# Data Structures & Algorithms in Java – Linked Lists- Linked List Cycle

## Problem:

Given a linked list and the head node of the linked list find if there is a loop / cycle in the linked list, that is if the tail node points back to any of the previous nodes.

For example:

The below linked list has a cycle:

Output is true for the above linked list.

Try out the solution here:

## Solution:

Hint:

• Have two pointers , a slow pointer moving one node at a time and a fast pointer moving two nodes at a time. If they meet each other there is a cycle.

## ALGORITHM:

STEP 1: Initialize two pointers , slow and fast pointing to the head

STEP 2: While the pointers are not null , increment slow pointer by one node and fast pointer by two nodes.

STEP 2a: If the pointers meet return true

STEP 3: Return false

## Code:

```/**
* class ListNode {
*     int val;
*     ListNode next;
*     ListNode(int x) {
*         val = x;
*         next = null;
*     }
* }
*/
public class Solution {

while(fast!=null &&  fast.next != null ){

slow = slow.next;

fast = fast.next.next;

if(slow == fast) return true;

}

return false;

}
}
```

Time complexity is O(n) where n is the number of nodes.

There is no extra space required apart from storing the slow and fast pointers.

That’s it!

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