - frequency: 1, amplitude: 0.25, phase: 0, re: 0.25, im: 0, - }, - { - frequency: 2, amplitude: 0.25, phase: 0, re: 0.25, im: 0, - }, - { - frequency: 3, amplitude: 0.25, phase: 0, re: 0.25, im: 0, - }, - ], - }, - { - input: [ - { amplitude: 0 }, - { amplitude: 1 }, - { amplitude: 0 }, - { amplitude: 0 }, - ], - output: [ - { - frequency: 0, amplitude: 0.25, phase: 0, re: 0.25, im: 0, - }, - { - frequency: 1, amplitude: 0.25, phase: -90, re: 0, im: -0.25, - }, - { - frequency: 2, amplitude: 0.25, phase: 180, re: -0.25, im: 0, - }, - { - frequency: 3, amplitude: 0.25, phase: 90, re: 0, im: 0.25, - }, - ], - }, - { - input: [ - { amplitude: 0 }, - { amplitude: 0 }, - { amplitude: 1 }, - { amplitude: 0 }, - ], - output: [ - { - frequency: 0, amplitude: 0.25, phase: 0, re: 0.25, im: 0, - }, - { - frequency: 1, amplitude: 0.25, phase: 180, re: -0.25, im: 0, - }, - { - frequency: 2, amplitude: 0.25, phase: 0, re: 0.25, im: 0, - }, - { - frequency: 3, amplitude: 0.25, phase: 180, re: -0.25, im: 0, - }, - ], - }, - { - input: [ - { amplitude: 0 }, - { amplitude: 0 }, - { amplitude: 0 }, - { amplitude: 2 }, - ], - output: [ - { - frequency: 0, amplitude: 0.5, phase: 0, re: 0.5, im: 0, - }, - { - frequency: 1, amplitude: 0.5, phase: 90, re: 0, im: 0.5, - }, - { - frequency: 2, amplitude: 0.5, phase: 180, re: -0.5, im: 0, - }, - { - frequency: 3, amplitude: 0.5, phase: -90, re: 0, im: -0.5, - }, - ], - }, - { - input: [ - { amplitude: 0 }, - { amplitude: 1 }, - { amplitude: 0 }, - { amplitude: 2 }, - ], - output: [ - { - frequency: 0, amplitude: 0.75, phase: 0, re: 0.75, im: 0, - }, - { - frequency: 1, amplitude: 0.25, phase: 90, re: 0, im: 0.25, - }, - { - frequency: 2, amplitude: 0.75, phase: 180, re: -0.75, im: 0, - }, - { - frequency: 3, amplitude: 0.25, phase: -90, re: 0, im: -0.25, - }, - ], - }, - { - input: [ - { amplitude: 4 }, - { amplitude: 1 }, - { amplitude: 0 }, - { amplitude: 2 }, - ], - output: [ - { - frequency: 0, amplitude: 1.75, phase: 0, re: 1.75, im: 0, - }, - { - frequency: 1, amplitude: 1.03077, phase: 14.03624, re: 0.99999, im: 0.25, - }, - { - frequency: 2, amplitude: 0.25, phase: 0, re: 0.25, im: 0, - }, - { - frequency: 3, amplitude: 1.03077, phase: -14.03624, re: 1, im: -0.25, - }, - ], - }, - { - input: [ - { amplitude: 4 }, - { amplitude: 1 }, - { amplitude: -3 }, - { amplitude: 2 }, - ], - output: [ - { - frequency: 0, amplitude: 1, phase: 0, re: 1, im: 0, - }, - { - frequency: 1, amplitude: 1.76776, phase: 8.13010, re: 1.75, im: 0.25, - }, - { - frequency: 2, amplitude: 0.5, phase: 180, re: -0.5, im: 0, - }, - { - frequency: 3, amplitude: 1.76776, phase: -8.13010, re: 1.75, im: -0.24999, - }, - ], - }, - { - input: [ - { amplitude: 1 }, - { amplitude: 2 }, - { amplitude: 3 }, - { amplitude: 4 }, - ], - output: [ - { - frequency: 0, amplitude: 2.5, phase: 0, re: 2.5, im: 0, - }, - { - frequency: 1, amplitude: 0.70710, phase: 135, re: -0.5, im: 0.49999, - }, - { - frequency: 2, amplitude: 0.5, phase: 180, re: -0.5, im: 0, - }, - { - frequency: 3, amplitude: 0.70710, phase: -134.99999, re: -0.49999, im: -0.5, - }, - ], - }, -]; - -export default class FourierTester { - /** - * @param {function} fourierTransform - */ - static testDirectFourierTransform(fourierTransform) { - fourierTestCases.forEach((testCase) => { - const { input, output: expectedOutput } = testCase; - - // Try to split input signal into sequence of pure sinusoids. - const formattedInput = input.map((sample) => sample.amplitude); - const currentOutput = fourierTransform(formattedInput); - - // Check the signal has been split into proper amount of sub-signals. - expect(currentOutput.length).toBeGreaterThanOrEqual(formattedInput.length); - - // Now go through all the signals and check their frequency, amplitude and phase. - expectedOutput.forEach((expectedSignal, frequency) => { - // Get template data we want to test against. - const currentSignal = currentOutput[frequency]; - const currentPolarSignal = currentSignal.getPolarForm(false); - - // Check all signal parameters. - expect(frequency).toBe(expectedSignal.frequency); - expect(currentSignal.re).toBeCloseTo(expectedSignal.re, 4); - expect(currentSignal.im).toBeCloseTo(expectedSignal.im, 4); - expect(currentPolarSignal.phase).toBeCloseTo(expectedSignal.phase, 4); - expect(currentPolarSignal.radius).toBeCloseTo(expectedSignal.amplitude, 4); - }); - }); - } - - /** - * @param {function} inverseFourierTransform - */ - static testInverseFourierTransform(inverseFourierTransform) { - fourierTestCases.forEach((testCase) => { - const { input: expectedOutput, output: inputFrequencies } = testCase; - - // Try to join frequencies into time signal. - const formattedInput = inputFrequencies.map((frequency) => { - return new ComplexNumber({ re: frequency.re, im: frequency.im }); - }); - const currentOutput = inverseFourierTransform(formattedInput); - - // Check the signal has been combined of proper amount of time samples. - expect(currentOutput.length).toBeLessThanOrEqual(formattedInput.length); - - // Now go through all the amplitudes and check their values. - expectedOutput.forEach((expectedAmplitudes, timer) => { - // Get template data we want to test against. - const currentAmplitude = currentOutput[timer]; - - // Check if current amplitude is close enough to the calculated one. - expect(currentAmplitude).toBeCloseTo(expectedAmplitudes.amplitude, 4); - }); - }); - } -} diff --git a/src/algorithms/math/fourier-transform/__test__/discreteFourierTransform.test.js b/src/algorithms/math/fourier-transform/__test__/discreteFourierTransform.test.js deleted file mode 100644 index 47da5c0b38..0000000000 --- a/src/algorithms/math/fourier-transform/__test__/discreteFourierTransform.test.js +++ /dev/null @@ -1,8 +0,0 @@ -import discreteFourierTransform from '../discreteFourierTransform'; -import FourierTester from './FourierTester'; - -describe('discreteFourierTransform', () => { - it('should split signal into frequencies', () => { - FourierTester.testDirectFourierTransform(discreteFourierTransform); - }); -}); diff --git a/src/algorithms/math/fourier-transform/__test__/fastFourierTransform.test.js b/src/algorithms/math/fourier-transform/__test__/fastFourierTransform.test.js deleted file mode 100644 index 2dcdc32f7c..0000000000 --- a/src/algorithms/math/fourier-transform/__test__/fastFourierTransform.test.js +++ /dev/null @@ -1,101 +0,0 @@ -import fastFourierTransform from '../fastFourierTransform'; -import ComplexNumber from '../../complex-number/ComplexNumber'; - -/** - * @param {ComplexNumber[]} sequence1 - * @param {ComplexNumber[]} sequence2 - * @param {Number} delta - * @return {boolean} - */ -function sequencesApproximatelyEqual(sequence1, sequence2, delta) { - if (sequence1.length !== sequence2.length) { - return false; - } - - for (let numberIndex = 0; numberIndex < sequence1.length; numberIndex += 1) { - if (Math.abs(sequence1[numberIndex].re - sequence2[numberIndex].re) > delta) { - return false; - } - - if (Math.abs(sequence1[numberIndex].im - sequence2[numberIndex].im) > delta) { - return false; - } - } - - return true; -} - -const delta = 1e-6; - -describe('fastFourierTransform', () => { - it('should calculate the radix-2 discrete fourier transform #1', () => { - const input = [new ComplexNumber({ re: 0, im: 0 })]; - const expectedOutput = [new ComplexNumber({ re: 0, im: 0 })]; - const output = fastFourierTransform(input); - const invertedOutput = fastFourierTransform(output, true); - - expect(sequencesApproximatelyEqual(expectedOutput, output, delta)).toBe(true); - expect(sequencesApproximatelyEqual(input, invertedOutput, delta)).toBe(true); - }); - - it('should calculate the radix-2 discrete fourier transform #2', () => { - const input = [ - new ComplexNumber({ re: 1, im: 2 }), - new ComplexNumber({ re: 2, im: 3 }), - new ComplexNumber({ re: 8, im: 4 }), - ]; - - const expectedOutput = [ - new ComplexNumber({ re: 11, im: 9 }), - new ComplexNumber({ re: -10, im: 0 }), - new ComplexNumber({ re: 7, im: 3 }), - new ComplexNumber({ re: -4, im: -4 }), - ]; - - const output = fastFourierTransform(input); - const invertedOutput = fastFourierTransform(output, true); - - expect(sequencesApproximatelyEqual(expectedOutput, output, delta)).toBe(true); - expect(sequencesApproximatelyEqual(input, invertedOutput, delta)).toBe(true); - }); - - it('should calculate the radix-2 discrete fourier transform #3', () => { - const input = [ - new ComplexNumber({ re: -83656.9359385182, im: 98724.08038374918 }), - new ComplexNumber({ re: -47537.415125808424, im: 88441.58381765135 }), - new ComplexNumber({ re: -24849.657029355192, im: -72621.79007878687 }), - new ComplexNumber({ re: 31451.27290052717, im: -21113.301128347346 }), - new ComplexNumber({ re: 13973.90836288876, im: -73378.36721594246 }), - new ComplexNumber({ re: 14981.520420492234, im: 63279.524958963884 }), - new ComplexNumber({ re: -9892.575367044381, im: -81748.44671677813 }), - new ComplexNumber({ re: -35933.00356823792, im: -46153.47157161784 }), - new ComplexNumber({ re: -22425.008561855735, im: -86284.24507370662 }), - new ComplexNumber({ re: -39327.43830818355, im: 30611.949874562706 }), - ]; - - const expectedOutput = [ - new ComplexNumber({ re: -203215.3322151, im: -100242.4827503 }), - new ComplexNumber({ re: 99217.0805705, im: 270646.9331932 }), - new ComplexNumber({ re: -305990.9040412, im: 68224.8435751 }), - new ComplexNumber({ re: -14135.7758282, im: 199223.9878095 }), - new ComplexNumber({ re: -306965.6350922, im: 26030.1025439 }), - new ComplexNumber({ re: -76477.6755206, im: 40781.9078990 }), - new ComplexNumber({ re: -48409.3099088, im: 54674.7959662 }), - new ComplexNumber({ re: -329683.0131713, im: 164287.7995937 }), - new ComplexNumber({ re: -50485.2048527, im: -330375.0546527 }), - new ComplexNumber({ re: 122235.7738708, im: 91091.6398019 }), - new ComplexNumber({ re: 47625.8850387, im: 73497.3981523 }), - new ComplexNumber({ re: -15619.8231136, im: 80804.8685410 }), - new ComplexNumber({ re: 192234.0276101, im: 160833.3072355 }), - new ComplexNumber({ re: -96389.4195635, im: 393408.4543872 }), - new ComplexNumber({ re: -173449.0825417, im: 146875.7724104 }), - new ComplexNumber({ re: -179002.5662573, im: 239821.0124341 }), - ]; - - const output = fastFourierTransform(input); - const invertedOutput = fastFourierTransform(output, true); - - expect(sequencesApproximatelyEqual(expectedOutput, output, delta)).toBe(true); - expect(sequencesApproximatelyEqual(input, invertedOutput, delta)).toBe(true); - }); -}); diff --git a/src/algorithms/math/fourier-transform/__test__/inverseDiscreteFourierTransform.test.js b/src/algorithms/math/fourier-transform/__test__/inverseDiscreteFourierTransform.test.js deleted file mode 100644 index 3919b3ad86..0000000000 --- a/src/algorithms/math/fourier-transform/__test__/inverseDiscreteFourierTransform.test.js +++ /dev/null @@ -1,8 +0,0 @@ -import inverseDiscreteFourierTransform from '../inverseDiscreteFourierTransform'; -import FourierTester from './FourierTester'; - -describe('inverseDiscreteFourierTransform', () => { - it('should calculate output signal out of input frequencies', () => { - FourierTester.testInverseFourierTransform(inverseDiscreteFourierTransform); - }); -}); diff --git a/src/algorithms/math/fourier-transform/discreteFourierTransform.js b/src/algorithms/math/fourier-transform/discreteFourierTransform.js deleted file mode 100644 index dcb0a014f5..0000000000 --- a/src/algorithms/math/fourier-transform/discreteFourierTransform.js +++ /dev/null @@ -1,69 +0,0 @@ -import ComplexNumber from '../complex-number/ComplexNumber'; - -const CLOSE_TO_ZERO_THRESHOLD = 1e-10; - -/** - * Discrete Fourier Transform (DFT): time to frequencies. - * - * Time complexity: O(N^2) - * - * @param {number[]} inputAmplitudes - Input signal amplitudes over time (complex - * numbers with real parts only). - * @param {number} zeroThreshold - Threshold that is used to convert real and imaginary numbers - * to zero in case if they are smaller then this. - * - * @return {ComplexNumber[]} - Array of complex number. Each of the number represents the frequency - * or signal. All signals together will form input signal over discrete time periods. Each signal's - * complex number has radius (amplitude) and phase (angle) in polar form that describes the signal. - * - * @see https://gist.github.com/anonymous/129d477ddb1c8025c9ac - * @see https://betterexplained.com/articles/an-interactive-guide-to-the-fourier-transform/ - */ -export default function dft(inputAmplitudes, zeroThreshold = CLOSE_TO_ZERO_THRESHOLD) { - const N = inputAmplitudes.length; - const signals = []; - - // Go through every discrete frequency. - for (let frequency = 0; frequency < N; frequency += 1) { - // Compound signal at current frequency that will ultimately - // take part in forming input amplitudes. - let frequencySignal = new ComplexNumber(); - - // Go through every discrete point in time. - for (let timer = 0; timer < N; timer += 1) { - const currentAmplitude = inputAmplitudes[timer]; - - // Calculate rotation angle. - const rotationAngle = -1 * (2 * Math.PI) * frequency * (timer / N); - - // Remember that e^ix = cos(x) + i * sin(x); - const dataPointContribution = new ComplexNumber({ - re: Math.cos(rotationAngle), - im: Math.sin(rotationAngle), - }).multiply(currentAmplitude); - - // Add this data point's contribution. - frequencySignal = frequencySignal.add(dataPointContribution); - } - - // Close to zero? You're zero. - if (Math.abs(frequencySignal.re) < zeroThreshold) { - frequencySignal.re = 0; - } - - if (Math.abs(frequencySignal.im) < zeroThreshold) { - frequencySignal.im = 0; - } - - // Average contribution at this frequency. - // The 1/N factor is usually moved to the reverse transform (going from frequencies - // back to time). This is allowed, though it would be nice to have 1/N in the forward - // transform since it gives the actual sizes for the time spikes. - frequencySignal = frequencySignal.divide(N); - - // Add current frequency signal to the list of compound signals. - signals[frequency] = frequencySignal; - } - - return signals; -} diff --git a/src/algorithms/math/fourier-transform/fastFourierTransform.js b/src/algorithms/math/fourier-transform/fastFourierTransform.js deleted file mode 100644 index ab51cf26e4..0000000000 --- a/src/algorithms/math/fourier-transform/fastFourierTransform.js +++ /dev/null @@ -1,77 +0,0 @@ -import ComplexNumber from '../complex-number/ComplexNumber'; -import bitLength from '../bits/bitLength'; - -/** - * Returns the number which is the flipped binary representation of input. - * - * @param {number} input - * @param {number} bitsCount - * @return {number} - */ -function reverseBits(input, bitsCount) { - let reversedBits = 0; - - for (let bitIndex = 0; bitIndex < bitsCount; bitIndex += 1) { - reversedBits *= 2; - - if (Math.floor(input / (1 << bitIndex)) % 2 === 1) { - reversedBits += 1; - } - } - - return reversedBits; -} - -/** - * Returns the radix-2 fast fourier transform of the given array. - * Optionally computes the radix-2 inverse fast fourier transform. - * - * @param {ComplexNumber[]} inputData - * @param {boolean} [inverse] - * @return {ComplexNumber[]} - */ -export default function fastFourierTransform(inputData, inverse = false) { - const bitsCount = bitLength(inputData.length - 1); - const N = 1 << bitsCount; - - while (inputData.length < N) { - inputData.push(new ComplexNumber()); - } - - const output = []; - for (let dataSampleIndex = 0; dataSampleIndex < N; dataSampleIndex += 1) { - output[dataSampleIndex] = inputData[reverseBits(dataSampleIndex, bitsCount)]; - } - - for (let blockLength = 2; blockLength <= N; blockLength *= 2) { - const imaginarySign = inverse ? -1 : 1; - const phaseStep = new ComplexNumber({ - re: Math.cos((2 * Math.PI) / blockLength), - im: imaginarySign * Math.sin((2 * Math.PI) / blockLength), - }); - - for (let blockStart = 0; blockStart < N; blockStart += blockLength) { - let phase = new ComplexNumber({ re: 1, im: 0 }); - - for (let signalId = blockStart; signalId < (blockStart + blockLength / 2); signalId += 1) { - const component = output[signalId + blockLength / 2].multiply(phase); - - const upd1 = output[signalId].add(component); - const upd2 = output[signalId].subtract(component); - - output[signalId] = upd1; - output[signalId + blockLength / 2] = upd2; - - phase = phase.multiply(phaseStep); - } - } - } - - if (inverse) { - for (let signalId = 0; signalId < N; signalId += 1) { - output[signalId] /= N; - } - } - - return output; -} diff --git a/src/algorithms/math/fourier-transform/inverseDiscreteFourierTransform.js b/src/algorithms/math/fourier-transform/inverseDiscreteFourierTransform.js deleted file mode 100644 index a9f0616351..0000000000 --- a/src/algorithms/math/fourier-transform/inverseDiscreteFourierTransform.js +++ /dev/null @@ -1,58 +0,0 @@ -import ComplexNumber from '../complex-number/ComplexNumber'; - -const CLOSE_TO_ZERO_THRESHOLD = 1e-10; - -/** - * Inverse Discrete Fourier Transform (IDFT): frequencies to time. - * - * Time complexity: O(N^2) - * - * @param {ComplexNumber[]} frequencies - Frequencies summands of the final signal. - * @param {number} zeroThreshold - Threshold that is used to convert real and imaginary numbers - * to zero in case if they are smaller then this. - * - * @return {number[]} - Discrete amplitudes distributed in time. - */ -export default function inverseDiscreteFourierTransform( - frequencies, - zeroThreshold = CLOSE_TO_ZERO_THRESHOLD, -) { - const N = frequencies.length; - const amplitudes = []; - - // Go through every discrete point of time. - for (let timer = 0; timer < N; timer += 1) { - // Compound amplitude at current time. - let amplitude = new ComplexNumber(); - - // Go through all discrete frequencies. - for (let frequency = 0; frequency < N; frequency += 1) { - const currentFrequency = frequencies[frequency]; - - // Calculate rotation angle. - const rotationAngle = (2 * Math.PI) * frequency * (timer / N); - - // Remember that e^ix = cos(x) + i * sin(x); - const frequencyContribution = new ComplexNumber({ - re: Math.cos(rotationAngle), - im: Math.sin(rotationAngle), - }).multiply(currentFrequency); - - amplitude = amplitude.add(frequencyContribution); - } - - // Close to zero? You're zero. - if (Math.abs(amplitude.re) < zeroThreshold) { - amplitude.re = 0; - } - - if (Math.abs(amplitude.im) < zeroThreshold) { - amplitude.im = 0; - } - - // Add current frequency signal to the list of compound signals. - amplitudes[timer] = amplitude.re; - } - - return amplitudes; -} diff --git a/src/algorithms/math/horner-method/README.md b/src/algorithms/math/horner-method/README.md deleted file mode 100644 index 991a674deb..0000000000 --- a/src/algorithms/math/horner-method/README.md +++ /dev/null @@ -1,20 +0,0 @@ -# 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: - -![Horner's rule](https://wikimedia.org/api/rest_v1/media/math/render/svg/2a576e42d875496f8b0f0dda5ebff7c2415532e4) - -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:** -`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 `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 - -- [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 deleted file mode 100644 index 8cdf950d6e..0000000000 --- a/src/algorithms/math/horner-method/__test__/classicPolynome.test.js +++ /dev/null @@ -1,14 +0,0 @@ -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 deleted file mode 100644 index 177ceb1aad..0000000000 --- a/src/algorithms/math/horner-method/__test__/hornerMethod.test.js +++ /dev/null @@ -1,21 +0,0 @@ -import hornerMethod from '../hornerMethod'; -import classicPolynome from '../classicPolynome'; - -describe('hornerMethod', () => { - 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); - }); - - 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 deleted file mode 100644 index 1f6aa8613c..0000000000 --- a/src/algorithms/math/horner-method/classicPolynome.js +++ /dev/null @@ -1,16 +0,0 @@ -/** - * 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 deleted file mode 100644 index 2236170ed1..0000000000 --- a/src/algorithms/math/horner-method/hornerMethod.js +++ /dev/null @@ -1,16 +0,0 @@ -/** - * Returns the evaluation of a polynomial function at a certain point. - * Uses Horner's rule. - * - * @param {number[]} coefficients - i.e. [4, 3, 2] for (4 * x^2 + 3 * x + 2) - * @param {number} xVal - * @return {number} - */ -export default function hornerMethod(coefficients, xVal) { - return coefficients.reduce( - (accumulator, currentCoefficient) => { - return accumulator * xVal + currentCoefficient; - }, - 0, - ); -} diff --git a/src/algorithms/math/integer-partition/README.md b/src/algorithms/math/integer-partition/README.md deleted file mode 100644 index 6023e1505a..0000000000 --- a/src/algorithms/math/integer-partition/README.md +++ /dev/null @@ -1,34 +0,0 @@ -# Integer Partition - -In number theory and combinatorics, a partition of a positive -integer `n`, also called an **integer partition**, is a way of -writing `n` as a sum of positive integers. - -Two sums that differ only in the order of their summands are -considered the same partition. For example, `4` can be partitioned -in five distinct ways: - -``` -4 -3 + 1 -2 + 2 -2 + 1 + 1 -1 + 1 + 1 + 1 -``` - -The order-dependent composition `1 + 3` is the same partition -as `3 + 1`, while the two distinct -compositions `1 + 2 + 1` and `1 + 1 + 2` represent the same -partition `2 + 1 + 1`. - -Young diagrams associated to the partitions of the positive -integers `1` through `8`. They are arranged so that images -under the reflection about the main diagonal of the square -are conjugate partitions. - -![Integer Partition](https://upload.wikimedia.org/wikipedia/commons/d/d8/Ferrer_partitioning_diagrams.svg) - -## References - -- [Wikipedia](https://en.wikipedia.org/wiki/Partition_(number_theory)) -- [YouTube](https://www.youtube.com/watch?v=ZaVM057DuzE&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8) diff --git a/src/algorithms/math/integer-partition/__test__/integerPartition.test.js b/src/algorithms/math/integer-partition/__test__/integerPartition.test.js deleted file mode 100644 index e78b1dfd2c..0000000000 --- a/src/algorithms/math/integer-partition/__test__/integerPartition.test.js +++ /dev/null @@ -1,14 +0,0 @@ -import integerPartition from '../integerPartition'; - -describe('integerPartition', () => { - it('should partition the number', () => { - expect(integerPartition(1)).toBe(1); - expect(integerPartition(2)).toBe(2); - expect(integerPartition(3)).toBe(3); - expect(integerPartition(4)).toBe(5); - expect(integerPartition(5)).toBe(7); - expect(integerPartition(6)).toBe(11); - expect(integerPartition(7)).toBe(15); - expect(integerPartition(8)).toBe(22); - }); -}); diff --git a/src/algorithms/math/integer-partition/integerPartition.js b/src/algorithms/math/integer-partition/integerPartition.js deleted file mode 100644 index 02cb31f69f..0000000000 --- a/src/algorithms/math/integer-partition/integerPartition.js +++ /dev/null @@ -1,57 +0,0 @@ -/** - * @param {number} number - * @return {number} - */ -export default function integerPartition(number) { - // Create partition matrix for solving this task using Dynamic Programming. - const partitionMatrix = Array(number + 1).fill(null).map(() => { - return Array(number + 1).fill(null); - }); - - // Fill partition matrix with initial values. - - // Let's fill the first row that represents how many ways we would have - // to combine the numbers 1, 2, 3, ..., n with number 0. We would have zero - // ways obviously since with zero number we may form only zero. - for (let numberIndex = 1; numberIndex <= number; numberIndex += 1) { - partitionMatrix[0][numberIndex] = 0; - } - - // Let's fill the first column. It represents the number of ways we can form - // number zero out of numbers 0, 0 and 1, 0 and 1 and 2, 0 and 1 and 2 and 3, ... - // Obviously there is only one way we could form number 0 - // and it is with number 0 itself. - for (let summandIndex = 0; summandIndex <= number; summandIndex += 1) { - partitionMatrix[summandIndex][0] = 1; - } - - // Now let's go through other possible options of how we could form number m out of - // summands 0, 1, ..., m using Dynamic Programming approach. - for (let summandIndex = 1; summandIndex <= number; summandIndex += 1) { - for (let numberIndex = 1; numberIndex <= number; numberIndex += 1) { - if (summandIndex > numberIndex) { - // If summand number is bigger then current number itself then just it won't add - // any new ways of forming the number. Thus we may just copy the number from row above. - partitionMatrix[summandIndex][numberIndex] = partitionMatrix[summandIndex - 1][numberIndex]; - } else { - /* - * The number of combinations would equal to number of combinations of forming the same - * number but WITHOUT current summand number PLUS number of combinations of forming the - * number but WITH current summand. - * - * Example: - * Number of ways to form 5 using summands {0, 1, 2} would equal the SUM of: - * - number of ways to form 5 using summands {0, 1} (we've excluded summand 2) - * - number of ways to form 3 (because 5 - 2 = 3) using summands {0, 1, 2} - * (we've included summand 2) - */ - const combosWithoutSummand = partitionMatrix[summandIndex - 1][numberIndex]; - const combosWithSummand = partitionMatrix[summandIndex][numberIndex - summandIndex]; - - partitionMatrix[summandIndex][numberIndex] = combosWithoutSummand + combosWithSummand; - } - } - } - - return partitionMatrix[number][number]; -} diff --git a/src/algorithms/math/is-power-of-two/README.md b/src/algorithms/math/is-power-of-two/README.md deleted file mode 100644 index 6ed1e92568..0000000000 --- a/src/algorithms/math/is-power-of-two/README.md +++ /dev/null @@ -1,51 +0,0 @@ -# Is a power of two - -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. - -**Bitwise solution** - -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`) - -``` -1: 0001 -2: 0010 -4: 0100 -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 -bit is set. - -``` -number & (number - 1) -``` - -For example for number `8` that operations will look like: - -``` - 1000 -- 0001 - ---- - 0111 - - 1000 -& 0111 - ---- - 0000 -``` - -## References - -- [GeeksForGeeks](https://www.geeksforgeeks.org/program-to-find-whether-a-no-is-power-of-two/) -- [Bitwise Solution on Stanford](http://www.graphics.stanford.edu/~seander/bithacks.html#DetermineIfPowerOf2) -- [Binary number subtraction on YouTube](https://www.youtube.com/watch?v=S9LJknZTyos&t=0s&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8&index=66) diff --git a/src/algorithms/math/is-power-of-two/__test__/isPowerOfTwo.test.js b/src/algorithms/math/is-power-of-two/__test__/isPowerOfTwo.test.js deleted file mode 100644 index d1271bab1a..0000000000 --- a/src/algorithms/math/is-power-of-two/__test__/isPowerOfTwo.test.js +++ /dev/null @@ -1,23 +0,0 @@ -import isPowerOfTwo from '../isPowerOfTwo'; - -describe('isPowerOfTwo', () => { - it('should check if the number is made by multiplying twos', () => { - expect(isPowerOfTwo(-1)).toBe(false); - expect(isPowerOfTwo(0)).toBe(false); - expect(isPowerOfTwo(1)).toBe(true); - expect(isPowerOfTwo(2)).toBe(true); - expect(isPowerOfTwo(3)).toBe(false); - expect(isPowerOfTwo(4)).toBe(true); - expect(isPowerOfTwo(5)).toBe(false); - expect(isPowerOfTwo(6)).toBe(false); - expect(isPowerOfTwo(7)).toBe(false); - expect(isPowerOfTwo(8)).toBe(true); - expect(isPowerOfTwo(10)).toBe(false); - expect(isPowerOfTwo(12)).toBe(false); - expect(isPowerOfTwo(16)).toBe(true); - expect(isPowerOfTwo(31)).toBe(false); - expect(isPowerOfTwo(64)).toBe(true); - expect(isPowerOfTwo(1024)).toBe(true); - expect(isPowerOfTwo(1023)).toBe(false); - }); -}); diff --git a/src/algorithms/math/is-power-of-two/__test__/isPowerOfTwoBitwise.test.js b/src/algorithms/math/is-power-of-two/__test__/isPowerOfTwoBitwise.test.js deleted file mode 100644 index bcba3a609c..0000000000 --- a/src/algorithms/math/is-power-of-two/__test__/isPowerOfTwoBitwise.test.js +++ /dev/null @@ -1,23 +0,0 @@ -import isPowerOfTwoBitwise from '../isPowerOfTwoBitwise'; - -describe('isPowerOfTwoBitwise', () => { - it('should check if the number is made by multiplying twos', () => { - expect(isPowerOfTwoBitwise(-1)).toBe(false); - expect(isPowerOfTwoBitwise(0)).toBe(false); - expect(isPowerOfTwoBitwise(1)).toBe(true); - expect(isPowerOfTwoBitwise(2)).toBe(true); - expect(isPowerOfTwoBitwise(3)).toBe(false); - expect(isPowerOfTwoBitwise(4)).toBe(true); - expect(isPowerOfTwoBitwise(5)).toBe(false); - expect(isPowerOfTwoBitwise(6)).toBe(false); - expect(isPowerOfTwoBitwise(7)).toBe(false); - expect(isPowerOfTwoBitwise(8)).toBe(true); - expect(isPowerOfTwoBitwise(10)).toBe(false); - expect(isPowerOfTwoBitwise(12)).toBe(false); - expect(isPowerOfTwoBitwise(16)).toBe(true); - expect(isPowerOfTwoBitwise(31)).toBe(false); - expect(isPowerOfTwoBitwise(64)).toBe(true); - expect(isPowerOfTwoBitwise(1024)).toBe(true); - expect(isPowerOfTwoBitwise(1023)).toBe(false); - }); -}); diff --git a/src/algorithms/math/is-power-of-two/isPowerOfTwo.js b/src/algorithms/math/is-power-of-two/isPowerOfTwo.js deleted file mode 100644 index 6f7590dd87..0000000000 --- a/src/algorithms/math/is-power-of-two/isPowerOfTwo.js +++ /dev/null @@ -1,25 +0,0 @@ -/** - * @param {number} number - * @return {boolean} - */ -export default function isPowerOfTwo(number) { - // 1 (2^0) is the smallest power of two. - if (number < 1) { - return false; - } - - // Let's find out if we can divide the number by two - // many times without remainder. - let dividedNumber = number; - while (dividedNumber !