How do you solve Counting Bits on LeetCode?

Counting Bits (LeetCode #338) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(n) space complexity. Key insight: Understanding how binary representation works is crucial for solving bit manipulation problems.

What is the brute force solution for Counting Bits?

The brute force approach for Counting Bits is Brute Force, with O(n log n) time complexity and O(n) space complexity. The brute-force approach involves converting each integer from 0 to n into its binary representation and counting the number of 1s. This is straightforward but inefficient for larger values of n. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Counting Bits?

Counting Bits uses the following concepts: Dynamic Programming, Bit Manipulation. The recommended patterns to study are: Bit Manipulation, Dynamic Programming.

What are the interview tips for Counting Bits?

Always consider the brute-force approach first; it helps in understanding the problem better. Look for patterns or relationships between numbers, especially in bit manipulation problems. Practice explaining your thought process clearly, as communication is key in interviews.

What are common mistakes when solving Counting Bits?

Relying too heavily on built-in functions for counting bits, which may not be allowed in interviews. Not recognizing patterns in how binary numbers relate to each other.

#338

Counting Bits

Easy

Dynamic ProgrammingBit ManipulationBit ManipulationDynamic Programming

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n log n)	O(n)
Space	O(n)	O(n)

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Intuition

Time O(n)Space O(n)

The optimal approach leverages the relationship between numbers. The number of 1s in the binary representation of a number can be derived from previously computed results, specifically using the formula: ans[i] = ans[i >> 1] + (i & 1). This means we can compute the number of 1s in constant time for each number.

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Algorithm

3 steps

1Step 1: Initialize an array ans of size n + 1 with all zeros.
2Step 2: For each integer i from 1 to n, calculate ans[i] using the formula: ans[i] = ans[i >> 1] + (i & 1).
3Step 3: Return the ans array.

solution.py5 lines

1def countBits(n):
2    ans = [0] * (n + 1)
3    for i in range(1, n + 1):
4        ans[i] = ans[i >> 1] + (i & 1)
5    return ans

ℹ

Complexity note: The time complexity is O(n) because we iterate through all numbers from 1 to n once, and each operation inside the loop is O(1).

1Understanding how binary representation works is crucial for solving bit manipulation problems.
2Leveraging previously computed results can significantly reduce time complexity.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.