c# Fluery算法构造欧拉回路

以下是使用C#实现Fleury算法构造欧拉回路的示例代码：

using System;
using System.Collections.Generic;

class Graph
{
    private int V; // 图中顶点的数量
    private List<int>[] adj; // 存储图的邻接表

    // 构造函数
    public Graph(int v)
    {
        V = v;
        adj = new List<int>[V];
        for (int i = 0; i < V; ++i)
        {
            adj[i] = new List<int>();
        }
    }

    // 添加一条边
    public void AddEdge(int v, int w)
    {
        adj[v].Add(w);
        adj[w].Add(v);
    }

    // 从顶点v开始进行DFS遍历
    private void DFS(int v, bool[] visited)
    {
        visited[v] = true;
        foreach (int i in adj[v])
        {
            if (!visited[i])
            {
                DFS(i, visited);
            }
        }
    }

    // 判断图是否连通
    private bool IsConnected()
    {
        bool[] visited = new bool[V];
        int i;
        for (i = 0; i < V; ++i)
        {
            visited[i] = false;
        }
        for (i = 0; i < V; ++i)
        {
            if (adj[i].Count != 0)
            {
                break;
            }
        }
        if (i == V)
        {
            return true;
        }
        DFS(i, visited);
        for (i = 0; i < V; ++i)
        {
            if (!visited[i] && adj[i].Count > 0)
            {
                return false;
            }
        }
        return true;
    }

    // 判断顶点v的度数
    private int Degree(int v)
    {
        int degree = 0;
        foreach (int i in adj[v])
        {
            ++degree;
        }
        return degree;
    }

    // 从顶点v开始进行Fleury算法构造欧拉回路
    private void Fleury(int v, List<int> circuit)
    {
        for (int i = 0; i < adj[v].Count; ++i)
        {
            int w = adj[v][i];
            if (Degree(v) == 1) // 如果顶点v的度数为1，则直接将v和w之间的边加入欧拉回路中
            {
                circuit.Add(w);
                adj[v].Remove(w);
                adj[w].Remove(v);
                Fleury(w, circuit);
            }
            else if (IsBridge(v, w)) // 如果v和w之间的边是桥，则将v和w之间的边加入欧拉回路中
            {
                circuit.Add(w);
                adj[v].Remove(w);
                adj[w].Remove(v);
                Fleury(w, circuit);
            }
        }
    }

    // 判断边(v, w)是否是桥
    private bool IsBridge(int v, int w)
    {
        adj[v].Remove(w);
        adj[w].Remove(v);
        bool[] visited = new bool[V];
        int count1 = CountComponents(visited);
        adj[v].Add(w);
        adj[w].Add(v);
        int count2 = CountComponents(visited);
        adj[v].Remove(w);
        adj[w].Remove(v);
        return (count1 > count2);
    }

    // 计算图的连通分量数量
    private int CountComponents(bool[] visited)
    {
        int count = 0;
        for (int i = 0; i < V; ++i)
        {
            visited[i] = false;
        }
        for (int i = 0; i < V; ++i)
        {
            if (!visited[i] && adj[i].Count > 0)
            {
                DFS(i, visited);
                ++count;
            }
        }
        return count;
    }

    // 构造欧拉回路
    public List<int> EulerianCircuit()
    {
        List<int> circuit = new List<int>();
        if (!IsConnected())
        {
            return circuit;
        }
        int oddDegreeVertices = 0;
        int startVertex = 0;
        for (int i = 0; i < V; ++i)
        {
            if (Degree(i) % 2 != 0)
            {
                ++oddDegreeVertices;
                startVertex = i;
            }
        }
        if (oddDegreeVertices > 2)
        {
            return circuit;
        }
        Fleury(startVertex, circuit);
        return circuit;
    }
}

class Program
{
    static void Main(string[] args)
    {
        Graph g = new Graph(5);
        g.AddEdge(1, 0);
        g.AddEdge(0, 2);
        g.AddEdge(2, 1);
        g.AddEdge(0, 3);
        g.AddEdge(3, 4);
        List<int> circuit = g.EulerianCircuit();
        if (circuit.Count == 0)
        {
            Console.WriteLine("No Eulerian circuit");
        }
        else
        {
            Console.Write("Eulerian circuit: ");
            foreach (int i in circuit)
            {
                Console.Write(i + " ");
            }
            Console.WriteLine();
        }
    }
}