Counting Bits

07/18/2016 Dynamic Programming Bit Manipulation


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.


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.


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


Result: Accepted Time: 40 ms

Here should be some explanations.

 * Return an array of size *returnSize.
 * Note: The returned array must be malloced, assume caller calls free().
int* countBits(int num, int* returnSize) {
    int * ary = malloc((num+2)*sizeof(int));
    *returnSize = num + 1;
    int ptr = 1;
    int cnt = 2;
    ary[0] = 0;
    ary[1] = 1;
    int limit = num / 2;
    while(ptr <= limit)
        ary[(ptr<<1)] = ary[ptr];
        ary[(ptr<<1)|1] = ary[ptr]+1;
    return ary;

Complexity Analytics

  • Time Complexity:
  • Space Complexity: