POJ1511 Invitation Cards (最短路+正反向建图)

题目链接

In the age of television, not many people attend theater performances. Antique Comedians of Malidinesia are aware of this fact. They want to propagate theater and, most of all, Antique Comedies. They have printed invitation cards with all the necessary information and with the programme. A lot of students were hired to distribute these invitations among the people. Each student volunteer has assigned exactly one bus stop and he or she stays there the whole day and gives invitation to people travelling by bus. A special course was taken where students learned how to influence people and what is the difference between influencing and robbery.The transport system is very special: all lines are unidirectional and connect exactly two stops. Buses leave the originating stop with passangers each half an hour. After reaching the destination stop they return empty to the originating stop, where they wait until the next full half an hour, e.g. X:00 or X:30, where ‘X’ denotes the hour. The fee for transport between two stops is given by special tables and is payable on the spot. The lines are planned in such a way, that each round trip (i.e. a journey starting and finishing at the same stop) passes through a Central Checkpoint Stop (CCS) where each passenger has to pass a thorough check including body scan.All the ACM student members leave the CCS each morning. Each volunteer is to move to one predetermined stop to invite passengers. There are as many volunteers as stops. At the end of the day, all students travel back to CCS. You are to write a computer program that helps ACM to minimize the amount of money to pay every day for the transport of their employees.

Input
The input consists of N cases. The first line of the input contains only positive integer N. Then follow the cases. Each case begins with a line containing exactly two integers P and Q, 1 <= P,Q <= 1000000. P is the number of stops including CCS and Q the number of bus lines. Then there are Q lines, each describing one bus line. Each of the lines contains exactly three numbers - the originating stop, the destination stop and the price. The CCS is designated by number 1. Prices are positive integers the sum of which is smaller than 1000000000. You can also assume it is always possible to get from any stop to any other stop.

Output
For each case, print one line containing the minimum amount of money to be paid each day by ACM for the travel costs of its volunteers.

1.题目很长，题意也就是求从起点1到其余各点的最短路，我们很容易想到Dijkstra。但是题目还要求每走到一个点就再返回到起点。这就很难受了，蒟蒻的我以为难道要再求从另外n-1个点到1的最短路吗？

2.如果求所有的的最短路不就成了Floyd吗，但是点这么多，不可能的。去网上看了看，确实是很巧妙的思维，由于是有向图，我们再反向建图，这样再求一次1到各点的最短路即可，tql

3.时间给的很足，写了链式前向星跑的还算快

代码：

#include <iostream>
#include <queue>
#include <algorithm>
#include <cstring>
#include <cstdio>
using namespace std;
#define INF 1e16
const int maxn=1e6+10;
typedef long long ll;
typedef pair<ll,int> P;

struct node{
    int next,to,w;
};

struct Dijkstra{
    int n,tot;
    node edge[maxn];
    int head[maxn];
    bool vis[maxn];
    ll d[maxn];

    void init(int n){
        this->n=n;
        tot=0;
        memset(head,0,sizeof head);
    }

    ll solve(){
        ll ans=0;
        for(int i=1;i<=n;i++){
            ans+=d[i];
        }
        return ans;
    }

    void add_edge(int from,int to,int w){
        tot++;
        edge[tot].w=w;
        edge[tot].to=to;
        edge[tot].next=head[from];
        head[from]=tot;
    }

    void dijkstra(int s){
        for(int i=1;i<=n;i++) d[i] = INF;
        memset(vis,0,sizeof vis);
        d[s]=0;
        priority_queue<P,vector<P>,greater<P> > q;
        q.push(make_pair(0,s));
        while(!q.empty()){
            P pr=q.top();q.pop();
            int u=pr.second;
            if(vis[u]) continue;
            vis[u]=1;
            for(int i=head[u];i;i=edge[i].next){
                int v=edge[i].to;
                int w=edge[i].w;
                if(d[v]>d[u]+w){
                    d[v]=d[u]+w;
                    q.push(make_pair(d[v],v));
                }
            }
        }
    }

};

Dijkstra dj1,dj2;

int main()
{
    int t,n,m,a,b,c;
    scanf("%d",&t);
    while(t--){
        scanf("%d%d",&n,&m);
        dj1.init(n);
        dj2.init(n);
        while(m--){
            scanf("%d%d%d",&a,&b,&c);
            dj1.add_edge(a,b,c);
            dj2.add_edge(b,a,c);
        }
        dj1.dijkstra(1);
        dj2.dijkstra(1);
        printf("%lld\n",dj1.solve()+dj2.solve());
    }
    return 0;
}