diff --git a/Data-Structures/Linked-List/CycleDetection.js b/Data-Structures/Linked-List/CycleDetection.js
index ba33cd0c4a..63b730eca1 100644
--- a/Data-Structures/Linked-List/CycleDetection.js
+++ b/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 }
diff --git a/Data-Structures/Linked-List/test/CycleDetection.test.js b/Data-Structures/Linked-List/test/CycleDetection.test.js
new file mode 100644
index 0000000000..0041dece59
--- /dev/null
+++ b/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)
+ })
+})
diff --git a/Maths/LiouvilleFunction.js b/Maths/LiouvilleFunction.js
new file mode 100644
index 0000000000..f13916d55d
--- /dev/null
+++ b/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 +} diff --git a/Maths/test/LiouvilleFunction.test.js b/Maths/test/LiouvilleFunction.test.js new file mode 100644 index 0000000000..58a79c9cc2 --- /dev/null +++ b/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)
+ })
+})
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