Codeforces 938.D Buy a Ticket

D. Buy a Ticket
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

Musicians of a popular band "Flayer" have announced that they are going to "make their exit" with a world tour. Of course, they will visit Berland as well.

There are n cities in Berland. People can travel between cities using two-directional train routes; there are exactly m routes, i-th route can be used to go from city vi to city ui (and from ui to vi), and it costs wi coins to use this route.

Each city will be visited by "Flayer", and the cost of the concert ticket in i-th city is ai coins.

You have friends in every city of Berland, and they, knowing about your programming skills, asked you to calculate the minimum possible number of coins they have to pay to visit the concert. For every city i you have to compute the minimum number of coins a person from city i has to spend to travel to some city j (or possibly stay in city i), attend a concert there, and return to city i (if j ≠ i).

Formally, for every  you have to calculate , where d(i, j) is the minimum number of coins you have to spend to travel from city i to city j. If there is no way to reach city j from city i, then we consider d(i, j) to be infinitely large.

Input

The first line contains two integers n and m (2 ≤ n ≤ 2·105, 1 ≤ m ≤ 2·105).

Then m lines follow, i-th contains three integers vi, ui and wi (1 ≤ vi, ui ≤ n, vi ≠ ui, 1 ≤ wi ≤ 1012) denoting i-th train route. There are no multiple train routes connecting the same pair of cities, that is, for each (v, u) neither extra (v, u) nor (u, v) present in input.

The next line contains n integers a1, a2, ... ak (1 ≤ ai ≤ 1012) — price to attend the concert in i-th city.

Output

Print n integers. i-th of them must be equal to the minimum number of coins a person from city i has to spend to travel to some city j (or possibly stay in city i), attend a concert there, and return to city i (if j ≠ i).

Examples
input
Copy
4 2
1 2 4
2 3 7
6 20 1 25
output
6 14 1 25
input
Copy
3 3
1 2 1
2 3 1
1 3 1
30 10 20
output
12 10 12 
题目大意：每个点有点权a[i],定义d[i][j]为i到j的最短路.对于每一个i,求一个任意的j,使得2*d[i][j] + a[j]最小.
分析：这道题应该属于那种想一会就能想到的题.
　　　题目让我们求的实际上是多源最短路.怎么求？floyd? 其实可以dijkstra来求.现将所有的点以及点权放到结构体里，并且加入到优先队列中.每扩展到一个点，这个点的答案就被确定了，因为是优先队列，每次都会找路径长度最小的扩展.然后再把这个点能扩展到的点以及路径长度放到优先队列中，不断处理，直到所有点的答案被确定.
          这道题利用了dijkstra每次取最短距离的点更新和可以处理多源最短路的特点，以前做过的一道类似的题：hdu6166

 

#include <cstdio>
#include <queue>
#include <cstring>
#include <iostream>
#include <algorithm>

using namespace std;

typedef long long ll;
const ll maxn = 200010;
ll n,m,head[maxn],to[maxn * 2],nextt[maxn * 2],w[maxn * 2],tot = 1,vis[maxn],ans[maxn];
priority_queue <pair<ll,ll>,vector<pair<ll,ll> >,greater<pair<ll,ll> > > q;

void add(ll x,ll y,ll z)
{
    w[tot] = z;
    to[tot] = y;
    nextt[tot] = head[x];
    head[x] = tot++;
}

int main()
{
    scanf("%I64d%I64d",&n,&m);
    for (ll i = 1; i <= m; i++)
    {
        ll a,b,c;
        scanf("%I64d%I64d%I64d",&a,&b,&c);
        add(a,b,2*c);
        add(b,a,2*c);
    }
    for (ll i = 1; i <= n; i++)
    {
        ll t;
        scanf("%I64d",&t);
        q.push(make_pair(t,i));
    }
    while (!q.empty())
    {
        pair <ll,ll> u = q.top();
        q.pop();
        if (vis[u.second])
            continue;
        vis[u.second] = 1;
        ans[u.second] = u.first;
        for (ll i = head[u.second];i;i = nextt[i])
        {
            ll v = to[i];
            q.push(make_pair(u.first + w[i],v));
        }
    }
    for (ll i = 1; i <= n; i++)
        printf("%I64d ",ans[i]);

    return 0;
}

 

 

posted @ 2018-02-17 14:57  zbtrs  阅读(579)  评论(0)  编辑  收藏  举报