UVa10806_Dijkstra, Dijkstra.(网络流/费用流)(小白书图论专题)

解题报告

思路：

从s->t 再从t->s等同与s->t两次，要求每条路只能走一次，要求最小花费，让每一条边容量为1，跑跑费用流

只要跑出流量为2就结束。

#include <iostream>
#include <cstring>
#include <cstdio>
#include <queue>
#define inf 0x3f3f3f3f
#define N 5000
#define M 50000

using namespace std;
int n,m,s,t,cnt,head[N],pre[N],vis[N],dis[N],f[N],cost,flow;
struct node {
    int v,cost,cap,next;
} edge[M];
void add(int u,int v,int cost,int cap) {
    edge[cnt].v=v,edge[cnt].cost=cost,edge[cnt].cap=cap;
    edge[cnt].next=head[u],head[u]=cnt++;
    edge[cnt].v=u,edge[cnt].cost=-cost,edge[cnt].cap=0;
    edge[cnt].next=head[v],head[v]=cnt++;
}
int _spfa() {
    for(int i=1; i<=n; i++) {
        dis[i]=inf;
        vis[i]=pre[i]=f[i]=0;
    }
    dis[1]=0;
    vis[1]=1;
    f[1]=inf;
    pre[1]=-1;
    queue<int >Q;
    Q.push(1);
    while(!Q.empty()) {
        int u=Q.front();
        Q.pop();
        vis[u]=0;
        for(int i=head[u]; i!=-1; i=edge[i].next) {
            int v=edge[i].v;
            if(edge[i].cap&&dis[v]>dis[u]+edge[i].cost) {
                dis[v]=dis[u]+edge[i].cost;
                f[v]=min(f[u],edge[i].cap);
                pre[v]=i;
                if(!vis[v]) {
                    vis[v]=1;
                    Q.push(v);
                }
            }
        }
    }
    if(dis[n]==inf)return 0;
    cost+=f[n]*dis[n];
    flow+=f[n];
    if(flow==2)return 0;
    for(int i=pre[n]; i!=-1; i=pre[edge[i^1].v]) {
        edge[i].cap-=f[n];
        edge[i^1].cap+=f[n];
    }
    return 1;
}
void mcmf() {
    cost=flow=0;
    while(_spfa());
}
int main() {
    int i,j,u,v,w;
    while(~scanf("%d",&n)) {
        if(!n)break;
        memset(head,-1,sizeof(head));
        cnt=0;
        scanf("%d",&m);
        while(m--) {
            scanf("%d%d%d",&u,&v,&w);
            add(u,v,w,1);
            add(v,u,w,1);
        }
        mcmf();
        if(flow!=2||cost==inf)
            printf("Back to jail\n");
        else printf("%d\n",cost);
    }
    return 0;
}

Problem ?

Dijkstra, Dijkstra.

Time Limit: 10 seconds

Jim Abrahams and Pat Proft,

"Hot Shots! Part Deux."

You are a political prisoner in jail. Things are looking grim, but fortunately, your jailmate has come up with an escape plan. He has found a way for both of you to get out of the cell and run through
the city to the train station, where you will leave the country. Your friend will escape first and run along the streets of the city to the train station. He will then call you from there on your cellphone (which somebody smuggled in to you inside a cake),
and you will start to run to the same train station. When you meet your friend there, you will both board a train and be on your way to freedom.

Your friend will be running along the streets during the day, wearing his jail clothes, so people will notice. This is why you can not follow any of the same streets that your friend follows - the
authorities may be waiting for you there. You have to pick a completely different path (although you may run across the same intersections as your friend).

What is the earliest time at which you and your friend can board a train?

Problem, in short

Given a weighed, undirected graph, find the shortest path from S to T and back without using the same edge twice.

Input

The input will contain several test cases. Each test case will begin with an integer n (2<=n<=100) - the number of nodes (intersections). The jail is at node number 1, and the train station is at node number n.
The next line will contain an integerm - the number of streets. The next m lines will describe the m streets. Each line will contain 3 integers - the two nodes connected by the street and the time it takes
to run the length of the street (in seconds). No street will be longer than 1000 or shorter than 1. Each street will connect two different nodes. No pair of nodes will be directly connected by more than one street. The last test case will be followed by a
line containing zero.

Output

For each test case, output a single integer on a line by itself - the number of seconds you and your friend need between the time he leaves the jail cell and the time both of you board the train. (Assume that you do not need to wait for the train - they leave
every second.) If there is no solution, print "Back to jail".

2
1
1 2 999
3
3
1 3 10
2 1 20
3 2 50
9
12
1 2 10
1 3 10
1 4 10
2 5 10
3 5 10
4 5 10
5 7 10
6 7 10
7 8 10
6 9 10
7 9 10
8 9 10
0

Back to jail
80
Back to jail