leetcode——338——Counting Bits

Given a non negative integer number num. For every numbers i in the range 0 ≤ i ≤ num calculate the number of 1's in their binary representation and return them as an array.
Example: For num = 5 you should return [0,1,1,2,1,2] .
Follow up:

It is very easy to come up with a solution with run time O(n*sizeof(integer)). But can you do it in linear time O(n)/possibly in a single pass?

Space complexity should be O(n).

Can you do it like a boss? Do it without using any builtin function like __builtin_popcount in c++ or in any other language.

class Solution {
public:
    vector<int> countBits(int num) {
          vector<int> ret(num + 1, 0);
         for (int i = 1; i <= num; ++i)
             ret[i] = ret[i&(i - 1)] + 1;
         return ret;


    }
};