Leetcode: Maximum XOR of Two Numbers in an Array

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.

Solution 1: Bit Manipulation:

这题真心有点难，get the max XOR bit by bit

note that if A^B=C, then A^C=B, B^C=A

 public class Solution {
     public int findMaximumXOR(int[] nums) {
         int mask = 0, max = 0;
         for (int i=31; i>=0; i--) {
             mask |= 1<<i;
             HashSet<Integer> prefixes = new HashSet<Integer>();
             for (int each : nums) {
                 prefixes.add(each & mask); // reserve Left bits and ignore Right bits
             }
             int tmpMax = max | (1<<i);
             //possible new max, for example: max right now is 11000, then tmpMax=11100, max is 11100, tmpMax is 11110
             for (int prefix : prefixes) {
                 if (prefixes.contains(tmpMax^prefix))
                     max = tmpMax;
             }
         }
         return max;
     }
 }        

Solution 2: Trie, (未研究)

https://discuss.leetcode.com/topic/63207/java-o-n-solution-using-trie

https://discuss.leetcode.com/topic/64753/31ms-o-n-java-solution-using-trie