Counting Bits

Problem

Given an integer n, return an array ans of length n+1 where ans[i] is the number of 1-bits in i's binary representation.

Constraints

• 0 ≤ n ≤ 10⁵

Approach — Dynamic Programming

This is a Dynamic Programming problem. The idea: break the problem into overlapping subproblems and build the answer up, caching results so nothing is recomputed. Work through the reference code below line by line, then re-derive it yourself in the editor — that's how the pattern sticks.

Complexity: O(n) to O(n²) time.

Solution code

Java

class Solution {
    public int[] countBits(int n) {
        int[] dp = new int[n + 1];
        for (int i = 1; i <= n; i++) dp[i] = dp[i >> 1] + (i & 1);
        return dp;
    }
}

Practice it

Reading a solution isn't the same as being able to write it under pressure. Open this problem in the in-browser editor, hide the solution, and solve it from scratch — your code runs against real test cases instantly.