== 1) { - if (dividedNumber % 2 !== 0) { - // For every case when remainder isn't zero we can say that this number - // couldn't be a result of power of two. - return false; - } - - dividedNumber /= 2; - } - - return true; -} diff --git a/src/algorithms/math/is-power-of-two/isPowerOfTwoBitwise.js b/src/algorithms/math/is-power-of-two/isPowerOfTwoBitwise.js deleted file mode 100644 index af1177355f..0000000000 --- a/src/algorithms/math/is-power-of-two/isPowerOfTwoBitwise.js +++ /dev/null @@ -1,26 +0,0 @@ -/** - * @param {number} number - * @return {boolean} - */ -export default function isPowerOfTwoBitwise(number) { - // 1 (2^0) is the smallest power of two. - if (number < 1) { - return false; - } - - /* - * Powers of two in binary look like this: - * 1: 0001 - * 2: 0010 - * 4: 0100 - * 8: 1000 - * - * Note that there is always exactly 1 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 - * - * So after checking that the number is greater than zero, we can use a clever little bit - * hack to test that one and only one bit is set. - */ - return (number & (number - 1)) === 0; -} diff --git a/src/algorithms/math/least-common-multiple/README.md b/src/algorithms/math/least-common-multiple/README.md deleted file mode 100644 index 3e49af9a5f..0000000000 --- a/src/algorithms/math/least-common-multiple/README.md +++ /dev/null @@ -1,62 +0,0 @@ -# Least common multiple - -In arithmetic and number theory, the least common multiple, -lowest common multiple, or smallest common multiple of -two integers `a` and `b`, usually denoted by `LCM(a, b)`, is -the smallest positive integer that is divisible by -both `a` and `b`. Since division of integers by zero is -undefined, this definition has meaning only if `a` and `b` are -both different from zero. However, some authors define `lcm(a,0)` -as `0` for all `a`, which is the result of taking the `lcm` -to be the least upper bound in the lattice of divisibility. - -## Example - -What is the LCM of 4 and 6? - -Multiples of `4` are: - -``` -4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, ... -``` - -and the multiples of `6` are: - -``` -6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, ... -``` - -Common multiples of `4` and `6` are simply the numbers -that are in both lists: - -``` -12, 24, 36, 48, 60, 72, .... -``` - -So, from this list of the first few common multiples of -the numbers `4` and `6`, their least common multiple is `12`. - -## Computing the least common multiple - -The following formula reduces the problem of computing the -least common multiple to the problem of computing the greatest -common divisor (GCD), also known as the greatest common factor: - -``` -lcm(a, b) = |a * b| / gcd(a, b) -``` - -![LCM](https://upload.wikimedia.org/wikipedia/commons/c/c9/Symmetrical_5-set_Venn_diagram_LCM_2_3_4_5_7.svg) - -A Venn diagram showing the least common multiples of -combinations of `2`, `3`, `4`, `5` and `7` (`6` is skipped as -it is `2 × 3`, both of which are already represented). - -For example, a card game which requires its cards to be -divided equally among up to `5` players requires at least `60` -cards, the number at the intersection of the `2`, `3`, `4` -and `5` sets, but not the `7` set. - -## References - -[Wikipedia](https://en.wikipedia.org/wiki/Least_common_multiple) diff --git a/src/algorithms/math/least-common-multiple/__test__/leastCommonMultiple.test.js b/src/algorithms/math/least-common-multiple/__test__/leastCommonMultiple.test.js deleted file mode 100644 index 2152e110a1..0000000000 --- a/src/algorithms/math/least-common-multiple/__test__/leastCommonMultiple.test.js +++ /dev/null @@ -1,18 +0,0 @@ -import leastCommonMultiple from '../leastCommonMultiple'; - -describe('leastCommonMultiple', () => { - it('should find least common multiple', () => { - expect(leastCommonMultiple(0, 0)).toBe(0); - expect(leastCommonMultiple(1, 0)).toBe(0); - expect(leastCommonMultiple(0, 1)).toBe(0); - expect(leastCommonMultiple(4, 6)).toBe(12); - expect(leastCommonMultiple(6, 21)).toBe(42); - expect(leastCommonMultiple(7, 2)).toBe(14); - expect(leastCommonMultiple(3, 5)).toBe(15); - expect(leastCommonMultiple(7, 3)).toBe(21); - expect(leastCommonMultiple(1000000, 2)).toBe(1000000); - expect(leastCommonMultiple(-9, -18)).toBe(18); - expect(leastCommonMultiple(-7, -9)).toBe(63); - expect(leastCommonMultiple(-7, 9)).toBe(63); - }); -}); diff --git a/src/algorithms/math/least-common-multiple/leastCommonMultiple.js b/src/algorithms/math/least-common-multiple/leastCommonMultiple.js deleted file mode 100644 index 26a7681039..0000000000 --- a/src/algorithms/math/least-common-multiple/leastCommonMultiple.js +++ /dev/null @@ -1,11 +0,0 @@ -import euclideanAlgorithm from '../euclidean-algorithm/euclideanAlgorithm'; - -/** - * @param {number} a - * @param {number} b - * @return {number} - */ - -export default function leastCommonMultiple(a, b) { - return ((a === 0) || (b === 0)) ? 0 : Math.abs(a * b) / euclideanAlgorithm(a, b); -} diff --git a/src/algorithms/math/liu-hui/README.md b/src/algorithms/math/liu-hui/README.md deleted file mode 100644 index c53257f8dd..0000000000 --- a/src/algorithms/math/liu-hui/README.md +++ /dev/null @@ -1,92 +0,0 @@ -# Liu Hui's π Algorithm - -Liu Hui remarked in his commentary to The Nine Chapters on the Mathematical Art, -that the ratio of the circumference of an inscribed hexagon to the diameter of -the circle was `three`, hence `π` must be greater than three. He went on to provide -a detailed step-by-step description of an iterative algorithm to calculate `π` to -any required accuracy based on bisecting polygons; he calculated `π` to -between `3.141024` and `3.142708` with a 96-gon; he suggested that `3.14` was -a good enough approximation, and expressed `π` as `157/50`; he admitted that -this number was a bit small. Later he invented an ingenious quick method to -improve on it, and obtained `π ≈ 3.1416` with only a 96-gon, with an accuracy -comparable to that from a 1536-gon. His most important contribution in this -area was his simple iterative `π` algorithm. - -## Area of a circle - -Liu Hui argued: - -> Multiply one side of a hexagon by the radius (of its -circumcircle), then multiply this by three, to yield the -area of a dodecagon; if we cut a hexagon into a -dodecagon, multiply its side by its radius, then again -multiply by six, we get the area of a 24-gon; the finer -we cut, the smaller the loss with respect to the area -of circle, thus with further cut after cut, the area of -the resulting polygon will coincide and become one with -the circle; there will be no loss - -![Liu Hui](https://upload.wikimedia.org/wikipedia/commons/6/69/Cutcircle2.svg) - -Liu Hui's method of calculating the area of a circle. - -Further, Liu Hui proved that the area of a circle is half of its circumference -multiplied by its radius. He said: - -> Between a polygon and a circle, there is excess radius. Multiply the excess -radius by a side of the polygon. The resulting area exceeds the boundary of -the circle - -In the diagram `d = excess radius`. Multiplying `d` by one side results in -oblong `ABCD` which exceeds the boundary of the circle. If a side of the polygon -is small (i.e. there is a very large number of sides), then the excess radius -will be small, hence excess area will be small. - -> Multiply the side of a polygon by its radius, and the area doubles; -hence multiply half the circumference by the radius to yield the area of circle. - -![Liu Hui](https://upload.wikimedia.org/wikipedia/commons/9/95/Cutcircle.svg) - -The area within a circle is equal to the radius multiplied by half the -circumference, or `A = r x C/2 = r x r x π`. - -## Iterative algorithm - -Liu Hui began with an inscribed hexagon. Let `M` be the length of one side `AB` of -hexagon, `r` is the radius of circle. - -![Liu Hui](https://upload.wikimedia.org/wikipedia/commons/4/46/Liuhui_geyuanshu.svg) - -Bisect `AB` with line `OPC`, `AC` becomes one side of dodecagon (12-gon), let -its length be `m`. Let the length of `PC` be `j` and the length of `OP` be `G`. - -`AOP`, `APC` are two right angle triangles. Liu Hui used -the [Gou Gu](https://en.wikipedia.org/wiki/Pythagorean_theorem) (Pythagorean theorem) -theorem repetitively: - -![](https://wikimedia.org/api/rest_v1/media/math/render/svg/dbfc192c78539c3901c7bad470302ededb76f813) - -![](https://wikimedia.org/api/rest_v1/media/math/render/svg/ccd12a402367c2d6614c88e75006d50bfc3a9929) - -![](https://wikimedia.org/api/rest_v1/media/math/render/svg/65d77869fc02c302d2d46d45f75ad7e79ae524fb) - -![](https://wikimedia.org/api/rest_v1/media/math/render/svg/a7a0d0d7f505a0f434e5dd80c2fef6d2b30d6100) - -![](https://wikimedia.org/api/rest_v1/media/math/render/svg/c31b9acf38f9d1a248d4023c3bf286bd03007f37) - -![](https://wikimedia.org/api/rest_v1/media/math/render/svg/0dee798efb0b1e3e64d6b3542106cb3ecaa4a383) - -![](https://wikimedia.org/api/rest_v1/media/math/render/svg/3ffeafe88d2983b364ad3442746063e3207fe842) - - -From here, there is now a technique to determine `m` from `M`, which gives the -side length for a polygon with twice the number of edges. Starting with a -hexagon, Liu Hui could determine the side length of a dodecagon using this -formula. Then continue repetitively to determine the side length of a -24-gon given the side length of a dodecagon. He could do this recursively as -many times as necessary. Knowing how to determine the area of these polygons, -Liu Hui could then approximate `π`. - -## References - -- [Wikipedia](https://en.wikipedia.org/wiki/Liu_Hui%27s_%CF%80_algorithm) diff --git a/src/algorithms/math/liu-hui/__test__/liuHui.test.js b/src/algorithms/math/liu-hui/__test__/liuHui.test.js deleted file mode 100644 index 44f7464bd3..0000000000 --- a/src/algorithms/math/liu-hui/__test__/liuHui.test.js +++ /dev/null @@ -1,19 +0,0 @@ -import liuHui from '../liuHui'; - -describe('liuHui', () => { - it('should calculate π based on 12-gon', () => { - expect(liuHui(1)).toBe(3); - }); - - it('should calculate π based on 24-gon', () => { - expect(liuHui(2)).toBe(3.105828541230249); - }); - - it('should calculate π based on 6144-gon', () => { - expect(liuHui(10)).toBe(3.1415921059992717); - }); - - it('should calculate π based on 201326592-gon', () => { - expect(liuHui(25)).toBe(3.141592653589793); - }); -}); diff --git a/src/algorithms/math/liu-hui/liuHui.js b/src/algorithms/math/liu-hui/liuHui.js deleted file mode 100644 index e289ed8113..0000000000 --- a/src/algorithms/math/liu-hui/liuHui.js +++ /dev/null @@ -1,54 +0,0 @@ -/* - * Let circleRadius is the radius of circle. - * circleRadius is also the side length of the inscribed hexagon - */ -const circleRadius = 1; - -/** - * @param {number} sideLength - * @param {number} splitCounter - * @return {number} - */ -function getNGonSideLength(sideLength, splitCounter) { - if (splitCounter <= 0) { - return sideLength; - } - - const halfSide = sideLength / 2; - - // Liu Hui used the Gou Gu (Pythagorean theorem) theorem repetitively. - const perpendicular = Math.sqrt((circleRadius ** 2) - (halfSide ** 2)); - const excessRadius = circleRadius - perpendicular; - const splitSideLength = Math.sqrt((excessRadius ** 2) + (halfSide ** 2)); - - return getNGonSideLength(splitSideLength, splitCounter - 1); -} - -/** - * @param {number} splitCount - * @return {number} - */ -function getNGonSideCount(splitCount) { - // Liu Hui began with an inscribed hexagon (6-gon). - const hexagonSidesCount = 6; - - // On every split iteration we make N-gons: 6-gon, 12-gon, 24-gon, 48-gon and so on. - return hexagonSidesCount * (splitCount ? 2 ** splitCount : 1); -} - -/** - * Calculate the π value using Liu Hui's π algorithm - * - * @param {number} splitCount - number of times we're going to split 6-gon. - * On each split we will receive 12-gon, 24-gon and so on. - * @return {number} - */ -export default function liuHui(splitCount = 1) { - const nGonSideLength = getNGonSideLength(circleRadius, splitCount - 1); - const nGonSideCount = getNGonSideCount(splitCount - 1); - const nGonPerimeter = nGonSideLength * nGonSideCount; - const approximateCircleArea = (nGonPerimeter / 2) * circleRadius; - - // Return approximate value of pi. - return approximateCircleArea / (circleRadius ** 2); -} diff --git a/src/algorithms/math/matrix/Matrix.js b/src/algorithms/math/matrix/Matrix.js deleted file mode 100644 index 2aee126ba2..0000000000 --- a/src/algorithms/math/matrix/Matrix.js +++ /dev/null @@ -1,309 +0,0 @@ -/** - * @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} - */ -export 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 - */ -export 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} - */ -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 - // 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 - */ -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 - // 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 deleted file mode 100644 index 8e084403b0..0000000000 --- a/src/algorithms/math/matrix/README.md +++ /dev/null @@ -1,63 +0,0 @@ -# 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, a2,1 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 deleted file mode 100644 index 37dc892b0a..0000000000 --- a/src/algorithms/math/matrix/__tests__/Matrix.test.js +++ /dev/null @@ -1,455 +0,0 @@ -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', - ); - }); -}); diff --git a/src/algorithms/math/pascal-triangle/README.md b/src/algorithms/math/pascal-triangle/README.md deleted file mode 100644 index ff5075414c..0000000000 --- a/src/algorithms/math/pascal-triangle/README.md +++ /dev/null @@ -1,64 +0,0 @@ -# Pascal's Triangle - -In mathematics, **Pascal's triangle** is a triangular array of -the [binomial coefficients](https://en.wikipedia.org/wiki/Binomial_coefficient). - -The rows of Pascal's triangle are conventionally enumerated -starting with row `n = 0` at the top (the `0th` row). The -entries in each row are numbered from the left beginning -with `k = 0` and are usually staggered relative to the -numbers in the adjacent rows. The triangle may be constructed -in the following manner: In row `0` (the topmost row), there -is a unique nonzero entry `1`. Each entry of each subsequent -row is constructed by adding the number above and to the -left with the number above and to the right, treating blank -entries as `0`. For example, the initial number in the -first (or any other) row is `1` (the sum of `0` and `1`), -whereas the numbers `1` and `3` in the third row are added -to produce the number `4` in the fourth row. - -![Pascal's Triangle](https://upload.wikimedia.org/wikipedia/commons/0/0d/PascalTriangleAnimated2.gif) - -## Formula - -The entry in the `nth` row and `kth` column of Pascal's -triangle is denoted ![Formula](https://wikimedia.org/api/rest_v1/media/math/render/svg/206415d3742167e319b2e52c2ca7563b799abad7). -For example, the unique nonzero entry in the topmost -row is ![Formula example](https://wikimedia.org/api/rest_v1/media/math/render/svg/b7e35f86368d5978b46c07fd6dddca86bd6e635c). - -With this notation, the construction of the previous -paragraph may be written as follows: - -![Formula](https://wikimedia.org/api/rest_v1/media/math/render/svg/203b128a098e18cbb8cf36d004bd7282b28461bf) - -for any non-negative integer `n` and any -integer `k` between `0` and `n`, inclusive. - -![Binomial Coefficient](https://wikimedia.org/api/rest_v1/media/math/render/svg/a2457a7ef3c77831e34e06a1fe17a80b84a03181) - -## Calculating triangle entries in O(n) time - -We know that `i`-th entry in a line number `lineNumber` is -Binomial Coefficient `C(lineNumber, i)` and all lines start -with value `1`. The idea is to -calculate `C(lineNumber, i)` using `C(lineNumber, i-1)`. It -can be calculated in `O(1)` time using the following: - -``` -C(lineNumber, i) = lineNumber! / ((lineNumber - i)! * i!) -C(lineNumber, i - 1) = lineNumber! / ((lineNumber - i + 1)! * (i - 1)!) -``` - -We can derive following expression from above two expressions: - -``` -C(lineNumber, i) = C(lineNumber, i - 1) * (lineNumber - i + 1) / i -``` - -So `C(lineNumber, i)` can be calculated -from `C(lineNumber, i - 1)` in `O(1)` time. - -## References - -- [Wikipedia](https://en.wikipedia.org/wiki/Pascal%27s_triangle) -- [GeeksForGeeks](https://www.geeksforgeeks.org/pascal-triangle/) diff --git a/src/algorithms/math/pascal-triangle/__test__/pascalTriangle.test.js b/src/algorithms/math/pascal-triangle/__test__/pascalTriangle.test.js deleted file mode 100644 index 152fc8ea35..0000000000 --- a/src/algorithms/math/pascal-triangle/__test__/pascalTriangle.test.js +++ /dev/null @@ -1,14 +0,0 @@ -import pascalTriangle from '../pascalTriangle'; - -describe('pascalTriangle', () => { - it('should calculate Pascal Triangle coefficients for specific line number', () => { - expect(pascalTriangle(0)).toEqual([1]); - expect(pascalTriangle(1)).toEqual([1, 1]); - expect(pascalTriangle(2)).toEqual([1, 2, 1]); - expect(pascalTriangle(3)).toEqual([1, 3, 3, 1]); - expect(pascalTriangle(4)).toEqual([1, 4, 6, 4, 1]); - expect(pascalTriangle(5)).toEqual([1, 5, 10, 10, 5, 1]); - expect(pascalTriangle(6)).toEqual([1, 6, 15, 20, 15, 6, 1]); - expect(pascalTriangle(7)).toEqual([1, 7, 21, 35, 35, 21, 7, 1]); - }); -}); diff --git a/src/algorithms/math/pascal-triangle/__test__/pascalTriangleRecursive.test.js b/src/algorithms/math/pascal-triangle/__test__/pascalTriangleRecursive.test.js deleted file mode 100644 index 2dfdad6bd3..0000000000 --- a/src/algorithms/math/pascal-triangle/__test__/pascalTriangleRecursive.test.js +++ /dev/null @@ -1,14 +0,0 @@ -import pascalTriangleRecursive from '../pascalTriangleRecursive'; - -describe('pascalTriangleRecursive', () => { - it('should calculate Pascal Triangle coefficients for specific line number', () => { - expect(pascalTriangleRecursive(0)).toEqual([1]); - expect(pascalTriangleRecursive(1)).toEqual([1, 1]); - expect(pascalTriangleRecursive(2)).toEqual([1, 2, 1]); - expect(pascalTriangleRecursive(3)).toEqual([1, 3, 3, 1]); - expect(pascalTriangleRecursive(4)).toEqual([1, 4, 6, 4, 1]); - expect(pascalTriangleRecursive(5)).toEqual([1, 5, 10, 10, 5, 1]); - expect(pascalTriangleRecursive(6)).toEqual([1, 6, 15, 20, 15, 6, 1]); - expect(pascalTriangleRecursive(7)).toEqual([1, 7, 21, 35, 35, 21, 7, 1]); - }); -}); diff --git a/src/algorithms/math/pascal-triangle/pascalTriangle.js b/src/algorithms/math/pascal-triangle/pascalTriangle.js deleted file mode 100644 index 35686fa5b0..0000000000 --- a/src/algorithms/math/pascal-triangle/pascalTriangle.js +++ /dev/null @@ -1,16 +0,0 @@ -/** - * @param {number} lineNumber - zero based. - * @return {number[]} - */ -export default function pascalTriangle(lineNumber) { - const currentLine = [1]; - - const currentLineSize = lineNumber + 1; - - for (let numIndex = 1; numIndex < currentLineSize; numIndex += 1) { - // See explanation of this formula in README. - currentLine[numIndex] = (currentLine[numIndex - 1] * (lineNumber - numIndex + 1)) / numIndex; - } - - return currentLine; -} diff --git a/src/algorithms/math/pascal-triangle/pascalTriangleRecursive.js b/src/algorithms/math/pascal-triangle/pascalTriangleRecursive.js deleted file mode 100644 index 120fe25199..0000000000 --- a/src/algorithms/math/pascal-triangle/pascalTriangleRecursive.js +++ /dev/null @@ -1,30 +0,0 @@ -/** - * @param {number} lineNumber - zero based. - * @return {number[]} - */ -export default function pascalTriangleRecursive(lineNumber) { - if (lineNumber === 0) { - return [1]; - } - - const currentLineSize = lineNumber + 1; - const previousLineSize = currentLineSize - 1; - - // Create container for current line values. - const currentLine = []; - - // We'll calculate current line based on previous one. - const previousLine = pascalTriangleRecursive(lineNumber - 1); - - // Let's go through all elements of current line except the first and - // last one (since they were and will be filled with 1's) and calculate - // current coefficient based on previous line. - for (let numIndex = 0; numIndex < currentLineSize; numIndex += 1) { - const leftCoefficient = (numIndex - 1) >= 0 ? previousLine[numIndex - 1] : 0; - const rightCoefficient = numIndex < previousLineSize ? previousLine[numIndex] : 0; - - currentLine[numIndex] = leftCoefficient + rightCoefficient; - } - - return currentLine; -} diff --git a/src/algorithms/math/primality-test/README.md b/src/algorithms/math/primality-test/README.md deleted file mode 100644 index 8a9852dc31..0000000000 --- a/src/algorithms/math/primality-test/README.md +++ /dev/null @@ -1,25 +0,0 @@ -# Primality Test - -A **prime number** (or a **prime**) is a natural number greater than `1` that -cannot be formed by multiplying two smaller natural numbers. A natural number -greater than `1` that is not prime is called a composite number. For -example, `5` is prime because the only ways of writing it as a -product, `1 × 5` or `5 × 1`, involve `5` itself. However, `6` is -composite because it is the product of two numbers `(2 × 3)` that are -both smaller than `6`. - -![Prime Numbers](https://upload.wikimedia.org/wikipedia/commons/f/f0/Primes-vs-composites.svg) - -A **primality test** is an algorithm for determining whether an input -number is prime. Among other fields of mathematics, it is used -for cryptography. Unlike integer factorization, primality tests -do not generally give prime factors, only stating whether the -input number is prime or not. Factorization is thought to be -a computationally difficult problem, whereas primality testing -is comparatively easy (its running time is polynomial in the -size of the input). - -## References - -- [Prime Numbers on Wikipedia](https://en.wikipedia.org/wiki/Prime_number) -- [Primality Test on Wikipedia](https://en.wikipedia.org/wiki/Primality_test) diff --git a/src/algorithms/math/primality-test/__test__/trialDivision.test.js b/src/algorithms/math/primality-test/__test__/trialDivision.test.js deleted file mode 100644 index 224e840ffc..0000000000 --- a/src/algorithms/math/primality-test/__test__/trialDivision.test.js +++ /dev/null @@ -1,37 +0,0 @@ -import trialDivision from '../trialDivision'; - -/** - * @param {function(n: number)} testFunction - */ -function primalityTest(testFunction) { - expect(testFunction(1)).toBe(false); - expect(testFunction(2)).toBe(true); - expect(testFunction(3)).toBe(true); - expect(testFunction(5)).toBe(true); - expect(testFunction(11)).toBe(true); - expect(testFunction(191)).toBe(true); - expect(testFunction(191)).toBe(true); - expect(testFunction(199)).toBe(true); - - expect(testFunction(-1)).toBe(false); - expect(testFunction(0)).toBe(false); - expect(testFunction(4)).toBe(false); - expect(testFunction(6)).toBe(false); - expect(testFunction(12)).toBe(false); - expect(testFunction(14)).toBe(false); - expect(testFunction(25)).toBe(false); - expect(testFunction(192)).toBe(false); - expect(testFunction(200)).toBe(false); - expect(testFunction(400)).toBe(false); - - // It should also deal with floats. - expect(testFunction(0.5)).toBe(false); - expect(testFunction(1.3)).toBe(false); - expect(testFunction(10.5)).toBe(false); -} - -describe('trialDivision', () => { - it('should detect prime numbers', () => { - primalityTest(trialDivision); - }); -}); diff --git a/src/algorithms/math/primality-test/trialDivision.js b/src/algorithms/math/primality-test/trialDivision.js deleted file mode 100644 index c347e05cad..0000000000 --- a/src/algorithms/math/primality-test/trialDivision.js +++ /dev/null @@ -1,35 +0,0 @@ -/** - * @param {number} number - * @return {boolean} - */ -export default function trialDivision(number) { - // Check if number is integer. - if (number % 1 !