专题测试四 图论 D - Dijkstra?

1. 题目
   

   You are given a weighted undirected graph. The vertices are enumerated from 1 to n. Your task is to find the shortest path between the vertex 1 and the vertex n.

   Input

   The first line contains two integers n and m (2 ≤ n ≤ 10⁵, 0 ≤ m ≤ 10⁵), where n is the number of vertices and m is the number of edges. Following m lines contain one edge each in form a_i, b_i and w_i (1 ≤ a_i, b_i ≤ n, 1 ≤ w_i ≤ 10⁶), where a_i, b_i are edge endpoints and w_i is the length of the edge.

   It is possible that the graph has loops and multiple edges between pair of vertices.

   Output

   Write the only integer -1 in case of no path. Write the shortest path in opposite case. If there are many solutions, print any of them.

   Sample

   Input	Output
   5 6 1 2 2 2 5 5 2 3 4 1 4 1 4 3 3 3 5 1	1 4 3 5

2. 思路
   众所周知，一个题目里，如果题目里写了某个算法的名字，那么实际操作里面肯定不会......哦这次还真的用了这个算法。
   题目很简单只是一个最短路径问题，但是直接上dijkstra会超时，要用优先队列优化一下，还要有一个前驱数组，存储每个节点的上一个中转点，然后递归输出
   很尴尬的是，因为忘了没有路径输出-1这件事，我WA了三次
3. 代码
   

   #include<iostream>
   #include<cstdio>
   #include<cstring>
   #include<algorithm>
   #include<queue>
   using namespace std;
   
   const int maxn = 100010;
   const long long INF=1145141919810;
   
   struct edge {
       int v, w;
   };
   
   struct node {
       long long dis;int u;
   
       bool operator>(const node& a) const { return dis > a.dis; }
   };
   
   vector<edge> e[maxn];
   long long dis[maxn];bool vis[maxn];int pre[maxn];
   priority_queue<node, vector<node>, greater<node> > q;
   
   void dijkstra(int n, int s) {
       for(int i=1;i<=n;i++) dis[i]=INF;
       dis[s] = 0;
       q.push({0, s});
       while (!q.empty()) {
           int u = q.top().u;
           q.pop();
           if (vis[u]) continue;
           vis[u] = 1;
   		if (vis[n]) return;
           for (auto ed : e[u]) {
               int v = ed.v, w = ed.w;
               if (dis[v] > dis[u] + w) {
                   dis[v] = dis[u] + w;
   				pre[v] = u;
                   q.push({dis[v], v});
               }
           }
       }
   }
   
   void print(int x)
   {
   	if(pre[x]==0) return;
   	print(pre[x]);
   	cout<<" "<<x;
   }
   
   int main()
   {
   	int n,m;
   	scanf("%d%d",&n,&m);
   	int a,b,w;
   	while(m--)
   	{
   		scanf("%d%d%d",&a,&b,&w);
   		edge aa,bb;
   		aa.v=b,aa.w=w;
   		bb.v=a,bb.w=w;
   		e[a].push_back(aa);
   		e[b].push_back(bb);
   	}
   	dijkstra(n,1);
   	if(dis[n]<INF-1)
   	{
   		pre[1] = 0;
   		cout<< 1 ;
   		print(n);
   		cout<<endl;
   	}
   	else
   	{
   		cout<< -1 <<endl;
   	}
   	return 0;
   }