What is graph theory in C++?

Can you explain what graph theory is in the context of 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.

How can I implement a graph in C++?

You can implement a graph in C++ using an adjacency list. Here's a simple example:

#include <iostream>
#include <vector>
using namespace std;

class Graph {
    int V; // Number of vertices
    vector<vector<int>> adj; // Adjacency list
public:
    Graph(int V) : V(V), adj(V) {}
    void addEdge(int v, int w) {
        adj[v].push_back(w); // Add w to v's list
    }
};

This code defines a basic graph class with a method to add edges.

What algorithms can I use with graphs in C++?

You can use various algorithms with graphs in C++, such as Depth-First Search (DFS), Breadth-First Search (BFS), Dijkstra's algorithm for shortest paths, and Kruskal's or Prim's algorithm for minimum spanning trees.

Can you give me an example of Dijkstra's algorithm in C++?

Sure! Here's a simple implementation of Dijkstra's algorithm:

#include <iostream>
#include <vector>
#include <queue>
#include <climits>
using namespace std;

void dijkstra(int src, vector<vector<pair<int, int>>>& graph) {
    vector<int> dist(graph.size(), INT_MAX);
    dist[src] = 0;
    priority_queue<pair<int, int>, vector<pair<int, int>>, greater<pair<int, int>>> pq;
    pq.push({0, src});

    while (!pq.empty()) {
        int u = pq.top().second;
        pq.pop();

        for (auto& edge : graph[u]) {
            int v = edge.first, weight = edge.second;
            if (dist[u] + weight < dist[v]) {
                dist[v] = dist[u] + weight;
                pq.push({dist[v], v});
            }
        }
    }
}

This code finds the shortest paths from the source vertex to all other vertices.