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.

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 solve more complex optimization problems on graphs, such as matching and network flow problems.

Learn Graph Algorithms in C++

## Recap

Congratulations on finishing this course on graph algorithms in C++! Let's recap what we learned in each chapter.

- First, we discovered the fundamental concepts and terminology of graph theory, such as directed, undirected, and weighted graphs.
- Next, we explored how graphs can be represented as data structures in programs, using adjacency lists and adjacency matrices.
- We traversed graphs using BFS and DFS and studied applications of graph traversal, such as computing strongly connected components.
- We also computed shortest paths in weighted graphs using Dijkstra’s algorithm and the Floyd-Warshall algorithm.
- We found optimal spanning trees using Kruskal’s algorithm.
- Finally, we solved flow problems using the Ford-Fulkerson method and applied it to find maximum bipartite matchings.

## Next steps

With the foundational knowledge of this course under your belt, you’ll be able to explore further topics of graph algorithms or dive deeper into rich fields such as max-flow algorithms. Below are some suggestions for further topics to check out next.

### Eulerian trails
Take a closer look at the eulerian trail problem, which was explored in the introductory lesson, and implement efficient algorithms for this problem, such as Fleury’s algorithm or Hierholzer’s algorithm.

### General matchings
We applied flow problems to solve the maximum matching problem in bipartite graphs. However, there are also more difficult variants of matching problems that need more complex algorithms to solve them efficiently. Some examples are computing maximum matchings non-bipartite graphs or even computing **maximum weighted matchings** in weighted graphs.

### Traveling salesmen
Explore the **Hamiltonian Cycle problem** and its weighted variant, the **Traveling Salesman problem (TSP)**. The objective of these problems is to find a cycle that visits all nodes and has minimal weight.

# Recap

Congratulations on finishing this course on graph algorithms in C++! Let's recap what we learned in each chapter.

- First, we discovered the fundamental concepts and terminology of graph theory, such as directed, undirected, and weighted graphs.
- Next, we explored how graphs can be represented as data structures in programs, using adjacency lists and adjacency matrices.
- We traversed graphs using BFS and DFS and studied applications of graph traversal, such as computing strongly connected components.
- We also computed shortest paths in weighted graphs using Dijkstra’s algorithm and the Floyd-Warshall algorithm.
- We found optimal spanning trees using Kruskal’s algorithm.
- Finally, we solved flow problems using the Ford-Fulkerson method and applied it to find maximum bipartite matchings.

# Next steps

With the foundational knowledge of this course under your belt, you’ll be able to explore further topics of graph algorithms or dive deeper into rich fields such as max-flow algorithms. Below are some suggestions for further topics to check out next.

## Eulerian trails
Take a closer look at the eulerian trail problem, which was explored in the introductory lesson, and implement efficient algorithms for this problem, such as Fleury’s algorithm or Hierholzer’s algorithm.

## General matchings
We applied flow problems to solve the maximum matching problem in bipartite graphs. However, there are also more difficult variants of matching problems that need more complex algorithms to solve them efficiently. Some examples are computing maximum matchings non-bipartite graphs or even computing **maximum weighted matchings** in weighted graphs.

## Traveling salesmen
Explore the **Hamiltonian Cycle problem** and its weighted variant, the **Traveling Salesman problem (TSP)**. The objective of these problems is to find a cycle that visits all nodes and has minimal weight.

Look back at what you learned. Get inspired by checking out further graph algorithm topics. 

Recap and Next Steps

Look back at what you learned. Get inspired by checking out further graph algorithm topics.

Introduction

Graph Representations

Graph Traversal

Shortest Paths

Spanning Trees

Flow Problems

Conclusion

Appendix

Recap and Next Steps

Recap