### Find First Node of Cycle in a Linked List - The Coding Shala

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## Find First Node of Cycle in a Linked List

Problem:

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 the 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 the 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 the 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.

### Find First Node of Cycle in a Linked List Java Program

Approach:
Take two-pointer slow and fast. Slow will move one step and fast will two steps. When slow meets fast then cycle exists. Initialize slow pointer to head and then move slow and fast by 1 step. Both slow and fast will meet at the first node of the cycle.

Java Code

```/**
* class ListNode {
*     int val;
*     ListNode next;
*     ListNode(int x) {
*         val = x;
*         next = null;
*     }
* }
*/
public class Solution {
while(fast != null && fast.next != null){
fast = fast.next.next;
slow = slow.next;

if(slow == fast){
slow = head;  //always meet to first node of cycle
while(slow != fast){
slow = slow.next;
fast = fast.next;
}
return slow;
}
}
return null;
}
}
```

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