[LeetCode] 477. Total Hamming Distance

轉自LeetCode

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.

<Solution>

461. Hamming Distance 的衍生題

想法如下

• 暴力解不會過，會TLE

• 用到排列組合的概念，假設有 n 個數，其中 k 個在位置 i 的 bit 是 1，n-k 個是 0，那麼，可以產生的 Hamming distance 會是 k * (n-k) 個，也就是在該 bit 的位置下，所有的配對情況

code 如下

Java(參考解答)