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https://github.com/ayusharyan143/graph-algorithms-dsa

Graph topics Algorithm
https://github.com/ayusharyan143/graph-algorithms-dsa

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Graph topics Algorithm

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# Graph-DSA
![image](https://github.com/ayusharyan143/Graph-DSA-/assets/141620322/36e134b1-50e2-430d-a0b6-8ca8313d4af5)

Released: 28 May, 2024

Written by Ayush Aryan.

(C) Copyright 2024-2025, by Ayush Aryan . All rights reserved.

Please address all contributions, suggestions, and inquiries to the user mailing list

Welcome to the Graph-DSA repository! This repository contains various algorithms and problems related to Graph Data Structures and Algorithms (DSA). Below is a list of implemented algorithms and their descriptions.

## Table of Contents

- [Introduction](#introduction)
- [Implemented Algorithms](#implemented-algorithms)
- [How to Use](#how-to-use)
- [Contributing](#contributing)
- [License](#license)

## Introduction

Graph-DSA is a collection of commonly used graph algorithms and problems solved using C++. This repository is intended to help students and professionals understand and implement these algorithms effectively.

## Implemented Algorithms

1. **Representation of Graph**
- File: `1.cpp`
- Description: Demonstrates different ways to represent graphs in C++ (Adjacency Matrix, Adjacency List, etc.).

2. **Breath-First Search (BFS)**
- File: `2.cpp`
- Description: Implements the BFS algorithm to traverse or search in a graph.

3. **Depth-First Search (DFS)**
- File: `3.cpp`
- Description: Implements the DFS algorithm to traverse or search in a graph.

4. **Detect Cycle in Graph**
- File: `4.cpp`
- Description: Detects cycles in a graph using DFS.

5. **Kruskal's Algorithm (MST)**
- File: `5.cpp`
- Description: Implements Kruskal's algorithm to find the Minimum Spanning Tree (MST) of a graph.

6. **Prim's Algorithm (MST)**
- File: `6.cpp`
- Description: Implements Prim's algorithm to find the MST of a graph.

7. **Dijkstra's Algorithm**
- File: `7.cpp`
- Description: Implements Dijkstra's algorithm to find the shortest path in a graph.

8. **Job Sequencing Problem**
- File: `8.cpp`
- Description: Solves the job sequencing problem to maximize profit.

9. **Fractional Knapsack Problem**
- File: `9.cpp`
- Description: Solves the fractional knapsack problem to maximize value.

10. **0-1 Knapsack Problem**
- File: `10.cpp`
- Description: Solves the 0-1 knapsack problem to maximize value.

11. **Length of Common Subsequence (LCS)**
- File: `11.cpp`
- Description: Finds the length of the longest common subsequence between two sequences.

12. **Matrix Chain Multiplication (MCM)**
- File: `12.cpp`
- Description: Solves the matrix chain multiplication problem to find the optimal order of matrix multiplication.

13. **Knuth-Morris-Pratt (KMP)**
- File: `14.cpp`
- Description: Implements the KMP string matching algorithm.

## How to Use

1. Clone the repository:
```sh
git clone https://github.com/ayusharyan143/Graph-DSA-.git