C＃实现基于广度优先BFS求解无权图最短路径----完整程序展示

本文介绍C#实现基于广度优先BFS求解无权图最短路径----完整程序展示

1、代码
using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace 图的应用__基于BFS算法求解的那元最短路径
{
using VertexType = System.Char;//顶点数据类型别名声明
using EdgeType = System.Int16;//带权图中边上权值的数据类型别名声明
class Program
{
public const int MAxVertexNum = 100;//顶点数目的最大值
public const int MAXSize = 100;
static void Main(string[] args)
{
MGraph G = new MGraph();
int u;
int[] d = new int[MAxVertexNum];
G.vexnum = 8;
G.arcnum = 8;
G.vex = new VertexType[MAxVertexNum];
G.Edge = new EdgeType[MAxVertexNum, MAxVertexNum];
for (int i = 0; i < MAxVertexNum; ++i)
{
for (int j = 0; j < MAxVertexNum; ++j)
{
G.Edge[i, j] = 0;
}
}
//图的赋值
G.vex[0] = ‘a’; G.vex[1] = ‘b’; G.vex[2] = ‘c’; G.vex[3] = ‘d’; G.vex[4] = ‘e’; G.vex[5] = ‘f’;
G.vex[6] = ‘g’; G.vex[7] = ‘h’;
G.Edge[0, 1] = 1; G.Edge[0, 2] = 1;
G.Edge[1, 0] = 1; G.Edge[1, 3] = 1; G.Edge[1, 4] = 1;
G.Edge[2, 0] = 1; G.Edge[2, 5] = 1; G.Edge[2, 6] = 1;
G.Edge[3, 1] = 1;
G.Edge[4, 1] = 1; G.Edge[4, 7] = 1;
G.Edge[5, 2] = 1;
G.Edge[6, 2] = 1;
G.Edge[7, 4] = 1;
//广度优先
Console.WriteLine(“广度优先：”);
BFSTraverse(G);
u = 3;
Console.WriteLine();
Console.WriteLine(“顶点”+G.vex[u]+“到各点最短路径：”);
BFS_MIN_Distance(G,u,ref d);
for (int i=0;i<G.vexnum;++i) {
Console.Write(d[i]+" ");

        }



        Console.Read();
    }



    /// <summary>
    /// 图的定义--邻接矩阵
    /// </summary>
    public struct MGraph
    {
        public VertexType[] vex;//顶点表数组
        public EdgeType[,] Edge;//临接矩阵、边表
        public int vexnum, arcnum;//图的当前顶点数和弧数
    }
    /// <summary>
    /// 图的定义--邻接表法
    /// </summary>
    public class ArcNode
    {//边表节点
        public int adjvex;
        public ArcNode next;
    }
    public class VNode
    {  //顶点表节点
        VertexType data;//顶点信息
        ArcNode first;//只想第一条依附改顶点的弧的指针
    }
    public class ALGraph
    {
        VNode[] vertices;   //邻接表
        int vexnum, arcnum;//图的顶点数和弧数
    }
    /// <summary>
    /// 对图G的广度优先遍历
    /// </summary>
    static void BFSTraverse(MGraph G)
    {
        bool[] visited = new bool[MAxVertexNum];//访问标记数组
        for (int i = 0; i < G.vexnum; ++i)
            visited[i] = false;//访问标记数组初始化
        SqQueue Q = new SqQueue();
        Q.data = new int[MAxVertexNum];//需要对队列数组进行new
        InitQueue(ref Q);//队列初始化
        for (int i = 0; i < G.vexnum; ++i)
        {
            if (!visited[i])
                BFS(G, i, ref visited, ref Q);

        }

    }

    static void BFS(MGraph G, int v, ref bool[] visited, ref SqQueue Q)
    {
        visit(G, v);//首先访问初始顶点v
        visited[v] = true;//对v做已访问标记
        EnQueue(ref Q, v);//顶点v入队列
        while (!isEmpty(Q))
        {
            DeQueue(ref Q, ref v);//顶点v出队列
            for (int w = FirstNeighbor(G, v); w >= 0; w = NextNeighbor(G, v, w))
            {
                if (!visited[w])
                {
                    visit(G, w);   //访问顶点w
                    visited[w] = true;//对w做已访问标记
                    EnQueue(ref Q, w);
                }


            }

        }

    }
    //控制台打印遍历点
    static void visit(MGraph G, int v)
    {
        Console.Write(G.vex[v] + " ");
    }
    //查找G中，V顶点的首个邻接点
    static int FirstNeighbor(MGraph G, int v)
    {
        int b = -1;
        for (int i = 0; i < G.vexnum; ++i)
        {
            if (G.Edge[v, i] == 1)
            {
                b = i;
                break;
            };
        }
        return b;//返回首个邻接点
    }
    //查找G中，V顶点的W邻节点后的下一个邻接点
    static int NextNeighbor(MGraph G, int v, int w)
    {
        int b = -1;
        for (int i = w + 1; i < G.vexnum; ++i)
        {
            if (G.Edge[v, i] == 1)
            {
                b = i;
                break;
            };
        }
        return b;//返回下一个邻接点
    }
    //求单源最短路径,即u到各顶点的最短路径长度
    static void BFS_MIN_Distance(MGraph G,int u,ref int[] d) {
        bool[] visited = new bool[MAxVertexNum];//访问标记数组
        SqQueue Q = new SqQueue();
        InitQueue(ref Q);
        Q.data = new int[MAxVertexNum];
        for (int i=0;i<G.vexnum;++i) {
            visited[i] = false;
            d[i] = -1;//初始化路径长度。-1表示没有
        }
        visited[u] = true;d[u] = 0;
        EnQueue(ref Q,u);
        while (!isEmpty(Q)) {
            DeQueue(ref Q, ref u);
            for (int w=FirstNeighbor(G,u);w>=0;w=NextNeighbor(G,u,w)) {
                if (!visited[w]) {
                    d[w] = d[u] + 1;
                    visited[w] = true;
                    EnQueue(ref Q, w);
                }


            }

        }


    }




    /// <summary>
    /// 队列结构体定义
    /// </summary>
    public struct SqQueue
    {
        public int[] data;//队列存放的元素
        public int front, real;//队头和队尾指针
    }
    /// <summary>
    /// 队列初始化
    /// </summary>
    /// <param name="Q"></param>
    static void InitQueue(ref SqQueue Q)
    {
        Q.real = Q.front = 0;
    }
    /// <summary>
    /// 判断队列是否为空
    /// </summary>
    /// <param name="Q"></param>
    /// <returns></returns>
    static bool isEmpty(SqQueue Q)
    {
        if (Q.front == Q.real) { return true; }
        else return false;
    }
    /// <summary>
    /// 入队
    /// </summary>
    /// <param name="Q"></param>
    /// <param name="x"></param>
    /// <returns></returns>
    static bool EnQueue(ref SqQueue Q, int x)
    {
        if ((Q.real + 1) % MAXSize == Q.front) { return false; }
        Q.data[Q.real] = x;
        Q.real = (Q.real + 1) % MAXSize;
        return true;
    }

    static bool DeQueue(ref SqQueue Q, ref int x)
    {
        if (Q.real == Q.front) { return false; }
        x = Q.data[Q.front];
        Q.front = (Q.front + 1) % MAXSize;
        return true;
    }
}

}
2、测试结果