What is the optimal time complexity of solving Number of 1 Bits?

The optimized solution achieves a time complexity of O(n) by using sorting, mathematical shortcuts, or hash table lookups.

What is the auxiliary space complexity for Number of 1 Bits?

The space complexity is O(1) since we only use a minimal/constant amount of extra memory for tracking variables (or auxiliary space if dynamic structures are allocated).

What are the typical edge cases we must handle in Number of 1 Bits?

Key edge cases include empty collections, negative or large bounds causing integer overflow, arrays with only one element, or inputs where target criteria are not met.

How can we optimize the brute force approach for Number of 1 Bits?

Brute force methods often inspect all possible combinations. We optimize this by sorting the input list to enable binary search, or tracking processed items in a set to avoid redundant nested loop lookups.

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Number of 1 Bits

Learn how to solve the 'Number of 1 Bits' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Easy

Write a function that takes the binary representation of a positive integer and returns the number of set bits it has (also known as the Hamming weight).

Write a function hammingWeight(n: int) -> int.

Constraints

•n must be a positive integer up to 2^32 - 1

Examples

Example 1

Input

n = 11

Output

Explanation

The binary representation of 11 is 1011, which has 3 set bits.

Example 2

Input

n = 128

Output

Explanation

The binary representation of 128 is 10000000, which has 1 set bit.

Need a Hint?

Analyze the input constraints. Try sorting first (O(n log n)) or using a hash map/set to track seen elements in O(n) time.

Edge Cases to Watch

Empty list or null input variables
Single item lists/arrays
Extremely large input bounds causing integer or stack overflow

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