多源最短路径Floyd算法

设d[i][j]为顶点 i 与顶点 j 的最短路径，设 k为i与j之间的点，那么d[i][j] = d[i][k] + d[k][j];

算法核心为：

void floyd()
{
int i,j,k;
for(k = 1; k <= n; k++)
{
for(i = 1; i <= n; i++)
{
for(j = 1; j <= n; j++)
{
if(d[i][k] + d[k][j] < d[i][j])
{
d[i][j] = d[i][k] + d[k][j];
path[i][j] = k;
}
}
}
}
}path[i][j]记录的是最短路径中到j的上一个点，初始化为-1，若最后path[i][j] = -1,说明j是与源点i相邻的点
例：

#include<iostream>
#include<vector>
#include<windows.h>
using namespace std;
#define NUM 101
#define INF 99999999
int d[NUM][NUM];
int path[NUM][NUM];
int n,m;
void floyd()
{
int i,j,k;
for(k = 1; k <= n; k++)
{
for(i = 1; i <= n; i++)
{
for(j = 1; j <= n; j++)
{
if(d[i][k] + d[k][j] < d[i][j])
{
d[i][j] = d[i][k] + d[k][j];
path[i][j] = k;
}
}
}
}
}

void findPre(int i,int j)
{
cout<<j<<"-";
if(path[i][j] == -1)
{
cout<<i;
return;
}
else
{
findPre(i,path[i][j]);
}
}
int main()
{
int i,j;
scanf("%d%d",&n,&m);
for(i = 1; i <= n; i++)
{
for(j = 1; j <= n; j++)
{
d[i][j] = INF;
path[i][j] = -1;
}
}
for(i = 1; i <= m; i++)
{
int a,b,c;
scanf("%d%d%d",&a,&b,&c);
d[a][b] = d[b][a] = c;
}
floyd();
for(i = 1; i <= n; i++)
{
for(j = 1; j <= n; j++)
{
if(d[i][j] < INF && i == 1 && j != 1)
{
printf("%d到%d的最短路径为：%d ",i,j,d[i][j]);
printf("路径为：");
findPre(i,j);
printf("\n");
}
}
}
system("pause");
return 0;

}