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++

## Defining the problem

The **minimum spanning tree (MST)** problem deals with connected, weighted, undirected graphs $G = (V, E, w)$. Here, the weights can be interpreted as costs, and the goal is to select some subset of edges $F \subseteq E$ that connect the nodes of $V$ in a cost-optimal way. In particular, we want
- $F$ contains enough edges such that they connect all nodes of $V$
- the total cost of the edges in $F$ is as small as possible.

As an example, consider the following weighted graph:

# Defining the problem

The **minimum spanning tree (MST)** problem deals with connected, weighted, undirected graphs $G = (V, E, w)$. Here, the weights can be interpreted as costs, and the goal is to select some subset of edges $F \subseteq E$ that connect the nodes of $V$ in a cost-optimal way. In particular, we want
- $F$ contains enough edges such that they connect all nodes of $V$
- the total cost of the edges in $F$ is as small as possible.

As an example, consider the following weighted graph:

Get introduced to the minimum spanning tree problem.

Introduction

Graph Representations

Graph Traversal

Shortest Paths

Spanning Trees

Flow Problems

Conclusion

Appendix

The Minimum Spanning Tree Problem

Defining the problem