merge: Add project-euler problem 12 (#767)

* Add project-euler problem 12

* Fix raised alert in problem 12

* Fixed for loop in Problem012

* fix alerts in Problem012

* Update Problem012

Author: aayushborkar14

DIRECTORY.md

@@ -210,6 +210,7 @@
   * [Problem008](https://github.com/TheAlgorithms/Javascript/blob/master/Project-Euler/Problem008.js)
   * [Problem009](https://github.com/TheAlgorithms/Javascript/blob/master/Project-Euler/Problem009.js)
   * [Problem010](https://github.com/TheAlgorithms/Javascript/blob/master/Project-Euler/Problem010.js)
+  * [Problem012](https://github.com/TheAlgorithms/Javascript/blob/master/Project-Euler/Problem012.js)
   * [Problem014](https://github.com/TheAlgorithms/Javascript/blob/master/Project-Euler/Problem014.js)
   * [Problem015](https://github.com/TheAlgorithms/Javascript/blob/master/Project-Euler/Problem015.js)
   * [Problem016](https://github.com/TheAlgorithms/Javascript/blob/master/Project-Euler/Problem016.js)

Project-Euler/Problem012.js

@@ -0,0 +1,64 @@
+/**
+ * Problem 12 - Highly divisible triangular number
+ *
+ * https://projecteuler.net/problem=11
+ *
+ * The sequence of triangle numbers is generated by adding the natural numbers.
+ * So the 7th triangle number would be 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28.
+ *
+ * The first ten terms would be: 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...
+ * Let us list the factors of the first seven triangle numbers:
+ *
+ * 1: 1
+ * 3: 1,3
+ * 6: 1,2,3,6
+ * 10: 1,2,5,10
+ * 15: 1,3,5,15
+ * 21: 1,3,7,21
+ * 28: 1,2,4,7,14,28
+ *
+ * We can see that 28 is the first triangle number to have over five divisors.
+ *
+ * What is the value of the first triangle number to have over five hundred divisors?
+*/
+
+/**
+ * Gets number of divisors of a given number
+ * @params num The number whose divisors to find
+ */
+const getNumOfDivisors = (num) => {
+  // initialize numberOfDivisors
+  let numberOfDivisors = 0
+
+  // if one divisor less than sqrt(num) exists
+  // then another divisor greater than sqrt(n) exists and its value is num/i
+  const sqrtNum = Math.sqrt(num)
+  for (let i = 0; i <= sqrtNum; i++) {
+    // check if i divides num
+    if (num % i === 0) {
+      if (i === sqrtNum) {
+        // if both divisors are equal, i.e., num is perfect square, then only 1 divisor
+        numberOfDivisors++
+      } else {
+        // 2 divisors, one of them is less than sqrt(n), other greater than sqrt(n)
+        numberOfDivisors += 2
+      }
+    }
+  }
+  return numberOfDivisors
+}
+
+/**
+ * Loops till first triangular number with 500 divisors is found
+ */
+const firstTriangularWith500Divisors = () => {
+  let triangularNum
+  // loop forever until numOfDivisors becomes greater than or equal to 500
+  for (let n = 1; ; n++) {
+    // nth triangular number is (1/2)*n*(n+1) by Arithmetic Progression
+    triangularNum = (1 / 2) * n * (n + 1)
+    if (getNumOfDivisors(triangularNum) >= 500) return triangularNum
+  }
+}
+
+export { firstTriangularWith500Divisors }

Project-Euler/test/Problem012.test.js

@@ -0,0 +1,8 @@
+import { firstTriangularWith500Divisors } from '../Problem012'
+
+describe('checkFirstTriangularWith500Divisors()', () => {
+  it('Problem Statement Answer', () => {
+    const firstTriangular = firstTriangularWith500Divisors()
+    expect(firstTriangular).toBe(76576500)
+  })
+})