Add longest-valid-parentheses

[shimmer12]

Description of Change

• Added implementation of Longest Valid Parentheses using Dynamic Programming.
• Provided detailed Doxygen-style documentation explaining the approach, logic, and example.
• Included a concise version of the algorithm for comparison.
• Added test cases in the main() function to demonstrate correctness and usage.
• Ensured adherence to C++17 standards and repository coding guidelines.

Checklist

• Added description of change
• File name matches File name guidelines
• Added tests and examples; all tests pass
• Added documentation so that the program is self-explanatory and educational — Doxygen guidelines
• Relevant documentation/comments added or updated
• PR title follows semantic commit guidelines
• Verified no duplicate implementations exist for the same problem
• Acknowledge that all contributions are made under the project’s license

Notes:
Added the Longest Valid Parentheses (DP Approach) implementation under dynamic_programming/ with comprehensive documentation and examples for educational clarity.