#include <iostream>#include <vector>#define INFINITY 32768#define VERTEX_MAX 50using namespace std;typedef char VertexType;//顶点类型typedef int AdjType;//边的关系类型typedef struct {VertexType vertex[VERTEX_MAX];//顶点集AdjType arcs[VERTEX_MAX][VERTEX_MAX];//边集int vexnum,arcnum;//图的当前顶点数和弧数}MGraph;void CreateDNGraph(MGraph *G);void ShortestPath_DJS(MGraph G,int v0,int dist[VERTEX_MAX],int path[VERTEX_MAX]);int main(){MGraph G;CreateDNGraph(&G);int dist[VERTEX_MAX];int path[VERTEX_MAX];ShortestPath_DJS(G,0,dist,path);return 0;}//求顶点位置函数int LocateVex(MGraph *G,VertexType v){int i;for(i=0;i<G->vexnum;i++){if(G->vertex[i] == v)return i;}return -1;}//创建又向带权图void CreateDNGraph(MGraph *G){ int i,j;VertexType v1,v2;int w;cout<<"请输入顶点数和边数：";cin>>G->vexnum>>G->arcnum;cout<<"请输入各顶点的数据:";for(int i=0;i<G->vexnum;i++)cin>>G->vertex[i];for (int i = 0; i < G->vexnum; i++){for(int j=0;j< G->vexnum;j++)G->arcs[i][j] = INFINITY;}cout<<"请输入"<<G->arcnum<<"对顶点和相应的权重：\n";for(int k=0; k<G->arcnum; k++){cin>>v1>>v2>>w;i = LocateVex(G,v1);j = LocateVex(G,v2);if(i>=0 && j>=0)G->arcs[i][j] = w;} }//dist[i]：存放目前已经找到的，从开始点v0到终点vi的当前最短路径长度//path[i]: 存放目前已经找到的，从开始点v0到终点vi的当前最短路径的顶点下标序列void ShortestPath_DJS(MGraph G,int v0,int dist[VERTEX_MAX],int path[VERTEX_MAX]){int min,j,k;int final[VERTEX_MAX];//为1代表已求得v0到v的最短路径（最短路径的终点集合）for (int i = 0; i < G.vexnum; i++){final[i] = 0;dist[i] = G.arcs[v0][i];//将v0到各顶点的最短路径长度初始化为权值if(dist[i]<INFINITY)path[i] = v0;//初始化各顶点的最短路径为边(v0,vi)}final[v0] = 1;//讲顶点v0加入终点集合dist[v0] = 0;//将最开始顶点(源点)的最短路径置为0for (int i = 0; i < G.vexnum; i++){min = INFINITY;for (j = 0; j < G.vexnum; j++){if (final[j]==0 && dist[j]<min)//查找未用顶点的最小权值{min = dist[j];k = j;}}final[k] = 1;//将顶点k加入终点集合for(j=0;j<G.vexnum;j++){//以顶点k为中间点，重新计算权重if (final[j]==0 && dist[k]+G.arcs[k][j]<dist[j]){dist[j] = dist[k]+G.arcs[k][j];//更新权值path[j] = k;//将k加入最短路径}}}cout<<"顶点"<<G.vertex[v0]<<"到各顶点的最短路径为:[(终点 <- 源点)倒序输出]"<<endl;for (int i = 1; i < G.vexnum; i++){if(final[i] == 1)//若顶点i在终点集合U中{k = i;while(k!=v0)//顶点序列不与源点相同{j = k;//由终点向前追溯cout<<"<- "<<G.vertex[k];//输出经过的顶点k = path[j];//上一个顶点}cout<<"<- "<<G.vertex[k]<<endl;//源点cout<<"最短路径长度为:";cout<<dist[i]<<endl;}else{cout<<G.vertex[v0]<<"->"<<G.vertex[i]<<":无路径"<<endl;}}}/*a b 50a c 10a e 45b c 15b e 10c a 20c d 15d b 20d e 35e d 30f d 3*/
，并且如此真实的活着——这，就是旅行的意义。
