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.

Follow up:
Can you solve it without using extra space?

 

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 Linked List Two Pointers

 

链接： http://leetcode.com/problems/linked-list-cycle-ii/

题解：

使用快慢指针，也就是Floyd's cycle-finding algorithm / Tortoise and the Hare algorithm，注意第一个循环结束后要判断是否有环，假如没有环的话return null。  

从快慢指针travel的距离得到  a + b + m * λ = 2(a + b) + n *λ， 得知   a + b = (m - n)λ ，  a = (m - n)λ - b。

就是此时可以设置fast= head，然后fast和slow每次均只前进一步，两指针会在环的起点相遇。

Time Complexity - O(λ + μ)， Space Complexity - O(1)。 λ 是环的周长，μ是环起点的index值。

public class Solution {
    public ListNode detectCycle(ListNode head) {
         if(head == null || head.next == null)
            return null;
         ListNode fast = head;
         ListNode slow = head;
         
         while(fast != null && fast.next != null){
            fast = fast.next.next;
            slow = slow.next;
            if(fast == slow)
                break;
         }
         
         if(fast == null || fast.next == null)
            return null;            
         fast = head;

         while(fast != slow){
             fast = fast.next;
             slow = slow.next;
         }
        
         return fast;
    }
}

 

Update:

/**
 * Definition for singly-linked list.
 * class ListNode {
 *     int val;
 *     ListNode next;
 *     ListNode(int x) {
 *         val = x;
 *         next = null;
 *     }
 * }
 */
public class Solution {
    public ListNode detectCycle(ListNode head) {
        if(head == null || head.next == null)
            return null;
        ListNode fast = head, slow = head;
        
        while(fast != null && fast.next != null) {
            fast = fast.next.next;
            slow = slow.next;
            if(slow == fast)
                break;
        }
        
        if(fast != slow)
            return null;
        
        fast = head;
        
        while(fast != slow) {
            fast = fast.next;
            slow = slow.next;
        }
        
        return fast;
    }
}

 

二刷:

跟一刷的方法一样，先用快慢指针确定是否有环，假如有环的话我们设置fast = head，然后两个指针每次走一步，这样碰到的地方就是环的起点。

Java:

Time Complexity - O(λ + μ)， Space Complexity - O(1)。 λ 是环的周长，μ是环起点的index值。

/**
 * Definition for singly-linked list.
 * class ListNode {
 *     int val;
 *     ListNode next;
 *     ListNode(int x) {
 *         val = x;
 *         next = null;
 *     }
 * }
 */
public class Solution {
    public ListNode detectCycle(ListNode head) {
        if (head == null || head.next == null) {
            return null;
        }
        ListNode fast = head, slow = head;
        while (fast != null && fast.next != null) {
            fast = fast.next.next;
            slow = slow.next;
            if (slow == fast) {
                break;
            }
        }
        if (fast != slow) {
            return null;
        }
        fast = head;
        while (fast != slow) {
            fast = fast.next;
            slow = slow.next;
        }
        return fast;
    }
}

 

三刷:

将fast重新设置为head之后，两个指针每次走一步。  这样当fast走到环的起点时， slow已经在环内走了 (x 圈 + 周长 - b)，所以也是到打环的起点。

Java:

/**
 * Definition for singly-linked list.
 * class ListNode {
 *     int val;
 *     ListNode next;
 *     ListNode(int x) {
 *         val = x;
 *         next = null;
 *     }
 * }
 */
public class Solution {
    public ListNode detectCycle(ListNode head) {
        if (head == null || head.next == null) return null;
        ListNode fast = head, slow = head;
        while (fast != null && fast.next != null) {
            fast = fast.next.next;
            slow = slow.next;
            if (fast == slow) break;
        }
        if (fast != slow) return null;
        fast = head;
        while (fast != slow) {
            fast = fast.next;
            slow = slow.next;
        }
        return slow;
    }
}

 

 

Reference:

http://en.wikipedia.org/wiki/Cycle_detection