I thought I had this one clean but the all-9s case tripped me up for a bit.
First, clarify the problem constraints and edge cases, then propose a two-pointer approach that mirrors the left half onto the right half and adjusts the middle if needed to ensure the palindrome is strictly greater. Emphasize O(n) time and O(1) space by modifying the string in place and handling carry propagation carefully.
Pro tip: Mention that you can avoid extra space by reusing the input string and that you should test edge cases like '9', '99', '12321', and '12921' to ensure correctness.
Confirm that the input is a non-negative integer string without leading zeros, and discuss edge cases such as all 9s, single-digit numbers, and cases where the result has more digits.
Explain that you will create a palindrome by mirroring the left half onto the right half, then compare it with the original to decide if an adjustment is needed.
If the mirrored palindrome is not greater, increment the middle digit(s) and propagate any carry, then re-mirror to maintain the palindrome property.
If the carry propagates beyond the most significant digit (e.g., all 9s), handle the case by creating a number with an additional digit, such as '1' + zeros + '1'.
Confirm O(n) time and O(1) extra space, then walk through examples to validate the solution.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
This is where I started to feel the pressure.
Generate the same set of candidate palindromes as in the 'next palindrome' problem (mirror of prefix, and mirror of prefix ±1), then compute the absolute difference between each candidate and the input. Compare differences without big integers by comparing lengths and lexicographic order, and return the candidate with the smallest difference, breaking ties by choosing the smaller palindrome.
Pro tip: Mention that you can avoid big integers by comparing the absolute differences as strings: if lengths differ, the longer difference is larger; if lengths are equal, lexicographic comparison works. This shows you understand the underlying numeric representation.
Create candidates by mirroring the first half of the input: (a) mirror of the prefix, (b) mirror of prefix+1, (c) mirror of prefix-1. Also consider edge cases like all 9s (e.g., 999 -> 1001) and single-digit numbers.
For each candidate, compute the absolute difference from the input as a string (or as a numeric value if within safe integer range). Since the input can be very large, represent differences as strings to avoid overflow.
Compare two differences by first comparing their lengths (longer string means larger number). If lengths are equal, compare lexicographically. This avoids converting to big integers.
Iterate through candidates, keeping track of the one with the smallest difference. If a tie occurs (equal differences), choose the smaller palindrome (compare palindromes as strings by length then lexicographically).
Ensure candidates are valid palindromes (e.g., no leading zeros). Return the selected palindrome as a string.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Treat the decimal string as two halves split by the decimal point, mirror the left half onto the right to form a palindrome, then if the result is not greater than the input, increment the left half and re-mirror. Handle carries that propagate across the decimal point by incrementing the integer part and resetting fractional digits as needed, ensuring the fractional length remains fixed.
Pro tip: Clarify edge cases upfront, such as all 9s (e.g., '99.99' → '100.001'? Actually with fixed fractional length, it's '100.01' if fractional length is 2) and inputs with leading zeros, to show thoroughness and avoid incorrect assumptions.
Separate the input into integer and fractional parts, noting the fixed number of fractional digits. Identify the left half (including the decimal point if odd length) that will be mirrored.
Create a candidate palindrome by copying the left half in reverse onto the right side, ensuring the decimal point stays in place and fractional digit count is preserved.
If the candidate is greater than the input, return it. Otherwise, increment the left half (as a number) by 1, handling carries that may propagate across the decimal point, then re-mirror.
When incrementing causes a carry beyond the most significant digit (e.g., all 9s), add a new digit and adjust the fractional part to maintain the fixed length, ensuring the decimal point remains correctly positioned.
Verify the result is a valid palindromic decimal with the correct fractional length and strictly greater than the input, then return it as a string.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.