Optimize Binary Search in C with 2D Index Tracking and Automated Tests

[adil-149120]

Description of Changes

This pull request upgrades the existing binary_search.h / binary_search.c logic with a production-grade, highly optimized binary search workflow in C.

• Dual Architectures: Implemented both clean Iterative and Recursive binary search routines.
• Index Retention: Added a 2D matrix layout tracking step so that sorted element lookups successfully yield the element's original index location.
• Universal Sort Integration: Built an optimized sorting configuration utilizing fast inlined Insertion Sort for small workloads ($N \le 16$) and robust qsort() for larger scaling profiles.
• Robust Verification Suite: Added a structural test_algorithm() harness that automatically handles standard search datasets alongside null/empty boundary conditions.

Closes #343

[github-actions]

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[github-actions]

🤖 Automated PR Status

🔍 Code Validation

❌ Failed - Please check file naming conventions and directory structure.

🧪 Compilation Tests

❌ Failed - Please fix compilation errors and try again.

📋 Overall Status

⚠️ Needs Work - Please address the issues above.
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[Zhiyilang074811]

Great optimization! Ready for review.