Maximum XOR of Two Numbers in an Array

首先，我们想一个简单的问题。
Given an array A, find the two numbers a, b in A that makes a * b == 1223.
我们可能首先想这么写

for i in range(len(nums)):
   for j in range(i + 1, len(nums)):
       if nums[i] * nums[j] == 1223:
           return True

但是我们想一下，其实可以优化位O(n), 用一个set就行了

set_ = set(nums)
for num in nums:
    if 1223 // num in set_:
            return True

然后我们看这个问题
https://leetcode.com/problems/maximum-xor-of-two-numbers-in-an-array/#/solutions
实际上就是把上面的过程重复了32遍

class Solution(object):
    def findMaximumXOR(self, nums):
        """
        :type nums: List[int]
        :rtype: int
        """
        max = 0
        for i in range(31, -1, -1):
            max <<= 1
            prefixes = {num >> i for num in nums}
            expect_max = max | 1
            for prefix in prefixes: # in prefixes, we want to find the a ^ b == expect_max. 
                if expect_max ^ prefix in prefixes:
                    max = expect_max
        return max