Problem

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.

Hint

You should make use of what you have produced already.
Divide the numbers in ranges like [2-3], [4-7], [8-15] and so on. And try to generate new range from previous.
Or does the odd/even status of the number help you in calculating the number of 1s?

Note

应用公式f[i] = f[i/2] + (i%2);
并优化此公式为f[i] = f[i>>2] + (i&1)，减少计算时间。

Solution

public class Solution {
    public int[] countBits(int num) {
        int[] dp = new int[num+1];
        for (int i = 1; i <= num; i++) dp[i] = dp[i>>1] + (i&1);
        return dp;
    }
}