338. Counting Bits

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.

Fornum = 5you 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.

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


  1. f[i] = f[i/2] (right shift by 1) + f[i%2] with f[0] = 0 and f[1] =1;
class Solution {
    vector<int> countBits(int num) {
        vector<int> f (num + 1);
        f[0] = 0;
        f[1] = 1;
        for(int i = 2; i <= num ; i ++){
            f[i] = f[i/2] + f[i%2];

        return f;

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