CF 20C Dijkstra?

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这是一个关于图论的问题，要求在给定的加权无向图中找到从顶点1到顶点n的最短路径。输入包含图的节点数n和边数m，以及每条边的起点、终点和权重。输出是-1表示没有路径，否则输出最短路径。题目描述中提到可以使用堆优化的Dijkstra算法，并提供了第一次使用C++链表存图的经历，这可能成为之后的模板。

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Dijkstra?

Time Limit:2000MS

Memory Limit:65536KB

64bit IO Format:%I64d & %I64u

[Submit] [Go Back] [Status]

Description

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

Input

Output

1 4 3 5

Input

Output

1 4 3 5

解析

最短路，堆优Dijkstra。这个题本身没什么，就是每次更新最短路的时候维护一个fa（fa[i]表示i的父亲）。第一次写堆优Dijkstra，第一次用C++链表存图。以后就是我的模板了

#include<stack>
#include<cstdio>
#include<cstring>
#include<utility>
#include<queue>

using namespace std;

#define INF 0x3f3f3f3f3f3f3f3fLL
typedef long long LL;

struct tnode
{
	tnode *next;
	int from,to;
	LL len;
};
typedef tnode* pnode; pnode Chain[100100];

typedef pair<LL,int> pii;
priority_queue<pii,vector<pii>,greater<pii> > heap;
bool vis[100100];

int N,M,pre[100100];
LL dist[100100];
void insert(int from,int to,LL len)
{
	pnode p=new tnode;
	p->next=Chain[from];
	p->from=from;
	p->to=to;
	p->len=len;
	Chain[from]=p;
}

void readdata()
{
	scanf("%d%d",&N,&M);
	for(int i=1;i<=N;i++) Chain[i]=NULL;
	for(int i=1;i<=M;i++)
	{
		int a,b;
		LL c;
		scanf("%d%d%I64d",&a,&b,&c);
		insert(a,b,c); insert(b,a,c);
	}
}

void dijkstra()
{
	for(int i=2;i<=N;i++) dist[i]=INF; dist[1]=0;
	memset(vis,0,sizeof(vis));

	heap.push(make_pair(dist[1],1));
	while(!heap.empty())
	{
		int v=heap.top().second; heap.pop();
		if(vis[v]) continue; vis[v]=1;
		for(pnode p=Chain[v];p;p=p->next)
		{
			int u=p->to,len=p->len;
			if(dist[u]>dist[v]+len)
			{
				pre[u]=v;
				dist[u]=dist[v]+len;
				heap.push(make_pair(dist[u],u));
			}
		}
	}

	//for(int i=1;i<=N;i++) printf("%I64d ",dist[i]); printf("%I64d\n",~0LL>>2);
	stack<int> Stack;
	if(dist[N]==INF) printf("-1");
	else
	{
		Stack.push(N);
		while(Stack.top()!=1) Stack.push(pre[Stack.top()]);
		while(!Stack.empty()) {printf("%d ",Stack.top());Stack.pop();}
	}
}

int main()
{
	freopen("CF20C.in","r",stdin);

	readdata();
	dijkstra();

	while(1);
	return 0;
}