最短路问题Dijkstra算法

Dijkstra算法可以解决源点到任意点的最短距离并输出最短路径

准备：

建立一个距离数组d[ n ]，记录每个点到源点的距离是多少

建立一个访问数组v[ n ]，记录每个点是否被访问到

建立一个祖先数组p[ n ]，记录每个节点的父亲节点是什么

选择一个起始点s

执行：

1初始化：所有点到源点的距离都是无穷大

2访问源点，源点到源点的距离自然就变成0，更新与源点相邻的点的距离数组（等于边的权值）

3加入距离最小的点到已访问集合，更新与已访问集合连接的点的距离数组（=min{ 直接距离, 间接距离}）以及更新祖先节点数组p[ n ]

4重复步骤3，直到寻找到终点或者访问完所有节点

#include<stdio.h>
#include<stdlib.h>
#include<string.h>
#define max 100
#define INF 999
int graph[max][max];
int vertex_num;
int edge_num;
int d[max];
int v[max];
int p[max];

Dijkstra(int s){
    int i,j,k;
    //init part
    for(i=;i<vertex_num;i++){
        if(graph[s][i]!=){ //if vertex i next to source vertex s
            d[i]=graph[s][i];//update the distance array
            p[i]=s;
            v[i]=;
        }else{
            d[i]=INF;
            p[i]=-;
            v[i]=;
        }

    }
    d[s]=;
    p[s]=;
    v[s]=;

    for(i=;i<vertex_num;i++){
        int min=INF;
        int u;
        for(j=;j<vertex_num;j++){  //find the shortest distance vertex form all the unvisited vertex
            if(v[j]==&&d[j]<min){
                min=d[j];   //mini distance
                u=j;        //mini distance vertex u
            }
        }
        v[u]=; //visit u
        for(k=;k<vertex_num;k++){
            if(v[k]==&&graph[u][k]>&&d[u]+graph[u][k]<d[k]){ //graph[u][k]>0 make sure u and k are connected;
                d[k]=d[u]+graph[u][k];
                p[k]=u;
            }
        }
    }
    printf("Shortest distance form %d:\n",s);
    for(i=;i<vertex_num;i++){
        printf("%d ",d[i]);
    }
    printf("\n\n");
}
void show_path(int s,int d){
    int cur=d;
    int tmp[vertex_num];

    int i=;
    while(cur!=s){
        tmp[i++]=cur;
        cur=p[cur];
    }
    tmp[i]=s;
    printf("The shortest path:\n");
    while(i>){
        printf("%d ->",tmp[i]);
        i--;
    }
    printf("%d",tmp[i]);
}
int main(){
    int i,j;
    FILE *fin  = fopen ("dij.in", "r");
    FILE *fout = fopen ("dij.out", "w");

    char buf[];
    fgets(buf,,fin);
    edge_num=atoi(buf);

    printf("edge_num:%d\n",edge_num);
    fgets(buf,,fin);
    vertex_num=atoi(buf);

    printf("vertex_num:%d\n",vertex_num);

    for(i=;i<edge_num;i++){
        int start,end,weight;//start point,end point and the weight of edge
        fgets(buf,,fin);
        sscanf(buf,"%d %d %d",&start,&end,&weight);

        printf("start:%d end:%d weight:%d\n",start,end,weight);
        graph[start][end]=weight;//init the graph matrix no direct

    }

    printf("\n");
    printf("Graph matrix:\n");
    for(i=;i<vertex_num;i++){
        for(j=;j<vertex_num;j++){
        printf("%-5d",graph[i][j]);
       }
       printf("\n");
    }
    printf("\n");
    Dijkstra();
    show_path(,);
    return ;
}