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Counting Bits

Explore dynamic programming techniques to count the number of 1s in the binary form of numbers from 0 to n. Understand the problem constraints and implement optimized solutions using memoization and tabulation to improve efficiency.

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Statement

For a given positive integer, n, your task is to return an array of length n+1n+1 such that for each xx where 0≤x≤n0 \leq x \leq n, result[x] is the count of 11s in the binary representation of xx.

Constraints:

  • 0≤n≤1040 \leq n \leq 10^4

Examples

Understand the problem

Let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

Counting Bits

1.

What will be the output if n=6n = 6?

A.

[0,1,1,2,1,2,2][0, 1, 1, 2, 1, 2, 2]

B.

[0,1,1,2,1,1,2][0, 1, 1, 2, 1, 1, 2]

C.

[0,1,2,2,1,2,1][0, 1, 2, 2, 1, 2, 1]

1 / 4

Figure it out!

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Sequence - Vertical
Drag and drop the cards to rearrange them in the correct sequence.
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Try it yourself

Implement your solution in the following coding playground.

Java
usercode > CountBits.java
import java.util.*;
public class CountBits {
    public static int[] countingBits(int n) {
        // Replace this placeholder return statement with your code
        return new int[]{};
    }
}
Counting Bits