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 1:
Input: 2 Output: [0,1,1]
Example 2:
Input: 5
Output: [0,1,1,2,1,2]
Follow up:
<li>It is very easy to come up with a solution with run time <b>O(n*sizeof(integer))</b>. But can you do it in linear time <b>O(n)</b> /possibly in a single pass?</li>
<li>Space complexity should be <b>O(n)</b>.</li>
<li>Can you do it like a boss? Do it without using any builtin function like <b>__builtin_popcount</b> in c++ or in any other language.</li>