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