Implement Manacher's Algorithm and Unit Tests for Longest Palindromic Substring

[Simranstha045]

PR Description:

This PR introduces the implementation of Manacher's Algorithm, an efficient algorithm to find the longest palindromic substring in linear time O(n). Additionally, the PR includes a set of comprehensive unit tests to verify the correctness and performance of the algorithm under different scenarios.

Manacher's Algorithm:

The algorithm is designed to find the longest palindromic substring by transforming the input string to handle both even-length and odd-length palindromes uniformly. It expands around potential center points and optimizes the search by leveraging symmetry (mirroring) properties of palindromes. The approach ensures a linear time complexity O(n), making it suitable for handling large strings efficiently.

Use Cases of Manacher's Algorithm:

In cryptography, palindromes might be used in certain algorithms. Identifying the longest palindromic substrings in a ciphered message could help analyze the underlying structure or potential weaknesses.

Unit Tests:

Unit tests have been added to cover a wide range of scenarios:

• Single-character strings: Ensures the algorithm works with the simplest input.
• Even-length and odd-length palindromes: Tests standard palindrome cases like "abba" and "racecar".
• Mixed palindromes: Accepts multiple valid longest palindromic substrings (e.g., "babad" can return either "aba" or "bab").
• Edge cases: Handles inputs like empty strings, no palindromes, and full-string palindromes.
• Special character handling: Verifies the algorithm can correctly identify palindromes when special characters (e.g., "a!b!a") are involved.

Test Case Adjustment:

• The test case for the input "babad" was adjusted to handle multiple valid outputs. Both "aba" and "bab" are correct longest palindromes for this input, so the test now accepts either of them.