I started with the obvious cases and worked inward.
Start by clarifying edge cases and constraints, then propose a solution that constructs the next palindrome rather than brute-force checking each number. Discuss how to handle carries and ensure the result is strictly greater than n, with no leading zeros.
Pro tip: Mention that a naive increment-and-check approach is O(n) in the worst case and may be too slow for large n, so an O(d) construction (where d is the number of digits) is preferred. Also, highlight that you would test edge cases like n=9, n=99, n=123, and n=9999.
Confirm that n is positive, no leading zeros, and the result must be strictly greater. Discuss examples like n=9 -> 11, n=99 -> 101, n=123 -> 131.
Decide between brute-force and constructive approach. Explain that constructing the next palindrome by mirroring the left half is O(d) and more efficient.
Describe how to split the number into left half, mirror it to form a palindrome, and if it's not greater than n, increment the left half and re-mirror, handling carries and digit growth.
Address cases where incrementing causes a carry that increases the number of digits (e.g., 999 -> 1001) and ensure no leading zeros.
State time and space complexity (O(d) time, O(d) space) and walk through test cases to validate correctness.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.