最短路径 Dijkstra算法

#include "stdio.h"

#define INFINITY 100
#define MAX_VERTEX_NUM 20

struct MGraph {
char vexs[MAX_VERTEX_NUM];
int arcs[6][6];
int vexnum, arcnum;
};

/*记录路径的数组, to[i].before 表示 v0 到 vi 的次短路径节点*/
struct PathArray{
int before;
}to[6];

/*lenth[i]表示v0到vi的最短路径长度*/
void myshortestpathfun(MGraph g, int v0, PathArray to[6], int lenth[6])
{
int i, j, k, t, num, temp[6];//temp[i]=1表示vi已经在最短路径上了，temp[i]= 0表示vi还不在最短路径上;

/*初始化*/
for (i = 0; i < 6; i++)
{
to[i].before = INFINITY;
lenth[i] = INFINITY;
temp[i] = 0;
}

/*第一轮比较*/
for (i = 0; i < 6; i ++)
{
if (g.arcs[v0][i] < INFINITY)
{
to[i].before = v0;
lenth[i] = g.arcs[v0][i];
}

}
temp[v0] = 1; //v0已经在最短路径了;

/*找出v0到vi中最短的一点vi，将节点下标保存到t中*/
int temp2 = INFINITY;
for (i = 0; i < 6; i++)
{
if (1 == temp[i])
continue; //从不在最短路径上的那些点中找出最短的;
if (lenth[i] < temp2)
{
temp2 = lenth[i];
t = i;
}
}

for (num = 0; num < 5; num++) //再比较5轮;
{
for (i = 0; i < 6; i++)
{
if (g.arcs[t][i] + lenth[t] < lenth[i])
{
to[i].before = t;
lenth[i] = g.arcs[t][i] + lenth[t];
}
}
temp[t] = 1; //vt已经在最短路径了;

temp2 = INFINITY;
for (i = 0; i < 6; i++)
{
if (1 == temp[i])
continue;
if (lenth[i] < temp2)
{
temp2 = lenth[i];
t = i;
}
}
}

printf("\nv%d 到各点的最短距离是：\n\n",v0);

for (num = 0; num < 6; num++)
{
printf("v%d -> v%d : %d\n", v0, num, lenth[num]);
}
printf("\n\n");

printf("v%d 到各点的最短路径： \n\n",v0);
for (j = 0; j < 6; j++)
{
printf("v%d -> v%d path:\t ",v0, j);
printf("v%d <- ", j);
for (i = j; to[i].before != v0; )
{
printf("v%d <- ", to[i].before);
i = to[i].before;

}
printf("v%d", v0);
printf("\n");
}
}

int main()
{
int i,j;
int p[6];
int d[6];

PathArray to[6];
int lenth[6];

MGraph a;

int arcs1[6][6]=
{
INFINITY,5,INFINITY,7,INFINITY,INFINITY,
INFINITY,INFINITY,4,INFINITY,INFINITY,INFINITY,
8,INFINITY,INFINITY,INFINITY,INFINITY,9,
INFINITY,INFINITY,5,INFINITY,INFINITY,6,
INFINITY,INFINITY,INFINITY,5,INFINITY,INFINITY,
3,INFINITY,INFINITY,INFINITY,1,INFINITY};
int vexs1[] = {1,2,3,4,5,6};
for(i = 0; i < 6;i++)
{
a.vexs[i] = vexs1[i];
}

/*初始化*/
a.vexnum = 6;
a.arcnum = 10;

for(i = 0;i < a.vexnum; i++ )
for(j = 0;j < a.vexnum;j++)
{
a.arcs[i][j] = arcs1[i][j];
}

printf("各节点的邻接关系为 :\n\n");

for (i = 0; i < 6; i++)
{
printf("\tv%d",i);
}

printf("\n");

for (i = 0; i < a.vexnum; i++)
{
printf("v%d\t",i);

for(j = 0; j < a.vexnum; j++)
{
printf("%d\t",a.arcs[i][j]);
}

printf("\n");
}

for (i = 0; i < 6; i++)
{
myshortestpathfun(a, i, to, lenth);
printf("\n");
}

return 0;
}