Dijkstra+Heap模板

普通Dijkstra：

 void DijkstraPath(int v0,int vis[],int dist[],int path[])
 {
     int onePath[maxn];
     int d;
     int k;
     for(int i = ;i < n;i++)
     {
         if( vis[i] && i != v0)
         {
             cout<<"Path->";
             d = ;
             onePath[d] = i;//添加路径上的终点
             k = path[i];
             if(k == -)
             {
                 cout<<"No paht"<<endl;
             }
             else
             {
                 while(k != v0)
                 {
                     d++;
                     onePath[d] = k;
                     k = path[k];
                 }
                 d++;
                 onePath[d] = v0;//添加起点
                 cout<<"Start :"<<onePath[d];//起点
                 for(int j = d - ;j>=;j--)
                 {
                     cout<<onePath[j]<<" ";
                 }
                 cout<<endl;
             }
         }
     }
 }

 void Dijkstra(int v0)
 {
     int dist[maxn];//距离数组，每个点到v0的直接距离
     int path[maxn];//路径数组，记录最短路径上的前驱结点
     int vis[maxn];
     int u;//中间结点
     memset(dist,,sizeof(dist));
     memset(path,,sizeof(path));
     memset(vis,,sizeof(vis));
     int mindist;
     for(int i = ;i < n;i++)
     {
         dist[i] = Graph[v0][i];
         if(Graph[v0][i] < INF)
         {
             path[i] = v0;//开始与v0直连的点记录
         }
         else
         {
             path[i] = -;
         }
     }
     vis[v0] = ;//开始时v0加入最短路中
     path[v0] = ;
     for(int i = ; i < n-;i++)
     {
         mindist = INF;
         for(int j = ;j < n;j++)
         {
             if( !(vis[i]) && dist[j] < mindist)//找最短路
             {
                 mindist = dist[j];
                 u = j;
             }
         }
         vis[u] = ;
         for(int i =  ; i < n;i++)//路径更新
         {
             if( !(vis[i]))////考虑剩下未访问的边
             {
                 if( Graph[u][i] < INF && dist[i] > dist[u] + Graph[u][i] )
                 //中间点的总路程比原来能直达的更短
                 {
                     dist[i] = dist[u] + Graph[u][i];
                     path[i] = u;//更新前驱结点
                 }
             }
         }
     }
     //DijkstraPath( v0, vis,dist,path);//输入最短路径
 }

优化后：

 const int maxn= ;
 int n;
 int m;
 int p;
 int cnt;
 int dist[];
 int head[];//init -1
 //存放以i为起点的第一条边存储的位置//以i为起点最后的那个编号
 int point[];

 struct Edge//建图
 {
     int v;//edge[i]表示第i条边的终点
     int w;//edge[i]表示第i条边的权值 即 距离
     int nxt;//edge[i]表示与第i条边同起点的下一条边的存储位置(上一条边)
 }edge[maxn];

 void Add(int x,int y,int w)// x -> y == w
 {//链式向前星
     edge[++cnt].v = y;
     edge[cnt].w = w;
     edge[cnt].nxt = head[x];
     head[x] = cnt;
 }

 struct node
 {
     int u;
     int d;
     bool operator< (const node& rhs)const
     {
         return d >rhs.d;
     }
 };

 void Dijkstra(int s)
 {
     for(int i=;i<=n;i++)
         dist[i] = (i==s)? :;
     priority_queue<node> Q;
     Q.push((node){s,});//开始结点进队
     while (!Q.empty())
     {
         node fr = Q.top(); Q.pop();
         int u = fr.u;//2,0
         int d = fr.d;
         //        cout<<"enqueue:u:"<<u<<" d:"<<d<<endl;
         //        cout<<"~~~";
         if (d != dist[u]) continue;//dijkstra中每个点只会出队一次 vis
         for (int i = head[u];i;i=edge[i].nxt)
         {
          //           cout<<"i =="<<i<<endl;
             int v = edge[i].v;//第i条边的终点
          //           cout<<"edge["<<i<<"].v :"<<v<<" ";
             int w = edge[i].w;
            //          cout<<"edge["<<i<<"].w :"<<w<<" ";
           //           cout<<endl<<"~~~~~~~~~~~"<<endl;
             if (dist[u]+w < dist[v])
             {
             //            cout<<"dist["<<v<<"]"<<dist[v]<<" "<<endl;
             ///         cout<<"dist["<<u<<"] + w :"<<dist[u]+w<<endl;
               //          cout<<"~~~~~~~~~"<<endl;
                 dist[v] = dist[u]+w;
              //        cout<<"dist["<<v<<"] = "<<dist[u]+w<<endl;
              //           cout<<v<<"v,dist["<<v<<"] enqueue"<<endl;
                 Q.push((node){v,dist[v]});
             }
         }
     }
 }
 int main()
 {
         cin>>n>>m>>p;//p为特殊点
         memset(point,,sizeof(point));
         memset(head,-,sizeof(head));
         for(int i=;i<=m;i++)
         {
             int x,y,z;
             scanf("%d%d%d",&x,&y,&z);
             Add(x,y,z);
         }
         //cout<<"~~~~~~~~~~~~~"<<endl;
         // for(int i = 1;i <= m;i++)
         // {
         //     cout<<"  head["<<i<<"]"<<head[i]<<" ||";
         //     cout<<"edge["<<i<<"] ="<<edge[i].v<<" next"<<edge[i].nxt<<endl;
         // }
         // cout<<"~~~~~~~~~~~~~~~~~~~~~"<<endl;
         Dijkstra(p);//p 到其他点的最小距离
         ...
        ....
        return ;
 }

以下题目可以拿来练练手，几乎是基本模板题

P3371 【模板】单源最短路径（弱化版)

P4779 【模板】单源最短路径（标准版）

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