[pull] master from TheAlgorithms:master

Data-Structures/Linked-List/CycleDetection.js

@@ -1,32 +1,24 @@
 /**
- * A LinkedList based solution for Detect a Cycle in a list
+ * A LinkedList based solution for Detecting a Cycle in a list.
  * https://en.wikipedia.org/wiki/Cycle_detection
  */
 
-function main () {
+function detectCycle (head) {
   /*
   Problem Statement:
   Given head, the head of a linked list, determine if the linked list has a cycle in it.
-
-  Note:
-  * While Solving the problem in given link below, don't use main() function.
-  * Just use only the code inside main() function.
-  * The purpose of using main() function here is to avoid global variables.
-
   Link for the Problem: https://leetcode.com/problems/linked-list-cycle/
   */
-  const head = '' // Reference to head is given in the problem. So please ignore this line
-  let fast = head
-  let slow = head
+  if (!head) { return false }
 
-  while (fast != null && fast.next != null && slow != null) {
+  let slow = head
+  let fast = head.next
+  while (fast && fast.next) {
+    if (fast === slow) { return true }
     fast = fast.next.next
     slow = slow.next
-    if (fast === slow) {
-      return true
-    }
   }
   return false
 }
 
-main()
+export { detectCycle }

Data-Structures/Linked-List/test/CycleDetection.test.js

@@ -0,0 +1,31 @@
+import { detectCycle } from '../CycleDetection'
+import { Node } from '../SinglyLinkedList'
+
+describe('Detect Cycle', () => {
+  it('should detect loop and return true', () => {
+    // Creating list and making a loop
+    const headNode = new Node(10)
+    headNode.next = new Node(20)
+    headNode.next.next = new Node(30)
+    headNode.next.next.next = new Node(40)
+    headNode.next.next.next.next = headNode
+    expect(detectCycle(headNode)).toEqual(true)
+  })
+
+  it('should not detect a loop and return false', () => {
+    // Case 0: When head is null, there is no loop.
+    expect(detectCycle(null)).toEqual(false)
+    const headNode = new Node(10)
+
+    // Case 1: List with single node doesn't have any loop
+    expect(detectCycle(headNode)).toEqual(false)
+
+    headNode.next = new Node(20)
+    headNode.next.next = new Node(30)
+    headNode.next.next.next = new Node(40)
+    headNode.next.next.next.next = new Node(50)
+
+    // Case 2: List not having any loops
+    expect(detectCycle(headNode)).toEqual(false)
+  })
+})

Maths/LiouvilleFunction.js

@@ -0,0 +1,25 @@
+/*
+ * Author: Akshay Dubey (https://github.com/itsAkshayDubey)
+ * Liouville Function: https://en.wikipedia.org/wiki/Liouville_function
+ * For any positive integer n, define λ(n) as the sum of the primitive nth roots of unity.
+ * It has values in {−1, 1} depending on the factorization of n into prime factors:
+ *   λ(n) = +1 if n positive integer with an even number of prime factors.
+ *   λ(n) = −1 if n positive integer with an odd number of prime factors.
+ */
+
+/**
+ * @function liouvilleFunction
+ * @description -> This method returns λ(n) of given number n
+ * returns 1 when number has even number of prime factors
+ * returns -1 when number has odd number of prime factors
+ * @param {Integer} number
+ * @returns {Integer} 1|-1
+ */
+
+import { PrimeFactors } from './PrimeFactors.js'
+export const liouvilleFunction = (number) => {
+  if (number <= 0) {
+    throw new Error('Number must be greater than zero.')
+  }
+  return PrimeFactors(number).length % 2 === 0 ? 1 : -1
+}

Maths/test/LiouvilleFunction.test.js

@@ -0,0 +1,19 @@
+import { liouvilleFunction } from '../LiouvilleFunction'
+
+const expectedValuesArray = [1, -1, -1, 1, -1, 1, -1, -1, 1, 1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, 1, 1, 1, -1, -1, -1, -1, -1, 1, -1, -1, 1, -1, 1, -1, -1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, 1, 1, -1, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1, 1, -1, -1, -1, 1, 1, -1, 1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, -1, -1, 1]
+
+describe('Testing liouville function', () => {
+  for (let i = 1; i <= 100; i++) {
+    it('Testing for number = ' + i + ', should return ' + expectedValuesArray[i], () => {
+      expect(liouvilleFunction(i)).toBe(expectedValuesArray[i - 1])
+    })
+  }
+
+  it('should throw error when supplied negative numbers', () => {
+    expect(() => { liouvilleFunction(-1) }).toThrow(Error)
+  })
+
+  it('should throw error when supplied zero', () => {
+    expect(() => { liouvilleFunction(0) }).toThrow(Error)
+  })
+})