IMPLEMENT CORE DP PROBLEMS

[durvaakadam]

Pull Request Description

What does this PR add?

• ✅ New algorithm implementations (Dynamic Programming)
• ✅ Test cases
• ✅ Documentation improvement

Algorithm/Feature Details

• Algorithms Added:

  1. fibonacci_sequence.c – Compute Fibonacci numbers using DP (bottom-up and memoization approaches)
  2. longest_common_subsequence.c – Find LCS of two strings with DP table
  3. coin_change_problem.c – Count minimum coins or ways to make change using DP
  4. maximum_subarray_sum.c – Kadane’s algorithm for maximum subarray sum

• Language: C

• Category: Dynamic Programming Algorithms

• Time Complexity: Varies per algorithm (usually O(n²) for LCS/coin change, O(n) for Fibonacci/Kadane)

• Space Complexity: Varies (O(n²) for LCS/coin change, O(n) for Fibonacci, O(1) for Kadane)

Implementation Highlights

• ✅ Comprehensive comments explaining each step
• ✅ Test cases covering normal and edge scenarios
• ✅ Efficient DP implementations (bottom-up or optimized space)
• ✅ Follows repository coding standards

Key Components

• DP tables for LCS and coin change
• Iterative and memoized Fibonacci implementations
• Kadane’s algorithm for maximum subarray sum
• Test drivers included in each file

Applications

• Computing optimized solutions for classical DP problems
• Useful for competitive programming and coding interviews
• Educational purposes for learning dynamic programming concepts

File Structure Added

C/dynamic_programming/
├── fibonacci_sequence.c
├── longest_common_subsequence.c
├── coin_change_problem.c
└── maximum_subarray_sum.c

Hacktoberfest 2025

This PR is submitted for Hacktoberfest 2025.
If possible, please add the hacktoberfest label. Thank you!

[github-actions]

🎉 Welcome to Hacktoberfest 2025, @durvaakadam! 🎃

Thank you for your first contribution to our DSA repository! Here's what happens next:

🔍 Automatic Checks

• ✅ Code Validation: Passed
• 🧪 Compilation Tests: Passed

📋 Next Steps

🎯 Great job! Your code compiled successfully. Maintainers @Karanjot786 and @Pradeepsingh61 will review your PR soon.

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💡 Tips for Success

• Follow our Contributing Guidelines
• Add comments explaining your algorithm
• Include time/space complexity analysis
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Welcome to the community! 🚀

[github-actions]

🤖 Automated PR Status

🔍 Code Validation

✅ Passed - File naming and structure look good!

🧪 Compilation Tests

✅ Passed - All code compiles successfully!

📋 Overall Status

🎉 Ready for Review - Your PR has passed all automated checks!
👥 Maintainers have been notified for review.

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[Karanjot786]

@Pradeepsingh61 merge it and @durvaakadam thanks for this PR