Dijkstra算法单源最短路径

使用邻接表存储图，最短路径的保存使用并查集。

---

#include<bits/stdc++.h>
using namespace std;

#define MAXSIZE 100
#define INF 9999999

/*
邻接表定义
*/
typedef struct ArcNode{
    int data;
    struct ArcNode *nextArc;
    int info;
}ArcNode;

typedef struct VNode{
    int data;
    ArcNode *firstArc;
}VNode,Adjlist;

typedef struct ALGraph{
    Adjlist vertices[MAXSIZE];
    int vexnum,arcnum;
}ALGraph;

/*
创建图（邻接表存储）
*/
void CreateALGraph(ALGraph &g){
    cout<<"Now create ALGraph: vexnum arcnum"<<endl;
    cin>>g.vexnum>>g.arcnum;
    for(int i=1;i<=g.arcnum;i++){
        g.vertices[i].firstArc=NULL;
        g.vertices[i].data=i;
    }
    //输入边
    cout<<"Now input the arcs:"<<endl;
    for(int i=0;i<g.arcnum;i++){
        //cout<<"input arc"<<i+1<<":";
        int u,v,info;
        cin>>u>>v>>info;
        if (g.vertices[u].firstArc==NULL){
            //cout<<"new firstArc"<<endl;
            ArcNode *q=(ArcNode*)malloc(sizeof(ArcNode));
            q->data=v;
            q->info=info;
            q->nextArc=NULL;
            g.vertices[u].firstArc=q;

        }
        else{
            ArcNode *p=g.vertices[u].firstArc;
            while (p->nextArc!=NULL){
                p=p->nextArc;
            }
            ArcNode *q=(ArcNode*)malloc(sizeof(ArcNode));
            q->data=v;
            q->info=info;
            q->nextArc=NULL;
            p->nextArc=q;
        }
    }

    //输出邻接表
    cout<<endl<<"Now output arcs info:"<<endl;
    for (int i = 1; i <= g.vexnum; i++){
        cout<<"vertex "<<g.vertices[i].data<<" :";
        ArcNode *p=g.vertices[i].firstArc;
        while (p!=NULL){
            cout<<p->data<<" ";
            p=p->nextArc;
        }
        cout<<endl<<endl;
    }
}


int visited[MAXSIZE];
int dist[MAXSIZE];
int path[MAXSIZE];

/*
清空visited[]
*/
void clearVisited(){
    for(int i=0;i<MAXSIZE;i++){
        visited[i]=0;
    }
}



void Dijkstra(ALGraph g,int u){
    for(int i=1;i<=g.vexnum;i++){   //初始化
        visited[i]=0;
        path[i]=-1;
        dist[i]=INF;
    }
    dist[u]=0;

    while (1){
        int min=-1;
        int mind=INF;
        for (int i = 1; i < g.vexnum; i++)
        {
            if(!visited[i]&&dist[i]<mind){
                min=i;
                mind=dist[i];
            }
        }
        if(min==-1)
            break;
        cout<<"select min"<<min<<endl;
        visited[min]=1;
        ArcNode *p=g.vertices[min].firstArc;
        while (p)
        {
            if(!visited[p->data]&&mind+p->info<dist[p->data]){
                cout<<"find shorter"<<p->data<<endl;
                dist[p->data]=mind+p->info;
                path[p->data]=min;
            }
            p=p->nextArc;
        }
        
    }
    
    for(int i=1;i<=g.vexnum;i++){
        cout<<dist[i]<<" ";
    }
    cout<<endl;
    
}


int main(){
    ALGraph g;
    CreateALGraph(g);       //创建图
    Dijkstra(g,1);

    return 0;
}


/*
6 16
1 2 7
1 3 11
2 4 9
2 3 10
3 4 5
3 5 7
3 6 8
5 6 6
6 5 6
6 3 8
5 3 7
4 3 5
3 2 10
4 2 9
3 1 11
2 1 7
*/