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> res;        for(int i = 0; i <= num; ++i){            int cnt = 0;            int n = i;            while(n){                cnt++;                n = n & (n - 1);            }            res.push_back(cnt);        }        return res;    }};