最短路径-Dijkstra详解-源代码

//算法6.10　迪杰斯特拉算法#include <iostream>using namespace std;#define MaxInt 32767                    //表示极大值，即∞#define MVNum 100                       //最大顶点数typedef char VerTexType;              //假设顶点的数据类型为字符型 typedef int ArcType;                  //假设边的权值类型为整型int *D=new int[MVNum];                    //用于记录最短路的长度bool *S=new bool[MVNum];          //标记顶点是否进入S集合int *Path=new int[MVNum];//用于记录最短路顶点的前驱//------------图的邻接矩阵-----------------typedef struct{ VerTexType vexs[MVNum];            //顶点表 ArcType arcs[MVNum][MVNum];      //邻接矩阵 int vexnum,arcnum;                //图的当前点数和边数 }AMGraph;int LocateVex(AMGraph G , VerTexType v){//确定点v在G中的位置for(int i = 0; i < G.vexnum; ++i)if(G.vexs[i] == v)return i;   return -1;}//LocateVexvoid CreateUDN(AMGraph &G){     //采用邻接矩阵表示法，创建无向网G int i , j , k;cout <<"请输入总顶点数，总边数，以空格隔开:";    cin >> G.vexnum >> G.arcnum;//输入总顶点数，总边数cout << endl;cout << "输入点的名称:，如a" << endl;    for(i = 0; i < G.vexnum; ++i){   cout << "请输入第" << (i+1) << "个点的名称:";cin >> G.vexs[i];                        //依次输入点的信息 }cout << endl;    for(i = 0; i < G.vexnum; ++i)                //初始化邻接矩阵，边的权值均置为极大值MaxInt for(j = 0; j < G.vexnum; ++j)   G.arcs[i][j] = MaxInt; cout << "输入边依附的顶点及权值，如a b 7" << endl;for(k = 0; k < G.arcnum;++k){//构造邻接矩阵 VerTexType v1 , v2;ArcType w;cout << "请输入第" << (k + 1) << "条边依附的顶点及权值:";cin >> v1 >> v2 >> w;//输入一条边依附的顶点及权值i = LocateVex(G, v1);  j = LocateVex(G, v2);//确定v1和v2在G中的位置，即顶点数组的下标 G.arcs[i][j] = w;//边<v1, v2>的权值置为w G.arcs[j][i] = G.arcs[i][j];//置<v1, v2>的对称边<v2, v1>的权值为w }//for}//CreateUDNvoid ShortestPath_DIJ(AMGraph G, int v0){     //用Dijkstra算法求有向网G的v0顶点到其余顶点的最短路径     int v , i , w , min;int n = G.vexnum;                    //n为G中顶点的个数 for(v = 0; v < n; ++v){             //n个顶点依次初始化 S[v] = false;                  //S初始为空集 D[v] = G.arcs[v0][v];           //将v0到各个终点的最短路径长度初始化为弧上的权值 if(D[v] < MaxInt)  Path [v] = v0;  //如果v0和v之间有弧，则将v的前驱置为v0 else Path [v] = -1;               //如果v0和v之间无弧，则将v的前驱置为-1 }//for S[v0]=true;                    //将v0加入S D[v0]=0;                      //源点到源点的距离为0 /*―初始化结束，开始主循环，每次求得v0到某个顶点v的最短路径，将v加到S集―*/ for(i = 1;i < n; ++i){//对其余n-1个顶点，依次进行计算         min= MaxInt;         for(w = 0; w < n; ++w) if(!S[w] && D[w] < min){//选择一条当前的最短路径，终点为v v = w; min = D[w];}//if         S[v]=true;                   //将v加入S for(w = 0;w < n; ++w)           //更新从v0出发到集合V?S上所有顶点的最短路径长度 if(!S[w] && (D[v] + G.arcs[v][w] < D[w])){ D[w] = D[v] + G.arcs[v][w];   //更新D[w] Path [w] = v;              //更改w的前驱为v }//if     }//for  }//ShortestPath_DIJvoid DisplayPath(AMGraph G , int begin ,int temp ){//显示最短路if(Path[temp] != -1){DisplayPath(G , begin ,Path[temp]);cout << G.vexs[Path[temp]] << "-->";}}//DisplayPathvoid main(){cout << "************算法6.10　迪杰斯特拉算法**************" << endl << endl;AMGraph G; int i , j ,num_start , num_destination;VerTexType start , destination;CreateUDN(G);cout <<endl;cout << "*****无向网G创建完成！*****" << endl;for(i = 0 ; i < G.vexnum ; ++i){for(j = 0; j < G.vexnum; ++j){if(j != G.vexnum - 1){if(G.arcs[i][j] != MaxInt)cout << G.arcs[i][j] << "\t";elsecout << "∞" << "\t";}else{if(G.arcs[i][j] != MaxInt)cout << G.arcs[i][j] <<endl;elsecout << "∞" <<endl;}}}//forcout << endl;cout << "请依次输入起始点、终点名称：";cin >> start >> destination;num_start = LocateVex(G , start);num_destination = LocateVex(G , destination);ShortestPath_DIJ(G , num_start);cout << endl <<"最短路径为：";DisplayPath(G , num_start , num_destination);cout << G.vexs[num_destination]<<endl;}//main