== 0) { - return false; - } - - if (number <= 1) { - // If number is less than one then it isn't prime by definition. - return false; - } - - if (number <= 3) { - // All numbers from 2 to 3 are prime. - return true; - } - - // If the number is not divided by 2 then we may eliminate all further even dividers. - if (number % 2 === 0) { - return false; - } - - // If there is no dividers up to square root of n then there is no higher dividers as well. - const dividerLimit = Math.sqrt(number); - for (let divider = 3; divider <= dividerLimit; divider += 2) { - if (number % divider === 0) { - return false; - } - } - - return true; -} diff --git a/src/algorithms/math/prime-factors/README.md b/src/algorithms/math/prime-factors/README.md deleted file mode 100644 index d8e0f96e3f..0000000000 --- a/src/algorithms/math/prime-factors/README.md +++ /dev/null @@ -1,37 +0,0 @@ -# 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**. - -![Composite numbers](https://www.mathsisfun.com/numbers/images/prime-composite.svg) - -_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`. - -![Factors](https://www.mathsisfun.com/numbers/images/factor-2x3.svg) - -_Image source: [Math is Fun](https://www.mathsisfun.com/prime-factorization.html)_ - -## Finding the prime factors and their count accurately - -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. - -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. - -## Hardy-Ramanujan formula for approximate calculation of prime-factor count - -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))`. - -Roughly speaking, this means that most numbers have about this number of distinct prime factors. - -## 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) diff --git a/src/algorithms/math/prime-factors/README.zh-CN.md b/src/algorithms/math/prime-factors/README.zh-CN.md deleted file mode 100644 index c6ab82e39b..0000000000 --- a/src/algorithms/math/prime-factors/README.zh-CN.md +++ /dev/null @@ -1,38 +0,0 @@ -# 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) 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 92c94d1f6f..0000000000 --- a/src/algorithms/math/prime-factors/__test__/primeFactors.test.js +++ /dev/null @@ -1,87 +0,0 @@ -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/primeFactors.js b/src/algorithms/math/prime-factors/primeFactors.js deleted file mode 100644 index 691436c49e..0000000000 --- a/src/algorithms/math/prime-factors/primeFactors.js +++ /dev/null @@ -1,42 +0,0 @@ -/** - * 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/radian/README.md b/src/algorithms/math/radian/README.md deleted file mode 100644 index 2de4655e7d..0000000000 --- a/src/algorithms/math/radian/README.md +++ /dev/null @@ -1,36 +0,0 @@ -# Radian - -The **radian** (symbol **rad**) is the unit for measuring angles, and is the -standard unit of angular measure used in many areas of mathematics. - -The length of an arc of a unit circle is numerically equal to the measurement -in radians of the angle that it subtends; one radian is just under `57.3` degrees. - -An arc of a circle with the same length as the radius of that circle subtends an -angle of `1 radian`. The circumference subtends an angle of `2π radians`. - -![Radian](https://upload.wikimedia.org/wikipedia/commons/4/4e/Circle_radians.gif) - -A complete revolution is 2π radians (shown here with a circle of radius one and -thus circumference `2π`). - -![2 pi Radian](https://upload.wikimedia.org/wikipedia/commons/6/67/2pi-unrolled.gif) - -**Conversions** - -| Radians | Degrees | -| :-----: | :-----: | -| 0 | 0° | -| π/12 | 15° | -| π/6 | 30° | -| π/4 | 45° | -| 1 | 57.3° | -| π/3 | 60° | -| π/2 | 90° | -| π | 180° | -| 2π | 360° | - - -## References - -- [Wikipedia](https://en.wikipedia.org/wiki/Radian) diff --git a/src/algorithms/math/radian/__test__/degreeToRadian.test.js b/src/algorithms/math/radian/__test__/degreeToRadian.test.js deleted file mode 100644 index dbf775168f..0000000000 --- a/src/algorithms/math/radian/__test__/degreeToRadian.test.js +++ /dev/null @@ -1,12 +0,0 @@ -import degreeToRadian from '../degreeToRadian'; - -describe('degreeToRadian', () => { - it('should convert degree to radian', () => { - expect(degreeToRadian(0)).toBe(0); - expect(degreeToRadian(45)).toBe(Math.PI / 4); - expect(degreeToRadian(90)).toBe(Math.PI / 2); - expect(degreeToRadian(180)).toBe(Math.PI); - expect(degreeToRadian(270)).toBe((3 * Math.PI) / 2); - expect(degreeToRadian(360)).toBe(2 * Math.PI); - }); -}); diff --git a/src/algorithms/math/radian/__test__/radianToDegree.test.js b/src/algorithms/math/radian/__test__/radianToDegree.test.js deleted file mode 100644 index 92f8b906d3..0000000000 --- a/src/algorithms/math/radian/__test__/radianToDegree.test.js +++ /dev/null @@ -1,12 +0,0 @@ -import radianToDegree from '../radianToDegree'; - -describe('radianToDegree', () => { - it('should convert radian to degree', () => { - expect(radianToDegree(0)).toBe(0); - expect(radianToDegree(Math.PI / 4)).toBe(45); - expect(radianToDegree(Math.PI / 2)).toBe(90); - expect(radianToDegree(Math.PI)).toBe(180); - expect(radianToDegree((3 * Math.PI) / 2)).toBe(270); - expect(radianToDegree(2 * Math.PI)).toBe(360); - }); -}); diff --git a/src/algorithms/math/radian/degreeToRadian.js b/src/algorithms/math/radian/degreeToRadian.js deleted file mode 100644 index fb3836cd41..0000000000 --- a/src/algorithms/math/radian/degreeToRadian.js +++ /dev/null @@ -1,7 +0,0 @@ -/** - * @param {number} degree - * @return {number} - */ -export default function degreeToRadian(degree) { - return degree * (Math.PI / 180); -} diff --git a/src/algorithms/math/radian/radianToDegree.js b/src/algorithms/math/radian/radianToDegree.js deleted file mode 100644 index e733f4152a..0000000000 --- a/src/algorithms/math/radian/radianToDegree.js +++ /dev/null @@ -1,7 +0,0 @@ -/** - * @param {number} radian - * @return {number} - */ -export default function radianToDegree(radian) { - return radian * (180 / Math.PI); -} diff --git a/src/algorithms/math/sieve-of-eratosthenes/README.md b/src/algorithms/math/sieve-of-eratosthenes/README.md deleted file mode 100644 index 876379a006..0000000000 --- a/src/algorithms/math/sieve-of-eratosthenes/README.md +++ /dev/null @@ -1,32 +0,0 @@ -# Sieve of Eratosthenes - -The Sieve of Eratosthenes is an algorithm for finding all prime numbers up to some limit `n`. - -It is attributed to Eratosthenes of Cyrene, an ancient Greek mathematician. - -## How it works - -1. Create a boolean array of `n + 1` positions (to represent the numbers `0` through `n`) -2. Set positions `0` and `1` to `false`, and the rest to `true` -3. Start at position `p = 2` (the first prime number) -4. Mark as `false` all the multiples of `p` (that is, positions `2 * p`, `3 * p`, `4 * p`... until you reach the end of the array) -5. Find the first position greater than `p` that is `true` in the array. If there is no such position, stop. Otherwise, let `p` equal this new number (which is the next prime), and repeat from step 4 - -When the algorithm terminates, the numbers remaining `true` in the array are all -the primes below `n`. - -An improvement of this algorithm is, in step 4, start marking multiples -of `p` from `p * p`, and not from `2 * p`. The reason why this works is because, -at that point, smaller multiples of `p` will have already been marked `false`. - -## Example - -![Sieve](https://upload.wikimedia.org/wikipedia/commons/b/b9/Sieve_of_Eratosthenes_animation.gif) - -## Complexity - -The algorithm has a complexity of `O(n log(log n))`. - -## References - -- [Wikipedia](https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes) diff --git a/src/algorithms/math/sieve-of-eratosthenes/__test__/sieveOfEratosthenes.test.js b/src/algorithms/math/sieve-of-eratosthenes/__test__/sieveOfEratosthenes.test.js deleted file mode 100644 index f2bce60d63..0000000000 --- a/src/algorithms/math/sieve-of-eratosthenes/__test__/sieveOfEratosthenes.test.js +++ /dev/null @@ -1,12 +0,0 @@ -import sieveOfEratosthenes from '../sieveOfEratosthenes'; - -describe('sieveOfEratosthenes', () => { - it('should find all primes less than or equal to n', () => { - expect(sieveOfEratosthenes(5)).toEqual([2, 3, 5]); - expect(sieveOfEratosthenes(10)).toEqual([2, 3, 5, 7]); - expect(sieveOfEratosthenes(100)).toEqual([ - 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, - 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, - ]); - }); -}); diff --git a/src/algorithms/math/sieve-of-eratosthenes/sieveOfEratosthenes.js b/src/algorithms/math/sieve-of-eratosthenes/sieveOfEratosthenes.js deleted file mode 100644 index 6b96583be6..0000000000 --- a/src/algorithms/math/sieve-of-eratosthenes/sieveOfEratosthenes.js +++ /dev/null @@ -1,36 +0,0 @@ -/** - * @param {number} maxNumber - * @return {number[]} - */ -export default function sieveOfEratosthenes(maxNumber) { - const isPrime = new Array(maxNumber + 1).fill(true); - isPrime[0] = false; - isPrime[1] = false; - - const primes = []; - - for (let number = 2; number <= maxNumber; number += 1) { - if (isPrime[number] === true) { - primes.push(number); - - /* - * Optimisation. - * Start marking multiples of `p` from `p * p`, and not from `2 * p`. - * The reason why this works is because, at that point, smaller multiples - * of `p` will have already been marked `false`. - * - * Warning: When working with really big numbers, the following line may cause overflow - * In that case, it can be changed to: - * let nextNumber = 2 * number; - */ - let nextNumber = number * number; - - while (nextNumber <= maxNumber) { - isPrime[nextNumber] = false; - nextNumber += number; - } - } - } - - return primes; -} diff --git a/src/algorithms/math/square-root/README.md b/src/algorithms/math/square-root/README.md deleted file mode 100644 index 7f9713b5f6..0000000000 --- a/src/algorithms/math/square-root/README.md +++ /dev/null @@ -1,62 +0,0 @@ -# Square Root (Newton's Method) - -In numerical analysis, a branch of mathematics, there are several square root -algorithms or methods of computing the principal square root of a non-negative real -number. As, generally, the roots of a function cannot be computed exactly. -The root-finding algorithms provide approximations to roots expressed as floating -point numbers. - -Finding ![](https://wikimedia.org/api/rest_v1/media/math/render/svg/bff86975b0e7944720b3e635c53c22c032a7a6f1) is -the same as solving the equation ![](https://wikimedia.org/api/rest_v1/media/math/render/svg/6cf57722151ef19ba1ca918d702b95c335e21cad) for a -positive `x`. Therefore, any general numerical root-finding algorithm can be used. - -**Newton's method** (also known as the Newton–Raphson method), named after -_Isaac Newton_ and _Joseph Raphson_, is one example of a root-finding algorithm. It is a -method for finding successively better approximations to the roots of a real-valued function. - -Let's start by explaining the general idea of Newton's method and then apply it to our particular -case with finding a square root of the number. - -## Newton's Method General Idea - -The Newton–Raphson method in one variable is implemented as follows: - -The method starts with a function `f` defined over the real numbers `x`, the function's derivative `f'`, and an -initial guess `x0` for a root of the function `f`. If the function satisfies the assumptions made in the derivation -of the formula and the initial guess is close, then a better approximation `x1` is: - -![](https://wikimedia.org/api/rest_v1/media/math/render/svg/52c50eca0b7c4d64ef2fdca678665b73e944cb84) - -Geometrically, `(x1, 0)` is the intersection of the `x`-axis and the tangent of -the graph of `f` at `(x0, f (x0))`. - -The process is repeated as: - -![](https://wikimedia.org/api/rest_v1/media/math/render/svg/710c11b9ec4568d1cfff49b7c7d41e0a7829a736) - -until a sufficiently accurate value is reached. - -![](https://upload.wikimedia.org/wikipedia/commons/e/e0/NewtonIteration_Ani.gif) - -## Newton's Method of Finding a Square Root - -As it was mentioned above, finding ![](https://wikimedia.org/api/rest_v1/media/math/render/svg/bff86975b0e7944720b3e635c53c22c032a7a6f1) is -the same as solving the equation ![](https://wikimedia.org/api/rest_v1/media/math/render/svg/6cf57722151ef19ba1ca918d702b95c335e21cad) for a -positive `x`. - -The derivative of the function `f(x)` in case of square root problem is `2x`. - -After applying the Newton's formula (see above) we get the following equation for our algorithm iterations: - -```text -x := x - (x² - S) / (2x) -``` - -The `x² − S` above is how far away `x²` is from where it needs to be, and the -division by `2x` is the derivative of `x²`, to scale how much we adjust `x` by how -quickly `x²` is changing. - -## References - -- [Methods of computing square roots on Wikipedia](https://en.wikipedia.org/wiki/Methods_of_computing_square_roots) -- [Newton's method on Wikipedia](https://en.wikipedia.org/wiki/Newton%27s_method) diff --git a/src/algorithms/math/square-root/__test__/squareRoot.test.js b/src/algorithms/math/square-root/__test__/squareRoot.test.js deleted file mode 100644 index 9679d1a1c5..0000000000 --- a/src/algorithms/math/square-root/__test__/squareRoot.test.js +++ /dev/null @@ -1,69 +0,0 @@ -import squareRoot from '../squareRoot'; - -describe('squareRoot', () => { - it('should throw for negative numbers', () => { - function failingSquareRoot() { - squareRoot(-5); - } - expect(failingSquareRoot).toThrow(); - }); - - it('should correctly calculate square root with default tolerance', () => { - expect(squareRoot(0)).toBe(0); - expect(squareRoot(1)).toBe(1); - expect(squareRoot(2)).toBe(1); - expect(squareRoot(3)).toBe(2); - expect(squareRoot(4)).toBe(2); - expect(squareRoot(15)).toBe(4); - expect(squareRoot(16)).toBe(4); - expect(squareRoot(256)).toBe(16); - expect(squareRoot(473)).toBe(22); - expect(squareRoot(14723)).toBe(121); - }); - - it('should correctly calculate square root for integers with custom tolerance', () => { - let tolerance = 1; - - expect(squareRoot(0, tolerance)).toBe(0); - expect(squareRoot(1, tolerance)).toBe(1); - expect(squareRoot(2, tolerance)).toBe(1.4); - expect(squareRoot(3, tolerance)).toBe(1.8); - expect(squareRoot(4, tolerance)).toBe(2); - expect(squareRoot(15, tolerance)).toBe(3.9); - expect(squareRoot(16, tolerance)).toBe(4); - expect(squareRoot(256, tolerance)).toBe(16); - expect(squareRoot(473, tolerance)).toBe(21.7); - expect(squareRoot(14723, tolerance)).toBe(121.3); - - tolerance = 3; - - expect(squareRoot(0, tolerance)).toBe(0); - expect(squareRoot(1, tolerance)).toBe(1); - expect(squareRoot(2, tolerance)).toBe(1.414); - expect(squareRoot(3, tolerance)).toBe(1.732); - expect(squareRoot(4, tolerance)).toBe(2); - expect(squareRoot(15, tolerance)).toBe(3.873); - expect(squareRoot(16, tolerance)).toBe(4); - expect(squareRoot(256, tolerance)).toBe(16); - expect(squareRoot(473, tolerance)).toBe(21.749); - expect(squareRoot(14723, tolerance)).toBe(121.338); - - tolerance = 10; - - expect(squareRoot(0, tolerance)).toBe(0); - expect(squareRoot(1, tolerance)).toBe(1); - expect(squareRoot(2, tolerance)).toBe(1.4142135624); - expect(squareRoot(3, tolerance)).toBe(1.7320508076); - expect(squareRoot(4, tolerance)).toBe(2); - expect(squareRoot(15, tolerance)).toBe(3.8729833462); - expect(squareRoot(16, tolerance)).toBe(4); - expect(squareRoot(256, tolerance)).toBe(16); - expect(squareRoot(473, tolerance)).toBe(21.7485631709); - expect(squareRoot(14723, tolerance)).toBe(121.3383698588); - }); - - it('should correctly calculate square root for integers with custom tolerance', () => { - expect(squareRoot(4.5, 10)).toBe(2.1213203436); - expect(squareRoot(217.534, 10)).toBe(14.7490338667); - }); -}); diff --git a/src/algorithms/math/square-root/squareRoot.js b/src/algorithms/math/square-root/squareRoot.js deleted file mode 100644 index 19779bf34c..0000000000 --- a/src/algorithms/math/square-root/squareRoot.js +++ /dev/null @@ -1,40 +0,0 @@ -/** - * Calculates the square root of the number with given tolerance (precision) - * by using Newton's method. - * - * @param number - the number we want to find a square root for. - * @param [tolerance] - how many precise numbers after the floating point we want to get. - * @return {number} - */ -export default function squareRoot(number, tolerance = 0) { - // For now we won't support operations that involves manipulation with complex numbers. - if (number < 0) { - throw new Error('The method supports only positive integers'); - } - - // Handle edge case with finding the square root of zero. - if (number === 0) { - return 0; - } - - // We will start approximation from value 1. - let root = 1; - - // Delta is a desired distance between the number and the square of the root. - // - if tolerance=0 then delta=1 - // - if tolerance=1 then delta=0.1 - // - if tolerance=2 then delta=0.01 - // - and so on... - const requiredDelta = 1 / (10 ** tolerance); - - // Approximating the root value to the point when we get a desired precision. - while (Math.abs(number - (root ** 2)) > requiredDelta) { - // Newton's method reduces in this case to the so-called Babylonian method. - // These methods generally yield approximate results, but can be made arbitrarily - // precise by increasing the number of calculation steps. - root -= ((root ** 2) - number) / (2 * root); - } - - // Cut off undesired floating digits and return the root value. - return Math.round(root * (10 ** tolerance)) / (10 ** tolerance); -} diff --git a/src/algorithms/ml/k-means/README.md b/src/algorithms/ml/k-means/README.md deleted file mode 100644 index fb58c1bfa4..0000000000 --- a/src/algorithms/ml/k-means/README.md +++ /dev/null @@ -1,40 +0,0 @@ -# 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. - -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) - -_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 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 - -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-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) diff --git a/src/algorithms/ml/k-means/README.pt-BR.md b/src/algorithms/ml/k-means/README.pt-BR.md deleted file mode 100644 index d814ac19bc..0000000000 --- a/src/algorithms/ml/k-means/README.pt-BR.md +++ /dev/null @@ -1,35 +0,0 @@ -# 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/k-means/__test__/kMeans.test.js b/src/algorithms/ml/k-means/__test__/kMeans.test.js deleted file mode 100644 index 44a6f538e2..0000000000 --- a/src/algorithms/ml/k-means/__test__/kMeans.test.js +++ /dev/null @@ -1,40 +0,0 @@ -import KMeans from '../kMeans'; - -describe('kMeans', () => { - it('should throw an error on invalid data', () => { - expect(() => { - KMeans(); - }).toThrowError('The data is empty'); - }); - - it('should throw an error on inconsistent data', () => { - expect(() => { - KMeans([[1, 2], [1]], 2); - }).toThrowError('Matrices have different shapes'); - }); - - it('should find the nearest neighbour', () => { - const data = [[1, 1], [6, 2], [3, 3], [4, 5], [9, 2], [2, 4], [8, 7]]; - const k = 2; - 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); - }); - - 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/k-means/kMeans.js b/src/algorithms/ml/k-means/kMeans.js deleted file mode 100644 index 4361eed689..0000000000 --- a/src/algorithms/ml/k-means/kMeans.js +++ /dev/null @@ -1,85 +0,0 @@ -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/knn/README.md b/src/algorithms/ml/knn/README.md deleted file mode 100644 index 1fc168eaf2..0000000000 --- a/src/algorithms/ml/knn/README.md +++ /dev/null @@ -1,44 +0,0 @@ -# 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. - -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/README.pt-BR.md b/src/algorithms/ml/knn/README.pt-BR.md deleted file mode 100644 index b2abdd784f..0000000000 --- a/src/algorithms/ml/knn/README.pt-BR.md +++ /dev/null @@ -1,44 +0,0 @@ -# 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/ml/knn/__test__/knn.test.js b/src/algorithms/ml/knn/__test__/knn.test.js deleted file mode 100644 index 302bf3b7a9..0000000000 --- a/src/algorithms/ml/knn/__test__/knn.test.js +++ /dev/null @@ -1,71 +0,0 @@ -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('Matrices have different shapes'); - }); - - 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 deleted file mode 100644 index 350e7ce176..0000000000 --- a/src/algorithms/ml/knn/kNN.js +++ /dev/null @@ -1,60 +0,0 @@ -/** - * 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 - */ - -import euclideanDistance from '../../math/euclidean-distance/euclideanDistance'; - -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; -} diff --git a/src/algorithms/search/binary-search/README.es-ES.md b/src/algorithms/search/binary-search/README.es-ES.md deleted file mode 100644 index f14aef985f..0000000000 --- a/src/algorithms/search/binary-search/README.es-ES.md +++ /dev/null @@ -1,27 +0,0 @@ -# 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 deleted file mode 100644 index 34d1bd7a40..0000000000 --- a/src/algorithms/search/binary-search/README.md +++ /dev/null @@ -1,27 +0,0 @@ -# Binary Search - -_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 the array. - -![Binary Search](https://upload.wikimedia.org/wikipedia/commons/8/83/Binary_Search_Depiction.svg) - -## Complexity - -**Time Complexity**: `O(log(n))` - since we split search area by two for every -next iteration. - -## References - -- [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.pt-BR.md b/src/algorithms/search/binary-search/README.pt-BR.md deleted file mode 100644 index 4f9de9f199..0000000000 --- a/src/algorithms/search/binary-search/README.pt-BR.md +++ /dev/null @@ -1,23 +0,0 @@ -# Busca Binária - -_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 -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) diff --git a/src/algorithms/search/binary-search/__test__/binarySearch.test.js b/src/algorithms/search/binary-search/__test__/binarySearch.test.js deleted file mode 100644 index 72c2b344f5..0000000000 --- a/src/algorithms/search/binary-search/__test__/binarySearch.test.js +++ /dev/null @@ -1,34 +0,0 @@ -import binarySearch from '../binarySearch'; - -describe('binarySearch', () => { - it('should search number in sorted array', () => { - expect(binarySearch([], 1)).toBe(-1); - expect(binarySearch([1], 1)).toBe(0); - expect(binarySearch([1, 2], 1)).toBe(0); - expect(binarySearch([1, 2], 2)).toBe(1); - expect(binarySearch([1, 5, 10, 12], 1)).toBe(0); - expect(binarySearch([1, 5, 10, 12, 14, 17, 22, 100], 17)).toBe(5); - expect(binarySearch([1, 5, 10, 12, 14, 17, 22, 100], 1)).toBe(0); - expect(binarySearch([1, 5, 10, 12, 14, 17, 22, 100], 100)).toBe(7); - expect(binarySearch([1, 5, 10, 12, 14, 17, 22, 100], 0)).toBe(-1); - }); - - it('should search object in sorted array', () => { - const sortedArrayOfObjects = [ - { key: 1, value: 'value1' }, - { key: 2, value: 'value2' }, - { key: 3, value: 'value3' }, - ]; - - const comparator = (a, b) => { - if (a.key === b.key) return 0; - return a.key < b.key ? -1 : 1; - }; - - expect(binarySearch([], { key: 1 }, comparator)).toBe(-1); - expect(binarySearch(sortedArrayOfObjects, { key: 4 }, comparator)).toBe(-1); - expect(binarySearch(sortedArrayOfObjects, { key: 1 }, comparator)).toBe(0); - expect(binarySearch(sortedArrayOfObjects, { key: 2 }, comparator)).toBe(1); - expect(binarySearch(sortedArrayOfObjects, { key: 3 }, comparator)).toBe(2); - }); -}); diff --git a/src/algorithms/search/binary-search/binarySearch.js b/src/algorithms/search/binary-search/binarySearch.js deleted file mode 100644 index 5c8d48fbea..0000000000 --- a/src/algorithms/search/binary-search/binarySearch.js +++ /dev/null @@ -1,44 +0,0 @@ -import Comparator from '../../../utils/comparator/Comparator'; - -/** - * Binary search implementation. - * - * @param {*[]} sortedArray - * @param {*} seekElement - * @param {function(a, b)} [comparatorCallback] - * @return {number} - */ - -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 lessThan(). - const comparator = new Comparator(comparatorCallback); - - // These two indices will contain current array (sub-array) boundaries. - let startIndex = 0; - let endIndex = sortedArray.length - 1; - - // Let's continue to split array until boundaries are collapsed - // and there is nothing to split anymore. - while (startIndex <= endIndex) { - // Let's calculate the index of the middle element. - const middleIndex = startIndex + Math.floor((endIndex - startIndex) / 2); - - // If we've found the element just return its position. - if (comparator.equal(sortedArray[middleIndex], seekElement)) { - return middleIndex; - } - - // Decide which half to choose for seeking next: left or right one. - if (comparator.lessThan(sortedArray[middleIndex], seekElement)) { - // Go to the right half of the array. - startIndex = middleIndex + 1; - } else { - // Go to the left half of the array. - endIndex = middleIndex - 1; - } - } - - // Return -1 if we have not found anything. - return -1; -} diff --git a/src/algorithms/search/interpolation-search/README.md b/src/algorithms/search/interpolation-search/README.md deleted file mode 100644 index e91154a8ff..0000000000 --- a/src/algorithms/search/interpolation-search/README.md +++ /dev/null @@ -1,40 +0,0 @@ -# Interpolation Search - -**Interpolation search** is an algorithm for searching for a key in an array that -has been ordered by numerical values assigned to the keys (key values). - -For example we have a sorted array of `n` uniformly distributed values `arr[]`, -and we need to write a function to search for a particular element `x` in the array. - -**Linear Search** finds the element in `O(n)` time, **Jump Search** takes `O(√ n)` time -and **Binary Search** take `O(Log n)` time. - -The **Interpolation Search** is an improvement over Binary Search for instances, -where the values in a sorted array are _uniformly_ distributed. Binary Search -always goes to the middle element to check. On the other hand, interpolation -search may go to different locations according to the value of the key being -searched. For example, if the value of the key is closer to the last element, -interpolation search is likely to start search toward the end side. - -To find the position to be searched, it uses following formula: - -``` -// The idea of formula is to return higher value of pos -// when element to be searched is closer to arr[hi]. And -// smaller value when closer to arr[lo] -pos = lo + ((x - arr[lo]) * (hi - lo) / (arr[hi] - arr[Lo])) - -arr[] - Array where elements need to be searched -x - Element to be searched -lo - Starting index in arr[] -hi - Ending index in arr[] -``` - -## Complexity - -**Time complexity**: `O(log(log(n))` - -## References - -- [GeeksForGeeks](https://www.geeksforgeeks.org/interpolation-search/) -- [Wikipedia](https://en.wikipedia.org/wiki/Interpolation_search) diff --git a/src/algorithms/search/interpolation-search/__test__/interpolationSearch.test.js b/src/algorithms/search/interpolation-search/__test__/interpolationSearch.test.js deleted file mode 100644 index 7ddc548b63..0000000000 --- a/src/algorithms/search/interpolation-search/__test__/interpolationSearch.test.js +++ /dev/null @@ -1,24 +0,0 @@ -import interpolationSearch from '../interpolationSearch'; - -describe('interpolationSearch', () => { - it('should search elements in sorted array of numbers', () => { - expect(interpolationSearch([], 1)).toBe(-1); - expect(interpolationSearch([1], 1)).toBe(0); - expect(interpolationSearch([1], 0)).toBe(-1); - expect(interpolationSearch([1, 1], 1)).toBe(0); - expect(interpolationSearch([1, 2], 1)).toBe(0); - expect(interpolationSearch([1, 2], 2)).toBe(1); - expect(interpolationSearch([10, 20, 30, 40, 50], 40)).toBe(3); - expect(interpolationSearch([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15], 14)).toBe(13); - expect(interpolationSearch([1, 6, 7, 8, 12, 13, 14, 19, 21, 23, 24, 24, 24, 300], 24)).toBe(10); - expect(interpolationSearch([1, 2, 3, 700, 800, 1200, 1300, 1400, 1900], 600)).toBe(-1); - expect(interpolationSearch([1, 2, 3, 700, 800, 1200, 1300, 1400, 1900], 1)).toBe(0); - expect(interpolationSearch([1, 2, 3, 700, 800, 1200, 1300, 1400, 1900], 2)).toBe(1); - expect(interpolationSearch([1, 2, 3, 700, 800, 1200, 1300, 1400, 1900], 3)).toBe(2); - expect(interpolationSearch([1, 2, 3, 700, 800, 1200, 1300, 1400, 1900], 700)).toBe(3); - expect(interpolationSearch([1, 2, 3, 700, 800, 1200, 1300, 1400, 1900], 800)).toBe(4); - expect(interpolationSearch([0, 2, 3, 700, 800, 1200, 1300, 1400, 1900], 1200)).toBe(5); - expect(interpolationSearch([1, 2, 3, 700, 800, 1200, 1300, 1400, 19000], 800)).toBe(4); - expect(interpolationSearch([0, 10, 11, 12, 13, 14, 15], 10)).toBe(1); - }); -}); diff --git a/src/algorithms/search/interpolation-search/interpolationSearch.js b/src/algorithms/search/interpolation-search/interpolationSearch.js deleted file mode 100644 index 8546c5be3b..0000000000 --- a/src/algorithms/search/interpolation-search/interpolationSearch.js +++ /dev/null @@ -1,52 +0,0 @@ -/** - * Interpolation search implementation. - * - * @param {*[]} sortedArray - sorted array with uniformly distributed values - * @param {*} seekElement - * @return {number} - */ -export default function interpolationSearch(sortedArray, seekElement) { - let leftIndex = 0; - let rightIndex = sortedArray.length - 1; - - while (leftIndex <= rightIndex) { - const rangeDelta = sortedArray[rightIndex] - sortedArray[leftIndex]; - const indexDelta = rightIndex - leftIndex; - const valueDelta = seekElement - sortedArray[leftIndex]; - - // If valueDelta is less then zero it means that there is no seek element - // exists in array since the lowest element from the range is already higher - // then seek element. - if (valueDelta < 0) { - return -1; - } - - // If range delta is zero then subarray contains all the same numbers - // and thus there is nothing to search for unless this range is all - // consists of seek number. - if (!rangeDelta) { - // By doing this we're also avoiding division by zero while - // calculating the middleIndex later. - return sortedArray[leftIndex] === seekElement ? leftIndex : -1; - } - - // Do interpolation of the middle index. - const middleIndex = leftIndex + Math.floor((valueDelta * indexDelta) / rangeDelta); - - // If we've found the element just return its position. - if (sortedArray[middleIndex] === seekElement) { - return middleIndex; - } - - // Decide which half to choose for seeking next: left or right one. - if (sortedArray[middleIndex] < seekElement) { - // Go to the right half of the array. - leftIndex = middleIndex + 1; - } else { - // Go to the left half of the array. - rightIndex = middleIndex - 1; - } - } - - return -1; -} diff --git a/src/algorithms/search/jump-search/README.md b/src/algorithms/search/jump-search/README.md deleted file mode 100644 index b711a7732d..0000000000 --- a/src/algorithms/search/jump-search/README.md +++ /dev/null @@ -1,27 +0,0 @@ -# Jump Search - -Like Binary Search, **Jump Search** (or **Block Search**) is a searching algorithm -for sorted arrays. The basic idea is to check fewer elements (than linear search) -by jumping ahead by fixed steps or skipping some elements in place of searching all -elements. - -For example, suppose we have an array `arr[]` of size `n` and block (to be jumped) -of size `m`. Then we search at the indexes `arr[0]`, `arr[m]`, `arr[2 * m]`, ..., `arr[k * m]` and -so on. Once we find the interval `arr[k * m] < x < arr[(k+1) * m]`, we perform a -linear search operation from the index `k * m` to find the element `x`. - -**What is the optimal block size to be skipped?