Dijkstra算法的C语言程序

Dijikstra算法是从一个顶点到其余各顶点的最短路径算法，解决的是有向图中最短路径问题。该算法是由荷兰计算机科学家迪杰斯特拉于1959年提出的。

程序来源：Dijkstra's Algorithm。

百度百科：Dijkstra算法。

维基百科：Dijkstra's Algorithm。

C语言程序（去除了原文中非标准的C语言代码）：

#include

#define INFINITY 9999
#define MAX 10

void dijikstra(int G[MAX][MAX], int n, int startnode);

int main(){
    int G[MAX][MAX], i, j, n, u;

    printf("\nEnter the no. of vertices:: ");
    scanf("%d", &n);
    printf("\nEnter the adjacency matrix::\n");
    for(i=0;i < n;i++)
        for(j=0;j < n;j++)
            scanf("%d", &G[i][j]);
    printf("\nEnter the starting node:: ");
    scanf("%d", &u);
    dijikstra(G,n,u);
}

void dijikstra(int G[MAX][MAX], int n, int startnode)
{
    int cost[MAX][MAX], distance[MAX], pred[MAX];
    int visited[MAX], count, mindistance, nextnode, i,j;
    for(i=0;i < n;i++)
        for(j=0;j < n;j++)
            if(G[i][j]==0)
                cost[i][j]=INFINITY;
            else
                cost[i][j]=G[i][j];

    for(i=0;i< n;i++) {
        distance[i]=cost[startnode][i];
        pred[i]=startnode;
        visited[i]=0;
    }
    distance[startnode]=0;
    visited[startnode]=1;
    count=1;
    while(count < n-1) {
        mindistance=INFINITY;
        for(i=0;i < n;i++)
            if(distance[i] < mindistance&&!visited[i]) {
                mindistance=distance[i];
                nextnode=i;
            }
        visited[nextnode]=1;
        for(i=0;i < n;i++)
            if(!visited[i])
                if(mindistance+cost[nextnode][i] < distance[i]) {
                    distance[i]=mindistance+cost[nextnode][i];
                    pred[i]=nextnode;
                }
            count++;
    }

    for(i=0;i < n;i++)
        if(i!=startnode) {
            printf("\nDistance of %d = %d", i, distance[i]);
            printf("\nPath = %d", i);
            j=i;
            do {
                j=pred[j];
                printf(" <-%d", j);
            }
            while(j!=startnode);
        }
    printf("\n");
}

程序运行结果：

Enter the no. of vertices:: 4

Enter the adjacency matrix::
0 1 1 1
1 0 1 0
1 1 0 1
1 0 1 0

Enter the starting node:: 1

Distance of 0 = 1
Path = 0 <-1
Distance of 2 = 1
Path = 2 <-1
Distance of 3 = 2
Path = 3 <-0 <-1