#43Hash Code Pattern Matching
In a distributed software system, every data object is assigned an alphanumeric hash code containing digits, lowercase letters, and uppercase letters. Given a hashCode, find the closest different palindromic hash code of the same length.
A hash code is palindromic if it reads exactly the same from left to right and right to left. Character case matters. To determine which palindrome is closest, assign every allowed character a numerical rank using this order:
- 0 1 2 3 4 5 6 7 8 9
- a b c d e ... z
- A B C D E ... Z
The cost of a palindrome is calculated as follows:
- For every pair of mirrored positions, calculate the absolute difference between their character ranks.
- For a pair to become equal, both characters are changed to the character chosen for that pair.
- The cost for a mirrored pair is the minimum total rank-change cost required to make the two characters equal.
- For the middle character of an odd-length hash, its cost is 0 unless the original hash is already a palindrome and a different palindrome is required.
- The original hashCode cannot be returned.
- If multiple different palindromic hash codes have the same minimum cost, return the lexicographically smaller one.
Real-World Applications: Distributed Hash Integrity Verification; Blockchain Hash Pattern Analysis; Cloud Storage Hash Validation;
Examples
Example 1
Input: hashCode = "a1Bc"
Output: "a11a"
Explanation: The mirrored pairs are, a ↔ c and 1 ↔ B. Using the smaller-ranked character for each pair, a ↔ a and 1 ↔ 1. The resulting hash is a11a which is a palindrome.
Example 2
Input: hashCode = "Ab3Cd"
Output: "Ab3bA"
Explanation: The mirrored pairs are: A ↔ d, b ↔ C, 3. Choosing the lower-ranked character for each pair gives: A ↔ A, b ↔ b, 3. Therefore Ab3bA is the closest palindromic hash code.
Example 3
Input: hashCode = "A7B7A"
Output: "A707A"
Explanation: A7B7A itself is a palindrome, so it cannot be returned. The algorithm searches for the closest different palindrome.
Constraints
- 1 <= hashCode.length <= 18
- hashCode contains only: digits 0-9, lowercase letters a-z, uppercase letters A-Z
- hashCode does not contain leading or trailing spaces.
- hashCode contains at least one character.
- The returned hash code must have the same length as hashCode.
- The returned hash code must be a palindrome.
- Character comparison is case-sensitive.
- The returned hash code must be different from hashCode.
- The solution must handle hash codes of length up to 18 without integer overflow.
- Base-62 arithmetic must be used for comparing candidate values.
- If two candidates have the same distance, return the lexicographically smaller candidate.