# LinkedListCycleII_142

###### tags: `cycle05_LinkedList`,`leetcode`,`medium`

**LinkedListCycleII_142**

>ref: https://leetcode.com/problems/linked-list-cycle-ii/
>git: https://github.com/chmonk/leetCodeTraining/blob/dev/src/cycle05_LinkedList/LinkedListCycleII_142.java
>
Given the head of a linked list, return the node where the cycle begins. If there is no cycle, return null.

There is a cycle in a linked list if there is some node in the list that can be reached again by continuously following the next pointer. Internally, pos is used to denote the index of the node that tail's next pointer is connected to (0-indexed). It is -1 if there is no cycle. Note that pos is not passed as a parameter.

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.

>Constraints:
The number of the nodes in the list is in the range [0, 10^4].
-10^5 <= Node.val <= 10^5
pos is -1 or a valid index in the linked-list.

>1. timeResolution:O(N)需go through 所有node(非環) 或起點到環形區塊
>2. 快慢兩者速度需查1步,當快慢兩者相見時,碰面點距離環形開始點會為"起點至環形開始點",此時再放置1.一者從起點與2.碰面點以相同速度前行會再環形開始點相見
t = X + nY + K
2t = X + mY + K
=>X+K = (m-2n)Y
=> X(環形扣除相碰點之距離;相碰點距離環形起始點)= Y-K
=> X多走K步即到環型起始點
>ref: https://leetcode.com/problems/linked-list-cycle-ii/discuss/44822/Java-two-pointer-solution.

	public ListNode detectCycle(ListNode head) {
		ListNode x = head;
		ListNode y = head;

		while (x != null && x.next != null) {
			x = x.next.next;
			y = y.next;
			if (x == y) {
				while (y != head) {
                                     //此時再放置1.一者從起點與2.碰面點以相同速度前行會再環形開始點相見
					y = y.next;
					head = head.next;
				}
				return y;
			}
		}

		return null;

	}

	public class ListNode {
		int val;
		ListNode next;

		ListNode() {
		}

		ListNode(int val) {
			this.val = val;
		}

		ListNode(int val, ListNode next) {
			this.val = val;
			this.next = next;
		}
	}
        
	}