Box

Online Assessment
Online Assessment//Number of 1 Bits
Q1
Easy50 Marks

Number of 1 Bits

Divide and ConquerBit Manipulation
Set 1 • 90 min
Problem Statement

In Box's technical coding assessment, candidates are evaluated on clean algorithmic problem-solving for "Number of 1 Bits".

Given standard input parameters adhering to Divide and Conquer principles, design an optimal algorithm that satisfies all constraints and handles boundary test scenarios efficiently.

Ensure your implementation minimizes memory overhead and executes within the allotted online assessment time limits.

Candidate Instructions
  • ▸Identify the core invariant related to Divide and Conquer.
  • ▸Verify edge cases including empty inputs and extreme bounds.
  • ▸Optimize time complexity before submitting.
Input Format
  • ▸The first line specifies the dimensions or count of test elements N.
  • ▸The subsequent line(s) contain the input array, string, or graph representation.
Output Format
  • ▸Print the computed result adhering to the required return format.
Constraints
  • 1 <= N <= 10^5
  • -10^9 <= element[i] <= 10^9
  • Time Limit: 2.0 seconds
  • Memory Limit: 256 MB
Edge Cases
  • ▸Empty or single-element input
  • ▸Input containing maximum or minimum boundary values
  • ▸Uniform elements or all-negative test cases
Sample Test Cases
Example 1
Input
nums = [2, 7, 11, 15], target = 9
Output
[0, 1]
Explanation

Applying the optimal Divide and Conquer approach yields the expected solution [0, 1].

Complexity
TimeO(log N)
SpaceO(1)
Expected Approach

Leverage Divide and Conquer combined with Bit Manipulation to process the input in optimal O(log N) time complexity.