graphs_basics README.md (Markdown)

graphs_basics

This repository contains clean and minimal implementations of classical graph algorithms in Java:

• BFS / DFS — basic graph traversals (graphs_algorithms/)
• Dijkstra's Algorithm — shortest path from a single source (dijkstra_shortest_path/)
• Kruskal's Algorithm — Minimum Spanning Tree (KruskalMST/)

🧰 Requirements

• JDK 17+ (the project uses plain Java, no build tools required)

🧪 How to Compile and Run

# 1. Compile all .java files into the out/ folder
mkdir -p out
find src -name "*.java" > sources.txt
javac -encoding UTF-8 -d out @sources.txt

# 2. Run a specific class with a main() method
# Example:
# java -cp out dijkstra_shortest_path.Dijkstra

Note: Replace the class name above with whichever algorithm’s entry point you want to test (e.g. graphs_algorithms.BFSGraph).

🧭 Project Structure

src/
 ├─ dijkstra_shortest_path/
 │   ├─ Dijkstra.java
 │   └─ Node.java
 ├─ graphs_algorithms/
 │   ├─ BFSGraph.java
 │   └─ DFSGraph.java
 └─ KruskalMST/
     ├─ Disjointset.java
     ├─ Edge.java
     └─ Kruskal.java

🧮 Complexity Overview

Algorithm	Time Complexity	Space Complexity
BFS / DFS	O(V + E)	O(V)
Dijkstra (naive)	O(V²)	O(V)
Kruskal (Union-Find)	O(E log E)	O(V)

V = number of vertices, E = number of edges

🚀 Future Improvements

• Add priority queue implementation for Dijkstra (O((V+E) log V))
• Add other MST algorithms (e.g. Prim)
• Add unit tests and visualization examples

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✨ Author: CellaIoana

📄 License

This project is licensed under the MIT License.
You are free to use, modify, and distribute this code as long as the original copyright notice is included.