dijkstra模板题 洛谷1339 邻接图建边

题目链接：https://www.luogu.com.cn/problem/P1339

朴素dijkstra算法的复杂度是O(n^2)，用堆优化的dijkstra复杂度是O(nlogn)的。在本题中前向星存边的时间消耗大约是113ms，空间消耗大约是8M，而在矩阵存边中时间消耗大约是125ms，空间消耗大约是30M，可见前向星是非常节省空间的。但点多边少的时候还是用前向星比较好。

代码如下：

 #include<bits/stdc++.h>
 using namespace std;
 typedef unsigned int ui;
 typedef long long ll;
 typedef unsigned long long ull;
 #define pf printf
 #define mem(a,b) memset(a,b,sizeof(a))
 #define prime1 1e9+7
 #define prime2 1e9+9
 #define pi 3.14159265
 #define lson l,mid,rt<<1
 #define rson mid+1,r,rt<<1|1
 #define scand(x) scanf("%llf",&x)
 #define f(i,a,b) for(int i=a;i<=b;i++)
 #define scan(a) scanf("%d",&a)
 #define dbg(args) cout<<#args<<":"<<args<<endl;
 #define inf 0x3f3f3f3f
 const int maxn=1e6+;
 int n,m,t;
 int d[maxn],head[maxn],nxt[maxn];
 int e=;
 struct node{
     int v,dis;
     node(int dis,int v):dis(dis),v(v){}
     node(){}
     bool  operator < (const node& a)const
     {
         return dis>a.dis;//priority_queue中按照dis递增
     }
 };
 struct edge{
     int v,w;
 }p[maxn];
 void init()
 {
     mem(head,-);
     mem(nxt,-);
     e=;
 }
 void addedge(int u,int v,int w)//邻接图单向建边
 {
     p[e].v=v;
     p[e].w=w;
     nxt[e]=head[u];
     head[u]=e++;
 }
 void dijkstra(int src)
 {
     f(i,,n)d[i]=inf;
     d[src]=;
     priority_queue<node> q;
     q.push(node(,src));
     while(!q.empty())
     {
         node u=q.top();
         q.pop();
         if(d[u.v]<u.dis)continue;
         int x=u.v;
         for(int i=head[x];~i;i=nxt[i])
         {
             if(d[p[i].v]>d[x]+p[i].w)
             {
                 d[p[i].v]=d[x]+p[i].w;
                 q.push(node(d[p[i].v],p[i].v));
             }
         }
     }
  }
 int main()
 {
     //freopen("input.txt","r",stdin);
     //freopen("output.txt","w",stdout);
     std::ios::sync_with_stdio(false);
     int st,ed;
     scanf("%d%d%d%d",&n,&m,&st,&ed);
     int u,v,w;
     init();
     f(i,,m)
     {
         scanf("%d%d%d",&u,&v,&w);
         addedge(u,v,w);
         addedge(v,u,w);
      }
      dijkstra(st);
      pf("%d",d[ed]);
  } 

邻接矩阵存边的代码如下：

 #include<bits/stdc++.h>
 using namespace std;
 typedef unsigned int ui;
 typedef long long ll;
 typedef unsigned long long ull;
 #define pf printf
 #define mem(a,b) memset(a,b,sizeof(a))
 #define prime1 1e9+7
 #define prime2 1e9+9
 #define pi 3.14159265
 #define lson l,mid,rt<<1
 #define rson mid+1,r,rt<<1|1
 #define scand(x) scanf("%llf",&x)
 #define f(i,a,b) for(int i=a;i<=b;i++)
 #define scan(a) scanf("%d",&a)
 #define P pair<int,int>
 #define  mp(a,b) make_pair((a),(b))
 #define dbg(args) cout<<#args<<":"<<args<<endl;
 #define inf 0x3f3f3f3f
 const int maxn=1e6+;
 #define maxm 3000
 int n,m,t;
 int edge[maxm][maxm],d[maxm];
 void init()
 {
     f(i,,n)
         f(j,,n)edge[i][j]=inf;
 }
 void dijkstra(int src)
 {
     f(i,,n)d[i]=inf;
     d[src]=;
     priority_queue<P,vector<P>,greater<P> >q;//先定义队列中的元素类型，在定义存放存放该元素的容器，最后决定是最大堆还是最小堆
     q.push(mp(,src));
     while(!q.empty())
     {
         P now=q.top();
         q.pop();
         if(d[now.second]<now.first)continue;
         int u=now.second;
         f(i,,n)
         {
             if(edge[u][i]!=inf&&d[i]>d[u]+edge[u][i])
             {
                 d[i]=d[u]+edge[u][i];
                 q.push(mp(d[i],i));
             }
         }
     }
 }
 int main()
 {
     //freopen("1339.txt","r",stdin);
     //freopen("output.txt","w",stdout);
     //std::ios::sync_with_stdio(false);
     int st,ed;
        cin>>n>>m>>st>>ed;
            init();
         int u,v,w;
         for(int i=;i<m;i++)
         {
             scanf("%d%d%d",&u,&v,&w);
             if(edge[u][v]>w)edge[u][v]=w,edge[v][u]=w;
         }
         dijkstra(st);
         cout<<d[ed]<<endl;
  }