** -In the worst case, we have to do `n/m` jumps and if the last checked value is -greater than the element to be searched for, we perform `m - 1` comparisons more -for linear search. Therefore the total number of comparisons in the worst case -will be `((n/m) + m - 1)`. The value of the function `((n/m) + m - 1)` will be -minimum when `m = √n`. Therefore, the best step size is `m = √n`. - -## Complexity - -**Time complexity**: `O(√n)` - because we do search by blocks of size `√n`. - -## References - -- [GeeksForGeeks](https://www.geeksforgeeks.org/jump-search/) -- [Wikipedia](https://en.wikipedia.org/wiki/Jump_search) diff --git a/src/algorithms/search/jump-search/__test__/jumpSearch.test.js b/src/algorithms/search/jump-search/__test__/jumpSearch.test.js deleted file mode 100644 index 32f4d3f7e0..0000000000 --- a/src/algorithms/search/jump-search/__test__/jumpSearch.test.js +++ /dev/null @@ -1,39 +0,0 @@ -import jumpSearch from '../jumpSearch'; - -describe('jumpSearch', () => { - it('should search for an element in sorted array', () => { - expect(jumpSearch([], 1)).toBe(-1); - expect(jumpSearch([1], 2)).toBe(-1); - expect(jumpSearch([1], 1)).toBe(0); - expect(jumpSearch([1, 2], 1)).toBe(0); - expect(jumpSearch([1, 2], 1)).toBe(0); - expect(jumpSearch([1, 1, 1], 1)).toBe(0); - expect(jumpSearch([1, 2, 5, 10, 20, 21, 24, 30, 48], 2)).toBe(1); - expect(jumpSearch([1, 2, 5, 10, 20, 21, 24, 30, 48], 0)).toBe(-1); - expect(jumpSearch([1, 2, 5, 10, 20, 21, 24, 30, 48], 0)).toBe(-1); - expect(jumpSearch([1, 2, 5, 10, 20, 21, 24, 30, 48], 7)).toBe(-1); - expect(jumpSearch([1, 2, 5, 10, 20, 21, 24, 30, 48], 5)).toBe(2); - expect(jumpSearch([1, 2, 5, 10, 20, 21, 24, 30, 48], 20)).toBe(4); - expect(jumpSearch([1, 2, 5, 10, 20, 21, 24, 30, 48], 30)).toBe(7); - expect(jumpSearch([1, 2, 5, 10, 20, 21, 24, 30, 48], 48)).toBe(8); - }); - - it('should search object in sorted array', () => { - const sortedArrayOfObjects = [ - { key: 1, value: 'value1' }, - { key: 2, value: 'value2' }, - { key: 3, value: 'value3' }, - ]; - - const comparator = (a, b) => { - if (a.key === b.key) return 0; - return a.key < b.key ? -1 : 1; - }; - - expect(jumpSearch([], { key: 1 }, comparator)).toBe(-1); - expect(jumpSearch(sortedArrayOfObjects, { key: 4 }, comparator)).toBe(-1); - expect(jumpSearch(sortedArrayOfObjects, { key: 1 }, comparator)).toBe(0); - expect(jumpSearch(sortedArrayOfObjects, { key: 2 }, comparator)).toBe(1); - expect(jumpSearch(sortedArrayOfObjects, { key: 3 }, comparator)).toBe(2); - }); -}); diff --git a/src/algorithms/search/jump-search/jumpSearch.js b/src/algorithms/search/jump-search/jumpSearch.js deleted file mode 100644 index b8c8c24ed4..0000000000 --- a/src/algorithms/search/jump-search/jumpSearch.js +++ /dev/null @@ -1,51 +0,0 @@ -import Comparator from '../../../utils/comparator/Comparator'; - -/** - * Jump (block) search implementation. - * - * @param {*[]} sortedArray - * @param {*} seekElement - * @param {function(a, b)} [comparatorCallback] - * @return {number} - */ -export default function jumpSearch(sortedArray, seekElement, comparatorCallback) { - const comparator = new Comparator(comparatorCallback); - const arraySize = sortedArray.length; - - if (!arraySize) { - // We can't find anything in empty array. - return -1; - } - - // Calculate optimal jump size. - // Total number of comparisons in the worst case will be ((arraySize/jumpSize) + jumpSize - 1). - // The value of the function ((arraySize/jumpSize) + jumpSize - 1) will be minimum - // when jumpSize = √array.length. - const jumpSize = Math.floor(Math.sqrt(arraySize)); - - // Find the block where the seekElement belong to. - let blockStart = 0; - let blockEnd = jumpSize; - while (comparator.greaterThan(seekElement, sortedArray[Math.min(blockEnd, arraySize) - 1])) { - // Jump to the next block. - blockStart = blockEnd; - blockEnd += jumpSize; - - // If our next block is out of array then we couldn't found the element. - if (blockStart > arraySize) { - return -1; - } - } - - // Do linear search for seekElement in subarray starting from blockStart. - let currentIndex = blockStart; - while (currentIndex < Math.min(blockEnd, arraySize)) { - if (comparator.equal(sortedArray[currentIndex], seekElement)) { - return currentIndex; - } - - currentIndex += 1; - } - - return -1; -} diff --git a/src/algorithms/search/linear-search/README.md b/src/algorithms/search/linear-search/README.md deleted file mode 100644 index 8feb422eb2..0000000000 --- a/src/algorithms/search/linear-search/README.md +++ /dev/null @@ -1,23 +0,0 @@ -# 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 -match is found or until all the elements have been searched. -Linear search runs in at worst linear time and makes at most `n` -comparisons, where `n` is the length of the list. - -![Linear Search](https://www.tutorialspoint.com/data_structures_algorithms/images/linear_search.gif) - -## Complexity - -**Time Complexity**: `O(n)` - since in worst case we're checking each element -exactly once. - -## References -- [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) diff --git a/src/algorithms/search/linear-search/README.pt-BR.md b/src/algorithms/search/linear-search/README.pt-BR.md deleted file mode 100644 index e0af42f4ea..0000000000 --- a/src/algorithms/search/linear-search/README.pt-BR.md +++ /dev/null @@ -1,19 +0,0 @@ -# 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) diff --git a/src/algorithms/search/linear-search/__test__/linearSearch.test.js b/src/algorithms/search/linear-search/__test__/linearSearch.test.js deleted file mode 100644 index c578fd1f78..0000000000 --- a/src/algorithms/search/linear-search/__test__/linearSearch.test.js +++ /dev/null @@ -1,40 +0,0 @@ -import linearSearch from '../linearSearch'; - -describe('linearSearch', () => { - it('should search all numbers in array', () => { - const array = [1, 2, 4, 6, 2]; - - expect(linearSearch(array, 10)).toEqual([]); - expect(linearSearch(array, 1)).toEqual([0]); - expect(linearSearch(array, 2)).toEqual([1, 4]); - }); - - it('should search all strings in array', () => { - const array = ['a', 'b', 'a']; - - expect(linearSearch(array, 'c')).toEqual([]); - expect(linearSearch(array, 'b')).toEqual([1]); - expect(linearSearch(array, 'a')).toEqual([0, 2]); - }); - - it('should search through objects as well', () => { - const comparatorCallback = (a, b) => { - if (a.key === b.key) { - return 0; - } - - return a.key <= b.key ? -1 : 1; - }; - - const array = [ - { key: 5 }, - { key: 6 }, - { key: 7 }, - { key: 6 }, - ]; - - expect(linearSearch(array, { key: 10 }, comparatorCallback)).toEqual([]); - expect(linearSearch(array, { key: 5 }, comparatorCallback)).toEqual([0]); - expect(linearSearch(array, { key: 6 }, comparatorCallback)).toEqual([1, 3]); - }); -}); diff --git a/src/algorithms/search/linear-search/linearSearch.js b/src/algorithms/search/linear-search/linearSearch.js deleted file mode 100644 index c5fb67c795..0000000000 --- a/src/algorithms/search/linear-search/linearSearch.js +++ /dev/null @@ -1,22 +0,0 @@ -import Comparator from '../../../utils/comparator/Comparator'; - -/** - * Linear search implementation. - * - * @param {*[]} array - * @param {*} seekElement - * @param {function(a, b)} [comparatorCallback] - * @return {number[]} - */ -export default function linearSearch(array, seekElement, comparatorCallback) { - const comparator = new Comparator(comparatorCallback); - const foundIndices = []; - - array.forEach((element, index) => { - if (comparator.equal(element, seekElement)) { - foundIndices.push(index); - } - }); - - return foundIndices; -} diff --git a/src/algorithms/sets/cartesian-product/README.md b/src/algorithms/sets/cartesian-product/README.md deleted file mode 100644 index ae58a15df1..0000000000 --- a/src/algorithms/sets/cartesian-product/README.md +++ /dev/null @@ -1,14 +0,0 @@ -# Cartesian Product - -In set theory a Cartesian product is a mathematical operation that returns a set -(or product set or simply product) from multiple sets. That is, for sets A and B, -the Cartesian product A × B is the set of all ordered pairs (a, b) -where a ∈ A and b ∈ B. - -Cartesian product `AxB` of two sets `A={x,y,z}` and `B={1,2,3}` - -![Cartesian Product of Two Sets](https://upload.wikimedia.org/wikipedia/commons/4/4e/Cartesian_Product_qtl1.svg) - -## References - -[Wikipedia](https://en.wikipedia.org/wiki/Cartesian_product) diff --git a/src/algorithms/sets/cartesian-product/__test__/cartesianProduct.test.js b/src/algorithms/sets/cartesian-product/__test__/cartesianProduct.test.js deleted file mode 100644 index f9154fa26b..0000000000 --- a/src/algorithms/sets/cartesian-product/__test__/cartesianProduct.test.js +++ /dev/null @@ -1,19 +0,0 @@ -import cartesianProduct from '../cartesianProduct'; - -describe('cartesianProduct', () => { - it('should return null if there is not enough info for calculation', () => { - const product1 = cartesianProduct([1], null); - const product2 = cartesianProduct([], null); - - expect(product1).toBeNull(); - expect(product2).toBeNull(); - }); - - it('should calculate the product of two sets', () => { - const product1 = cartesianProduct([1], [1]); - const product2 = cartesianProduct([1, 2], [3, 5]); - - expect(product1).toEqual([[1, 1]]); - expect(product2).toEqual([[1, 3], [1, 5], [2, 3], [2, 5]]); - }); -}); diff --git a/src/algorithms/sets/cartesian-product/cartesianProduct.js b/src/algorithms/sets/cartesian-product/cartesianProduct.js deleted file mode 100644 index 14924fae36..0000000000 --- a/src/algorithms/sets/cartesian-product/cartesianProduct.js +++ /dev/null @@ -1,27 +0,0 @@ -/** - * Generates Cartesian Product of two sets. - * @param {*[]} setA - * @param {*[]} setB - * @return {*[]} - */ -export default function cartesianProduct(setA, setB) { - // Check if input sets are not empty. - // Otherwise return null since we can't generate Cartesian Product out of them. - if (!setA || !setB || !setA.length || !setB.length) { - return null; - } - - // Init product set. - const product = []; - - // Now, let's go through all elements of a first and second set and form all possible pairs. - for (let indexA = 0; indexA < setA.length; indexA += 1) { - for (let indexB = 0; indexB < setB.length; indexB += 1) { - // Add current product pair to the product set. - product.push([setA[indexA], setB[indexB]]); - } - } - - // Return cartesian product set. - return product; -} diff --git a/src/algorithms/sets/combination-sum/README.md b/src/algorithms/sets/combination-sum/README.md deleted file mode 100644 index cb14f1bae8..0000000000 --- a/src/algorithms/sets/combination-sum/README.md +++ /dev/null @@ -1,60 +0,0 @@ -# Combination Sum Problem - -Given a **set** of candidate numbers (`candidates`) **(without duplicates)** and -a target number (`target`), find all unique combinations in `candidates` where -the candidate numbers sums to `target`. - -The **same** repeated number may be chosen from `candidates` unlimited number -of times. - -**Note:** - -- All numbers (including `target`) will be positive integers. -- The solution set must not contain duplicate combinations. - -## Examples - -``` -Input: candidates = [2,3,6,7], target = 7, - -A solution set is: -[ - [7], - [2,2,3] -] -``` - -``` -Input: candidates = [2,3,5], target = 8, - -A solution set is: -[ - [2,2,2,2], - [2,3,3], - [3,5] -] -``` - -## Explanations - -Since the problem is to get all the possible results, not the best or the -number of result, thus we don’t need to consider DP (dynamic programming), -backtracking approach using recursion is needed to handle it. - -Here is an example of decision tree for the situation when `candidates = [2, 3]` and `target = 6`: - -``` - 0 - / \ - +2 +3 - / \ \ - +2 +3 +3 - / \ / \ \ - +2 ✘ ✘ ✘ ✓ - / \ - ✓ ✘ -``` - -## References - -- [LeetCode](https://leetcode.com/problems/combination-sum/description/) diff --git a/src/algorithms/sets/combination-sum/__test__/combinationSum.test.js b/src/algorithms/sets/combination-sum/__test__/combinationSum.test.js deleted file mode 100644 index 7b196bf2a2..0000000000 --- a/src/algorithms/sets/combination-sum/__test__/combinationSum.test.js +++ /dev/null @@ -1,24 +0,0 @@ -import combinationSum from '../combinationSum'; - -describe('combinationSum', () => { - it('should find all combinations with specific sum', () => { - expect(combinationSum([1], 4)).toEqual([ - [1, 1, 1, 1], - ]); - - expect(combinationSum([2, 3, 6, 7], 7)).toEqual([ - [2, 2, 3], - [7], - ]); - - expect(combinationSum([2, 3, 5], 8)).toEqual([ - [2, 2, 2, 2], - [2, 3, 3], - [3, 5], - ]); - - expect(combinationSum([2, 5], 3)).toEqual([]); - - expect(combinationSum([], 3)).toEqual([]); - }); -}); diff --git a/src/algorithms/sets/combination-sum/combinationSum.js b/src/algorithms/sets/combination-sum/combinationSum.js deleted file mode 100644 index dd396a8cb4..0000000000 --- a/src/algorithms/sets/combination-sum/combinationSum.js +++ /dev/null @@ -1,65 +0,0 @@ -/** - * @param {number[]} candidates - candidate numbers we're picking from. - * @param {number} remainingSum - remaining sum after adding candidates to currentCombination. - * @param {number[][]} finalCombinations - resulting list of combinations. - * @param {number[]} currentCombination - currently explored candidates. - * @param {number} startFrom - index of the candidate to start further exploration from. - * @return {number[][]} - */ -function combinationSumRecursive( - candidates, - remainingSum, - finalCombinations = [], - currentCombination = [], - startFrom = 0, -) { - if (remainingSum < 0) { - // By adding another candidate we've gone below zero. - // This would mean that the last candidate was not acceptable. - return finalCombinations; - } - - if (remainingSum === 0) { - // If after adding the previous candidate our remaining sum - // became zero - we need to save the current combination since it is one - // of the answers we're looking for. - finalCombinations.push(currentCombination.slice()); - - return finalCombinations; - } - - // If we haven't reached zero yet let's continue to add all - // possible candidates that are left. - for (let candidateIndex = startFrom; candidateIndex < candidates.length; candidateIndex += 1) { - const currentCandidate = candidates[candidateIndex]; - - // Let's try to add another candidate. - currentCombination.push(currentCandidate); - - // Explore further option with current candidate being added. - combinationSumRecursive( - candidates, - remainingSum - currentCandidate, - finalCombinations, - currentCombination, - candidateIndex, - ); - - // BACKTRACKING. - // Let's get back, exclude current candidate and try another ones later. - currentCombination.pop(); - } - - return finalCombinations; -} - -/** - * Backtracking algorithm of finding all possible combination for specific sum. - * - * @param {number[]} candidates - * @param {number} target - * @return {number[][]} - */ -export default function combinationSum(candidates, target) { - return combinationSumRecursive(candidates, target); -} diff --git a/src/algorithms/sets/combinations/README.md b/src/algorithms/sets/combinations/README.md deleted file mode 100644 index 69fc0603f9..0000000000 --- a/src/algorithms/sets/combinations/README.md +++ /dev/null @@ -1,68 +0,0 @@ -# Combinations - -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", -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) -we win! - -No Repetition: such as lottery numbers `(2,14,15,27,30,33)` - -**Number of combinations** - -![Formula](https://www.mathsisfun.com/combinatorics/images/combinations-no-repeat.png) - -where `n` is the number of things to choose from, and we choose `r` of them, -no repetition, order doesn't matter. - -It is often called "n choose r" (such as "16 choose 3"). And is also known as the Binomial Coefficient. - -## Combinations with repetitions - -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: -`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}`. -Example selections include: - -- `{c, c, c}` (3 scoops of chocolate) -- `{b, l, v}` (one each of banana, lemon and vanilla) -- `{b, v, v}` (one of banana, two of vanilla) - -**Number of combinations** - -![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, -order doesn't matter. - -## Cheatsheet - -![Permutations and Combinations Overview](./images/overview.png) - -![Combinations overview](./images/combinations-overview.jpg) - -| | | -| --- | --- | -|![Combinations with repetition](./images/combinations-with-repetitions.jpg) | ![Combinations without repetition](./images/combinations-without-repetitions.jpg) | - -*Made with [okso.app](https://okso.app)* - -## References - -- [Math Is Fun](https://www.mathsisfun.com/combinatorics/combinations-permutations.html) -- [Permutations/combinations cheat sheets](https://medium.com/@trekhleb/permutations-combinations-algorithms-cheat-sheet-68c14879aba5) diff --git a/src/algorithms/sets/combinations/__test__/combineWithRepetitions.test.js b/src/algorithms/sets/combinations/__test__/combineWithRepetitions.test.js deleted file mode 100644 index 90c38958e0..0000000000 --- a/src/algorithms/sets/combinations/__test__/combineWithRepetitions.test.js +++ /dev/null @@ -1,59 +0,0 @@ -import combineWithRepetitions from '../combineWithRepetitions'; -import factorial from '../../../math/factorial/factorial'; - -describe('combineWithRepetitions', () => { - it('should combine string with repetitions', () => { - expect(combineWithRepetitions(['A'], 1)).toEqual([ - ['A'], - ]); - - expect(combineWithRepetitions(['A', 'B'], 1)).toEqual([ - ['A'], - ['B'], - ]); - - expect(combineWithRepetitions(['A', 'B'], 2)).toEqual([ - ['A', 'A'], - ['A', 'B'], - ['B', 'B'], - ]); - - expect(combineWithRepetitions(['A', 'B'], 3)).toEqual([ - ['A', 'A', 'A'], - ['A', 'A', 'B'], - ['A', 'B', 'B'], - ['B', 'B', 'B'], - ]); - - expect(combineWithRepetitions(['A', 'B', 'C'], 2)).toEqual([ - ['A', 'A'], - ['A', 'B'], - ['A', 'C'], - ['B', 'B'], - ['B', 'C'], - ['C', 'C'], - ]); - - expect(combineWithRepetitions(['A', 'B', 'C'], 3)).toEqual([ - ['A', 'A', 'A'], - ['A', 'A', 'B'], - ['A', 'A', 'C'], - ['A', 'B', 'B'], - ['A', 'B', 'C'], - ['A', 'C', 'C'], - ['B', 'B', 'B'], - ['B', 'B', 'C'], - ['B', 'C', 'C'], - ['C', 'C', 'C'], - ]); - - const combinationOptions = ['A', 'B', 'C', 'D', 'E', 'F', 'G', 'H']; - const combinationSlotsNumber = 4; - const combinations = combineWithRepetitions(combinationOptions, combinationSlotsNumber); - const n = combinationOptions.length; - const r = combinationSlotsNumber; - const expectedNumberOfCombinations = factorial((r + n) - 1) / (factorial(r) * factorial(n - 1)); - - expect(combinations.length).toBe(expectedNumberOfCombinations); - }); -}); diff --git a/src/algorithms/sets/combinations/__test__/combineWithoutRepetitions.test.js b/src/algorithms/sets/combinations/__test__/combineWithoutRepetitions.test.js deleted file mode 100644 index d35e00f342..0000000000 --- a/src/algorithms/sets/combinations/__test__/combineWithoutRepetitions.test.js +++ /dev/null @@ -1,64 +0,0 @@ -import combineWithoutRepetitions from '../combineWithoutRepetitions'; -import factorial from '../../../math/factorial/factorial'; -import pascalTriangle from '../../../math/pascal-triangle/pascalTriangle'; - -describe('combineWithoutRepetitions', () => { - it('should combine string without repetitions', () => { - expect(combineWithoutRepetitions(['A', 'B'], 3)).toEqual([]); - - expect(combineWithoutRepetitions(['A', 'B'], 1)).toEqual([ - ['A'], - ['B'], - ]); - - expect(combineWithoutRepetitions(['A'], 1)).toEqual([ - ['A'], - ]); - - expect(combineWithoutRepetitions(['A', 'B'], 2)).toEqual([ - ['A', 'B'], - ]); - - expect(combineWithoutRepetitions(['A', 'B', 'C'], 2)).toEqual([ - ['A', 'B'], - ['A', 'C'], - ['B', 'C'], - ]); - - expect(combineWithoutRepetitions(['A', 'B', 'C'], 3)).toEqual([ - ['A', 'B', 'C'], - ]); - - expect(combineWithoutRepetitions(['A', 'B', 'C', 'D'], 3)).toEqual([ - ['A', 'B', 'C'], - ['A', 'B', 'D'], - ['A', 'C', 'D'], - ['B', 'C', 'D'], - ]); - - expect(combineWithoutRepetitions(['A', 'B', 'C', 'D', 'E'], 3)).toEqual([ - ['A', 'B', 'C'], - ['A', 'B', 'D'], - ['A', 'B', 'E'], - ['A', 'C', 'D'], - ['A', 'C', 'E'], - ['A', 'D', 'E'], - ['B', 'C', 'D'], - ['B', 'C', 'E'], - ['B', 'D', 'E'], - ['C', 'D', 'E'], - ]); - - const combinationOptions = ['A', 'B', 'C', 'D', 'E', 'F', 'G', 'H']; - const combinationSlotsNumber = 4; - const combinations = combineWithoutRepetitions(combinationOptions, combinationSlotsNumber); - const n = combinationOptions.length; - const r = combinationSlotsNumber; - const expectedNumberOfCombinations = factorial(n) / (factorial(r) * factorial(n - r)); - - expect(combinations.length).toBe(expectedNumberOfCombinations); - - // This one is just to see one of the way of Pascal's triangle application. - expect(combinations.length).toBe(pascalTriangle(n)[r]); - }); -}); diff --git a/src/algorithms/sets/combinations/combineWithRepetitions.js b/src/algorithms/sets/combinations/combineWithRepetitions.js deleted file mode 100644 index 5e25635dac..0000000000 --- a/src/algorithms/sets/combinations/combineWithRepetitions.js +++ /dev/null @@ -1,32 +0,0 @@ -/** - * @param {*[]} comboOptions - * @param {number} comboLength - * @return {*[]} - */ -export default function combineWithRepetitions(comboOptions, comboLength) { - // If the length of the combination is 1 then each element of the original array - // is a combination itself. - if (comboLength === 1) { - return comboOptions.map((comboOption) => [comboOption]); - } - - // Init combinations array. - const combos = []; - - // Remember characters one by one and concatenate them to combinations of smaller lengths. - // We don't extract elements here because the repetitions are allowed. - comboOptions.forEach((currentOption, optionIndex) => { - // Generate combinations of smaller size. - const smallerCombos = combineWithRepetitions( - comboOptions.slice(optionIndex), - comboLength - 1, - ); - - // Concatenate currentOption with all combinations of smaller size. - smallerCombos.forEach((smallerCombo) => { - combos.push([currentOption].concat(smallerCombo)); - }); - }); - - return combos; -} diff --git a/src/algorithms/sets/combinations/combineWithoutRepetitions.js b/src/algorithms/sets/combinations/combineWithoutRepetitions.js deleted file mode 100644 index 38fb8507f1..0000000000 --- a/src/algorithms/sets/combinations/combineWithoutRepetitions.js +++ /dev/null @@ -1,32 +0,0 @@ -/** - * @param {*[]} comboOptions - * @param {number} comboLength - * @return {*[]} - */ -export default function combineWithoutRepetitions(comboOptions, comboLength) { - // If the length of the combination is 1 then each element of the original array - // is a combination itself. - if (comboLength === 1) { - return comboOptions.map((comboOption) => [comboOption]); - } - - // Init combinations array. - const combos = []; - - // Extract characters one by one and concatenate them to combinations of smaller lengths. - // We need to extract them because we don't want to have repetitions after concatenation. - comboOptions.forEach((currentOption, optionIndex) => { - // Generate combinations of smaller size. - const smallerCombos = combineWithoutRepetitions( - comboOptions.slice(optionIndex + 1), - comboLength - 1, - ); - - // Concatenate currentOption with all combinations of smaller size. - smallerCombos.forEach((smallerCombo) => { - combos.push([currentOption].concat(smallerCombo)); - }); - }); - - return combos; -} diff --git a/src/algorithms/sets/combinations/images/combinations-overview.jpg b/src/algorithms/sets/combinations/images/combinations-overview.jpg deleted file mode 100644 index 9f54477492b0c9772a2b2493e3f22364e3160f30..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 352932 zcmeFYbyQqWlrGwY00|l#f(3U7+B6oy-Q5B--nd%`5ZoL0;L^A|fj~D-a1Rh@2<|Sq z{ASj?xqr-)S@+Fb@2xlctaIvHRl9b5wYyfyIlKSP|6K#Tl9!f~2B4q-04Prv;P3Be zEOHVOCaUTx(sGJY|5EUb4Dck+-vR*k4sI^$G9TaQ>gm7vC-2|H)ZEqS-|&BsKH0sT z{l_{0Fva;Fl>eV)y#!mhnm;KWKizIFPmMp31wUaTtAE8_|6sF!#nJy@7fp4EC!KFk zn8oUU!e;*y_H=V{d(s*BN8jAZ#i2i%sfB!B1cl!F~sSf2+KOLVgD*yyw0eAzD12_Q8 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a/src/algorithms/sets/fisher-yates/README.md +++ /dev/null @@ -1,15 +0,0 @@ -# Fisher–Yates shuffle - -The Fisher–Yates shuffle is an algorithm for generating a random -permutation of a finite sequence—in plain terms, the algorithm -shuffles the sequence. The algorithm effectively puts all the -elements into a hat; it continually determines the next element -by randomly drawing an element from the hat until no elements -remain. The algorithm produces an unbiased permutation: every -permutation is equally likely. The modern version of the -algorithm is efficient: it takes time proportional to the -number of items being shuffled and shuffles them in place. - -## References - -[Wikipedia](https://en.wikipedia.org/wiki/Fisher%E2%80%93Yates_shuffle) diff --git a/src/algorithms/sets/fisher-yates/__test__/fisherYates.test.js b/src/algorithms/sets/fisher-yates/__test__/fisherYates.test.js deleted file mode 100644 index f43a7b7cf3..0000000000 --- a/src/algorithms/sets/fisher-yates/__test__/fisherYates.test.js +++ /dev/null @@ -1,19 +0,0 @@ -import fisherYates from '../fisherYates'; -import { sortedArr } from '../../../sorting/SortTester'; -import QuickSort from '../../../sorting/quick-sort/QuickSort'; - -describe('fisherYates', () => { - it('should shuffle small arrays', () => { - expect(fisherYates([])).toEqual([]); - expect(fisherYates([1])).toEqual([1]); - }); - - it('should shuffle array randomly', () => { - const shuffledArray = fisherYates(sortedArr); - const sorter = new QuickSort(); - - expect(shuffledArray.length).toBe(sortedArr.length); - expect(shuffledArray).not.toEqual(sortedArr); - expect(sorter.sort(shuffledArray)).toEqual(sortedArr); - }); -}); diff --git a/src/algorithms/sets/fisher-yates/fisherYates.js b/src/algorithms/sets/fisher-yates/fisherYates.js deleted file mode 100644 index 23b710b9f6..0000000000 --- a/src/algorithms/sets/fisher-yates/fisherYates.js +++ /dev/null @@ -1,15 +0,0 @@ -/** - * @param {*[]} originalArray - * @return {*[]} - */ -export default function fisherYates(originalArray) { - // Clone array from preventing original array from modification (for testing purpose). - const array = originalArray.slice(0); - - for (let i = (array.length - 1); i > 0; i -= 1) { - const randomIndex = Math.floor(Math.random() * (i + 1)); - [array[i], array[randomIndex]] = [array[randomIndex], array[i]]; - } - - return array; -} diff --git a/src/algorithms/sets/knapsack-problem/Knapsack.js b/src/algorithms/sets/knapsack-problem/Knapsack.js deleted file mode 100644 index 5d14911102..0000000000 --- a/src/algorithms/sets/knapsack-problem/Knapsack.js +++ /dev/null @@ -1,195 +0,0 @@ -import MergeSort from '../../sorting/merge-sort/MergeSort'; - -export default class Knapsack { - /** - * @param {KnapsackItem[]} possibleItems - * @param {number} weightLimit - */ - constructor(possibleItems, weightLimit) { - this.selectedItems = []; - this.weightLimit = weightLimit; - this.possibleItems = possibleItems; - } - - sortPossibleItemsByWeight() { - this.possibleItems = new MergeSort({ - /** - * @var KnapsackItem itemA - * @var KnapsackItem itemB - */ - compareCallback: (itemA, itemB) => { - if (itemA.weight === itemB.weight) { - return 0; - } - - return itemA.weight < itemB.weight ? -1 : 1; - }, - }).sort(this.possibleItems); - } - - sortPossibleItemsByValue() { - this.possibleItems = new MergeSort({ - /** - * @var KnapsackItem itemA - * @var KnapsackItem itemB - */ - compareCallback: (itemA, itemB) => { - if (itemA.value === itemB.value) { - return 0; - } - - return itemA.value > itemB.value ? -1 : 1; - }, - }).sort(this.possibleItems); - } - - sortPossibleItemsByValuePerWeightRatio() { - this.possibleItems = new MergeSort({ - /** - * @var KnapsackItem itemA - * @var KnapsackItem itemB - */ - compareCallback: (itemA, itemB) => { - if (itemA.valuePerWeightRatio === itemB.valuePerWeightRatio) { - return 0; - } - - return itemA.valuePerWeightRatio > itemB.valuePerWeightRatio ? -1 : 1; - }, - }).sort(this.possibleItems); - } - - // Solve 0/1 knapsack problem - // Dynamic Programming approach. - solveZeroOneKnapsackProblem() { - // We do two sorts because in case of equal weights but different values - // we need to take the most valuable items first. - this.sortPossibleItemsByValue(); - this.sortPossibleItemsByWeight(); - - this.selectedItems = []; - - // Create knapsack values matrix. - const numberOfRows = this.possibleItems.length; - const numberOfColumns = this.weightLimit; - const knapsackMatrix = Array(numberOfRows).fill(null).map(() => { - return Array(numberOfColumns + 1).fill(null); - }); - - // Fill the first column with zeros since it would mean that there is - // no items we can add to knapsack in case if weight limitation is zero. - for (let itemIndex = 0; itemIndex < this.possibleItems.length; itemIndex += 1) { - knapsackMatrix[itemIndex][0] = 0; - } - - // Fill the first row with max possible values we would get by just adding - // or not adding the first item to the knapsack. - for (let weightIndex = 1; weightIndex <= this.weightLimit; weightIndex += 1) { - const itemIndex = 0; - const itemWeight = this.possibleItems[itemIndex].weight; - const itemValue = this.possibleItems[itemIndex].value; - knapsackMatrix[itemIndex][weightIndex] = itemWeight <= weightIndex ? itemValue : 0; - } - - // Go through combinations of how we may add items to knapsack and - // define what weight/value we would receive using Dynamic Programming - // approach. - for (let itemIndex = 1; itemIndex < this.possibleItems.length; itemIndex += 1) { - for (let weightIndex = 1; weightIndex <= this.weightLimit; weightIndex += 1) { - const currentItemWeight = this.possibleItems[itemIndex].weight; - const currentItemValue = this.possibleItems[itemIndex].value; - - if (currentItemWeight > weightIndex) { - // In case if item's weight is bigger then currently allowed weight - // then we can't add it to knapsack and the max possible value we can - // gain at the moment is the max value we got for previous item. - knapsackMatrix[itemIndex][weightIndex] = knapsackMatrix[itemIndex - 1][weightIndex]; - } else { - // Else we need to consider the max value we can gain at this point by adding - // current value or just by keeping the previous item for current weight. - knapsackMatrix[itemIndex][weightIndex] = Math.max( - currentItemValue + knapsackMatrix[itemIndex - 1][weightIndex - currentItemWeight], - knapsackMatrix[itemIndex - 1][weightIndex], - ); - } - } - } - - // Now let's trace back the knapsack matrix to see what items we're going to add - // to the knapsack. - let itemIndex = this.possibleItems.length - 1; - let weightIndex = this.weightLimit; - - while (itemIndex > 0) { - const currentItem = this.possibleItems[itemIndex]; - const prevItem = this.possibleItems[itemIndex - 1]; - - // Check if matrix value came from top (from previous item). - // In this case this would mean that we need to include previous item - // to the list of selected items. - if ( - knapsackMatrix[itemIndex][weightIndex] - && knapsackMatrix[itemIndex][weightIndex] === knapsackMatrix[itemIndex - 1][weightIndex] - ) { - // Check if there are several items with the same weight but with the different values. - // We need to add highest item in the matrix that is possible to get the highest value. - const prevSumValue = knapsackMatrix[itemIndex - 1][weightIndex]; - const prevPrevSumValue = knapsackMatrix[itemIndex - 2][weightIndex]; - if ( - !prevSumValue - || (prevSumValue && prevPrevSumValue !