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Early-stage Startup·Software Engineer·Online Assessment (OA)·Intermediate

IntermediatePrefer not to say
Jun 2026

Summary

Ran into a binary palindrome problem on an OA and posted asking for help since I couldn't figure out the optimal approach during the assessment.

Questions Asked (1)

Q1

Given a number n, find the minimum number of +1 or -1 steps needed to reach the nearest binary palindrome (a number whose binary representation reads the same forwards and backwards).

Algorithms & Data Structures
Author's notes

Saw this and immediately thought it'd be straightforward, then spent way too long going in circles.

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AI HintsAI Generated

Suggested Approach

Clarify the problem constraints (e.g., n's size, whether n itself can be a palindrome) and discuss a brute-force approach first. Then propose an efficient method: generate candidate palindromes by mirroring prefixes of n's binary representation, and check distances. Finally, analyze time complexity and edge cases.

Pro tip: Mention that you can generate the nearest palindrome by considering the mirrored value of n's binary prefix and its immediate neighbors (increment/decrement the prefix), which avoids scanning all numbers. This shows you understand the structure of binary palindromes and can optimize beyond brute force.

1. Clarify and define

Confirm what 'nearest' means (absolute difference) and whether n itself can be a palindrome. Discuss input size and expected output.

2. Brute force baseline

Explain a simple approach: check n, n±1, n±2, ... until a binary palindrome is found. Note its O(k * log n) time where k is the distance.

3. Optimized approach

Describe generating candidate palindromes by taking the binary representation of n, mirroring its first half to form a palindrome, and also considering the prefix incremented and decremented by 1. Compute distances to these candidates and pick the minimum.

4. Handle edge cases

Consider cases like n=0, n=1, powers of two, and when the mirrored palindrome has a different bit-length. Ensure the algorithm checks palindromes of both lengths (e.g., all 1s for next length).

5. Complexity and testing

State time complexity O(log n) for generating candidates and space O(log n). Walk through a small example (e.g., n=10) to verify correctness.

Key Points to Mention

  • Binary representation and palindrome definition
  • Brute force vs. optimized approach
  • Mirroring the first half of the binary string to generate palindromes
  • Considering prefix ±1 to find nearest candidates
  • Edge cases: n=0, n=1, powers of two, and bit-length changes
  • Time and space complexity analysis

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.