Dijkstra’s Algorithm – Shortest Path Finder

A comprehensive implementation of Dijkstra’s Algorithm for finding the shortest paths from a source node to all other nodes in a weighted graph.
This project focuses on algorithmic correctness, performance, scalability, and real-world use cases, making it suitable for academic study, competitive programming, and production systems.

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📌 Table of Contents

1. Introduction
2. Problem Statement
3. Algorithm Overview
4. Why Dijkstra’s Algorithm
5. Applications
6. Graph Representation
7. Data Structures Used
8. Time & Space Complexity
9. Project Features
10. Input & Output Format
11. Implementation Details
12. Example Walkthrough
13. Edge Cases Handled
14. Limitations
15. Optimization Techniques
16. Comparison with Other Algorithms
17. Real-World Use Cases
18. Project Structure
19. How to Run
20. Testing Strategy
21. Future Enhancements
22. Academic Relevance
23. Interview Relevance
24. License
25. Author

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🧠 Introduction

Dijkstra’s Algorithm is one of the most fundamental and widely used graph algorithms in computer science.
It computes the shortest path from a given source vertex to all other vertices in a graph with non-negative edge weights.

This project demonstrates:

• Correct implementation of Dijkstra’s Algorithm
• Efficient use of data structures
• Clean, modular, and readable code
• Practical considerations for real-world systems

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❓ Problem Statement

Given:

• A weighted graph G(V, E)
• A source vertex S

Find:

• The shortest distance from S to every other vertex in the graph
• Optionally, the actual shortest path

Constraints:

• Edge weights must be non-negative
• Graph may be directed or undirected

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⚙️ Algorithm Overview

Dijkstra’s Algorithm works by:

1. Initializing distances from the source to all vertices as infinity
2. Setting the source distance to 0
3. Using a priority queue (min-heap) to always expand the closest unvisited node
4. Relaxing edges and updating distances
5. Repeating until all nodes are visited or the queue is empty

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💡 Why Dijkstra’s Algorithm?

✔ Guarantees optimal shortest paths
✔ Efficient for sparse graphs
✔ Widely used in real-world systems
✔ Simple yet powerful
✔ Foundation for advanced routing algorithms

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🌍 Applications

• GPS Navigation Systems
• Google Maps routing
• Network routing protocols
• Traffic management systems
• Game AI pathfinding
• Robotics navigation
• Logistics and supply chain optimization
• Social network analysis

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🗺️ Graph Representation

The graph is represented using:

• Adjacency List
• Each node maintains a list of (neighbor, weight) pairs

Advantages:

• Space efficient
• Faster iteration over neighbors
• Suitable for sparse graphs

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🧱 Data Structures Used

Data Structure	Purpose
Priority Queue (Min Heap)	Select next closest node
HashMap / Array	Store distances
Visited Set	Prevent reprocessing
Parent Map	Path reconstruction

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⏱️ Time Complexity

Implementation	Time Complexity
Array-based	O(V²)
Priority Queue	O((V + E) log V)

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💾 Space Complexity

• O(V + E)
• Stores graph, distance array, and priority queue

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✨ Project Features

• Supports directed & undirected graphs
• Supports weighted graphs
• Efficient priority queue implementation
• Path reconstruction
• Handles disconnected graphs
• Clean modular code
• Easy to extend

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📥 Input Format