'''
Given an integer n, return an array ans of length n + 1 such that for each i (0 <= i <= n), ans[i] is the number of 1's in the binary representation of i.

 

Example 1:

Input: n = 2
Output: [0,1,1]
Explanation:
0 --> 0
1 --> 1
2 --> 10
Example 2:

Input: n = 5
Output: [0,1,1,2,1,2]
Explanation:
0 --> 0
1 --> 1
2 --> 10
3 --> 11
4 --> 100
5 --> 101
'''
class Solution:
    def countBits(self, num: int) -> List[int]:
        dp     = [0]*(num+1)
        offset = 1
        for i in range(1, num+1):
            if offset*2==i:
                offset = i
            dp[i] = 1+dp[i-offset]
            
        return dp
