338. Counting Bits

• Difficulty: Medium

• Topics: Dynamic Programming, Bit Manipulation

• Similar Questions:

  • Number of 1 Bits

Problem:

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:

• 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.

Solutions:

class Solution {
public:
    vector<int> countBits(int num) {
        vector<int> ret(num + 1, 0);
        for (int i = 1; i <= num; ++i) {
            ret[i] = ret[i&(i-1)] + 1;
        }

        return ret;
    }
};