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> result(num+1, 0);
	    for (int i = 1; i <= num; i++)
	    {
		    result[i] = result[i&(i-1)] + 1;
	    }

	    return result;
    }
};