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Learn Graph Algorithms in C++

Explore the basics of graph theory, learn to represent graphs in C++, and master essential algorithms like DFS and Dijkstra to solve complex optimization problems, including matching and network flow.

Intermediate

42 Lessons

Certificate of Completion

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This course includes

18 Playgrounds

5 Challenges

11 Quizzes

Course Overview

What You'll Learn

Course Content

Course Overview

Graph algorithms are the core of many real-world applications of computer science, such as automotive navigation or routing in computer networks. They’re also a common subject in coding interviews at top-tier tech companies. In this course, we’ll learn about the basic concepts of graph theory and how to represent graphs as data structures in code. We’ll study essential graph algorithms such as depth-first search or Dijkstra's algorithm to traverse graphs and find shortest paths. Finally, we’ll learn to s...Show More

What You'll Learn

Learn how graphs can be represented as data structures

Traverse graphs using search algorithms

Find the shortest paths in graphs

Find maximum matchings

Solve flow problems

Compute minimum spanning trees

Learn how graphs can be represented as data structures

Course Content

Introduction

7 Lessons

Get familiar with fundamental graph concepts, key terminology, and algorithm efficiency analysis.

Introduction to Graph Algorithms

Directed and Undirected Graphs

Graph Terminology I

Graph Terminology II

Weighted Graphs

Excursion: Algorithm Analysis

Quiz: Introduction to Graph Algorithms

Graph Representations

6 Lessons

Discover the logic behind graph representations, including adjacency matrices, adjacency lists, and their comparisons.

Adjacency Matrix

Adjacency List

Representing Weighted Graphs

Comparison of Graph Representations

Quiz: Graph Representations

Challenge: Converting Graph Representations

Graph Traversal

9 Lessons

Work your way through DFS and BFS implementations, topological sort, SCCs, and bipartite graphs.

Depth-first Search (DFS)

Implementation of DFS

Breadth First Search (BFS)

Implementation of BFS

Application 1: Topological Sort

Application 2: Strongly Connected Components

Implementation of Kosaraju's Algorithm

Quiz: Graph Traversal

Challenge: Bipartite Graph Check

Shortest Paths

7 Lessons

Break down complex ideas on shortest path algorithms and their implementation techniques.

Shortest Path Problems

Dijkstra's Algorithm for the SSSP

Implementation of Dijkstra

Floyd-Warshall Algorithm for the ASSP

Implementation of Floyd-Warshall

Quiz: Shortest Paths

Challenge: Bellmann-Ford

Spanning Trees

5 Lessons

Deepen your knowledge of minimum spanning trees, Kruskal's algorithm, and maximum spanning tree challenges.

The Minimum Spanning Tree Problem

Kruskal's Algorithm

Implementation of Kruskal's Algorithm

Quiz: Spanning Trees

Challenge: Maximum Spanning Trees

Flow Problems

6 Lessons

Focus on solving max flow problems, Ford-Fulkerson method, and bipartite matching challenges.

The Max Flow Problem

The Ford-Fulkerson Method

Max Flow = Min Cut

Implementation of Ford Fulkerson (Edmonds-Karp)

Quiz: Flow Problems

Challenge: Bipartite Matchings

Conclusion

1 Lessons

Master the steps to understanding graph algorithms, solving fundamental problems, and exploring advanced topics.

Recap and Next Steps

Appendix

1 Lessons

Step through the Disjoint Set Union structure and its optimizations for dynamic connectivity.

Disjoint Set Union Data Structure

Course Author

Lukas Huwald

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