最短路径（Dijkstra）

#include<iostream>

using  namespace  std;

typedef  char VertexType;
typedef  int EdgeType;

const  int   MAXVEX = 100;
const  int   INFINITY = 65535;

typedef  int Patharc[MAXVEX];
typedef  int shortPathTable[MAXVEX];

typedef  struct
{
    VertexType  vexs[MAXVEX];
    EdgeType    arc[MAXVEX][MAXVEX];
    int numVertexes,numEdges;
}MGraph;


//D记录V0点到其他顶点的路劲总权值，P记录所经过哪些点
void  ShortestPath_Dijkastra(MGraph *G,Patharc *P,shortPathTable *D)
{
    int i , j, k, min;
    int final[MAXVEX];
    for(i = 0;i < G->numVertexes;++i)
    {
        (*D)[i] = G->arc[0][i];
        (*P)[i] = 0;
        final[i] = 0;
    }
     final[0] = 1;
     for(i = 0;i < G->numVertexes;++i)
     {
         min = INFINITY;
         for(j = 0;j < G->numEdges;++j)
         {
             if(!final[j] && (*D)[j] < min)
             {
                 k = j;
                 min = (*D)[j];
             }
         }
         final[k] = 1;
         for(j = 0;j < G->numEdges;++j)
         {
             if(!final[j] && (min + G->arc[k][j]) <  (*D)[j])
             {
                 (*D)[j] = min + G->arc[k][j];
                 (*P)[j] = k;
             }
         }
     }
}


/*
建立无向网图的邻接矩阵表示
*/

void  CreateMGraph_Undirected(MGraph *G)
{
    int i,j,k,w;
    cin>>G->numVertexes>>G->numEdges;
    for(i = 0;i < G->numVertexes;++i)//输入顶点
    {       
        cin>>G->vexs[i];
    }

    for(i = 0;i < G->numVertexes;++i)//初始化邻接矩阵,除对角线元素 = 0，其余为INFINITY;
    {
        for(j = 0;j < G->numVertexes;++j)
        {
            if(i == j)
            {
                G->arc[i][j] = 0;
            }
            else
            {
                G->arc[i][j] = INFINITY;
            }
        }
    }

    for(k = 0;k < G->numEdges;++k)//完成邻接矩阵的填写工作
    {
        cin>>i>>j>>w;
        G->arc[i][j] = G->arc[j][i] = w;
    }
}

void  ShowMGraph(MGraph *G)//打印图的信息
{
    cout<<"图的顶点，边数为："<<G->numVertexes<<","<<G->numEdges<<endl;
    cout<<"邻接矩阵为："<<endl;
    
    for(int i = 0;i < G->numVertexes;++i)
    {
        for(int j = 0;j < G->numVertexes;++j)
        {
            if(G->arc[i][j] == INFINITY)
            {
                cout<<"#  ";
            }
            else
            {
                cout<<"  "<<G->arc[i][j]<<"  ";
            }
        }
        cout<<endl;
    }
}




int main()
{
    MGraph *G = new MGraph();
    Patharc P;
    shortPathTable D;
    CreateMGraph_Undirected(G);
    ShowMGraph(G);
    ShortestPath_Dijkastra(G,&P,&D);
    delete G;
}