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

/**
 * Return an array of size *returnSize.
 * Note: The returned array must be malloced, assume caller calls free().
 */
int* countBits(int num, int* returnSize) {
    int *ary;
    int i;
    int k;
    ary = (int *)malloc((num + 1) * sizeof(int));
    for(i = 0; i <= num; i++)
    {
        ary[i] = 0;
        k = i;
        while(k)
        {
            k &= (k-1);
            ary[i]++;
        }
    }
    *returnSize = num + 1;
    return ary;
}