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Saw this and immediately thought it'd be straightforward, then spent way too long going in circles.
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.
Confirm what 'nearest' means (absolute difference) and whether n itself can be a palindrome. Discuss input size and expected output.
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.
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.
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).
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.
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