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Grokking the Coding Interview Patterns in Python

Counting Bits

Explore how to count the number of 1s in the binary representation of integers using dynamic programming. This lesson helps you understand the problem statement and develop an efficient solution approach through hands-on coding practice.

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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.

Python
usercode > main.py
def counting_bits(n):

    

    # Replace this placeholder return statement with your code

    return []
Counting Bits