求链表环的起始位置

leetcode中题目位置

https://leetcode.cn/problems/linked-list-cycle-ii/submissions/?envType=study-plan-v2&envId=top-100-liked

代码：

public class Solution {
    public ListNode detectCycle(ListNode head) {
        if (head == null || head.next == null) {
            return null;
        }
        // a + b = slow = cnt;
        // a + b + (b + c)x = fast = 2 * slow = 2cnt ----> bx+cx = cnt
        // a = b(x-1) + cx = (b + c)(x - 1) + c, 即从 相遇节点、root节点出发，经过(a+1)节点后，他们会在头结点相遇；
        ListNode slow = head;
        ListNode fast = head.next;
        while (slow != fast) {
            if (fast.next == null || fast.next.next == null) {
                return null;
            }
            slow = slow.next;
            fast = fast.next.next;
        }
        slow = slow.next;
        while (head != slow) {
            head = head.next;
            slow = slow.next;
        }
        return head;
    }
}

重点：快慢指针相遇后，慢指针继续往前，同时root也开始往前（root.next = head), 他们必然会相遇，即a = (b + c)(x - 1) + c

* a+1是root到环起点的步数；

* c+1是慢指针从相遇节点 到 环起点的步数；

* b+c是环的节点数