What are the key concepts of graph theory in C++?

What are the key concepts of graph theory in C++?

Graph theory involves concepts like vertices, edges, paths, and cycles. In C++, you can represent graphs using adjacency lists or matrices.

Can you explain how to implement a graph using an adjacency list?

Sure! In C++, you can use a vector of lists to represent an adjacency list. Each index represents a vertex, and the list at that index contains its adjacent vertices.

What are the advantages of using an adjacency list over an adjacency matrix?

Adjacency lists are more space-efficient for sparse graphs, as they only store edges that exist, while adjacency matrices use O(V^2) space regardless of the number of edges.

How can I perform a depth-first search (DFS) on a graph in C++?

You can implement DFS using recursion or a stack. Start from a vertex, mark it as visited, and recursively visit all its unvisited adjacent vertices.