⚙️ Naive vs Optimized Algorithms (C++ Implementation)

This project explores and compares naive and optimized versions of three foundational algorithms:

• Dijkstra’s Algorithm
• String Matching using Trie (with KMP Hybrid)
• Union-Find (Disjoint Set)

Each algorithm is implemented in its own header file, and driven from a main.cpp runner.

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📁 Project Structure

├── Dijkstra.h        # Naive and optimized Dijkstra's algorithm
├── DisjointSet.h     # Naive and optimized Union-Find (Disjoint Set)
├── KMPTrie.h         # Trie-based pattern matching and KMP-Trie hybrid
├── main.cpp          # Entry point: allows you to test all implementations
└── main.exe          # Precompiled executable (for Windows)

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🚀 How to Run

🖥️ Compile (on any system with a C++ compiler)

g++ main.cpp -o main
./main

Or, on Windows if you prefer:

g++ main.cpp -o main.exe
main.exe

You can also directly use the provided main.exe if you're on Windows.

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📌 Algorithm Overview

1. Dijkstra’s Algorithm

Version	Description	Time Complexity
Naive	Scans all vertices to find minimum distance	O(V²)
Optimized	Uses min-heap (priority queue) for fast selection	O((V + E) log V)

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2. String Matching (Trie vs KMP-Trie Hybrid)

Version	Description	Time Complexity
Naive Trie	Basic trie, character-by-character search	O(m) per pattern
KMP-Trie Hybrid	Uses KMP’s LPS array to skip unnecessary comparisons during search	O(m + k)

Where:

• m = pattern length
• k = number of matches in the text

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3. Union-Find (Disjoint Set)

Version	Description	Time Complexity
Naive	Simple tree structure, no balancing	O(n)
Optimized	Path Compression + Union by Rank for flat trees	O(α(n)) (amortized)

Where:

• α(n) is the inverse Ackermann function, practically constant

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📊 Benchmarking

Benchmark tests are run within main.cpp for side-by-side comparisons of performance between naive and optimized versions.

You can customize input sizes and operations inside main.cpp for your own benchmarking.

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💡 Learn More

This project is great for:

• Understanding the importance of data structures in algorithm performance
• Studying the effect of optimization techniques like heaps, path compression, and KMP
• Comparing real-world runtimes of theoretical complexities

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📝 License

This project is open-source and licensed under the MIT License.