Cycle Detection of A Linked List in JavaScript

Cycle detection is the algorithmic problem of finding a cycle in a sequence of iterated function values, for example, the classic linked list loop detection problem. There are different solution. For the following Leetcode example, I’ll explain true solutions.

Example of Floyd’s algorithm

Given head, the head of a linked list, determine if the linked list has a cycle in it.

There is a cycle in a linked list if there is some node in the list that can be reached again by continuously following the next pointer. Internally, pos is used to denote the index of the node that tail's next pointer is connected to. Note that pos is not passed as a parameter.

Return true if there is a cycle in the linked list. Otherwise, return false.

Example 1: 
Input: head = [3,2,0,-4], pos = 1
Output: true
Explanation: There is a cycle in the linked list, where the tail connects to the 1st node (0-indexed).

Example 1

Example 2:
Input: head = [1,2], pos = 0
Output: true
Explanation: There is a cycle in the linked list, where the tail connects to the 0th node.

Example 2

Example 3:
Input: head = [1], pos = -1
Output: false
Explanation: There is no cycle in the linked list.

Example 3

Constraints:

• The number of the nodes in the list is in the range [0, 104].
• -105 <= Node.val <= 105
• pos is -1 or a valid index in the linked-list.

Solution 1: Hashing

1. Traverse the given linked list and store nodes in Set() object to avoid duplicated value
2. If the duplication occurs, the linked list is a loop, the function returns true
3. After traversed, if no duplicated node is found, the function returns false

https://gist.github.com/GAierken/226126a8998ed219de9921aa5cf0c195

Time complexity: O(n). Only one traversal of the linked list is needed.

Space complexity: O(n). n is the space required to store nodes in the Set().

Solution 2: Floyd’s Tortoise and Hare Algorithm

1. Traverse the given list with two pointers
2. Slow pointer moves by one and fast pointer by two
3. If two pointers meet, returns true, if not returns false

https://gist.github.com/GAierken/5e66d1fbf3e4c5b7adf367520e46004f

Time complexity: O(n). Only one traversal of the linked list is needed.

Space complexity: O(1). No space is needed, it’s constant.

Resources:

Linked List Cycle - LeetCode

Cycle detection

Detect loop in a linked list - GeeksforGeeks