feat: add longest repeating subsequence algorithm

[JPisOP007]

Describe your change:

Add a dynamic programming implementation of the Longest Repeating Subsequence (LRS) algorithm to the dynamic_programming directory.

The Longest Repeating Subsequence finds the longest subsequence that occurs at least twice in a string, using a variation of LCS where the string is compared with itself but characters at the same index cannot be reused.

Features:

• O(n²) time and space complexity using dynamic programming
• Comprehensive doctests covering valid inputs, edge cases, and error handling
• Python type hints for parameters and return values
• Proper error handling with TypeError for invalid input types

Reference: https://en.wikipedia.org/wiki/Longest_common_subsequence_problem

• Add an algorithm?
• Fix a bug or typo in an existing algorithm?
• An existing algorithm or test needs improvement?
• Documentation change?

Checklist:

• I have read CONTRIBUTING.md.
• This pull request is all my own work -- I have not plagiarized.
• I know that pull requests will not be merged if they fail the automated tests.
• This PR only changes one algorithm file.
• All new Python files are placed inside an existing directory.
• All filenames are in all lowercase characters with no spaces or dashes.
• All functions and variable names follow Python naming conventions.
• All function parameters and return values are annotated with Python type hints.
• All functions have doctests that pass the automated testing.
• All new algorithms include at least one URL that points to Wikipedia or another similar explanation.