README: Shortest Path Algorithm Notebook

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Overview

Welcome to the Shortest Path Algorithm Notebook! This repository is designed to guide you through the fundamental concepts and implementations of various shortest path algorithms. Whether you're a beginner or seeking a refresher, this resource aims to provide you with comprehensive tutorials, code examples, GIFs, videos, and more.

Subjects Covered

1. Heap and Priority Queue (Construction of Dijkstra)

   • Understand the importance of heaps and priority queues in implementing Dijkstra's algorithm efficiently.

2. Dijkstra's Algorithm

   • Dive into one of the most popular and widely used algorithms for finding the shortest path between nodes in a graph.

3. Bellman-Ford Algorithm

   • Explore the Bellman-Ford algorithm, which handles graphs with negative edge weights and detects negative cycles.

4. Shortest Path Optimality Condition

   • Learn about the conditions that define the optimality of the shortest path in a graph.

5. Negative Cycle Detection

   • Understand how to detect negative cycles in graphs and their significance in shortest path algorithms.

6. Difference Constraint System

   • Explore the concept of a difference constraint system and its applications in solving optimization problems.

7. Johnson's Algorithm and All Pairs Shortest Paths

   • Delve into Johnson's algorithm, which efficiently computes all pairs shortest paths in a graph, even with negative edge weights.

How to use

you just need to clone the repo and run all blocks of the shortest_path.ipynb in google colab or on your local to see the videos.

Getting Started

To make the most out of this notebook, follow these steps:

1. Review the Materials: Take some time to review the tutorials, codes, GIFs, and videos provided for each subject.
2. Experiment with Code: Experiment with the provided code examples to deepen your understanding of the algorithms.
3. Engage with Visuals: Visual aids such as GIFs and videos can help you grasp complex concepts more effectively.
4. Practice Problems: Test your understanding by solving practice problems related to each algorithm.
5. Contribute and Share: Feel free to contribute additional materials or share your insights with the community to enhance the learning experience.