== prevSumValue) - ) { - this.selectedItems.push(prevItem); - } - } else if (knapsackMatrix[itemIndex - 1][weightIndex - currentItem.weight]) { - this.selectedItems.push(prevItem); - weightIndex -= currentItem.weight; - } - - itemIndex -= 1; - } - } - - // Solve unbounded knapsack problem. - // Greedy approach. - solveUnboundedKnapsackProblem() { - this.sortPossibleItemsByValue(); - this.sortPossibleItemsByValuePerWeightRatio(); - - for (let itemIndex = 0; itemIndex < this.possibleItems.length; itemIndex += 1) { - if (this.totalWeight < this.weightLimit) { - const currentItem = this.possibleItems[itemIndex]; - - // Detect how much of current items we can push to knapsack. - const availableWeight = this.weightLimit - this.totalWeight; - const maxPossibleItemsCount = Math.floor(availableWeight / currentItem.weight); - - if (maxPossibleItemsCount > currentItem.itemsInStock) { - // If we have more items in stock then it is allowed to add - // let's add the maximum allowed number of them. - currentItem.quantity = currentItem.itemsInStock; - } else if (maxPossibleItemsCount) { - // In case if we don't have specified number of items in stock - // let's add only items we have in stock. - currentItem.quantity = maxPossibleItemsCount; - } - - this.selectedItems.push(currentItem); - } - } - } - - get totalValue() { - /** @var {KnapsackItem} item */ - return this.selectedItems.reduce((accumulator, item) => { - return accumulator + item.totalValue; - }, 0); - } - - get totalWeight() { - /** @var {KnapsackItem} item */ - return this.selectedItems.reduce((accumulator, item) => { - return accumulator + item.totalWeight; - }, 0); - } -} diff --git a/src/algorithms/sets/knapsack-problem/KnapsackItem.js b/src/algorithms/sets/knapsack-problem/KnapsackItem.js deleted file mode 100644 index 4c84eeee6f..0000000000 --- a/src/algorithms/sets/knapsack-problem/KnapsackItem.js +++ /dev/null @@ -1,33 +0,0 @@ -export default class KnapsackItem { - /** - * @param {Object} itemSettings - knapsack item settings, - * @param {number} itemSettings.value - value of the item. - * @param {number} itemSettings.weight - weight of the item. - * @param {number} itemSettings.itemsInStock - how many items are available to be added. - */ - constructor({ value, weight, itemsInStock = 1 }) { - this.value = value; - this.weight = weight; - this.itemsInStock = itemsInStock; - // Actual number of items that is going to be added to knapsack. - this.quantity = 1; - } - - get totalValue() { - return this.value * this.quantity; - } - - get totalWeight() { - return this.weight * this.quantity; - } - - // This coefficient shows how valuable the 1 unit of weight is - // for current item. - get valuePerWeightRatio() { - return this.value / this.weight; - } - - toString() { - return `v${this.value} w${this.weight} x ${this.quantity}`; - } -} diff --git a/src/algorithms/sets/knapsack-problem/README.md b/src/algorithms/sets/knapsack-problem/README.md deleted file mode 100644 index 1d86019f62..0000000000 --- a/src/algorithms/sets/knapsack-problem/README.md +++ /dev/null @@ -1,69 +0,0 @@ -# Knapsack Problem - -The knapsack problem or rucksack problem is a problem in -combinatorial optimization: Given a set of items, each with -a weight and a value, determine the number of each item to -include in a collection so that the total weight is less -than or equal to a given limit and the total value is as -large as possible. - -It derives its name from the problem faced by someone who is -constrained by a fixed-size knapsack and must fill it with the -most valuable items. - -Example of a one-dimensional (constraint) knapsack problem: -which boxes should be chosen to maximize the amount of money -while still keeping the overall weight under or equal to 15 kg? - -![knapsack problem](https://upload.wikimedia.org/wikipedia/commons/f/fd/Knapsack.svg) - -## Definition - -### 0/1 knapsack problem - -The most common problem being solved is the **0/1 knapsack problem**, -which restricts the number `xi` of copies of each kind of item to zero or one. - -Given a set of n items numbered from `1` up to `n`, each with a -weight `wi` and a value `vi`, along with a maximum weight -capacity `W`, - -maximize ![0/1 knapsack](https://wikimedia.org/api/rest_v1/media/math/render/svg/85620037d368d2136fb3361702df6a489416931b) - -subject to ![0/1 knapsack](https://wikimedia.org/api/rest_v1/media/math/render/svg/dd6e7c9bca4397980976ea6d19237500ce3b8176) -and ![0/1 knapsack](https://wikimedia.org/api/rest_v1/media/math/render/svg/07dda71da2a630762c7b21b51ea54f86f422f951) - -Here `xi` represents the number of instances of item `i` to -include in the knapsack. Informally, the problem is to maximize -the sum of the values of the items in the knapsack so that the -sum of the weights is less than or equal to the knapsack's -capacity. - -### Bounded knapsack problem (BKP) - -The **bounded knapsack problem (BKP)** removes the restriction -that there is only one of each item, but restricts the number -`xi` of copies of each kind of item to a maximum non-negative -integer value `c`: - -maximize ![bounded knapsack](https://wikimedia.org/api/rest_v1/media/math/render/svg/85620037d368d2136fb3361702df6a489416931b) - -subject to ![bounded knapsack](https://wikimedia.org/api/rest_v1/media/math/render/svg/dd6e7c9bca4397980976ea6d19237500ce3b8176) -and ![bounded knapsack](https://wikimedia.org/api/rest_v1/media/math/render/svg/6c8c5ac4f8247b3b8e01e89de76a1df0ea969821) - -### Unbounded knapsack problem (UKP) - -The **unbounded knapsack problem (UKP)** places no upper bound -on the number of copies of each kind of item and can be -formulated as above except for that the only restriction -on `xi` is that it is a non-negative integer. - -maximize ![unbounded knapsack](https://wikimedia.org/api/rest_v1/media/math/render/svg/85620037d368d2136fb3361702df6a489416931b) - -subject to ![unbounded knapsack](https://wikimedia.org/api/rest_v1/media/math/render/svg/dd6e7c9bca4397980976ea6d19237500ce3b8176) -and ![unbounded knapsack](https://wikimedia.org/api/rest_v1/media/math/render/svg/90a99710f61d5dea19e49ae5b31164d2b56b07e3) - -## References - -- [Wikipedia](https://en.wikipedia.org/wiki/Knapsack_problem) -- [0/1 Knapsack Problem on YouTube](https://www.youtube.com/watch?v=8LusJS5-AGo&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8) diff --git a/src/algorithms/sets/knapsack-problem/__test__/Knapsack.test.js b/src/algorithms/sets/knapsack-problem/__test__/Knapsack.test.js deleted file mode 100644 index d322445a72..0000000000 --- a/src/algorithms/sets/knapsack-problem/__test__/Knapsack.test.js +++ /dev/null @@ -1,162 +0,0 @@ -import Knapsack from '../Knapsack'; -import KnapsackItem from '../KnapsackItem'; - -describe('Knapsack', () => { - it('should solve 0/1 knapsack problem', () => { - const possibleKnapsackItems = [ - new KnapsackItem({ value: 1, weight: 1 }), - new KnapsackItem({ value: 4, weight: 3 }), - new KnapsackItem({ value: 5, weight: 4 }), - new KnapsackItem({ value: 7, weight: 5 }), - ]; - - const maxKnapsackWeight = 7; - - const knapsack = new Knapsack(possibleKnapsackItems, maxKnapsackWeight); - - knapsack.solveZeroOneKnapsackProblem(); - - expect(knapsack.totalValue).toBe(9); - expect(knapsack.totalWeight).toBe(7); - expect(knapsack.selectedItems.length).toBe(2); - expect(knapsack.selectedItems[0].toString()).toBe('v5 w4 x 1'); - expect(knapsack.selectedItems[1].toString()).toBe('v4 w3 x 1'); - }); - - it('should solve 0/1 knapsack problem regardless of items order', () => { - const possibleKnapsackItems = [ - new KnapsackItem({ value: 5, weight: 4 }), - new KnapsackItem({ value: 1, weight: 1 }), - new KnapsackItem({ value: 7, weight: 5 }), - new KnapsackItem({ value: 4, weight: 3 }), - ]; - - const maxKnapsackWeight = 7; - - const knapsack = new Knapsack(possibleKnapsackItems, maxKnapsackWeight); - - knapsack.solveZeroOneKnapsackProblem(); - - expect(knapsack.totalValue).toBe(9); - expect(knapsack.totalWeight).toBe(7); - expect(knapsack.selectedItems.length).toBe(2); - expect(knapsack.selectedItems[0].toString()).toBe('v5 w4 x 1'); - expect(knapsack.selectedItems[1].toString()).toBe('v4 w3 x 1'); - }); - - it('should solve 0/1 knapsack problem with impossible items set', () => { - const possibleKnapsackItems = [ - new KnapsackItem({ value: 5, weight: 40 }), - new KnapsackItem({ value: 1, weight: 10 }), - new KnapsackItem({ value: 7, weight: 50 }), - new KnapsackItem({ value: 4, weight: 30 }), - ]; - - const maxKnapsackWeight = 7; - - const knapsack = new Knapsack(possibleKnapsackItems, maxKnapsackWeight); - - knapsack.solveZeroOneKnapsackProblem(); - - expect(knapsack.totalValue).toBe(0); - expect(knapsack.totalWeight).toBe(0); - expect(knapsack.selectedItems.length).toBe(0); - }); - - it('should solve 0/1 knapsack problem with all equal weights', () => { - const possibleKnapsackItems = [ - new KnapsackItem({ value: 5, weight: 1 }), - new KnapsackItem({ value: 1, weight: 1 }), - new KnapsackItem({ value: 7, weight: 1 }), - new KnapsackItem({ value: 4, weight: 1 }), - new KnapsackItem({ value: 4, weight: 1 }), - new KnapsackItem({ value: 4, weight: 1 }), - ]; - - const maxKnapsackWeight = 3; - - const knapsack = new Knapsack(possibleKnapsackItems, maxKnapsackWeight); - - knapsack.solveZeroOneKnapsackProblem(); - - expect(knapsack.totalValue).toBe(16); - expect(knapsack.totalWeight).toBe(3); - expect(knapsack.selectedItems.length).toBe(3); - expect(knapsack.selectedItems[0].toString()).toBe('v4 w1 x 1'); - expect(knapsack.selectedItems[1].toString()).toBe('v5 w1 x 1'); - expect(knapsack.selectedItems[2].toString()).toBe('v7 w1 x 1'); - }); - - it('should solve unbound knapsack problem', () => { - const possibleKnapsackItems = [ - new KnapsackItem({ value: 84, weight: 7 }), // v/w ratio is 12 - new KnapsackItem({ value: 5, weight: 2 }), // v/w ratio is 2.5 - new KnapsackItem({ value: 12, weight: 3 }), // v/w ratio is 4 - new KnapsackItem({ value: 10, weight: 1 }), // v/w ratio is 10 - new KnapsackItem({ value: 20, weight: 2 }), // v/w ratio is 10 - ]; - - const maxKnapsackWeight = 15; - - const knapsack = new Knapsack(possibleKnapsackItems, maxKnapsackWeight); - - knapsack.solveUnboundedKnapsackProblem(); - - expect(knapsack.totalValue).toBe(84 + 20 + 12 + 10 + 5); - expect(knapsack.totalWeight).toBe(15); - expect(knapsack.selectedItems.length).toBe(5); - expect(knapsack.selectedItems[0].toString()).toBe('v84 w7 x 1'); - expect(knapsack.selectedItems[1].toString()).toBe('v20 w2 x 1'); - expect(knapsack.selectedItems[2].toString()).toBe('v10 w1 x 1'); - expect(knapsack.selectedItems[3].toString()).toBe('v12 w3 x 1'); - expect(knapsack.selectedItems[4].toString()).toBe('v5 w2 x 1'); - }); - - it('should solve unbound knapsack problem with items in stock', () => { - const possibleKnapsackItems = [ - new KnapsackItem({ value: 84, weight: 7, itemsInStock: 3 }), // v/w ratio is 12 - new KnapsackItem({ value: 5, weight: 2, itemsInStock: 2 }), // v/w ratio is 2.5 - new KnapsackItem({ value: 12, weight: 3, itemsInStock: 1 }), // v/w ratio is 4 - new KnapsackItem({ value: 10, weight: 1, itemsInStock: 6 }), // v/w ratio is 10 - new KnapsackItem({ value: 20, weight: 2, itemsInStock: 8 }), // v/w ratio is 10 - ]; - - const maxKnapsackWeight = 17; - - const knapsack = new Knapsack(possibleKnapsackItems, maxKnapsackWeight); - - knapsack.solveUnboundedKnapsackProblem(); - - expect(knapsack.totalValue).toBe(84 + 84 + 20 + 10); - expect(knapsack.totalWeight).toBe(17); - expect(knapsack.selectedItems.length).toBe(3); - expect(knapsack.selectedItems[0].toString()).toBe('v84 w7 x 2'); - expect(knapsack.selectedItems[1].toString()).toBe('v20 w2 x 1'); - expect(knapsack.selectedItems[2].toString()).toBe('v10 w1 x 1'); - }); - - it('should solve unbound knapsack problem with items in stock and max weight more than sum of all items', () => { - const possibleKnapsackItems = [ - new KnapsackItem({ value: 84, weight: 7, itemsInStock: 3 }), // v/w ratio is 12 - new KnapsackItem({ value: 5, weight: 2, itemsInStock: 2 }), // v/w ratio is 2.5 - new KnapsackItem({ value: 12, weight: 3, itemsInStock: 1 }), // v/w ratio is 4 - new KnapsackItem({ value: 10, weight: 1, itemsInStock: 6 }), // v/w ratio is 10 - new KnapsackItem({ value: 20, weight: 2, itemsInStock: 8 }), // v/w ratio is 10 - ]; - - const maxKnapsackWeight = 60; - - const knapsack = new Knapsack(possibleKnapsackItems, maxKnapsackWeight); - - knapsack.solveUnboundedKnapsackProblem(); - - expect(knapsack.totalValue).toBe((3 * 84) + (2 * 5) + (1 * 12) + (6 * 10) + (8 * 20)); - expect(knapsack.totalWeight).toBe((3 * 7) + (2 * 2) + (1 * 3) + (6 * 1) + (8 * 2)); - expect(knapsack.selectedItems.length).toBe(5); - expect(knapsack.selectedItems[0].toString()).toBe('v84 w7 x 3'); - expect(knapsack.selectedItems[1].toString()).toBe('v20 w2 x 8'); - expect(knapsack.selectedItems[2].toString()).toBe('v10 w1 x 6'); - expect(knapsack.selectedItems[3].toString()).toBe('v12 w3 x 1'); - expect(knapsack.selectedItems[4].toString()).toBe('v5 w2 x 2'); - }); -}); diff --git a/src/algorithms/sets/knapsack-problem/__test__/KnapsackItem.test.js b/src/algorithms/sets/knapsack-problem/__test__/KnapsackItem.test.js deleted file mode 100644 index d8ea8b8b39..0000000000 --- a/src/algorithms/sets/knapsack-problem/__test__/KnapsackItem.test.js +++ /dev/null @@ -1,35 +0,0 @@ -import KnapsackItem from '../KnapsackItem'; - -describe('KnapsackItem', () => { - it('should create knapsack item and count its total weight and value', () => { - const knapsackItem = new KnapsackItem({ value: 3, weight: 2 }); - - expect(knapsackItem.value).toBe(3); - expect(knapsackItem.weight).toBe(2); - expect(knapsackItem.quantity).toBe(1); - expect(knapsackItem.valuePerWeightRatio).toBe(1.5); - expect(knapsackItem.toString()).toBe('v3 w2 x 1'); - expect(knapsackItem.totalValue).toBe(3); - expect(knapsackItem.totalWeight).toBe(2); - - knapsackItem.quantity = 0; - - expect(knapsackItem.value).toBe(3); - expect(knapsackItem.weight).toBe(2); - expect(knapsackItem.quantity).toBe(0); - expect(knapsackItem.valuePerWeightRatio).toBe(1.5); - expect(knapsackItem.toString()).toBe('v3 w2 x 0'); - expect(knapsackItem.totalValue).toBe(0); - expect(knapsackItem.totalWeight).toBe(0); - - knapsackItem.quantity = 2; - - expect(knapsackItem.value).toBe(3); - expect(knapsackItem.weight).toBe(2); - expect(knapsackItem.quantity).toBe(2); - expect(knapsackItem.valuePerWeightRatio).toBe(1.5); - expect(knapsackItem.toString()).toBe('v3 w2 x 2'); - expect(knapsackItem.totalValue).toBe(6); - expect(knapsackItem.totalWeight).toBe(4); - }); -}); diff --git a/src/algorithms/sets/longest-common-subsequence/README.md b/src/algorithms/sets/longest-common-subsequence/README.md deleted file mode 100644 index 7c9328e073..0000000000 --- a/src/algorithms/sets/longest-common-subsequence/README.md +++ /dev/null @@ -1,25 +0,0 @@ -# Longest common subsequence problem - -The longest common subsequence (LCS) problem is the problem of finding -the longest subsequence common to all sequences in a set of sequences -(often just two sequences). It differs from the longest common substring -problem: unlike substrings, subsequences are not required to occupy -consecutive positions within the original sequences. - -## Application - -The longest common subsequence problem is a classic computer science -problem, the basis of data comparison programs such as the diff utility, -and has applications in bioinformatics. It is also widely used by -revision control systems such as Git for reconciling multiple changes -made to a revision-controlled collection of files. - -## Example - -- LCS for input Sequences `ABCDGH` and `AEDFHR` is `ADH` of length 3. -- LCS for input Sequences `AGGTAB` and `GXTXAYB` is `GTAB` of length 4. - -## References - -- [Wikipedia](https://en.wikipedia.org/wiki/Longest_common_subsequence_problem) -- [YouTube](https://www.youtube.com/watch?v=NnD96abizww&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8) diff --git a/src/algorithms/sets/longest-common-subsequence/__test__/longestCommonSubsequence.test.js b/src/algorithms/sets/longest-common-subsequence/__test__/longestCommonSubsequence.test.js deleted file mode 100644 index 9cddc52bc0..0000000000 --- a/src/algorithms/sets/longest-common-subsequence/__test__/longestCommonSubsequence.test.js +++ /dev/null @@ -1,31 +0,0 @@ -import longestCommonSubsequence from '../longestCommonSubsequence'; - -describe('longestCommonSubsequence', () => { - it('should find longest common subsequence for two strings', () => { - expect(longestCommonSubsequence([''], [''])).toEqual(['']); - - expect(longestCommonSubsequence([''], ['A', 'B', 'C'])).toEqual(['']); - - expect(longestCommonSubsequence(['A', 'B', 'C'], [''])).toEqual(['']); - - expect(longestCommonSubsequence( - ['A', 'B', 'C'], - ['D', 'E', 'F', 'G'], - )).toEqual(['']); - - expect(longestCommonSubsequence( - ['A', 'B', 'C', 'D', 'G', 'H'], - ['A', 'E', 'D', 'F', 'H', 'R'], - )).toEqual(['A', 'D', 'H']); - - expect(longestCommonSubsequence( - ['A', 'G', 'G', 'T', 'A', 'B'], - ['G', 'X', 'T', 'X', 'A', 'Y', 'B'], - )).toEqual(['G', 'T', 'A', 'B']); - - expect(longestCommonSubsequence( - ['A', 'B', 'C', 'D', 'A', 'F'], - ['A', 'C', 'B', 'C', 'F'], - )).toEqual(['A', 'B', 'C', 'F']); - }); -}); diff --git a/src/algorithms/sets/longest-common-subsequence/__test__/longestCommonSubsequenceRecursive.test.js b/src/algorithms/sets/longest-common-subsequence/__test__/longestCommonSubsequenceRecursive.test.js deleted file mode 100644 index 3d5c9d802a..0000000000 --- a/src/algorithms/sets/longest-common-subsequence/__test__/longestCommonSubsequenceRecursive.test.js +++ /dev/null @@ -1,17 +0,0 @@ -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/sets/longest-common-subsequence/longestCommonSubsequence.js b/src/algorithms/sets/longest-common-subsequence/longestCommonSubsequence.js deleted file mode 100644 index 412482736d..0000000000 --- a/src/algorithms/sets/longest-common-subsequence/longestCommonSubsequence.js +++ /dev/null @@ -1,60 +0,0 @@ -/** - * @param {string[]} set1 - * @param {string[]} set2 - * @return {string[]} - */ -export default function longestCommonSubsequence(set1, set2) { - // Init LCS matrix. - const lcsMatrix = Array(set2.length + 1).fill(null).map(() => Array(set1.length + 1).fill(null)); - - // Fill first row with zeros. - for (let columnIndex = 0; columnIndex <= set1.length; columnIndex += 1) { - lcsMatrix[0][columnIndex] = 0; - } - - // Fill first column with zeros. - for (let rowIndex = 0; rowIndex <= set2.length; rowIndex += 1) { - lcsMatrix[rowIndex][0] = 0; - } - - // Fill rest of the column that correspond to each of two strings. - for (let rowIndex = 1; rowIndex <= set2.length; rowIndex += 1) { - for (let columnIndex = 1; columnIndex <= set1.length; columnIndex += 1) { - if (set1[columnIndex - 1] === set2[rowIndex - 1]) { - lcsMatrix[rowIndex][columnIndex] = lcsMatrix[rowIndex - 1][columnIndex - 1] + 1; - } else { - lcsMatrix[rowIndex][columnIndex] = Math.max( - lcsMatrix[rowIndex - 1][columnIndex], - lcsMatrix[rowIndex][columnIndex - 1], - ); - } - } - } - - // Calculate LCS based on LCS matrix. - if (!lcsMatrix[set2.length][set1.length]) { - // If the length of largest common string is zero then return empty string. - return ['']; - } - - const longestSequence = []; - let columnIndex = set1.length; - let rowIndex = set2.length; - - while (columnIndex > 0 || rowIndex > 0) { - if (set1[columnIndex - 1] === set2[rowIndex - 1]) { - // Move by diagonal left-top. - longestSequence.unshift(set1[columnIndex - 1]); - columnIndex -= 1; - rowIndex -= 1; - } else if (lcsMatrix[rowIndex][columnIndex] === lcsMatrix[rowIndex][columnIndex - 1]) { - // Move left. - columnIndex -= 1; - } else { - // Move up. - rowIndex -= 1; - } - } - - return longestSequence; -} diff --git a/src/algorithms/sets/longest-common-subsequence/longestCommonSubsequenceRecursive.js b/src/algorithms/sets/longest-common-subsequence/longestCommonSubsequenceRecursive.js deleted file mode 100644 index 580ba8c72f..0000000000 --- a/src/algorithms/sets/longest-common-subsequence/longestCommonSubsequenceRecursive.js +++ /dev/null @@ -1,36 +0,0 @@ -/* eslint-disable no-param-reassign */ -/** - * Longest Common Subsequence (LCS) (Recursive Approach). - * - * @param {string} string1 - * @param {string} string2 - * @return {number} - */ -export default function longestCommonSubsequenceRecursive(string1, string2) { - /** - * - * @param {string} s1 - * @param {string} s2 - * @return {string} - returns the LCS (Longest Common Subsequence) - */ - 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); -} diff --git a/src/algorithms/sets/longest-increasing-subsequence/README.md b/src/algorithms/sets/longest-increasing-subsequence/README.md deleted file mode 100644 index bcb2665c2d..0000000000 --- a/src/algorithms/sets/longest-increasing-subsequence/README.md +++ /dev/null @@ -1,46 +0,0 @@ -# Longest Increasing Subsequence - -The longest increasing subsequence problem is to find a subsequence of a -given sequence in which the subsequence's elements are in sorted order, -lowest to highest, and in which the subsequence is as long as possible. -This subsequence is not necessarily contiguous, or unique. - -## Complexity - -The longest increasing subsequence problem is solvable in -time `O(n log n)`, where `n` denotes the length of the input sequence. - -Dynamic programming approach has complexity `O(n * n)`. - -## Example - -In the first 16 terms of the binary Van der Corput sequence - -``` -0, 8, 4, 12, 2, 10, 6, 14, 1, 9, 5, 13, 3, 11, 7, 15 -``` - -a longest increasing subsequence is - -``` -0, 2, 6, 9, 11, 15. -``` - -This subsequence has length six; -the input sequence has no seven-member increasing subsequences. -The longest increasing subsequence in this example is not unique: for -instance, - -``` -0, 4, 6, 9, 11, 15 or -0, 2, 6, 9, 13, 15 or -0, 4, 6, 9, 13, 15 -``` - -are other increasing subsequences of equal length in the same -input sequence. - -## References - -- [Wikipedia](https://en.wikipedia.org/wiki/Longest_increasing_subsequence) -- [Dynamic Programming Approach on YouTube](https://www.youtube.com/watch?v=CE2b_-XfVDk&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8) diff --git a/src/algorithms/sets/longest-increasing-subsequence/__test__/dpLongestIncreasingSubsequence.test.js b/src/algorithms/sets/longest-increasing-subsequence/__test__/dpLongestIncreasingSubsequence.test.js deleted file mode 100644 index 13160b6192..0000000000 --- a/src/algorithms/sets/longest-increasing-subsequence/__test__/dpLongestIncreasingSubsequence.test.js +++ /dev/null @@ -1,36 +0,0 @@ -import dpLongestIncreasingSubsequence from '../dpLongestIncreasingSubsequence'; - -describe('dpLongestIncreasingSubsequence', () => { - it('should find longest increasing subsequence length', () => { - // Should be: - // 9 or - // 8 or - // 7 or - // 6 or - // ... - expect(dpLongestIncreasingSubsequence([ - 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, - ])).toBe(1); - - // Should be: - // 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 - expect(dpLongestIncreasingSubsequence([ - 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, - ])).toBe(10); - - // Should be: - // -1, 0, 2, 3 - expect(dpLongestIncreasingSubsequence([ - 3, 4, -1, 0, 6, 2, 3, - ])).toBe(4); - - // Should be: - // 0, 2, 6, 9, 11, 15 or - // 0, 4, 6, 9, 11, 15 or - // 0, 2, 6, 9, 13, 15 or - // 0, 4, 6, 9, 13, 15 - expect(dpLongestIncreasingSubsequence([ - 0, 8, 4, 12, 2, 10, 6, 14, 1, 9, 5, 13, 3, 11, 7, 15, - ])).toBe(6); - }); -}); diff --git a/src/algorithms/sets/longest-increasing-subsequence/dpLongestIncreasingSubsequence.js b/src/algorithms/sets/longest-increasing-subsequence/dpLongestIncreasingSubsequence.js deleted file mode 100644 index e5f2ec6dbf..0000000000 --- a/src/algorithms/sets/longest-increasing-subsequence/dpLongestIncreasingSubsequence.js +++ /dev/null @@ -1,53 +0,0 @@ -/** - * Dynamic programming approach to find longest increasing subsequence. - * Complexity: O(n * n) - * - * @param {number[]} sequence - * @return {number} - */ -export default function dpLongestIncreasingSubsequence(sequence) { - // Create array with longest increasing substrings length and - // fill it with 1-s that would mean that each element of the sequence - // is itself a minimum increasing subsequence. - const lengthsArray = Array(sequence.length).fill(1); - - let previousElementIndex = 0; - let currentElementIndex = 1; - - while (currentElementIndex < sequence.length) { - if (sequence[previousElementIndex] < sequence[currentElementIndex]) { - // If current element is bigger then the previous one then - // current element is a part of increasing subsequence which - // length is by one bigger then the length of increasing subsequence - // for previous element. - const newLength = lengthsArray[previousElementIndex] + 1; - if (newLength > lengthsArray[currentElementIndex]) { - // Increase only if previous element would give us bigger subsequence length - // then we already have for current element. - lengthsArray[currentElementIndex] = newLength; - } - } - - // Move previous element index right. - previousElementIndex += 1; - - // If previous element index equals to current element index then - // shift current element right and reset previous element index to zero. - if (previousElementIndex === currentElementIndex) { - currentElementIndex += 1; - previousElementIndex = 0; - } - } - - // Find the biggest element in lengthsArray. - // This number is the biggest length of increasing subsequence. - let longestIncreasingLength = 0; - - for (let i = 0; i < lengthsArray.length; i += 1) { - if (lengthsArray[i] > longestIncreasingLength) { - longestIncreasingLength = lengthsArray[i]; - } - } - - return longestIncreasingLength; -} diff --git a/src/algorithms/sets/maximum-subarray/README.md b/src/algorithms/sets/maximum-subarray/README.md deleted file mode 100644 index f06300f500..0000000000 --- a/src/algorithms/sets/maximum-subarray/README.md +++ /dev/null @@ -1,29 +0,0 @@ -# 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 -which has the largest sum, where, - -![Maximum subarray](https://wikimedia.org/api/rest_v1/media/math/render/svg/e8960f093107b71b21827e726e2bad8b023779b2) - -![Maximum subarray](https://www.geeksforgeeks.org/wp-content/uploads/kadane-Algorithm.png) - -## 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 -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) -- [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) diff --git a/src/algorithms/sets/maximum-subarray/__test__/bfMaximumSubarray.test.js b/src/algorithms/sets/maximum-subarray/__test__/bfMaximumSubarray.test.js deleted file mode 100644 index 6bff427110..0000000000 --- a/src/algorithms/sets/maximum-subarray/__test__/bfMaximumSubarray.test.js +++ /dev/null @@ -1,16 +0,0 @@ -import bfMaximumSubarray from '../bfMaximumSubarray'; - -describe('bfMaximumSubarray', () => { - 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]); - expect(bfMaximumSubarray([0, 0, 1, 2])).toEqual([0, 0, 1, 2]); - expect(bfMaximumSubarray([0, 0, -1, 2])).toEqual([2]); - expect(bfMaximumSubarray([-1, -2, -3, -4, -5])).toEqual([-1]); - expect(bfMaximumSubarray([1, 2, 3, 2, 3, 4, 