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++

The second option to represent graph edges in code is the adjacency list. 

# Adjacency list

In this data structure, we store a list of each node’s neighbors. 

Let’s look at our example graph again. We use the same integer encoding of nodes that we did for the adjacency matrix.


digraph g {
    bgcolor="transparent"
    nodesep=0.4
    {rank=same 2}
    {rank=same 0,1,3}
    0 -> 1
    1 -> 0
    1 -> 2
    1 -> 3
    2 -> 0
    2 -> 3
}

The node with index $1$ has three neighbors: $0$, $2$ and $3$. Its adjacency list looks like this:

Discover how graphs can be represented in code using adjacency lists.

Introduction

Graph Representations

Graph Traversal

Shortest Paths

Spanning Trees

Flow Problems

Conclusion

Appendix

Adjacency List

Adjacency list