/*
 * @lc app=leetcode id=142 lang=java
 *
 * [142] Linked List Cycle II
 */

// @lc code=start
/**
 * Definition for singly-linked list.
 * class ListNode {
 *     int val;
 *     ListNode next;
 *     ListNode(int x) {
 *         val = x;
 *         next = null;
 *     }
 * }
 */
public class Solution {
    /**
     * 2 * k - s - (k - s) = p * r
     * 2 * k - s - k + s = p * r
     * k = p * r, 且 k > s
     * 
     * s + p * r + m - 2m = q * r
     * s = q * r - p * r  + m
     * 
     * @param head
     * @return
     */
    public ListNode detectCycle(ListNode head) {
        if(head == null) {
            return null;
        }
        Set<ListNode> tracked = new HashSet<>();
        ListNode cur = head, r = null;
        while(cur != null) {
            if(tracked.contains(cur)) {
                r = cur;
                break;
            }
            tracked.add(cur);
            cur = cur.next;
        }
        return r;
    }
}
// @lc code=end