Graph Theory Algorithms

A complete overview of graph theory algorithms in computer science and mathematics.

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What You Will Learn!

Storage and representation of graphs (networks) on a computer
Common graph theory problems
Breadth first search algorithm
Depth first search algorithm
Various tree algorithms including: the height or a tree, finding the center of a tree, rooting a tree, and etc...
Dijkstra's algorithm
Topological sort algorithm
Shortest/longest path on a acyclic graph
Bellman Ford's algorithm
Floyd-Warshall all pairs shortest path algorithm
Finding bridges/articulation points
Finding strongly connected components (Tarjan's)
Travelling salesman problem (TSP)
How to find the maximum flow of a flow graph
Finding bipartite graph matchings
Various network flow algorithms including: Edmonds-Karp, Capacity Scaling, and Dinic's algorithm
Kruskal's Minimum Spanning Tree algorithm
The Lowest Common Ancestor (LCA) Problem

Description

Welcome to this Graph Theory Algorithms course!

Graph theory is a fundamental branch of mathematics that deals with the study of graphs, networks, and their applications in real-world scenarios. This course is designed to equip you with the necessary skills and knowledge to understand, analyze, and solve problems related to graph theory.

In this course, you will receive a thorough introduction to graph theory algorithms as they apply to computer science. Throughout the videos, we will cover a range of topics, including how to represent and store graphs on a computer, common graph theory problems encountered in real-world scenarios, famous graph traversal algorithms like DFS and BFS, as well as the lazy and eager versions of Dijkstra's shortest path algorithm. Additionally, we will explore what a topological sort is, how to identify one, and its applications. You will also learn about detecting negative cycles and finding shortest paths using the Bellman-Ford and Floyd-Warshall algorithms, discovering bridges and articulation points in graphs, understanding and detecting strongly connected components using Tarjan's algorithm, and finally, solving the traveling salesman problem with dynamic programming.

Throughout the course, we will use a hands-on approach to teaching, with plenty of examples and exercises to reinforce your understanding of the material. By the end of this course, you will have a deep understanding of graph theory algorithms and be able to apply them to solve real-world problems.

So, whether you are a computer science student, a software developer, or just someone interested in the fascinating world of graph theory, this course is for you! Join today and take your first step towards mastering the art of graph theory algorithms.