5])).toEqual([1, 2, 3, 2, 3, 4, 5]); - expect(bfMaximumSubarray([-2, 1, -3, 4, -1, 2, 1, -5, 4])).toEqual([4, -1, 2, 1]); - expect(bfMaximumSubarray([-2, -3, 4, -1, -2, 1, 5, -3])).toEqual([4, -1, -2, 1, 5]); - expect(bfMaximumSubarray([1, -3, 2, -5, 7, 6, -1, 4, 11, -23])).toEqual([7, 6, -1, 4, 11]); - }); -}); diff --git a/src/algorithms/sets/maximum-subarray/__test__/dcMaximumSubarraySum.test.js b/src/algorithms/sets/maximum-subarray/__test__/dcMaximumSubarraySum.test.js deleted file mode 100644 index 3b3ace08d3..0000000000 --- a/src/algorithms/sets/maximum-subarray/__test__/dcMaximumSubarraySum.test.js +++ /dev/null @@ -1,16 +0,0 @@ -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 deleted file mode 100644 index c00727cc66..0000000000 --- a/src/algorithms/sets/maximum-subarray/__test__/dpMaximumSubarray.test.js +++ /dev/null @@ -1,16 +0,0 @@ -import dpMaximumSubarray from '../dpMaximumSubarray'; - -describe('dpMaximumSubarray', () => { - 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]); - expect(dpMaximumSubarray([0, 0, 1, 2])).toEqual([0, 0, 1, 2]); - expect(dpMaximumSubarray([0, 0, -1, 2])).toEqual([2]); - expect(dpMaximumSubarray([-1, -2, -3, -4, -5])).toEqual([-1]); - expect(dpMaximumSubarray([1, 2, 3, 2, 3, 4, 5])).toEqual([1, 2, 3, 2, 3, 4, 5]); - expect(dpMaximumSubarray([-2, 1, -3, 4, -1, 2, 1, -5, 4])).toEqual([4, -1, 2, 1]); - expect(dpMaximumSubarray([-2, -3, 4, -1, -2, 1, 5, -3])).toEqual([4, -1, -2, 1, 5]); - expect(dpMaximumSubarray([1, -3, 2, -5, 7, 6, -1, 4, 11, -23])).toEqual([7, 6, -1, 4, 11]); - }); -}); diff --git a/src/algorithms/sets/maximum-subarray/bfMaximumSubarray.js b/src/algorithms/sets/maximum-subarray/bfMaximumSubarray.js deleted file mode 100644 index 20c0b38e72..0000000000 --- a/src/algorithms/sets/maximum-subarray/bfMaximumSubarray.js +++ /dev/null @@ -1,26 +0,0 @@ -/** - * Brute Force solution. - * Complexity: O(n^2) - * - * @param {Number[]} inputArray - * @return {Number[]} - */ -export default function bfMaximumSubarray(inputArray) { - let maxSubarrayStartIndex = 0; - let maxSubarrayLength = 0; - let maxSubarraySum = null; - - for (let startIndex = 0; startIndex < inputArray.length; startIndex += 1) { - let subarraySum = 0; - for (let arrLength = 1; arrLength <= (inputArray.length - startIndex); arrLength += 1) { - subarraySum += inputArray[startIndex + (arrLength - 1)]; - if (maxSubarraySum === null || subarraySum > maxSubarraySum) { - maxSubarraySum = subarraySum; - maxSubarrayStartIndex = startIndex; - maxSubarrayLength = arrLength; - } - } - } - - return inputArray.slice(maxSubarrayStartIndex, maxSubarrayStartIndex + maxSubarrayLength); -} diff --git a/src/algorithms/sets/maximum-subarray/dcMaximumSubarraySum.js b/src/algorithms/sets/maximum-subarray/dcMaximumSubarraySum.js deleted file mode 100644 index 3ed9ab3ee7..0000000000 --- a/src/algorithms/sets/maximum-subarray/dcMaximumSubarraySum.js +++ /dev/null @@ -1,33 +0,0 @@ -/** - * 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); -} diff --git a/src/algorithms/sets/maximum-subarray/dpMaximumSubarray.js b/src/algorithms/sets/maximum-subarray/dpMaximumSubarray.js deleted file mode 100644 index ef1734b486..0000000000 --- a/src/algorithms/sets/maximum-subarray/dpMaximumSubarray.js +++ /dev/null @@ -1,45 +0,0 @@ -/** - * Dynamic Programming solution. - * Complexity: O(n) - * - * @param {Number[]} inputArray - * @return {Number[]} - */ -export default function dpMaximumSubarray(inputArray) { - // We iterate through the inputArray once, using a greedy approach to keep track of the maximum - // sum we've seen so far and the current sum. - // - // The currentSum variable gets reset to 0 every time it drops below 0. - // - // The maxSum variable is set to -Infinity so that if all numbers are negative, the highest - // negative number will constitute the maximum subarray. - - let maxSum = -Infinity; - let currentSum = 0; - - // We need to keep track of the starting and ending indices that contributed to our maxSum - // so that we can return the actual subarray. From the beginning let's assume that whole array - // is contributing to maxSum. - let maxStartIndex = 0; - let maxEndIndex = inputArray.length - 1; - let currentStartIndex = 0; - - inputArray.forEach((currentNumber, currentIndex) => { - currentSum += currentNumber; - - // Update maxSum and the corresponding indices if we have found a new max. - if (maxSum < currentSum) { - maxSum = currentSum; - maxStartIndex = currentStartIndex; - maxEndIndex = currentIndex; - } - - // Reset currentSum and currentStartIndex if currentSum drops below 0. - if (currentSum < 0) { - currentSum = 0; - currentStartIndex = currentIndex + 1; - } - }); - - return inputArray.slice(maxStartIndex, maxEndIndex + 1); -} diff --git a/src/algorithms/sets/permutations/README.md b/src/algorithms/sets/permutations/README.md deleted file mode 100644 index 4b6a268adc..0000000000 --- a/src/algorithms/sets/permutations/README.md +++ /dev/null @@ -1,55 +0,0 @@ -# Permutations - -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`. -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. - -Below are the permutations of string `ABC`. - -`ABC ACB BAC BCA CBA CAB` - -Or for example the first three people in a running race: you can't be first and second. - -**Number of combinations** - -``` -n * (n-1) * (n -2) * ... * 1 = n! -``` - -## Permutations with repetitions - -When repetition is allowed we have permutations with repetitions. -For example the the lock below: it could be `333`. - -![Permutation Lock](https://www.mathsisfun.com/combinatorics/images/combination-lock.jpg) - -**Number of combinations** - -``` -n * n * n ... (r times) = n^r -``` - -## Cheatsheet - -![Permutations and Combinations Overview](./images/overview.png) - -![Permutations overview](./images/permutations-overview.jpeg) - -| | | -| --- | --- | -|![Permutations with repetition](./images/permutations-with-repetitions.jpg) | ![Permutations without repetition](./images/permutations-without-repetitions.jpg) | - -*Made with [okso.app](https://okso.app)* - -## References - -- [Math Is Fun](https://www.mathsisfun.com/combinatorics/combinations-permutations.html) -- [Permutations/combinations cheat sheets](https://medium.com/@trekhleb/permutations-combinations-algorithms-cheat-sheet-68c14879aba5) diff --git a/src/algorithms/sets/permutations/__test__/permutateWithRepetitions.test.js b/src/algorithms/sets/permutations/__test__/permutateWithRepetitions.test.js deleted file mode 100644 index 0d53def1ae..0000000000 --- a/src/algorithms/sets/permutations/__test__/permutateWithRepetitions.test.js +++ /dev/null @@ -1,52 +0,0 @@ -import permutateWithRepetitions from '../permutateWithRepetitions'; - -describe('permutateWithRepetitions', () => { - it('should permutate string with repetition', () => { - const permutations1 = permutateWithRepetitions(['A']); - expect(permutations1).toEqual([ - ['A'], - ]); - - const permutations2 = permutateWithRepetitions(['A', 'B']); - expect(permutations2).toEqual([ - ['A', 'A'], - ['A', 'B'], - ['B', 'A'], - ['B', 'B'], - ]); - - const permutations3 = permutateWithRepetitions(['A', 'B', 'C']); - expect(permutations3).toEqual([ - ['A', 'A', 'A'], - ['A', 'A', 'B'], - ['A', 'A', 'C'], - ['A', 'B', 'A'], - ['A', 'B', 'B'], - ['A', 'B', 'C'], - ['A', 'C', 'A'], - ['A', 'C', 'B'], - ['A', 'C', 'C'], - ['B', 'A', 'A'], - ['B', 'A', 'B'], - ['B', 'A', 'C'], - ['B', 'B', 'A'], - ['B', 'B', 'B'], - ['B', 'B', 'C'], - ['B', 'C', 'A'], - ['B', 'C', 'B'], - ['B', 'C', 'C'], - ['C', 'A', 'A'], - ['C', 'A', 'B'], - ['C', 'A', 'C'], - ['C', 'B', 'A'], - ['C', 'B', 'B'], - ['C', 'B', 'C'], - ['C', 'C', 'A'], - ['C', 'C', 'B'], - ['C', 'C', 'C'], - ]); - - const permutations4 = permutateWithRepetitions(['A', 'B', 'C', 'D']); - expect(permutations4.length).toBe(4 * 4 * 4 * 4); - }); -}); diff --git a/src/algorithms/sets/permutations/__test__/permutateWithoutRepetitions.test.js b/src/algorithms/sets/permutations/__test__/permutateWithoutRepetitions.test.js deleted file mode 100644 index 6125e58e3c..0000000000 --- a/src/algorithms/sets/permutations/__test__/permutateWithoutRepetitions.test.js +++ /dev/null @@ -1,68 +0,0 @@ -import permutateWithoutRepetitions from '../permutateWithoutRepetitions'; -import factorial from '../../../math/factorial/factorial'; - -describe('permutateWithoutRepetitions', () => { - it('should permutate string', () => { - const permutations1 = permutateWithoutRepetitions(['A']); - expect(permutations1).toEqual([ - ['A'], - ]); - - const permutations2 = permutateWithoutRepetitions(['A', 'B']); - expect(permutations2.length).toBe(2); - expect(permutations2).toEqual([ - ['A', 'B'], - ['B', 'A'], - ]); - - const permutations6 = permutateWithoutRepetitions(['A', 'A']); - expect(permutations6.length).toBe(2); - expect(permutations6).toEqual([ - ['A', 'A'], - ['A', 'A'], - ]); - - const permutations3 = permutateWithoutRepetitions(['A', 'B', 'C']); - expect(permutations3.length).toBe(factorial(3)); - expect(permutations3).toEqual([ - ['A', 'B', 'C'], - ['B', 'A', 'C'], - ['B', 'C', 'A'], - ['A', 'C', 'B'], - ['C', 'A', 'B'], - ['C', 'B', 'A'], - ]); - - const permutations4 = permutateWithoutRepetitions(['A', 'B', 'C', 'D']); - expect(permutations4.length).toBe(factorial(4)); - expect(permutations4).toEqual([ - ['A', 'B', 'C', 'D'], - ['B', 'A', 'C', 'D'], - ['B', 'C', 'A', 'D'], - ['B', 'C', 'D', 'A'], - ['A', 'C', 'B', 'D'], - ['C', 'A', 'B', 'D'], - ['C', 'B', 'A', 'D'], - ['C', 'B', 'D', 'A'], - ['A', 'C', 'D', 'B'], - ['C', 'A', 'D', 'B'], - ['C', 'D', 'A', 'B'], - ['C', 'D', 'B', 'A'], - ['A', 'B', 'D', 'C'], - ['B', 'A', 'D', 'C'], - ['B', 'D', 'A', 'C'], - ['B', 'D', 'C', 'A'], - ['A', 'D', 'B', 'C'], - ['D', 'A', 'B', 'C'], - ['D', 'B', 'A', 'C'], - ['D', 'B', 'C', 'A'], - ['A', 'D', 'C', 'B'], - ['D', 'A', 'C', 'B'], - ['D', 'C', 'A', 'B'], - ['D', 'C', 'B', 'A'], - ]); - - const permutations5 = permutateWithoutRepetitions(['A', 'B', 'C', 'D', 'E', 'F']); - expect(permutations5.length).toBe(factorial(6)); - }); -}); diff --git a/src/algorithms/sets/permutations/images/overview.png b/src/algorithms/sets/permutations/images/overview.png deleted file mode 100644 index fa8d6a66f5403d99a5367a006d9bca788b2e9534..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 145014 zcmeFYby$>L*EftHf*_#?C`c+GInq6(APv$vATTh%&^?q2(k&gM(%oH(gtRcg&<#U( z4f&3DT-W`)&-ecO{dLcAoU`}rJojF)e`~Ehq3WvgLSXfv@3U6fJVqxLBV`1T# z;NQcP)S`3}u&^G8L1bjq6=Y=S)tw!{5IajOtT&+vx_Ek;JrtRSZxy8P%StM)tB}S< zeI_-)x>N8WGUhHm(Yc-Rzfx<|;y*4wC8o+QZnWvlhD 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permutations. - const smallerPermutations = permutateWithRepetitions( - permutationOptions, - permutationLength - 1, - ); - - // Go through all options and join it to the smaller permutations. - permutationOptions.forEach((currentOption) => { - smallerPermutations.forEach((smallerPermutation) => { - permutations.push([currentOption].concat(smallerPermutation)); - }); - }); - - return permutations; -} diff --git a/src/algorithms/sets/permutations/permutateWithoutRepetitions.js b/src/algorithms/sets/permutations/permutateWithoutRepetitions.js deleted file mode 100644 index 7b2f002c74..0000000000 --- a/src/algorithms/sets/permutations/permutateWithoutRepetitions.js +++ /dev/null @@ -1,31 +0,0 @@ -/** - * @param {*[]} permutationOptions - * @return {*[]} - */ -export default function permutateWithoutRepetitions(permutationOptions) { - if (permutationOptions.length === 1) { - return [permutationOptions]; - } - - // Init permutations array. - const permutations = []; - - // Get all permutations for permutationOptions excluding the first element. - const smallerPermutations = permutateWithoutRepetitions(permutationOptions.slice(1)); - - // Insert first option into every possible position of every smaller permutation. - const firstOption = permutationOptions[0]; - - for (let permIndex = 0; permIndex < smallerPermutations.length; permIndex += 1) { - const smallerPermutation = smallerPermutations[permIndex]; - - // Insert first option into every possible position of smallerPermutation. - for (let positionIndex = 0; positionIndex <= smallerPermutation.length; positionIndex += 1) { - const permutationPrefix = smallerPermutation.slice(0, positionIndex); - const permutationSuffix = smallerPermutation.slice(positionIndex); - permutations.push(permutationPrefix.concat([firstOption], permutationSuffix)); - } - } - - return permutations; -} diff --git a/src/algorithms/sets/power-set/README.md b/src/algorithms/sets/power-set/README.md deleted file mode 100644 index e96961dd8f..0000000000 --- a/src/algorithms/sets/power-set/README.md +++ /dev/null @@ -1,112 +0,0 @@ -# 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)`. - -For example for `{x, y, z}`, the subsets -are: - -```text -{ - {}, // (also denoted empty set ∅ or the null set) - {x}, - {y}, - {z}, - {x, y}, - {x, z}, - {y, z}, - {x, y, z} -} -``` - -![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 -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 -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 -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 -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 -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}` | -| `3` | `011` | `{c, b}` | -| `4` | `100` | `{a}` | -| `5` | `101` | `{a, c}` | -| `6` | `110` | `{a, b}` | -| `7` | `111` | `{a, b, c}` | - -> See [bwPowerSet.js](./bwPowerSet.js) file for bitwise solution. - -### Backtracking Solution - -In backtracking approach we're constantly trying to add next element of the set -to the subset, memorizing it and then removing it and try the same with the next -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) -* [Math is Fun](https://www.mathsisfun.com/sets/power-set.html) diff --git a/src/algorithms/sets/power-set/__test__/btPowerSet.test.js b/src/algorithms/sets/power-set/__test__/btPowerSet.test.js deleted file mode 100644 index acfb1730a6..0000000000 --- a/src/algorithms/sets/power-set/__test__/btPowerSet.test.js +++ /dev/null @@ -1,21 +0,0 @@ -import btPowerSet from '../btPowerSet'; - -describe('btPowerSet', () => { - it('should calculate power set of given set using backtracking approach', () => { - expect(btPowerSet([1])).toEqual([ - [], - [1], - ]); - - expect(btPowerSet([1, 2, 3])).toEqual([ - [], - [1], - [1, 2], - [1, 2, 3], - [1, 3], - [2], - [2, 3], - [3], - ]); - }); -}); diff --git a/src/algorithms/sets/power-set/__test__/bwPowerSet.test.js b/src/algorithms/sets/power-set/__test__/bwPowerSet.test.js deleted file mode 100644 index e2ed179300..0000000000 --- a/src/algorithms/sets/power-set/__test__/bwPowerSet.test.js +++ /dev/null @@ -1,21 +0,0 @@ -import bwPowerSet from '../bwPowerSet'; - -describe('bwPowerSet', () => { - it('should calculate power set of given set using bitwise approach', () => { - expect(bwPowerSet([1])).toEqual([ - [], - [1], - ]); - - expect(bwPowerSet([1, 2, 3])).toEqual([ - [], - [1], - [2], - [1, 2], - [3], - [1, 3], - [2, 3], - [1, 2, 3], - ]); - }); -}); diff --git a/src/algorithms/sets/power-set/__test__/caPowerSet.test.js b/src/algorithms/sets/power-set/__test__/caPowerSet.test.js deleted file mode 100644 index 4fad5efe20..0000000000 --- a/src/algorithms/sets/power-set/__test__/caPowerSet.test.js +++ /dev/null @@ -1,28 +0,0 @@ -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/btPowerSet.js b/src/algorithms/sets/power-set/btPowerSet.js deleted file mode 100644 index 2007c124bf..0000000000 --- a/src/algorithms/sets/power-set/btPowerSet.js +++ /dev/null @@ -1,41 +0,0 @@ -/** - * @param {*[]} originalSet - Original set of elements we're forming power-set of. - * @param {*[][]} allSubsets - All subsets that have been formed so far. - * @param {*[]} currentSubSet - Current subset that we're forming at the moment. - * @param {number} startAt - The position of in original set we're starting to form current subset. - * @return {*[][]} - All subsets of original set. - */ -function btPowerSetRecursive(originalSet, allSubsets = [[]], currentSubSet = [], startAt = 0) { - // Let's iterate over originalSet elements that may be added to the subset - // without having duplicates. The value of startAt prevents adding the duplicates. - for (let position = startAt; position < originalSet.length; position += 1) { - // Let's push current element to the subset - currentSubSet.push(originalSet[position]); - - // Current subset is already valid so let's memorize it. - // We do array destruction here to save the clone of the currentSubSet. - // We need to save a clone since the original currentSubSet is going to be - // mutated in further recursive calls. - allSubsets.push([...currentSubSet]); - - // Let's try to generate all other subsets for the current subset. - // We're increasing the position by one to avoid duplicates in subset. - btPowerSetRecursive(originalSet, allSubsets, currentSubSet, position + 1); - - // BACKTRACK. Exclude last element from the subset and try the next valid one. - currentSubSet.pop(); - } - - // Return all subsets of a set. - return allSubsets; -} - -/** - * Find power-set of a set using BACKTRACKING approach. - * - * @param {*[]} originalSet - * @return {*[][]} - */ -export default function btPowerSet(originalSet) { - return btPowerSetRecursive(originalSet); -} diff --git a/src/algorithms/sets/power-set/bwPowerSet.js b/src/algorithms/sets/power-set/bwPowerSet.js deleted file mode 100644 index b8417bea4b..0000000000 --- a/src/algorithms/sets/power-set/bwPowerSet.js +++ /dev/null @@ -1,34 +0,0 @@ -/** - * Find power-set of a set using BITWISE approach. - * - * @param {*[]} originalSet - * @return {*[][]} - */ -export default function bwPowerSet(originalSet) { - const subSets = []; - - // We will have 2^n possible combinations (where n is a length of original set). - // It is because for every element of original set we will decide whether to include - // it or not (2 options for each set element). - const numberOfCombinations = 2 ** originalSet.length; - - // 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. - for (let combinationIndex = 0; combinationIndex < numberOfCombinations; combinationIndex += 1) { - const subSet = []; - - for (let setElementIndex = 0; setElementIndex < originalSet.length; setElementIndex += 1) { - // Decide whether we need to include current element into the subset or not. - if (combinationIndex & (1 << setElementIndex)) { - subSet.push(originalSet[setElementIndex]); - } - } - - // Add current subset to the list of all subsets. - subSets.push(subSet); - } - - return subSets; -} diff --git a/src/algorithms/sets/power-set/caPowerSet.js b/src/algorithms/sets/power-set/caPowerSet.js deleted file mode 100644 index 45b9eb6169..0000000000 --- a/src/algorithms/sets/power-set/caPowerSet.js +++ /dev/null @@ -1,37 +0,0 @@ -/** - * 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; -} diff --git a/src/algorithms/sets/shortest-common-supersequence/README.md b/src/algorithms/sets/shortest-common-supersequence/README.md deleted file mode 100644 index 5af90a8337..0000000000 --- a/src/algorithms/sets/shortest-common-supersequence/README.md +++ /dev/null @@ -1,24 +0,0 @@ -# Shortest Common Supersequence - -The shortest common supersequence (SCS) of two sequences `X` and `Y` -is the shortest sequence which has `X` and `Y` as subsequences. - -In other words assume we're given two strings str1 and str2, find -the shortest string that has both str1 and str2 as subsequences. - -This is a problem closely related to the longest common -subsequence problem. - -## Example - -``` -Input: str1 = "geek", str2 = "eke" -Output: "geeke" - -Input: str1 = "AGGTAB", str2 = "GXTXAYB" -Output: "AGXGTXAYB" -``` - -## References - -- [GeeksForGeeks](https://www.geeksforgeeks.org/shortest-common-supersequence/) diff --git a/src/algorithms/sets/shortest-common-supersequence/__test__/shortestCommonSupersequence.test.js b/src/algorithms/sets/shortest-common-supersequence/__test__/shortestCommonSupersequence.test.js deleted file mode 100644 index 8adf27d159..0000000000 --- a/src/algorithms/sets/shortest-common-supersequence/__test__/shortestCommonSupersequence.test.js +++ /dev/null @@ -1,35 +0,0 @@ -import shortestCommonSupersequence from '../shortestCommonSupersequence'; - -describe('shortestCommonSupersequence', () => { - it('should find shortest common supersequence of two sequences', () => { - // LCS (longest common subsequence) is empty - expect(shortestCommonSupersequence( - ['A', 'B', 'C'], - ['D', 'E', 'F'], - )).toEqual(['A', 'B', 'C', 'D', 'E', 'F']); - - // LCS (longest common subsequence) is "EE" - expect(shortestCommonSupersequence( - ['G', 'E', 'E', 'K'], - ['E', 'K', 'E'], - )).toEqual(['G', 'E', 'K', 'E', 'K']); - - // LCS (longest common subsequence) is "GTAB" - expect(shortestCommonSupersequence( - ['A', 'G', 'G', 'T', 'A', 'B'], - ['G', 'X', 'T', 'X', 'A', 'Y', 'B'], - )).toEqual(['A', 'G', 'G', 'X', 'T', 'X', 'A', 'Y', 'B']); - - // LCS (longest common subsequence) is "BCBA". - expect(shortestCommonSupersequence( - ['A', 'B', 'C', 'B', 'D', 'A', 'B'], - ['B', 'D', 'C', 'A', 'B', 'A'], - )).toEqual(['A', 'B', 'D', 'C', 'A', 'B', 'D', 'A', 'B']); - - // LCS (longest common subsequence) is "BDABA". - expect(shortestCommonSupersequence( - ['B', 'D', 'C', 'A', 'B', 'A'], - ['A', 'B', 'C', 'B', 'D', 'A', 'B', 'A', 'C'], - )).toEqual(['A', 'B', 'C', 'B', 'D', 'C', 'A', 'B', 'A', 'C']); - }); -}); diff --git a/src/algorithms/sets/shortest-common-supersequence/shortestCommonSupersequence.js b/src/algorithms/sets/shortest-common-supersequence/shortestCommonSupersequence.js deleted file mode 100644 index 8b14b54e22..0000000000 --- a/src/algorithms/sets/shortest-common-supersequence/shortestCommonSupersequence.js +++ /dev/null @@ -1,71 +0,0 @@ -import longestCommonSubsequence from '../longest-common-subsequence/longestCommonSubsequence'; - -/** - * @param {string[]} set1 - * @param {string[]} set2 - * @return {string[]} - */ - -export default function shortestCommonSupersequence(set1, set2) { - // Let's first find the longest common subsequence of two sets. - const lcs = longestCommonSubsequence(set1, set2); - - // If LCS is empty then the shortest common supersequence would be just - // concatenation of two sequences. - if (lcs.length === 1 && lcs[0] === '') { - return set1.concat(set2); - } - - // Now let's add elements of set1 and set2 in order before/inside/after the LCS. - let supersequence = []; - - let setIndex1 = 0; - let setIndex2 = 0; - let lcsIndex = 0; - let setOnHold1 = false; - let setOnHold2 = false; - - while (lcsIndex < lcs.length) { - // Add elements of the first set to supersequence in correct order. - if (setIndex1 < set1.length) { - if (!setOnHold1 && set1[setIndex1] !== lcs[lcsIndex]) { - supersequence.push(set1[setIndex1]); - setIndex1 += 1; - } else { - setOnHold1 = true; - } - } - - // Add elements of the second set to supersequence in correct order. - if (setIndex2 < set2.length) { - if (!setOnHold2 && set2[setIndex2] !== lcs[lcsIndex]) { - supersequence.push(set2[setIndex2]); - setIndex2 += 1; - } else { - setOnHold2 = true; - } - } - - // Add LCS element to the supersequence in correct order. - if (setOnHold1 && setOnHold2) { - supersequence.push(lcs[lcsIndex]); - lcsIndex += 1; - setIndex1 += 1; - setIndex2 += 1; - setOnHold1 = false; - setOnHold2 = false; - } - } - - // Attach set1 leftovers. - if (setIndex1 < set1.length) { - supersequence = supersequence.concat(set1.slice(setIndex1)); - } - - // Attach set2 leftovers. - if (setIndex2 < set2.length) { - supersequence = supersequence.concat(set2.slice(setIndex2)); - } - - return supersequence; -} diff --git a/src/algorithms/sorting/Sort.js b/src/algorithms/sorting/Sort.js deleted file mode 100644 index e0290881a7..0000000000 --- a/src/algorithms/sorting/Sort.js +++ /dev/null @@ -1,34 +0,0 @@ -import Comparator from '../../utils/comparator/Comparator'; - -/** - * @typedef {Object} SorterCallbacks - * @property {function(a: *, b: *)} compareCallback - If provided then all elements comparisons - * will be done through this callback. - * @property {function(a: *)} visitingCallback - If provided it will be called each time the sorting - * function is visiting the next element. - */ - -export default class Sort { - constructor(originalCallbacks) { - this.callbacks = Sort.initSortingCallbacks(originalCallbacks); - this.comparator = new Comparator(this.callbacks.compareCallback); - } - - /** - * @param {SorterCallbacks} originalCallbacks - * @returns {SorterCallbacks} - */ - static initSortingCallbacks(originalCallbacks) { - const callbacks = originalCallbacks || {}; - const stubCallback = () => {}; - - callbacks.compareCallback = callbacks.compareCallback || undefined; - callbacks.visitingCallback = callbacks.visitingCallback || stubCallback; - - return callbacks; - } - - sort() { - throw new Error('sort method must be implemented'); - } -} diff --git a/src/algorithms/sorting/SortTester.js b/src/algorithms/sorting/SortTester.js deleted file mode 100644 index e92ea39adb..0000000000 --- a/src/algorithms/sorting/SortTester.js +++ /dev/null @@ -1,72 +0,0 @@ -export const sortedArr = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]; -export const reverseArr = [20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]; -export const notSortedArr = [15, 8, 5, 12, 10, 1, 16, 9, 11, 7, 20, 3, 2, 6, 17, 18, 4, 13, 14, 19]; -export const equalArr = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]; -export const negativeArr = [-1, 0, 5, -10, 20, 13, -7, 3, 2, -3]; -export const negativeArrSorted = [-10, -7, -3, -1, 0, 2, 3, 5, 13, 20]; - -export class SortTester { - static testSort(SortingClass) { - const sorter = new SortingClass(); - - expect(sorter.sort([])).toEqual([]); - expect(sorter.sort([1])).toEqual([1]); - expect(sorter.sort([1, 2])).toEqual([1, 2]); - expect(sorter.sort([2, 1])).toEqual([1, 2]); - expect(sorter.sort([3, 4, 2, 1, 0, 0, 4, 3, 4, 2])).toEqual([0, 0, 1, 2, 2, 3, 3, 4, 4, 4]); - expect(sorter.sort(sortedArr)).toEqual(sortedArr); - expect(sorter.sort(reverseArr)).toEqual(sortedArr); - expect(sorter.sort(notSortedArr)).toEqual(sortedArr); - expect(sorter.sort(equalArr)).toEqual(equalArr); - } - - static testNegativeNumbersSort(SortingClass) { - const sorter = new SortingClass(); - expect(sorter.sort(negativeArr)).toEqual(negativeArrSorted); - } - - static testSortWithCustomComparator(SortingClass) { - const callbacks = { - compareCallback: (a, b) => { - if (a.length === b.length) { - return 0; - } - return a.length < b.length ? -1 : 1; - }, - }; - - const sorter = new SortingClass(callbacks); - - expect(sorter.sort([''])).toEqual(['']); - expect(sorter.sort(['a'])).toEqual(['a']); - expect(sorter.sort(['aa', 'a'])).toEqual(['a', 'aa']); - expect(sorter.sort(['aa', 'q', 'bbbb', 'ccc'])).toEqual(['q', 'aa', 'ccc', 'bbbb']); - expect(sorter.sort(['aa', 'aa'])).toEqual(['aa', 'aa']); - } - - static testSortStability(SortingClass) { - const callbacks = { - compareCallback: (a, b) => { - if (a.length === b.length) { - return 0; - } - return a.length < b.length ? -1 : 1; - }, - }; - - const sorter = new SortingClass(callbacks); - - expect(sorter.sort(['bb', 'aa', 'c'])).toEqual(['c', 'bb', 'aa']); - expect(sorter.sort(['aa', 'q', 'a', 'bbbb', 'ccc'])).toEqual(['q', 'a', 'aa', 'ccc', 'bbbb']); - } - - static testAlgorithmTimeComplexity(SortingClass, arrayToBeSorted, numberOfVisits) { - const visitingCallback = jest.fn(); - const callbacks = { visitingCallback }; - const sorter = new SortingClass(callbacks); - - sorter.sort(arrayToBeSorted); - - expect(visitingCallback).toHaveBeenCalledTimes(numberOfVisits); - } -} diff --git a/src/algorithms/sorting/__test__/Sort.test.js b/src/algorithms/sorting/__test__/Sort.test.js deleted file mode 100644 index 989f3e7786..0000000000 --- a/src/algorithms/sorting/__test__/Sort.test.js +++ /dev/null @@ -1,12 +0,0 @@ -import Sort from '../Sort'; - -describe('Sort', () => { - it('should throw an error when trying to call Sort.sort() method directly', () => { - function doForbiddenSort() { - const sorter = new Sort(); - sorter.sort(); - } - - expect(doForbiddenSort).toThrow(); - }); -}); diff --git a/src/algorithms/sorting/bubble-sort/BubbleSort.js b/src/algorithms/sorting/bubble-sort/BubbleSort.js deleted file mode 100644 index d78ebcbdc1..0000000000 --- a/src/algorithms/sorting/bubble-sort/BubbleSort.js +++ /dev/null @@ -1,38 +0,0 @@ -import Sort from '../Sort'; - -export default class BubbleSort extends Sort { - sort(originalArray) { - // Flag that holds info about whether the swap has occur or not. - let swapped = false; - // Clone original array to prevent its modification. - const array = [...originalArray]; - - for (let i = 1; i < array.length; i += 1) { - swapped = false; - - // Call visiting callback. - this.callbacks.visitingCallback(array[i]); - - for (let j = 0; j < array.length - i; j += 1) { - // Call visiting callback. - this.callbacks.visitingCallback(array[j]); - - // Swap elements if they are in wrong order. - if (this.comparator.lessThan(array[j + 1], array[j])) { - [array[j], array[j + 1]] = [array[j + 1], array[j]]; - - // Register the swap. - swapped = true; - } - } - - // If there were no swaps then array is already sorted and there is - // no need to proceed. - if (!swapped) { - return array; - } - } - - return array; - } -} diff --git a/src/algorithms/sorting/bubble-sort/README.md b/src/algorithms/sorting/bubble-sort/README.md deleted file mode 100644 index 66347d86c7..0000000000 --- a/src/algorithms/sorting/bubble-sort/README.md +++ /dev/null @@ -1,25 +0,0 @@ -# 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 -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 -indicates that the list is sorted. - -![Algorithm Visualization](https://upload.wikimedia.org/wikipedia/commons/c/c8/Bubble-sort-example-300px.gif) - -## Complexity - -| Name | Best | Average | Worst | Memory | Stable | Comments | -| --------------------- | :-------------: | :-----------------: | :-----------------: | :-------: | :-------: | :-------- | -| **Bubble sort** | n | n2 | n2 | 1 | Yes | | - -## References - -- [Wikipedia](https://en.