【leetcode 两个链表的交集点】Intersection of Two Linked Lists

Intersection of Two Linked Lists

 

1、题目

Write a program to find the node at which the intersection of two singly linked lists begins.

For example, the following two linked lists:

A:          a1 → a2
                   ↘
                     c1 → c2 → c3
                   ↗            
B:     b1 → b2 → b3

begin to intersect at node c1.

Notes:

• If the two linked lists have no intersection at all, return null.
• The linked lists must retain their original structure after the function returns.
• You may assume there are no cycles anywhere in the entire linked structure.
• Your code should preferably run in O(n) time and use only O(1) memory.

2、分析

题目大意：给两个链表，找出它们交集的那个节点，要求时间复杂度O(n)，空间复杂度O(1)。

有以下几种思路：

（1）暴力破解，遍历链表A的所有节点，并且对于每个节点，都与链表B中的所有节点比较，退出条件是在B中找到第一个相等的节点。时间复杂度O(lengthA*lengthB)，空间复杂度O(1)。

（2）哈希表。遍历链表A，并且将节点存储到哈希表中。接着遍历链表B，对于B中的每个节点，查找哈希表，如果在哈希表中找到了，说明是交集开始的那个节点。时间复杂度O(lengthA+lengthB)，空间复杂度O(lengthA)或O(lengthB)。

（3）双指针法，指针pa、pb分别指向链表A和B的首节点。

遍历链表A，记录其长度lengthA，遍历链表B，记录其长度lengthB。

因为两个链表的长度可能不相同，比如题目所给的case，lengthA=5，lengthB=6，则作差得到lengthB-lengthA=1，将指针pb从链表B的首节点开始走1步，即指向了第二个节点，pa指向链表A首节点，然后它们同时走，每次都走一步，当它们相等时，就是交集的节点。

时间复杂度O(lengthA+lengthB)，空间复杂度O(1)。双指针法的代码如下：

3、代码

 ListNode *getIntersectionNode(ListNode *headA, ListNode *headB) {
        ListNode *pa=headA,*pb=headB;
        int lengthA=0,lengthB=0;
        while(pa) {pa=pa->next;lengthA++;}
        while(pb) {pb=pb->next;lengthB++;}
        if(lengthA<=lengthB){
            int n=lengthB-lengthA;
            pa=headA;pb=headB;
            while(n) {pb=pb->next;n--;}
        }else{
            int n=lengthA-lengthB;
            pa=headA;pb=headB;
            while(n) {pa=pa->next;n--;}
        }
        while(pa!=pb){
            pa=pa->next;
            pb=pb->next;
        }
        return pa;
    }

4、题目作者的解答（英文）

作者双指针法花费的时间比我的方法更少

There are many solutions to this problem:

• Brute-force solution (O(mn) running time, O(1) memory):

  For each node ai in list A, traverse the entire list B and check if any node in list B coincides with ai.

• Hashset solution (O(n+m) running time, O(n) or O(m) memory):

  Traverse list A and store the address / reference to each node in a hash set. Then check every node bi in list B: if bi appears in the hash set, then bi is the intersection node.

• Two pointer solution (O(n+m) running time, O(1) memory):
  • Maintain two pointers pA and pB initialized at the head of A and B, respectively. Then let them both traverse through the lists, one node at a time.
  • When pA reaches the end of a list, then redirect it to the head of B (yes, B, that's right.); similarly when pB reaches the end of a list, redirect it the head of A.
  • If at any point pA meets pB, then pA/pB is the intersection node.
  • To see why the above trick would work, consider the following two lists: A = {1,3,5,7,9,11} and B = {2,4,9,11}, which are intersected at node '9'. Since B.length (=4) < A.length (=6), pB would reach the end of the merged list first, because pB traverses exactly 2 nodes less than pA does. By redirecting pB to head A, and pA to head B, we now ask pB to travel exactly 2 more nodes than pA would. So in the second iteration, they are guaranteed to reach the intersection node at the same time.
  • If two lists have intersection, then their last nodes must be the same one. So when pA/pB reaches the end of a list, record the last element of A/B respectively. If the two last elements are not the same one, then the two lists have no intersections.