feat: modified implementation of the Manacher algorithm

[oulaindex]

Description

This pull request updates the implementation of the Manacher algorithm for finding the longest palindromic substring.
Summary of changes:

• The old implementation in manacher.rs contains a critical logic bug:
  • The variables

    let mut current_center: usize = 0;
    let mut right_from_current_center: usize = 0;

    are only updated within the block guarded by
    if right_from_current_center > i && i > current_center,
    which is never true when both variables are zero at initialization.
    As a result, the logic for updating current_center and right_from_current_center can never execute inside the conditional block at the start, causing these variables to remain unchanged at zero during the initial iterations. Although the final result remains correct due to redundant expansions, this leads to unnecessary repeated checks and significantly reduces the efficiency of the algorithm.
• The new implementation (manacher.rs) fixes this by:
  • Ensuring the logic for updating the center and right boundary always functions correctly, using the standard and widely accepted method for Manacher’s algorithm.
  • Initializing and updating these variables in a manner consistent with canonical implementations and literature, ensuring correct and complete palindrome detection.

Type of change

• Bug fix (non-breaking change which fixes an issue)

Checklist:

• I ran bellow commands using the latest version of rust nightly.
• I ran cargo clippy --all -- -D warnings just before my last commit and fixed any issue that was found.
• I ran cargo fmt just before my last commit.
• I ran cargo test just before my last commit and all tests passed.

Note:
This PR not only clarifies and streamlines the code, but, most importantly, it fixes a functional bug in the center and boundary assignment logic.
All tests pass, and the implementation follows the best practices and guidelines for Manacher’s algorithm.

[codecov-commenter]

Codecov Report

❌ Patch coverage is 95.83333% with 1 line in your changes missing coverage. Please review.
✅ Project coverage is 95.36%. Comparing base (f2a23e9) to head (2f4c748).

Files with missing lines	Patch %	Lines
src/string/manacher.rs	95.83%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #911      +/-   ##
==========================================
+ Coverage   95.32%   95.36%   +0.04%     
==========================================
  Files         319      319              
  Lines       20807    20802       -5     
==========================================
+ Hits        19834    19838       +4     
+ Misses        973      964       -9     

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[github-actions]

This pull request has been automatically marked as abandoned because it has not had recent activity. It will be closed if no further activity occurs. Thank you for your contributions.

[github-actions]

Please ping one of the maintainers once you commit the changes requested or make improvements on the code. If this is not the case and you need some help, feel free to ask for help in our Gitter channel. Thank you for your contributions!