迪杰斯特拉算法 源程序

/**********************迪杰斯特拉算法*********************************************/
#include <stdio.h>

#define INFINITY 10000
#define TRUE 1
#define FALSE 0
#define VERTEX_NUM 6

typedef struct Graph
{
    char vexs[VERTEX_NUM];  /*顶点*/
    int arcs[VERTEX_NUM][VERTEX_NUM];   /*邻接矩阵*/
    int vexnum;     /*顶点数*/
    int arcnum;     /*弧数*/
}Graph;

void ShortestPath(Graph g,int v0,int p[][VERTEX_NUM],int d[])
{
/*迪杰斯特拉算法求最短路径，g为图的邻接矩阵，v0为起始顶点，
p[v][w]储存v0到v路径上w的后继顶点(无后继置-1)，d[v]为路径v0到v的带权长度*/
    int v;
    int w;
    int min;
    int i,j;
    int final[VERTEX_NUM];  /*final[v]=TRUE当且仅当v属于S*/
    
    /*初始化数组*/
    for (v = 0; v < g.vexnum; v++)
    {
        final[v] = FALSE;
        d[v] = g.arcs[v0][v];
        for (w = 0; w < g.vexnum; w++)
        {
            p[v][w] = -1;
        }
        if (d[v] < INFINITY)
        {
            p[v][0] = v0;
            p[v][1] = v;
        }
    }
    /*初始化，顶点v0属于S集合*/
    d[v0] = 0;
    final[v0] = TRUE;
    /*循环n-1次求最短路径*/
    for (i = 1; i < g.vexnum; i++)      
    {
        min=INFINITY;
        for (w = 0; w<g.vexnum; w++)
        {
            if (!final[w])  /* w属于V-S */
            {
                if (d[w] < min)
                {
                    /* w顶点离v0更近 */
                    v=w;
                    min=d[w];
                 }
             }
        }
        final[v] = TRUE;    /*离v0顶点最近的v加入S集*/
        for (w = 0; w<g.vexnum; w++)    /*更新当前最短路径及距离*/
        {
            if (!final[w] && (min+g.arcs[v][w] < d[w]) )
            {   
                                           /*修改d[w]和p[w] (w属于V-S) */
                d[w] = min + g.arcs[v][w];
                for (j = 0; p[v][j]> -1 && j < VERTEX_NUM; j++)
                {
                    p[w][j] = p[v][j];  /* p[w]=p[v] */
                 }
                p[w][j] = w;        /* p[w]=p[v]+w */
             }
        }
    }
}

void main()
{
    int i,
        j;
    Graph g;
    int p[VERTEX_NUM][VERTEX_NUM];
    int d[VERTEX_NUM];
    int v0;

    /*初始化图g*/
    g.vexs[0]='A',g.vexs[1]='B',g.vexs[2]='C',g.vexs[3]='D',g.vexs[4]='E',g.vexs[5]='F';
    for(i=0;i<VERTEX_NUM;i++)
        for(j=0;j<VERTEX_NUM;j++)       
            g.arcs[i][j]=INFINITY;
    g.arcs[0][2]=10,g.arcs[0][4]=30,g.arcs[0][5]=100,g.arcs[1][2]=5,
        g.arcs[2][3]=50,g.arcs[3][5]=10,g.arcs[4][3]=20,g.arcs[4][5]=60;
    g.vexnum=g.arcnum=VERTEX_NUM;

    /*输出图的有关信息*/
    for(i=0;i<VERTEX_NUM;i++)
    {
        printf("%c\t",g.vexs[i]);
        for(j=0;j<VERTEX_NUM;j++)
        {
            printf("%5d ",g.arcs[i][j]);
        }
        printf("\n");
    }
    printf("\n");

    /*求最短路径*/
    v0 = 0;
    ShortestPath(g,v0,p,d);

    /*输出最短路径*/
    for (i = 0; i < g.vexnum; i++)
    {
        printf("Path %c to %c:\n",g.vexs[v0],g.vexs[i]);
        if ( p[i][v0] != -1 )   /*存在路径则输出*/
        {
            for (j = 0; p[i][j]!=-1; j++)
            {
                if (j != 0)
                    printf("→");
                printf("  %c",g.vexs[p[i][j]]);
            }
            printf("\n");
        }
        printf("Length:%d\n",d[i]);
        printf("\n");
    }
}
/**********************迪杰斯特拉算法*********************************************/