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.

Analysis:

0 | 0+1| 0+1 1+1| 0+1 1+1 1+1 2+1 |..........

0 | 1    | 1       2  | 1      2    2     3     |................

Solution:

public class Solution {
public int[] countBits(int num) {
int[] res = new int[num + 1]; res[0] = 0;
int nextNum = 1;
int nextCount = 1;
while (nextNum <= num) {
for (int i = 0; i < nextCount && nextNum <= num; i++) {
res[nextNum++] = res[i] + 1;
}
nextCount *= 2;
}
return res;
}
}

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