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/bubble-sort/README.pt-BR.md b/src/algorithms/sorting/bubble-sort/README.pt-BR.md deleted file mode 100644 index e650523d71..0000000000 --- a/src/algorithms/sorting/bubble-sort/README.pt-BR.md +++ /dev/null @@ -1,20 +0,0 @@ -# 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) - -## Complexidade - -| Nome | Melhor | Média | Pior | Memória | Estável | Comentários | -| --------------------- | :-------------: | :-----------------: | :-----------------: | :-------: | :-------: | :-------- | -| **Bubble sort** | n | n2 | n2 | 1 | Sim | | - -## 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/bubble-sort/__test__/BubbleSort.test.js b/src/algorithms/sorting/bubble-sort/__test__/BubbleSort.test.js deleted file mode 100644 index 7e71a0b643..0000000000 --- a/src/algorithms/sorting/bubble-sort/__test__/BubbleSort.test.js +++ /dev/null @@ -1,64 +0,0 @@ -import BubbleSort from '../BubbleSort'; -import { - equalArr, - notSortedArr, - reverseArr, - sortedArr, - SortTester, -} from '../../SortTester'; - -// Complexity constants. -const SORTED_ARRAY_VISITING_COUNT = 20; -const NOT_SORTED_ARRAY_VISITING_COUNT = 189; -const REVERSE_SORTED_ARRAY_VISITING_COUNT = 209; -const EQUAL_ARRAY_VISITING_COUNT = 20; - -describe('BubbleSort', () => { - it('should sort array', () => { - SortTester.testSort(BubbleSort); - }); - - it('should sort array with custom comparator', () => { - SortTester.testSortWithCustomComparator(BubbleSort); - }); - - it('should do stable sorting', () => { - SortTester.testSortStability(BubbleSort); - }); - - it('should sort negative numbers', () => { - SortTester.testNegativeNumbersSort(BubbleSort); - }); - - it('should visit EQUAL array element specified number of times', () => { - SortTester.testAlgorithmTimeComplexity( - BubbleSort, - equalArr, - EQUAL_ARRAY_VISITING_COUNT, - ); - }); - - it('should visit SORTED array element specified number of times', () => { - SortTester.testAlgorithmTimeComplexity( - BubbleSort, - sortedArr, - SORTED_ARRAY_VISITING_COUNT, - ); - }); - - it('should visit NOT SORTED array element specified number of times', () => { - SortTester.testAlgorithmTimeComplexity( - BubbleSort, - notSortedArr, - NOT_SORTED_ARRAY_VISITING_COUNT, - ); - }); - - it('should visit REVERSE SORTED array element specified number of times', () => { - SortTester.testAlgorithmTimeComplexity( - BubbleSort, - reverseArr, - REVERSE_SORTED_ARRAY_VISITING_COUNT, - ); - }); -}); diff --git a/src/algorithms/sorting/bucket-sort/BucketSort.js b/src/algorithms/sorting/bucket-sort/BucketSort.js deleted file mode 100644 index a41e5892d2..0000000000 --- a/src/algorithms/sorting/bucket-sort/BucketSort.js +++ /dev/null @@ -1,46 +0,0 @@ -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 deleted file mode 100644 index 673ba80b71..0000000000 --- a/src/algorithms/sorting/bucket-sort/README.md +++ /dev/null @@ -1,35 +0,0 @@ -# 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 deleted file mode 100644 index 9cab525d9b..0000000000 --- a/src/algorithms/sorting/bucket-sort/__test__/BucketSort.test.js +++ /dev/null @@ -1,33 +0,0 @@ -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 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zmsvf_NJBhx*xw80mbRu3ZWep(g&`x;CmXPB3s3!hR842a=0_+a7=rmOV0G12D_F|} zW6>!TpM4nHWGK8V)RgKGHco!Buz8g8Yov^{nZ69Uy1zaP%f?Dqj%@>m9D2`oLxdZ% zX@G!+XEo2i-a%OdgkymnI1dIlRiBRH(0~701Dq)E?R-E$Ub8CG7g@xEKP>@Bipq)9 I2pI(aFLR8DQvd(} diff --git a/src/algorithms/sorting/counting-sort/CountingSort.js b/src/algorithms/sorting/counting-sort/CountingSort.js deleted file mode 100644 index 7e810dc525..0000000000 --- a/src/algorithms/sorting/counting-sort/CountingSort.js +++ /dev/null @@ -1,78 +0,0 @@ -import Sort from '../Sort'; - -export default class CountingSort extends Sort { - /** - * @param {number[]} originalArray - * @param {number} [smallestElement] - * @param {number} [biggestElement] - */ - sort(originalArray, smallestElement = undefined, biggestElement = undefined) { - // Init biggest and smallest elements in array in order to build number bucket array later. - let detectedSmallestElement = smallestElement || 0; - let detectedBiggestElement = biggestElement || 0; - - if (smallestElement === undefined || biggestElement === undefined) { - originalArray.forEach((element) => { - // Visit element. - this.callbacks.visitingCallback(element); - - // Detect biggest element. - if (this.comparator.greaterThan(element, detectedBiggestElement)) { - detectedBiggestElement = element; - } - - // Detect smallest element. - if (this.comparator.lessThan(element, detectedSmallestElement)) { - detectedSmallestElement = element; - } - }); - } - - // Init buckets array. - // This array will hold frequency of each number from originalArray. - const buckets = Array(detectedBiggestElement - detectedSmallestElement + 1).fill(0); - - originalArray.forEach((element) => { - // Visit element. - this.callbacks.visitingCallback(element); - - buckets[element - detectedSmallestElement] += 1; - }); - - // Add previous frequencies to the current one for each number in bucket - // to detect how many numbers less then current one should be standing to - // the left of current one. - for (let bucketIndex = 1; bucketIndex < buckets.length; bucketIndex += 1) { - buckets[bucketIndex] += buckets[bucketIndex - 1]; - } - - // Now let's shift frequencies to the right so that they show correct numbers. - // I.e. if we won't shift right than the value of buckets[5] will display how many - // elements less than 5 should be placed to the left of 5 in sorted array - // INCLUDING 5th. After shifting though this number will not include 5th anymore. - buckets.pop(); - buckets.unshift(0); - - // Now let's assemble sorted array. - const sortedArray = Array(originalArray.length).fill(null); - for (let elementIndex = 0; elementIndex < originalArray.length; elementIndex += 1) { - // Get the element that we want to put into correct sorted position. - const element = originalArray[elementIndex]; - - // Visit element. - this.callbacks.visitingCallback(element); - - // Get correct position of this element in sorted array. - const elementSortedPosition = buckets[element - detectedSmallestElement]; - - // Put element into correct position in sorted array. - sortedArray[elementSortedPosition] = element; - - // Increase position of current element in the bucket for future correct placements. - buckets[element - detectedSmallestElement] += 1; - } - - // Return sorted array. - return sortedArray; - } -} diff --git a/src/algorithms/sorting/counting-sort/README.md b/src/algorithms/sorting/counting-sort/README.md deleted file mode 100644 index 40a9539a22..0000000000 --- a/src/algorithms/sorting/counting-sort/README.md +++ /dev/null @@ -1,70 +0,0 @@ -# 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 -counting the number of objects that have each distinct key value, -and using arithmetic on those counts to determine the positions -of each key value in the output sequence. Its running time is -linear in the number of items and the difference between the -maximum and minimum key values, so it is only suitable for direct -use in situations where the variation in keys is not significantly -greater than the number of items. However, it is often used as a -subroutine in another sorting algorithm, radix sort, that can -handle larger keys more efficiently. - -Because counting sort uses key values as indexes into an array, -it is not a comparison sort, and the `Ω(n log n)` lower bound for -comparison sorting does not apply to it. Bucket sort may be used -for many of the same tasks as counting sort, with a similar time -analysis; however, compared to counting sort, bucket sort requires -linked lists, dynamic arrays or a large amount of preallocated -memory to hold the sets of items within each bucket, whereas -counting sort instead stores a single number (the count of items) -per bucket. - -Counting sorting works best when the range of numbers for each array -element is very small. - -## Algorithm - -**Step I** - -In first step we calculate the count of all the elements of the -input array `A`. Then Store the result in the count array `C`. -The way we count is depicted below. - -![Counting Sort](https://3.bp.blogspot.com/-jJchly1BkTc/WLGqCFDdvCI/AAAAAAAAAHA/luljAlz2ptMndIZNH0KLTTuQMNsfzDeFQCLcB/s1600/CSortUpdatedStepI.gif) - -**Step II** - -In second step we calculate how many elements exist in the input -array `A` which are less than or equals for the given index. -`Ci` = numbers of elements less than or equals to `i` in input array. - -![Counting Sort](https://1.bp.blogspot.com/-1vFu-VIRa9Y/WLHGuZkdF3I/AAAAAAAAAHs/8jKu2dbQee4ap9xlVcNsILrclqw0UxAVACLcB/s1600/Step-II.png) - -**Step III** - -In this step we place the input array `A` element at sorted -position by taking help of constructed count array `C` ,i.e what -we constructed in step two. We used the result array `B` to store -the sorted elements. Here we handled the index of `B` start from -zero. - -![Counting Sort](https://1.bp.blogspot.com/-xPqylngqASY/WLGq3p9n9vI/AAAAAAAAAHM/JHdtXAkJY8wYzDMBXxqarjmhpPhM0u8MACLcB/s1600/ResultArrayCS.gif) - -## Complexity - -| Name | Best | Average | Worst | Memory | Stable | Comments | -| --------------------- | :-------------: | :-----------------: | :-----------------: | :-------: | :-------: | :-------- | -| **Counting sort** | n + r | n + r | n + r | n + r | Yes | r - biggest number in array | - -## References - -- [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/counting-sort/README.pt-br.md b/src/algorithms/sorting/counting-sort/README.pt-br.md deleted file mode 100644 index af2c75f6af..0000000000 --- a/src/algorithms/sorting/counting-sort/README.pt-br.md +++ /dev/null @@ -1,70 +0,0 @@ -# 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/counting-sort/__test__/CountingSort.test.js b/src/algorithms/sorting/counting-sort/__test__/CountingSort.test.js deleted file mode 100644 index 9bf5d5c513..0000000000 --- a/src/algorithms/sorting/counting-sort/__test__/CountingSort.test.js +++ /dev/null @@ -1,74 +0,0 @@ -import CountingSort from '../CountingSort'; -import { - equalArr, - notSortedArr, - reverseArr, - sortedArr, - SortTester, -} from '../../SortTester'; - -// Complexity constants. -const SORTED_ARRAY_VISITING_COUNT = 60; -const NOT_SORTED_ARRAY_VISITING_COUNT = 60; -const REVERSE_SORTED_ARRAY_VISITING_COUNT = 60; -const EQUAL_ARRAY_VISITING_COUNT = 60; - -describe('CountingSort', () => { - it('should sort array', () => { - SortTester.testSort(CountingSort); - }); - - it('should sort negative numbers', () => { - SortTester.testNegativeNumbersSort(CountingSort); - }); - - it('should allow to use specify max/min integer value in array to make sorting faster', () => { - const visitingCallback = jest.fn(); - const sorter = new CountingSort({ visitingCallback }); - - // Detect biggest number in array in prior. - const biggestElement = Math.max(...notSortedArr); - - // Detect smallest number in array in prior. - const smallestElement = Math.min(...notSortedArr); - - const sortedArray = sorter.sort(notSortedArr, smallestElement, biggestElement); - - expect(sortedArray).toEqual(sortedArr); - // Normally visitingCallback is being called 60 times but in this case - // it should be called only 40 times. - expect(visitingCallback).toHaveBeenCalledTimes(40); - }); - - it('should visit EQUAL array element specified number of times', () => { - SortTester.testAlgorithmTimeComplexity( - CountingSort, - equalArr, - EQUAL_ARRAY_VISITING_COUNT, - ); - }); - - it('should visit SORTED array element specified number of times', () => { - SortTester.testAlgorithmTimeComplexity( - CountingSort, - sortedArr, - SORTED_ARRAY_VISITING_COUNT, - ); - }); - - it('should visit NOT SORTED array element specified number of times', () => { - SortTester.testAlgorithmTimeComplexity( - CountingSort, - notSortedArr, - NOT_SORTED_ARRAY_VISITING_COUNT, - ); - }); - - it('should visit REVERSE SORTED array element specified number of times', () => { - SortTester.testAlgorithmTimeComplexity( - CountingSort, - reverseArr, - REVERSE_SORTED_ARRAY_VISITING_COUNT, - ); - }); -}); diff --git a/src/algorithms/sorting/heap-sort/HeapSort.js b/src/algorithms/sorting/heap-sort/HeapSort.js deleted file mode 100644 index 06e58e1ef2..0000000000 --- a/src/algorithms/sorting/heap-sort/HeapSort.js +++ /dev/null @@ -1,30 +0,0 @@ -import Sort from '../Sort'; -import MinHeap from '../../../data-structures/heap/MinHeap'; - -export default class HeapSort extends Sort { - sort(originalArray) { - const sortedArray = []; - const minHeap = new MinHeap(this.callbacks.compareCallback); - - // Insert all array elements to the heap. - originalArray.forEach((element) => { - // Call visiting callback. - this.callbacks.visitingCallback(element); - - minHeap.add(element); - }); - - // Now we have min heap with minimal element always on top. - // Let's poll that minimal element one by one and thus form the sorted array. - while (!minHeap.isEmpty()) { - const nextMinElement = minHeap.poll(); - - // Call visiting callback. - this.callbacks.visitingCallback(nextMinElement); - - sortedArray.push(nextMinElement); - } - - return sortedArray; - } -} diff --git a/src/algorithms/sorting/heap-sort/README.md b/src/algorithms/sorting/heap-sort/README.md deleted file mode 100644 index 2370776f1b..0000000000 --- a/src/algorithms/sorting/heap-sort/README.md +++ /dev/null @@ -1,27 +0,0 @@ -# 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 -a sorted and an unsorted region, and it iteratively -shrinks the unsorted region by extracting the largest -element and moving that to the sorted region. The -improvement consists of the use of a heap data structure -rather than a linear-time search to find the maximum. - -![Algorithm Visualization](https://upload.wikimedia.org/wikipedia/commons/1/1b/Sorting_heapsort_anim.gif) - -![Algorithm Visualization](https://upload.wikimedia.org/wikipedia/commons/4/4d/Heapsort-example.gif) - -## Complexity - -| Name | Best | Average | Worst | Memory | Stable | Comments | -| --------------------- | :-------------: | :-----------------: | :-----------------: | :-------: | :-------: | :-------- | -| **Heap sort** | n log(n) | n log(n) | n log(n) | 1 | No | | - -## References - -[Wikipedia](https://en.wikipedia.org/wiki/Heapsort) diff --git a/src/algorithms/sorting/heap-sort/README.pt-BR.md b/src/algorithms/sorting/heap-sort/README.pt-BR.md deleted file mode 100644 index 6d5a2d4849..0000000000 --- a/src/algorithms/sorting/heap-sort/README.pt-BR.md +++ /dev/null @@ -1,20 +0,0 @@ -# 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 log(n) | n log(n) | n log(n) | 1 | Não | | - -## Referências - -[Wikipedia](https://en.wikipedia.org/wiki/Heapsort) diff --git a/src/algorithms/sorting/heap-sort/__test__/HeapSort.test.js b/src/algorithms/sorting/heap-sort/__test__/HeapSort.test.js deleted file mode 100644 index 75f690d438..0000000000 --- a/src/algorithms/sorting/heap-sort/__test__/HeapSort.test.js +++ /dev/null @@ -1,62 +0,0 @@ -import HeapSort from '../HeapSort'; -import { - equalArr, - notSortedArr, - reverseArr, - sortedArr, - SortTester, -} from '../../SortTester'; - -// Complexity constants. -// These numbers don't take into account up/dow heapifying of the heap. -// Thus these numbers are higher in reality. -const SORTED_ARRAY_VISITING_COUNT = 40; -const NOT_SORTED_ARRAY_VISITING_COUNT = 40; -const REVERSE_SORTED_ARRAY_VISITING_COUNT = 40; -const EQUAL_ARRAY_VISITING_COUNT = 40; - -describe('HeapSort', () => { - it('should sort array', () => { - SortTester.testSort(HeapSort); - }); - - it('should sort array with custom comparator', () => { - SortTester.testSortWithCustomComparator(HeapSort); - }); - - it('should sort negative numbers', () => { - SortTester.testNegativeNumbersSort(HeapSort); - }); - - it('should visit EQUAL array element specified number of times', () => { - SortTester.testAlgorithmTimeComplexity( - HeapSort, - equalArr, - EQUAL_ARRAY_VISITING_COUNT, - ); - }); - - it('should visit SORTED array element specified number of times', () => { - SortTester.testAlgorithmTimeComplexity( - HeapSort, - sortedArr, - SORTED_ARRAY_VISITING_COUNT, - ); - }); - - it('should visit NOT SORTED array element specified number of times', () => { - SortTester.testAlgorithmTimeComplexity( - HeapSort, - notSortedArr, - NOT_SORTED_ARRAY_VISITING_COUNT, - ); - }); - - it('should visit REVERSE SORTED array element specified number of times', () => { - SortTester.testAlgorithmTimeComplexity( - HeapSort, - reverseArr, - REVERSE_SORTED_ARRAY_VISITING_COUNT, - ); - }); -}); diff --git a/src/algorithms/sorting/insertion-sort/InsertionSort.js b/src/algorithms/sorting/insertion-sort/InsertionSort.js deleted file mode 100644 index 7a80161379..0000000000 --- a/src/algorithms/sorting/insertion-sort/InsertionSort.js +++ /dev/null @@ -1,39 +0,0 @@ -import Sort from '../Sort'; - -export default class InsertionSort extends Sort { - sort(originalArray) { - const array = [...originalArray]; - - // Go through all array elements... - for (let i = 1; i < array.length; i += 1) { - let currentIndex = i; - - // Call visiting callback. - this.callbacks.visitingCallback(array[i]); - - // 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]) - ) { - // Call visiting callback. - this.callbacks.visitingCallback(array[currentIndex - 1]); - - // Swap the elements. - [ - array[currentIndex - 1], - array[currentIndex], - ] = [ - array[currentIndex], - array[currentIndex - 1], - ]; - - // Shift current index left. - currentIndex -= 1; - } - } - - return array; - } -} diff --git a/src/algorithms/sorting/insertion-sort/README.md b/src/algorithms/sorting/insertion-sort/README.md deleted file mode 100644 index 8bc922683f..0000000000 --- a/src/algorithms/sorting/insertion-sort/README.md +++ /dev/null @@ -1,24 +0,0 @@ -# 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 -advanced algorithms such as quicksort, heapsort, or merge -sort. - -![Algorithm Visualization](https://upload.wikimedia.org/wikipedia/commons/4/42/Insertion_sort.gif) - -![Algorithm Visualization](https://upload.wikimedia.org/wikipedia/commons/0/0f/Insertion-sort-example-300px.gif) - -## Complexity - -| Name | Best | Average | Worst | Memory | Stable | Comments | -| --------------------- | :-------------: | :-----------------: | :-----------------: | :-------: | :-------: | :-------- | -| **Insertion sort** | n | n2 | n2 | 1 | Yes | | - -## References - -[Wikipedia](https://en.wikipedia.org/wiki/Insertion_sort) diff --git a/src/algorithms/sorting/insertion-sort/README.pt-BR.md b/src/algorithms/sorting/insertion-sort/README.pt-BR.md deleted file mode 100644 index a36d2742be..0000000000 --- a/src/algorithms/sorting/insertion-sort/README.pt-BR.md +++ /dev/null @@ -1,22 +0,0 @@ -# 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 | n2 | n2 | 1 | Sim | | - -## Referências - -[Wikipedia](https://en.wikipedia.org/wiki/Insertion_sort) diff --git a/src/algorithms/sorting/insertion-sort/__test__/InsertionSort.test.js b/src/algorithms/sorting/insertion-sort/__test__/InsertionSort.test.js deleted file mode 100644 index 8453b7db16..0000000000 --- a/src/algorithms/sorting/insertion-sort/__test__/InsertionSort.test.js +++ /dev/null @@ -1,64 +0,0 @@ -import InsertionSort from '../InsertionSort'; -import { - equalArr, - notSortedArr, - reverseArr, - sortedArr, - SortTester, -} from '../../SortTester'; - -// Complexity constants. -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', () => { - SortTester.testSort(InsertionSort); - }); - - it('should sort array with custom comparator', () => { - SortTester.testSortWithCustomComparator(InsertionSort); - }); - - it('should do stable sorting', () => { - SortTester.testSortStability(InsertionSort); - }); - - it('should sort negative numbers', () => { - SortTester.testNegativeNumbersSort(InsertionSort); - }); - - it('should visit EQUAL array element specified number of times', () => { - SortTester.testAlgorithmTimeComplexity( - InsertionSort, - equalArr, - EQUAL_ARRAY_VISITING_COUNT, - ); - }); - - it('should visit SORTED array element specified number of times', () => { - SortTester.testAlgorithmTimeComplexity( - InsertionSort, - sortedArr, - SORTED_ARRAY_VISITING_COUNT, - ); - }); - - it('should visit NOT SORTED array element specified number of times', () => { - SortTester.testAlgorithmTimeComplexity( - InsertionSort, - notSortedArr, - NOT_SORTED_ARRAY_VISITING_COUNT, - ); - }); - - it('should visit REVERSE SORTED array element specified number of times', () => { - SortTester.testAlgorithmTimeComplexity( - InsertionSort, - reverseArr, - REVERSE_SORTED_ARRAY_VISITING_COUNT, - ); - }); -}); diff --git a/src/algorithms/sorting/merge-sort/MergeSort.js b/src/algorithms/sorting/merge-sort/MergeSort.js deleted file mode 100644 index 23fca74e49..0000000000 --- a/src/algorithms/sorting/merge-sort/MergeSort.js +++ /dev/null @@ -1,60 +0,0 @@ -import Sort from '../Sort'; - -export default class MergeSort extends Sort { - sort(originalArray) { - // Call visiting callback. - this.callbacks.visitingCallback(null); - - // If array is empty or consists of one element then return this array since it is sorted. - if (originalArray.length <= 1) { - return originalArray; - } - - // Split array on two halves. - const middleIndex = Math.floor(originalArray.length / 2); - const leftArray = originalArray.slice(0, middleIndex); - const rightArray = originalArray.slice(middleIndex, originalArray.length); - - // Sort two halves of split array - const leftSortedArray = this.sort(leftArray); - const rightSortedArray = this.sort(rightArray); - - // Merge two sorted arrays into one. - return this.mergeSortedArrays(leftSortedArray, rightSortedArray); - } - - mergeSortedArrays(leftArray, rightArray) { - const sortedArray = []; - - // Use array pointers to exclude old elements after they have been added to the sorted array. - let leftIndex = 0; - let rightIndex = 0; - - while (leftIndex < leftArray.length && rightIndex < rightArray.length) { - let minElement = null; - - // Find the minimum element between the left and right array. - if (this.comparator.lessThanOrEqual(leftArray[leftIndex], rightArray[rightIndex])) { - minElement = leftArray[leftIndex]; - // Increment index pointer to the right - leftIndex += 1; - } else { - minElement = rightArray[rightIndex]; - // Increment index pointer to the right - rightIndex += 1; - } - - // Add the minimum element to the sorted array. - sortedArray.push(minElement); - - // Call visiting callback. - this.callbacks.visitingCallback(minElement); - } - - // There will be elements remaining from either the left OR the right - // Concatenate the remaining elements into the sorted array - return sortedArray - .concat(leftArray.slice(leftIndex)) - .concat(rightArray.slice(rightIndex)); - } -} diff --git a/src/algorithms/sorting/merge-sort/README.ko-KR.md b/src/algorithms/sorting/merge-sort/README.ko-KR.md deleted file mode 100644 index 5447fd217e..0000000000 --- a/src/algorithms/sorting/merge-sort/README.ko-KR.md +++ /dev/null @@ -1,22 +0,0 @@ -# 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 log(n) | n log(n) | n 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 deleted file mode 100644 index 2931329482..0000000000 --- a/src/algorithms/sorting/merge-sort/README.md +++ /dev/null @@ -1,38 +0,0 @@ -# Merge Sort - -_Read this in other languages:_ -[_한국어_](README.ko-KR.md), -[_Português_](README.pt-BR.