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.

Counting Bits Solution

public class CountingBits {
    public int[] countBits(int num) {
        int[] bits = new int[num + 1];

        bits[0] = 0;

        for(int i = 1; i <= num; i++) {
            bits[i] = bits[i >> 1] + (i & 1);
        }

        return bits;
    }
}