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.



Credits:Special thanks to @ syedee  for adding this problem and creating all test cases.

Difficulty: interview

Starter code:

class Solution:
    def countBits(self, num: int) -> List[int]:
        

Solutions:
class Solution:
     def countBits(self, num):
         """
         :type num: int
         :rtype: List[int]
         """
         ans = [0]
         while len(ans) < num + 1:
             ans += [1 + x for x in ans]
         # len(ans) > num
         return ans[:num+1]