LeetCode 421. Maximum XOR of Two Numbers in an Array
原题链接在这里:https://leetcode.com/problems/maximum-xor-of-two-numbers-in-an-array/
题目:
Given a non-empty array of numbers, a0, a1, a2, … , an-1, where 0 ≤ ai < 231.
Find the maximum result of ai XOR aj, where 0 ≤ i, j < n.
Could you do this in O(n) runtime?
Example:
Input: [3, 10, 5, 25, 2, 8] Output: 28 Explanation: The maximum result is 5 ^ 25 = 28.
题解:
利用Trie. 每个TrieNode.nexts array有两个分支,一个0, 一个1.
把nums中每一个num插入Trie中.
然后,对于一个num, 从首位bit开始,若是该bit^1对应的TrieNode存在,就说明nums中有该bit位和num是相反的数存在. 就沿着bit^1的分支走下去. 同时更新这个bit到这个num的sum中.
若bit^1对应的TrieNode 是null, 说明nums中没有该bit位和num相反的数存在,沿着该bit的分支走下去.
最后返回所有数中最大的res.
Time Complexity: O(n). n = nums.length. insert 用了O(n). 求res也用了O(n).
Space: O(1). Trie最大2^32-1.
AC Java:
1 class Solution { 2 public int findMaximumXOR(int[] nums) { 3 TrieNode root = new TrieNode(); 4 5 //insert each num into trie 6 for(int num : nums){ 7 TrieNode p = root; 8 for(int i = 31; i>=0; i--){ 9 int cur = (num>>i)&1; 10 if(p.nexts[cur] == null){ 11 p.nexts[cur] = new TrieNode(); 12 } 13 14 p = p.nexts[cur]; 15 } 16 } 17 18 int res = 0; 19 for(int num : nums){ 20 TrieNode p = root; 21 int sum = 0; 22 for(int i = 31; i>=0; i--){ 23 int cur = (num>>i)&1; 24 if(p.nexts[cur^1] != null){ 25 sum += (1<<i); 26 p = p.nexts[cur^1]; 27 }else{ 28 p = p.nexts[cur]; 29 } 30 } 31 32 res = Math.max(res, sum); 33 } 34 35 return res; 36 } 37 } 38 39 class TrieNode{ 40 TrieNode [] nexts; 41 42 public TrieNode(){ 43 nexts = new TrieNode[2]; 44 } 45 }