单源最短路径－－－－Dijkstra算法

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#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0    for (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*/
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