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 -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 -emulate merge sort (top-down). - -![Merge Sort](https://upload.wikimedia.org/wikipedia/commons/e/e6/Merge_sort_algorithm_diagram.svg) - -## Complexity - -| Name | Best | Average | Worst | Memory | Stable | Comments | -| --------------------- | :-------------: | :-----------------: | :-----------------: | :-------: | :-------: | :-------- | -| **Merge sort** | n log(n) | n log(n) | n log(n) | n | Yes | | - -## References - -- [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.pt-BR.md b/src/algorithms/sorting/merge-sort/README.pt-BR.md deleted file mode 100644 index f7be449f04..0000000000 --- a/src/algorithms/sorting/merge-sort/README.pt-BR.md +++ /dev/null @@ -1,38 +0,0 @@ -# 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 log(n) | n log(n) | n 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/merge-sort/__test__/MergeSort.test.js b/src/algorithms/sorting/merge-sort/__test__/MergeSort.test.js deleted file mode 100644 index 0112003bb8..0000000000 --- a/src/algorithms/sorting/merge-sort/__test__/MergeSort.test.js +++ /dev/null @@ -1,64 +0,0 @@ -import MergeSort from '../MergeSort'; -import { - equalArr, - notSortedArr, - reverseArr, - sortedArr, - SortTester, -} from '../../SortTester'; - -// Complexity constants. -const SORTED_ARRAY_VISITING_COUNT = 79; -const NOT_SORTED_ARRAY_VISITING_COUNT = 102; -const REVERSE_SORTED_ARRAY_VISITING_COUNT = 87; -const EQUAL_ARRAY_VISITING_COUNT = 79; - -describe('MergeSort', () => { - it('should sort array', () => { - SortTester.testSort(MergeSort); - }); - - it('should sort array with custom comparator', () => { - SortTester.testSortWithCustomComparator(MergeSort); - }); - - it('should do stable sorting', () => { - SortTester.testSortStability(MergeSort); - }); - - it('should sort negative numbers', () => { - SortTester.testNegativeNumbersSort(MergeSort); - }); - - it('should visit EQUAL array element specified number of times', () => { - SortTester.testAlgorithmTimeComplexity( - MergeSort, - equalArr, - EQUAL_ARRAY_VISITING_COUNT, - ); - }); - - it('should visit SORTED array element specified number of times', () => { - SortTester.testAlgorithmTimeComplexity( - MergeSort, - sortedArr, - SORTED_ARRAY_VISITING_COUNT, - ); - }); - - it('should visit NOT SORTED array element specified number of times', () => { - SortTester.testAlgorithmTimeComplexity( - MergeSort, - notSortedArr, - NOT_SORTED_ARRAY_VISITING_COUNT, - ); - }); - - it('should visit REVERSE SORTED array element specified number of times', () => { - SortTester.testAlgorithmTimeComplexity( - MergeSort, - reverseArr, - REVERSE_SORTED_ARRAY_VISITING_COUNT, - ); - }); -}); diff --git a/src/algorithms/sorting/quick-sort/QuickSort.js b/src/algorithms/sorting/quick-sort/QuickSort.js deleted file mode 100644 index 1c63c86e8b..0000000000 --- a/src/algorithms/sorting/quick-sort/QuickSort.js +++ /dev/null @@ -1,48 +0,0 @@ -import Sort from '../Sort'; - -export default class QuickSort extends Sort { - /** - * @param {*[]} originalArray - * @return {*[]} - */ - sort(originalArray) { - // Clone original array to prevent it from modification. - const array = [...originalArray]; - - // If array has less than or equal to one elements then it is already sorted. - if (array.length <= 1) { - return array; - } - - // Init left and right arrays. - const leftArray = []; - const rightArray = []; - - // Take the first element of array as a pivot. - const pivotElement = array.shift(); - const centerArray = [pivotElement]; - - // Split all array elements between left, center and right arrays. - while (array.length) { - const currentElement = array.shift(); - - // Call visiting callback. - this.callbacks.visitingCallback(currentElement); - - if (this.comparator.equal(currentElement, pivotElement)) { - centerArray.push(currentElement); - } else if (this.comparator.lessThan(currentElement, pivotElement)) { - leftArray.push(currentElement); - } else { - rightArray.push(currentElement); - } - } - - // Sort left and right arrays. - const leftArraySorted = this.sort(leftArray); - const rightArraySorted = this.sort(rightArray); - - // Let's now join sorted left array with center array and with sorted right array. - return leftArraySorted.concat(centerArray, rightArraySorted); - } -} diff --git a/src/algorithms/sorting/quick-sort/QuickSortInPlace.js b/src/algorithms/sorting/quick-sort/QuickSortInPlace.js deleted file mode 100644 index d02298b230..0000000000 --- a/src/algorithms/sorting/quick-sort/QuickSortInPlace.js +++ /dev/null @@ -1,78 +0,0 @@ -import Sort from '../Sort'; - -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: https://www.hackerearth.com/practice/algorithms/sorting/quick-sort/visualize/ - * - * @param {*[]} originalArray - Not sorted array. - * @param {number} inputLowIndex - * @param {number} inputHighIndex - * @param {boolean} recursiveCall - * @return {*[]} - Sorted array. - */ - sort( - originalArray, - inputLowIndex = 0, - inputHighIndex = originalArray.length - 1, - recursiveCall = false, - ) { - // Copies array on initial call, and then sorts in place. - const array = recursiveCall ? originalArray : [...originalArray]; - - /** - * The partitionArray() operates on the subarray between lowIndex and highIndex, inclusive. - * It arbitrarily chooses the last element in the subarray as the pivot. - * Then, it partially sorts the subarray into elements than are less than the pivot, - * and elements that are greater than or equal to the pivot. - * Each time partitionArray() is executed, the pivot element is in its final sorted position. - * - * @param {number} lowIndex - * @param {number} highIndex - * @return {number} - */ - const partitionArray = (lowIndex, highIndex) => { - /** - * Swaps two elements in array. - * @param {number} leftIndex - * @param {number} rightIndex - */ - const swap = (leftIndex, rightIndex) => { - const temp = array[leftIndex]; - array[leftIndex] = array[rightIndex]; - array[rightIndex] = temp; - }; - - const pivot = array[highIndex]; - // visitingCallback is used for time-complexity analysis. - this.callbacks.visitingCallback(pivot); - - let partitionIndex = lowIndex; - for (let currentIndex = lowIndex; currentIndex < highIndex; currentIndex += 1) { - if (this.comparator.lessThan(array[currentIndex], pivot)) { - swap(partitionIndex, currentIndex); - partitionIndex += 1; - } - } - - // The element at the partitionIndex is guaranteed to be greater than or equal to pivot. - // All elements to the left of partitionIndex are guaranteed to be less than pivot. - // Swapping the pivot with the partitionIndex therefore places the pivot in its - // final sorted position. - swap(partitionIndex, highIndex); - - return partitionIndex; - }; - - // Base case is when low and high converge. - if (inputLowIndex < inputHighIndex) { - const partitionIndex = partitionArray(inputLowIndex, inputHighIndex); - const RECURSIVE_CALL = true; - this.sort(array, inputLowIndex, partitionIndex - 1, RECURSIVE_CALL); - this.sort(array, partitionIndex + 1, inputHighIndex, RECURSIVE_CALL); - } - - return array; - } -} diff --git a/src/algorithms/sorting/quick-sort/README.md b/src/algorithms/sorting/quick-sort/README.md deleted file mode 100644 index 9dcec0f12f..0000000000 --- a/src/algorithms/sorting/quick-sort/README.md +++ /dev/null @@ -1,39 +0,0 @@ -# Quicksort - -_Read this in other languages:_ -[_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 -sub-arrays: the low elements and the high elements. -Quicksort can then recursively sort the sub-arrays - -The steps are: - -1. Pick an element, called a pivot, from the array. -2. Partitioning: reorder the array so that all elements with -values less than the pivot come before the pivot, while all -elements with values greater than the pivot come after it -(equal values can go either way). After this partitioning, -the pivot is in its final position. This is called the -partition operation. -3. Recursively apply the above steps to the sub-array of -elements with smaller values and separately to the -sub-array of elements with greater values. - -Animated visualization of the quicksort algorithm. -The horizontal lines are pivot values. - -![Quicksort](https://upload.wikimedia.org/wikipedia/commons/6/6a/Sorting_quicksort_anim.gif) - -## Complexity - -| Name | Best | Average | Worst | Memory | Stable | Comments | -| --------------------- | :-------------: | :-----------------: | :-----------------: | :-------: | :-------: | :-------- | -| **Quick sort** | n log(n) | n log(n) | n2 | log(n) | No | Quicksort is usually done in-place with O(log(n)) stack space | - -## References - -- [Wikipedia](https://en.wikipedia.org/wiki/Quicksort) -- [YouTube](https://www.youtube.com/watch?v=SLauY6PpjW4&index=28&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8) diff --git a/src/algorithms/sorting/quick-sort/README.pt-BR.md b/src/algorithms/sorting/quick-sort/README.pt-BR.md deleted file mode 100644 index ca3a45699f..0000000000 --- a/src/algorithms/sorting/quick-sort/README.pt-BR.md +++ /dev/null @@ -1,39 +0,0 @@ -# Quicksort - -_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. - -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 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 -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 log(n) | n log(n) | n2 | log(n) | Não | 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) diff --git a/src/algorithms/sorting/quick-sort/README.zh-CN.md b/src/algorithms/sorting/quick-sort/README.zh-CN.md deleted file mode 100644 index 96b2e44de8..0000000000 --- a/src/algorithms/sorting/quick-sort/README.zh-CN.md +++ /dev/null @@ -1,27 +0,0 @@ -# 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 log(n) | n log(n) | n2 | 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) diff --git a/src/algorithms/sorting/quick-sort/__test__/QuickSort.test.js b/src/algorithms/sorting/quick-sort/__test__/QuickSort.test.js deleted file mode 100644 index 71c1fe71e0..0000000000 --- a/src/algorithms/sorting/quick-sort/__test__/QuickSort.test.js +++ /dev/null @@ -1,64 +0,0 @@ -import QuickSort from '../QuickSort'; -import { - equalArr, - notSortedArr, - reverseArr, - sortedArr, - SortTester, -} from '../../SortTester'; - -// Complexity constants. -const SORTED_ARRAY_VISITING_COUNT = 190; -const NOT_SORTED_ARRAY_VISITING_COUNT = 62; -const REVERSE_SORTED_ARRAY_VISITING_COUNT = 190; -const EQUAL_ARRAY_VISITING_COUNT = 19; - -describe('QuickSort', () => { - it('should sort array', () => { - SortTester.testSort(QuickSort); - }); - - it('should sort array with custom comparator', () => { - SortTester.testSortWithCustomComparator(QuickSort); - }); - - it('should do stable sorting', () => { - SortTester.testSortStability(QuickSort); - }); - - it('should sort negative numbers', () => { - SortTester.testNegativeNumbersSort(QuickSort); - }); - - it('should visit EQUAL array element specified number of times', () => { - SortTester.testAlgorithmTimeComplexity( - QuickSort, - equalArr, - EQUAL_ARRAY_VISITING_COUNT, - ); - }); - - it('should visit SORTED array element specified number of times', () => { - SortTester.testAlgorithmTimeComplexity( - QuickSort, - sortedArr, - SORTED_ARRAY_VISITING_COUNT, - ); - }); - - it('should visit NOT SORTED array element specified number of times', () => { - SortTester.testAlgorithmTimeComplexity( - QuickSort, - notSortedArr, - NOT_SORTED_ARRAY_VISITING_COUNT, - ); - }); - - it('should visit REVERSE SORTED array element specified number of times', () => { - SortTester.testAlgorithmTimeComplexity( - QuickSort, - reverseArr, - REVERSE_SORTED_ARRAY_VISITING_COUNT, - ); - }); -}); diff --git a/src/algorithms/sorting/quick-sort/__test__/QuickSortInPlace.test.js b/src/algorithms/sorting/quick-sort/__test__/QuickSortInPlace.test.js deleted file mode 100644 index 0e103f2ef2..0000000000 --- a/src/algorithms/sorting/quick-sort/__test__/QuickSortInPlace.test.js +++ /dev/null @@ -1,60 +0,0 @@ -import QuickSortInPlace from '../QuickSortInPlace'; -import { - equalArr, - notSortedArr, - reverseArr, - sortedArr, - SortTester, -} from '../../SortTester'; - -// Complexity constants. -const SORTED_ARRAY_VISITING_COUNT = 19; -const NOT_SORTED_ARRAY_VISITING_COUNT = 12; -const REVERSE_SORTED_ARRAY_VISITING_COUNT = 19; -const EQUAL_ARRAY_VISITING_COUNT = 19; - -describe('QuickSortInPlace', () => { - it('should sort array', () => { - SortTester.testSort(QuickSortInPlace); - }); - - it('should sort array with custom comparator', () => { - SortTester.testSortWithCustomComparator(QuickSortInPlace); - }); - - it('should sort negative numbers', () => { - SortTester.testNegativeNumbersSort(QuickSortInPlace); - }); - - it('should visit EQUAL array element specified number of times', () => { - SortTester.testAlgorithmTimeComplexity( - QuickSortInPlace, - equalArr, - EQUAL_ARRAY_VISITING_COUNT, - ); - }); - - it('should visit SORTED array element specified number of times', () => { - SortTester.testAlgorithmTimeComplexity( - QuickSortInPlace, - sortedArr, - SORTED_ARRAY_VISITING_COUNT, - ); - }); - - it('should visit NOT SORTED array element specified number of times', () => { - SortTester.testAlgorithmTimeComplexity( - QuickSortInPlace, - notSortedArr, - NOT_SORTED_ARRAY_VISITING_COUNT, - ); - }); - - it('should visit REVERSE SORTED array element specified number of times', () => { - SortTester.testAlgorithmTimeComplexity( - QuickSortInPlace, - reverseArr, - REVERSE_SORTED_ARRAY_VISITING_COUNT, - ); - }); -}); diff --git a/src/algorithms/sorting/radix-sort/README.md b/src/algorithms/sorting/radix-sort/README.md deleted file mode 100644 index 108d7d19b6..0000000000 --- a/src/algorithms/sorting/radix-sort/README.md +++ /dev/null @@ -1,48 +0,0 @@ -# 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 -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 -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 -comparison-based sorts (and worse if keys are much longer than `log n`). - -![Radix Sort](./images/radix-sort.png) - -## Complexity - -| Name | Best | Average | Worst | Memory | Stable | Comments | -| --------------------- | :-------------: | :-----------------: | :-----------------: | :-------: | :-------: | :-------- | -| **Radix sort** | n * k | n * k | n * k | n + k | Yes | k - length of longest key | - -## References - -- [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/radix-sort/README.pt-BR.md b/src/algorithms/sorting/radix-sort/README.pt-BR.md deleted file mode 100644 index 2274440984..0000000000 --- a/src/algorithms/sorting/radix-sort/README.pt-BR.md +++ /dev/null @@ -1,48 +0,0 @@ -# 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/radix-sort/RadixSort.js b/src/algorithms/sorting/radix-sort/RadixSort.js deleted file mode 100644 index 8e8dccfb0d..0000000000 --- a/src/algorithms/sorting/radix-sort/RadixSort.js +++ /dev/null @@ -1,152 +0,0 @@ -import Sort from '../Sort'; - -// Using charCode (a = 97, b = 98, etc), we can map characters to buckets from 0 - 25 -const BASE_CHAR_CODE = 97; -const NUMBER_OF_POSSIBLE_DIGITS = 10; -const ENGLISH_ALPHABET_LENGTH = 26; - -export default class RadixSort extends Sort { - /** - * @param {*[]} originalArray - * @return {*[]} - */ - sort(originalArray) { - // Assumes all elements of array are of the same type - const isArrayOfNumbers = this.isArrayOfNumbers(originalArray); - - let sortedArray = [...originalArray]; - const numPasses = this.determineNumPasses(sortedArray); - - for (let currentIndex = 0; currentIndex < numPasses; currentIndex += 1) { - const buckets = isArrayOfNumbers - ? this.placeElementsInNumberBuckets(sortedArray, currentIndex) - : this.placeElementsInCharacterBuckets(sortedArray, currentIndex, numPasses); - - // Flatten buckets into sortedArray, and repeat at next index - sortedArray = buckets.reduce((acc, val) => { - return [...acc, ...val]; - }, []); - } - - return sortedArray; - } - - /** - * @param {*[]} array - * @param {number} index - * @return {*[]} - */ - placeElementsInNumberBuckets(array, index) { - // See below. These are used to determine which digit to use for bucket allocation - const modded = 10 ** (index + 1); - const divided = 10 ** index; - const buckets = this.createBuckets(NUMBER_OF_POSSIBLE_DIGITS); - - array.forEach((element) => { - this.callbacks.visitingCallback(element); - if (element < divided) { - buckets[0].push(element); - } else { - /** - * Say we have element of 1,052 and are currently on index 1 (starting from 0). This means - * we want to use '5' as the bucket. `modded` would be 10 ** (1 + 1), which - * is 100. So we take 1,052 % 100 (52) and divide it by 10 (5.2) and floor it (5). - */ - const currentDigit = Math.floor((element % modded) / divided); - buckets[currentDigit].push(element); - } - }); - - return buckets; - } - - /** - * @param {*[]} array - * @param {number} index - * @param {number} numPasses - * @return {*[]} - */ - placeElementsInCharacterBuckets(array, index, numPasses) { - const buckets = this.createBuckets(ENGLISH_ALPHABET_LENGTH); - - array.forEach((element) => { - this.callbacks.visitingCallback(element); - const currentBucket = this.getCharCodeOfElementAtIndex(element, index, numPasses); - buckets[currentBucket].push(element); - }); - - return buckets; - } - - /** - * @param {string} element - * @param {number} index - * @param {number} numPasses - * @return {number} - */ - getCharCodeOfElementAtIndex(element, index, numPasses) { - // Place element in last bucket if not ready to organize - if ((numPasses - index) > element.length) { - return ENGLISH_ALPHABET_LENGTH - 1; - } - - /** - * If each character has been organized, use first character to determine bucket, - * otherwise iterate backwards through element - */ - const charPos = index > element.length - 1 ? 0 : element.length - index - 1; - - return element.toLowerCase().charCodeAt(charPos) - BASE_CHAR_CODE; - } - - /** - * Number of passes is determined by the length of the longest element in the array. - * For integers, this log10(num), and for strings, this would be the length of the string. - */ - determineNumPasses(array) { - return this.getLengthOfLongestElement(array); - } - - /** - * @param {*[]} array - * @return {number} - */ - getLengthOfLongestElement(array) { - if (this.isArrayOfNumbers(array)) { - return Math.floor(Math.log10(Math.max(...array))) + 1; - } - - return array.reduce((acc, val) => { - return val.length > acc ? val.length : acc; - }, -Infinity); - } - - /** - * @param {*[]} array - * @return {boolean} - */ - isArrayOfNumbers(array) { - // Assumes all elements of array are of the same type - return this.isNumber(array[0]); - } - - /** - * @param {number} numBuckets - * @return {*[]} - */ - createBuckets(numBuckets) { - /** - * Mapping buckets to an array instead of filling them with - * an array prevents each bucket from containing a reference to the same array - */ - return new Array(numBuckets).fill(null).map(() => []); - } - - /** - * @param {*} element - * @return {boolean} - */ - isNumber(element) { - return Number.isInteger(element); - } -} diff --git a/src/algorithms/sorting/radix-sort/__test__/RadixSort.test.js b/src/algorithms/sorting/radix-sort/__test__/RadixSort.test.js deleted file mode 100644 index ece713609d..0000000000 --- a/src/algorithms/sorting/radix-sort/__test__/RadixSort.test.js +++ /dev/null @@ -1,27 +0,0 @@ -import RadixSort from '../RadixSort'; -import { SortTester } from '../../SortTester'; - -// Complexity constants. -const ARRAY_OF_STRINGS_VISIT_COUNT = 24; -const ARRAY_OF_INTEGERS_VISIT_COUNT = 77; -describe('RadixSort', () => { - it('should sort array', () => { - SortTester.testSort(RadixSort); - }); - - it('should visit array of strings n (number of strings) x m (length of longest element) times', () => { - SortTester.testAlgorithmTimeComplexity( - RadixSort, - ['zzz', 'bb', 'a', 'rr', 'rrb', 'rrba'], - ARRAY_OF_STRINGS_VISIT_COUNT, - ); - }); - - it('should visit array of integers n (number of elements) x m (length of longest integer) times', () => { - SortTester.testAlgorithmTimeComplexity( - RadixSort, - [3, 1, 75, 32, 884, 523, 4343456, 232, 123, 656, 343], - ARRAY_OF_INTEGERS_VISIT_COUNT, - ); - }); -}); diff --git a/src/algorithms/sorting/radix-sort/images/radix-sort.png b/src/algorithms/sorting/radix-sort/images/radix-sort.png deleted file mode 100644 index 0cf9bf9e4de3c8799b0d8949cb6ea059b3b489dc..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 12619 zcmcJ0XF$_Wvu;A~y*KHhN)-sb1f>QLr79f)QiOmMDTWTxtCY|b0SmqNDg=ShCDNpX 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It has O(n2) time complexity, -making it inefficient on large lists, and generally -performs worse than the similar insertion sort. -Selection sort is noted for its simplicity, and it has -performance advantages over more complicated algorithms -in certain situations, particularly where auxiliary -memory is limited. - -![Algorithm Visualization](https://upload.wikimedia.org/wikipedia/commons/b/b0/Selection_sort_animation.gif) - -![Algorithm Visualization](https://upload.wikimedia.org/wikipedia/commons/9/94/Selection-Sort-Animation.gif) - -## Complexity - -| Name | Best | Average | Worst | Memory | Stable | Comments | -| --------------------- | :-------------: | :-----------------: | :-----------------: | :-------: | :-------: | :-------- | -| **Selection sort** | n2 | n2 | n2 | 1 | No | | - -## References - -[Wikipedia](https://en.wikipedia.org/wiki/Selection_sort) diff --git a/src/algorithms/sorting/selection-sort/README.pt-BR.md b/src/algorithms/sorting/selection-sort/README.pt-BR.md deleted file mode 100644 index 0c45b73f61..0000000000 --- a/src/algorithms/sorting/selection-sort/README.pt-BR.md +++ /dev/null @@ -1,20 +0,0 @@ -# Selection Sort - -_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. - -![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** | n2 | n2 | n2 | 1 | Não | | - -## Referências - -[Wikipedia](https://en.wikipedia.org/wiki/Selection_sort) diff --git a/src/algorithms/sorting/selection-sort/SelectionSort.js b/src/algorithms/sorting/selection-sort/SelectionSort.js deleted file mode 100644 index fa4a720b2f..0000000000 --- a/src/algorithms/sorting/selection-sort/SelectionSort.js +++ /dev/null @@ -1,32 +0,0 @@ -import Sort from '../Sort'; - -export default class SelectionSort extends Sort { - sort(originalArray) { - // Clone original array to prevent its modification. - const array = [...originalArray]; - - for (let i = 0; i < array.length - 1; i += 1) { - let minIndex = i; - - // Call visiting callback. - this.callbacks.visitingCallback(array[i]); - - // Find minimum element in the rest of array. - for (let j = i + 1; j < array.length; j += 1) { - // Call visiting callback. - this.callbacks.visitingCallback(array[j]); - - if (this.comparator.lessThan(array[j], array[minIndex])) { - minIndex = j; - } - } - - // If new minimum element has been found then swap it with current i-th element. - if (minIndex !== i) { - [array[i], array[minIndex]] = [array[minIndex], array[i]]; - } - } - - return array; - } -} diff --git a/src/algorithms/sorting/selection-sort/__test__/SelectionSort.test.js b/src/algorithms/sorting/selection-sort/__test__/SelectionSort.test.js deleted file mode 100644 index d52385d132..0000000000 --- a/src/algorithms/sorting/selection-sort/__test__/SelectionSort.test.js +++ /dev/null @@ -1,60 +0,0 @@ -import SelectionSort from '../SelectionSort'; -import { - equalArr, - notSortedArr, - reverseArr, - sortedArr, - SortTester, -} from '../../SortTester'; - -// Complexity constants. -const SORTED_ARRAY_VISITING_COUNT = 209; -const NOT_SORTED_ARRAY_VISITING_COUNT = 209; -const REVERSE_SORTED_ARRAY_VISITING_COUNT = 209; -const EQUAL_ARRAY_VISITING_COUNT = 209; - -describe('SelectionSort', () => { - it('should sort array', () => { - SortTester.testSort(SelectionSort); - }); - - it('should sort array with custom comparator', () => { - SortTester.testSortWithCustomComparator(SelectionSort); - }); - - it('should sort negative numbers', () => { - SortTester.testNegativeNumbersSort(SelectionSort); - }); - - it('should visit EQUAL array element specified number of times', () => { - SortTester.testAlgorithmTimeComplexity( - SelectionSort, - equalArr, - EQUAL_ARRAY_VISITING_COUNT, - ); - }); - - it('should visit SORTED array element specified number of times', () => { - SortTester.testAlgorithmTimeComplexity( - SelectionSort, - sortedArr, - SORTED_ARRAY_VISITING_COUNT, - ); - }); - - it('should visit NOT SORTED array element specified number of times', () => { - SortTester.testAlgorithmTimeComplexity( - SelectionSort, - notSortedArr, - NOT_SORTED_ARRAY_VISITING_COUNT, - ); - }); - - it('should visit REVERSE SORTED array element specified number of times', () => { - SortTester.testAlgorithmTimeComplexity( - SelectionSort, - reverseArr, - REVERSE_SORTED_ARRAY_VISITING_COUNT, - ); - }); -}); diff --git a/src/algorithms/sorting/shell-sort/README.md b/src/algorithms/sorting/shell-sort/README.md deleted file mode 100644 index f93338e2eb..0000000000 --- a/src/algorithms/sorting/shell-sort/README.md +++ /dev/null @@ -1,60 +0,0 @@ -# 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 -by insertion (insertion sort). The method starts by sorting -pairs of elements far apart from each other, then progressively -reducing the gap between elements to be compared. Starting -with far apart elements, it can move some out-of-place -elements into position faster than a simple nearest neighbor -exchange - -![Shellsort](https://upload.wikimedia.org/wikipedia/commons/d/d8/Sorting_shellsort_anim.gif) - -## How Shell Sort Works - -For our example and ease of understanding, we take the interval -of `4`. Make a virtual sub-list of all values located at the -interval of 4 positions. Here these values are -`{35, 14}`, `{33, 19}`, `{42, 27}` and `{10, 44}` - -![Shellsort](https://www.tutorialspoint.com/data_structures_algorithms/images/shell_sort_gap_4.jpg) - -We compare values in each sub-list and swap them (if necessary) -in the original array. After this step, the new array should -look like this - -![Shellsort](https://www.tutorialspoint.com/data_structures_algorithms/images/shell_sort_step_1.jpg) - -Then, we take interval of 2 and this gap generates two sub-lists -- `{14, 27, 35, 42}`, `{19, 10, 33, 44}` - -![Shellsort](https://www.tutorialspoint.com/data_structures_algorithms/images/shell_sort_gap_2.jpg) - -We compare and swap the values, if required, in the original array. -After this step, the array should look like this - -![Shellsort](https://www.tutorialspoint.com/data_structures_algorithms/images/shell_sort_step_2.jpg) - -> UPD: On the picture below there is a typo and result array is supposed to be `[14, 10, 27, 19, 35, 33, 42, 44]`. - -Finally, we sort the rest of the array using interval of value 1. -Shell sort uses insertion sort to sort the array. - -![Shellsort](https://www.tutorialspoint.com/data_structures_algorithms/images/shell_sort.jpg) - -## Complexity - -| Name | Best | Average | Worst | Memory | Stable | Comments | -| --------------------- | :-------------: | :-----------------: | :-----------------: | :-------: | :-------: | :-------- | -| **Shell sort** | n log(n) | depends on gap sequence | n (log(n))2 | 1 | No | | - -## References - -- [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/algorithms/sorting/shell-sort/README.pt-BR.md b/src/algorithms/sorting/shell-sort/README.pt-BR.md deleted file mode 100644 index 14de1a517e..0000000000 --- a/src/algorithms/sorting/shell-sort/README.pt-BR.md +++ /dev/null @@ -1,60 +0,0 @@ -# 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 log(n) | depends on gap sequence | n (log(n))2 | 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/algorithms/sorting/shell-sort/ShellSort.js b/src/algorithms/sorting/shell-sort/ShellSort.js deleted file mode 100644 index cdbba99720..0000000000 --- a/src/algorithms/sorting/shell-sort/ShellSort.js +++ /dev/null @@ -1,41 +0,0 @@ -import Sort from '../Sort'; - -export default class ShellSort extends Sort { - sort(originalArray) { - // Prevent original array from mutations. - const array = [...originalArray]; - - // Define a gap distance. - let gap = Math.floor(array.length / 2); - - // Until gap is bigger then zero do elements comparisons and swaps. - while (gap > 0) { - // Go and compare all distant element pairs. - for (let i = 0; i < (array.length - gap); i += 1) { - let currentIndex = i; - let gapShiftedIndex = i + gap; - - while (currentIndex >= 0) { - // Call visiting callback. - this.callbacks.visitingCallback(array[currentIndex]); - - // Compare and swap array elements if needed. - if (this.comparator.lessThan(array[gapShiftedIndex], array[currentIndex])) { - const tmp = array[currentIndex]; - array[currentIndex] = array[gapShiftedIndex]; - array[gapShiftedIndex] = tmp; - } - - gapShiftedIndex = currentIndex; - currentIndex -= gap; - } - } - - // Shrink the gap. - gap = Math.floor(gap / 2); - } - - // Return sorted copy of an original array. - return array; - } -} diff --git a/src/algorithms/sorting/shell-sort/__test__/ShellSort.test.js b/src/algorithms/sorting/shell-sort/__test__/ShellSort.test.js deleted file mode 100644 index 454845f44c..0000000000 --- a/src/algorithms/sorting/shell-sort/__test__/ShellSort.test.js +++ /dev/null @@ -1,60 +0,0 @@ -import ShellSort from '../ShellSort'; -import { - equalArr, - notSortedArr, - reverseArr, - sortedArr, - SortTester, -} from '../../SortTester'; - -// Complexity constants. -const SORTED_ARRAY_VISITING_COUNT = 320; -const NOT_SORTED_ARRAY_VISITING_COUNT = 320; -const REVERSE_SORTED_ARRAY_VISITING_COUNT = 320; -const EQUAL_ARRAY_VISITING_COUNT = 320; - -describe('ShellSort', () => { - it('should sort array', () => { - SortTester.testSort(ShellSort); - }); - - it('should sort array with custom comparator', () => { - SortTester.testSortWithCustomComparator(ShellSort); - }); - - it('should sort negative numbers', () => { - SortTester.testNegativeNumbersSort(ShellSort); - }); - - it('should visit EQUAL array element specified number of times', () => { - SortTester.testAlgorithmTimeComplexity( - ShellSort, - equalArr, - EQUAL_ARRAY_VISITING_COUNT, - ); - }); - - it('should visit SORTED array element specified number of times', () => { - SortTester.testAlgorithmTimeComplexity( - ShellSort, - sortedArr, - SORTED_ARRAY_VISITING_COUNT, - ); - }); - - it('should visit NOT SORTED array element specified number of times', () => { - SortTester.testAlgorithmTimeComplexity( - ShellSort, - notSortedArr, - NOT_SORTED_ARRAY_VISITING_COUNT, - ); - }); - - it('should visit REVERSE SORTED array element specified number of times', () => { - SortTester.testAlgorithmTimeComplexity( - ShellSort, - reverseArr, - REVERSE_SORTED_ARRAY_VISITING_COUNT, - ); - }); -}); diff --git a/src/algorithms/stack/valid-parentheses/README.md b/src/algorithms/stack/valid-parentheses/README.md deleted file mode 100644 index 31d7fd60f3..0000000000 --- a/src/algorithms/stack/valid-parentheses/README.md +++ /dev/null @@ -1,44 +0,0 @@ -# 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 deleted file mode 100644 index e286688dfd..0000000000 --- a/src/algorithms/stack/valid-parentheses/__test__/validParentheses.test.js +++ /dev/null @@ -1,23 +0,0 @@ -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 deleted file mode 100644 index a327780768..0000000000 --- a/src/algorithms/stack/valid-parentheses/validParentheses.js +++ /dev/null @@ -1,42 +0,0 @@ -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(); -} diff --git a/src/algorithms/statistics/weighted-random/README.md b/src/algorithms/statistics/weighted-random/README.md deleted file mode 100644 index 16e459704b..0000000000 --- a/src/algorithms/statistics/weighted-random/README.md +++ /dev/null @@ -1,143 +0,0 @@ -# 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: `[ '🍌', '🍎', '🥕' ]`. - -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 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: - -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 deleted file mode 100644 index 1b0b267627..0000000000 --- a/src/algorithms/statistics/weighted-random/__test__/weightedRandom.test.js +++ /dev/null @@ -1,64 +0,0 @@ -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/images/cover.png b/src/algorithms/statistics/weighted-random/images/cover.png deleted file mode 100644 index a4bf41b65ffe1aa0598b6febb17a415ba70dc3a1..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 305130 zcmeEt1zTKAmT=?l?iyT!25H}+1^@tPa=-o5=noTZ~GCypd3`g%(tUcVq1LX9Yk2MVT*S2mVK 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