What is graph theory and how can I implement it in C#?

What is graph theory and how can I implement it in C#?

Graph theory is a field of mathematics that studies graphs, which are structures made up of nodes (or vertices) connected by edges. In C#, you can implement graph theory concepts using data structures like adjacency lists or matrices.

Can you show me an example of how to create a graph in C#?

Sure! Here's a simple example using an adjacency list:

using System;
using System.Collections.Generic;

class Graph {
    private Dictionary<int, List<int>> adjList;

    public Graph() {
        adjList = new Dictionary<int, List<int>>();
    }

    public void AddEdge(int v, int w) {
        if (!adjList.ContainsKey(v)) {
            adjList[v] = new List<int>();
        }
        adjList[v].Add(w);
    }
}

How do I perform a depth-first search on this graph?

You can implement depth-first search (DFS) using recursion. Here's a simple method to do that:

public void DFS(int start) {
    HashSet<int> visited = new HashSet<int>();
    DFSUtil(start, visited);
}

private void DFSUtil(int v, HashSet<int> visited) {
    visited.Add(v);
    Console.WriteLine(v);

    foreach (var neighbor in adjList[v]) {
        if (!visited.Contains(neighbor)) {
            DFSUtil(neighbor, visited);
        }
    }
}

What are some common applications of graph theory?

Graph theory has many applications, including network routing, social network analysis, scheduling problems, and more. It's widely used in computer science, biology, and logistics.