LeetCode 477. Total Hamming Distance

题目描述：

The Hamming distance between two integers is the number of positions at which the corresponding bits are different.

Now your job is to find the total Hamming distance between all pairs of the given numbers.

Example:

Input: 4, 14, 2

Output: 6

Explanation: In binary representation, the 4 is 0100, 14 is 1110, and 2 is 0010 (just
showing the four bits relevant in this case). So the answer will be:
HammingDistance(4, 14) + HammingDistance(4, 2) + HammingDistance(14, 2) = 2 + 2 + 2 = 6.

Note:

1. Elements of the given array are in the range of 0 to 10^9
2. Length of the array will not exceed 10^4.

跟 461. Hamming Distance 这道题类似，不过数量增加了。我们可以对int的每一位分别求HammingDistance再求和。n个二进制位中有i个0和j个1，那么它们两两组合成0与1的种类有i*j种。

class Solution {
public:
    int totalHammingDistance(vector<int>& nums) {
        int ans = 0;
        for(int i = 0; i < 32; i++){
            int num[2] = {0, 0};
            for(auto j : nums){
                if(j & (1 << i))
                    num[1]++;
                else
                    num[0]++;
            }
            ans += (num[0] * num[1]);
        }
        return ans;
    }
};