421. 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.

思路：
利用了异或的”自反性“： a ^ b = c，而a ^ b ^ b = a, 则 c ^ b = a
其他运算定律有：交换律、结合律、分配律。

class Solution {
    public int findMaximumXOR(int[] nums) {
        int max = 0;
        int flag = 0;

        // from left to right
        for (int i = 31; i >= 0; i--) {
            Set<Integer> prefixSet = new HashSet();
            // flag : 11110000
            flag = flag | (1 << i);
            for (int num : nums) {
                prefixSet.add(num & flag);
            }

            // tmp, max: 10101000000, add more 1 
            int tmp = max | (1 << i);
            for (int prefix : prefixSet) {
                // 利用了 ^ 的 a ^ b = c，则 b ^ c = a
                if (prefixSet.contains(tmp ^ prefix)) {
                    max = tmp;
                    break;
                }
            }
        }
        return