142. Linked List Cycle II

题目

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.

题目大意

判断链表是否有环，不能使用额外的空间。如果有环，输出环的起点指针，如果没有环，则输出空。

解题思路

这道题是第 141 题的加强版。在判断是否有环的基础上，还需要输出环的第一个点。

分析一下判断环的原理。fast 指针一次都 2 步，slow 指针一次走 1 步。令链表 head 到环的一个点需要 x1 步，从环的第一个点到相遇点需要 x2 步，从环中相遇点回到环的第一个点需要 x3 步。那么环的总长度是 x2 + x3 步。

fast 和 slow 会相遇，说明他们走的时间是相同的，可以知道他们走的路程有以下的关系：

fast 的 t = (x1 + x2 + x3 + x2) / 2
slow 的 t = (x1 + x2) / 1

x1 + x2 + x3 + x2 = 2 * (x1 + x2)

所以 x1 = x3

所以 2 个指针相遇以后，如果 slow 继续往前走，fast 指针回到起点 head，两者都每次走一步，那么必定会在环的起点相遇，相遇以后输出这个点即是结果。

代码

package leetcode

/**
 * Definition for singly-linked list.
 * type ListNode struct {
 *     Val int
 *     Next *ListNode
 * }
 */
func detectCycle(head *ListNode) *ListNode {
	if head == nil || head.Next == nil {
		return nil
	}
	isCycle, slow := hasCycle142(head)
	if !isCycle {
		return nil
	}
	fast := head
	for fast != slow {
		fast = fast.Next
		slow = slow.Next
	}
	return fast
}

func hasCycle142(head *ListNode) (bool, *ListNode) {
	fast := head
	slow := head
	for slow != nil && fast != nil && fast.Next != nil {
		fast = fast.Next.Next
		slow = slow.Next
		if fast == slow {
			return true, slow
		}
	}
	return false, nil
}

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