LeetCode - Counting Bits

Question Definition

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.

  Java Solution

  public int[] countBits(int num) {
    int[] dp = new int[num + 1];
    dp[0] = 0;
    if(num >= 1) dp[1] = 1;
    if(num >= 2) dp[2] = 1;
    for(int i = 3; i <= num; i++){
        if(i % 2 == 0)
            dp[i] = dp[i / 2];
        else
            dp[i] = dp[i - 1] + 1;
    }
    return dp;
  }