> For the complete documentation index, see [llms.txt](https://blog.yushunchen.com/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://blog.yushunchen.com/algo/linked-list/linked-list-cycle.md).

# Linked List Cycle

{% embed url="<https://leetcode.com/problems/linked-list-cycle/>" %}

{% embed url="<https://www.lintcode.com/problem/102/>" %}

## Solution 1 (Go)

```go
/**
 * Definition for singly-linked list.
 * type ListNode struct {
 *     Val int
 *     Next *ListNode
 * }
 */
func hasCycle(head *ListNode) bool {
    m := make(map[*ListNode]bool)
    for head != nil {
        if _,found := m[head]; found {
            return true
        }
        m[head] = true
        head = head.Next
    }
    return false
}
```

## Solution 2 (Go)

```go
/**
 * Definition for singly-linked list.
 * type ListNode struct {
 *     Val int
 *     Next *ListNode
 * }
 */
func hasCycle(head *ListNode) bool {
    tortoise, hare := head, head
    for tortoise != nil && hare != nil && hare.Next != nil {
        tortoise = tortoise.Next
        hare = hare.Next.Next
        if tortoise == hare {
            return true
        }
    }
    return false
    
}
```

## Solution 3 (Java)

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

public class Solution {
    /**
     * @param head: The first node of linked list.
     * @return: True if it has a cycle, or false
     */
    public boolean hasCycle(ListNode head) {
        if (head == null || head.next == null)
            return false;
        
        ListNode slow = head;
        ListNode fast = head;
        
        while (fast.next != null && fast.next.next != null) {
            slow = slow.next;
            fast = fast.next.next;
            if (slow == fast) return true;
        }

        return false;
    }
}
```

### Floyd's tortoise and hare cycle-finding algorithm

{% embed url="<https://en.wikipedia.org/wiki/Cycle_detection#Floyd's_tortoise_and_hare>" %}

The tortoise move by 1 step each time and the hare moves by 2 steps at a time. If there is a cycle, the hare will eventually catch the tortoise at a position.

A simple idea of the proof can be tracking the **gap** between the tortoise and the hare. By construction, the gap increases by 1 each iteration. Eventually, the gap with become n, where n is the number of elements in the **cycle** (not the whole list). This is the time when the tortoise and the hare meet. More proofs:

{% embed url="<https://math.stackexchange.com/questions/913499/proof-of-floyd-cycle-chasing-tortoise-and-hare>" %}


---

# Agent Instructions
This documentation is published with GitBook. GitBook is the documentation platform designed so that both humans and AI agents can read, navigate, and reason over technical content effectively. Learn more at gitbook.com.

## Querying This Documentation
If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.

Perform an HTTP GET request on the current page URL with the `ask` query parameter, and the optional `goal` query parameter:

```
GET https://blog.yushunchen.com/algo/linked-list/linked-list-cycle.md?ask=<question>&goal=<endgoal>
```

`ask` is the immediate question: it should be specific, self-contained, and written in natural language.
`goal` is optional and describes the broader end goal you are ultimately trying to accomplish on behalf of the user. GitBook uses it to tailor the answer towards what is most useful for that goal.

The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.