Counting Bits Solutions in C++

// Source : https://leetcode.com/problems/counting-bits/
// Author : Hao Chen
// Date   : 2016-05-30



class Solution {
public:
    /* 
     * Initialization
     * 
     *   bits_cnt[0] => 0000 => 0
     *   bits_cnt[1] => 0001 => 1
     * 
     * if the number has 2 bits (2, 3), then we can split the binary to two parts, 
     * 2 = 10 + 0  and  3= 10 + 1, then we can reuse the bits_cnt[0] and bits_cnt[1] 
     *
     *   bits_cnt[2] => 0010 => 0010 + 0 => 1 + bits_cnt[0];
     *   bits_cnt[3] => 0011 => 0010 + 1 => 1 + bits_cnt[1];
     *
     * if the number has 3 bits (4,5,6,7), then we can split the binary to two parts, 
     * 4 = 100 + 0,  5 = 100 + 01, 6= 100 + 10, 7 = 100 +11
     * then we can reuse the bits_cnt[0] and bits_cnt[1] 
     * 
     *   bits_cnt[4] => 0110 => 0100 + 00 => 1 + bits_cnt[0];
     *   bits_cnt[5] => 0101 => 0100 + 01 => 1 + bits_cnt[1];
     *   bits_cnt[6] => 0110 => 0100 + 10 => 1 + bits_cnt[2];
     *   bits_cnt[7] => 0111 => 0100 + 11 => 1 + bits_cnt[3];
     *
     * so, we can have the solution:
     *
     *   bits_cnt[x] = bits_cnt[x & (x-1) ] + 1;
     *
     */
    vector<int> countBits(int num) {
        vector<int> bits_cnt(num+1, 0); 
        
        for (int i=1; i<=num; i++) {
            bits_cnt[i] = bits_cnt[i & (i-1)] + 1;
        }
        return bits_cnt;
    }
};