What are the basics of graph theory in C++?

What are the basics of graph theory in C++?

Graph theory is a field of mathematics and computer science that studies graphs, which are structures made up of nodes (or vertices) connected by edges. In C++, you can represent graphs using various data structures like adjacency lists or matrices.

Can you explain how to implement an adjacency list in C++?

Sure! An adjacency list can be implemented using a vector of lists in C++. Each index of the vector represents a vertex, and the list at that index contains the vertices that are adjacent to it. Here's a simple example:

#include <iostream>
#include <vector>
#include <list>

class Graph {
    int V; // Number of vertices
    std::vector<std::list<int>> adj;
public:
    Graph(int V);
    void addEdge(int v, int w);
    void printGraph();
};

Graph::Graph(int V) {
    this->V = V;
    adj.resize(V);
}

void Graph::addEdge(int v, int w) {
    adj[v].push_back(w);
}

void Graph::printGraph() {
    for (int v = 0; v < V; v++) {
        std::cout << "Vertex " << v << " : ";
        for (int w : adj[v]) {
            std::cout << w << " ";
        }
        std::cout << std::endl;
    }
}

This code defines a simple graph class with methods to add edges and print the graph.

What are some common algorithms used in graph theory?

Some common algorithms in graph theory include:

1. Depth-First Search (DFS)
2. Breadth-First Search (BFS)
3. Dijkstra's algorithm for shortest paths
4. Kruskal's and Prim's algorithms for minimum spanning trees
5. Floyd-Warshall algorithm for all pairs shortest paths.