implemented CycleDetectionII code in LinkedList (TheAlgorithms#1482)

* implemented CycleTectionII code

* changes made per review by appgurueu

* made the changes per review by appgurueu

* changes made per review by appgurueu

* did some changes

* fixed the test file with prettier

* Simplify code, renames for clarity

---------

Co-authored-by: Lars Mueller <[email protected]>

Author: Akshay73c

DIRECTORY.md

@@ -82,6 +82,7 @@
   * **Linked-List**
     * [AddTwoNumbers](Data-Structures/Linked-List/AddTwoNumbers.js)
     * [CycleDetection](Data-Structures/Linked-List/CycleDetection.js)
+    * [CycleDetectionII](Data-Structures/Linked-List/CycleDetectionII.js)
     * [DoublyLinkedList](Data-Structures/Linked-List/DoublyLinkedList.js)
     * [MergeTwoSortedLinkedLists](Data-Structures/Linked-List/MergeTwoSortedLinkedLists.js)
     * [ReverseSinglyLinkedList](Data-Structures/Linked-List/ReverseSinglyLinkedList.js)

Data-Structures/Linked-List/CycleDetectionII.js

@@ -0,0 +1,57 @@
+/**
+ * A LinkedList based solution for finding the starting node of the cycle in a list.
+ * @returns the node where cycle begins in the linked list. If there is no cycle present, returns null.
+ * @see https://en.wikipedia.org/wiki/Cycle_detection
+ * @see https://leetcode.com/problems/linked-list-cycle-ii/
+ */
+
+function findCycleStart(head) {
+  let length = 0
+  let fast = head
+  let slow = head
+
+  while (fast !== null && fast.next !== null) {
+    fast = fast.next.next
+    slow = slow.next
+    if (fast === slow) {
+      length = cycleLength(slow)
+      break
+    }
+  }
+
+  if (length === 0) {
+    // If there is no cycle, return null.
+    return null
+  }
+
+  let ahead = head
+  let behind = head
+  // Move slow pointer ahead 'length' of cycle times
+  while (length > 0) {
+    ahead = ahead.next
+    length--
+  }
+
+  // Now move both pointers until they meet - this will be the start of cycle
+  while (ahead !== behind) {
+    ahead = ahead.next
+    behind = behind.next
+  }
+
+  // return the meeting node
+  return ahead
+}
+
+// head is a node on a cycle
+function cycleLength(head) {
+  // How long until we visit head again?
+  let cur = head
+  let len = 0
+  do {
+    cur = cur.next
+    len++
+  } while (cur != head)
+  return len
+}
+
+export { findCycleStart }

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

@@ -0,0 +1,39 @@
+import { findCycleStart } from '../CycleDetectionII'
+import { Node } from '../SinglyLinkedList'
+
+describe('Detect Cycle', () => {
+  it('no cycle', () => {
+    const head = new Node(1)
+    head.next = new Node(2)
+
+    expect(findCycleStart(head)).toBeNull()
+  })
+
+  it('simple cycle', () => {
+    const head = new Node(1)
+    head.next = new Node(2)
+    head.next.next = new Node(3)
+    head.next.next.next = head.next // Creates a cycle
+
+    expect(findCycleStart(head)).toBe(head.next)
+  })
+
+  it('long list with cycle', () => {
+    const head = new Node(1)
+    head.next = new Node(2)
+    head.next.next = new Node(3)
+    head.next.next.next = new Node(4)
+    head.next.next.next.next = new Node(5)
+    head.next.next.next.next.next = head.next.next // Cycle
+
+    expect(findCycleStart(head)).toBe(head.next.next)
+  })
+
+  it('cycle on last node', () => {
+    const head = new Node(1)
+    head.next = new Node(2)
+    head.next.next = head
+
+    expect(findCycleStart(head)).toBe(head)
+  })
+})