9) Linked List Cycle II

In this article we going to see about how to Detect Loop in a Linked List and Return the Loop Node.

Below is our given problem from Leetcode,

Given a linked list, return the node where the cycle begins. If there is no cycle, return null.

To represent a cycle in the given linked list, we use an integer pos which represents the position (0-indexed) in the linked list where tail connects to. If pos is -1, then there is no cycle in the linked list.

Note: Do not modify the linked list.

Example 1:

Input: head = [3,2,0,-4], pos = 1
Output: tail connects to node index 1
Explanation: There is a cycle in the linked list, where tail connects to the second node.

Example 2:

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

Example 3:

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

Can you solve it without using extra space?

Basic Knowledge:

Before proceeding you must have good knowledge of detecting loop in a linked list. For that, I made an with detailed explanations.

  1. How to detect cycle in linked list


Once you find the cycle, return the node which meeting each other.

Make one pointer from head(Let’s say q) and another pointer(Let’s say p from node(which met each other).

Move p from one node to another node. Similarly move q from one node to another node, still both meets each other.

Repeat this process, until the node meets each other.

When both pointer meets at some point, it the starting node of cycle­čśť


 * Definition for singly-linked list.
 * class ListNode {
 *     int val;
 *     ListNode next;
 *     ListNode(int x) {
 *         val = x;
 *         next = null;
 *     }
 * }
public class Solution {
    public ListNode detectCycle(ListNode head) {
        ListNode temp = head;
        ListNode p = findWhereNodesMeeting(temp);
        if(p != null)
            ListNode q = head;
            while(p != q)
                p = p.next;
                q = q.next;
            return p;
        return null;
    public ListNode findWhereNodesMeeting(ListNode head)
        ListNode p = head;
        ListNode q = head;
        while(p != null && q != null && q.next != null)
            p = p.next;
            q = q.next.next;
            if(p == q)
                return p;
        return null;

Time Complexity: O(n)

Space Complexity: O(1)


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