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Linked List Cycle

ID: 141; easy

Solution 1 (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)

/**
* 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)

/**
* 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

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: