题目地址:https://icpcarchive.ecs.baylor.edu/index.php?option=com_onlinejudge&Itemid=8&page=show_problem&problem=1646
思路:拆点,将航线看做点。设一源点与汇点。对于每个航线i,将其拆为两点,i和i',连一条容量为最大客容量的边;对于所有起点为出发点的航线j,连一条源点到j的容量为INF的边;对于所有终点为目标点的航线k,连一条k到汇点的容量为INF的边;对于可换乘的航线i、j,连一条i-->j'容量为INF的边。求从源点到汇点的最大流即可。注意换乘时在同一地点。
#include<map>
#include<queue>
#include<cstdio>
#include<vector>
#include<cstring>
#include<iostream>
#include<algorithm>
#define debu
using namespace std;
const int maxn=10000+10;
const int maxm=5000+50;
const int INF=0x3f3f3f3f;
struct Edge
{
int from,to,cap,flow;
Edge(int a=0,int b=0,int c=0,int d=0):from(a),to(b),cap(c),flow(d) {}
};
struct Node
{
string x,y;
int Tst,Ted,c;
};
struct Dinic
{
int n,m,s,t;
vector<Edge> edges;
vector<int> G[maxn];
bool vis[maxn];
int d[maxn];
int cur[maxn];
void init(int n)
{
this->n=n;
for(int i=0; i<=n; i++) G[i].clear();
edges.clear();
}
void addedge(int from,int to,int cap)
{
edges.push_back(Edge(from,to,cap,0));
edges.push_back(Edge(to,from,0,0));
int m=edges.size();
G[from].push_back(m-2);
G[to].push_back(m-1);
}
bool BFS()
{
memset(vis,0,sizeof(vis));
queue<int> Q;
Q.push(s);
vis[s]=1;
d[s]=0;
while(!Q.empty())
{
int x=Q.front();
Q.pop();
for(int i=0; i<G[x].size(); i++)
{
Edge& e=edges[G[x][i]];
if(!vis[e.to]&&e.cap>e.flow)
{
vis[e.to]=1;
d[e.to]=d[x]+1;
Q.push(e.to);
}
}
}
return vis[t];
}
int DFS(int x,int a)
{
if(x==t||a==0) return a;
int flow=0,f;
for(int& i=cur[x]; i<G[x].size(); i++)
{
Edge& e=edges[G[x][i]];
if(d[x]+1==d[e.to]&&(f=DFS(e.to,min(a,e.cap-e.flow)))>0)
{
e.flow+=f;
edges[G[x][i]^1].flow-=f;
flow+=f;
a-=f;
if(a==0) break;
}
}
return flow;
}
int Maxflow(int s,int t)
{
this->s=s;
this->t=t;
int flow=0;
while(BFS())
{
memset(cur,0,sizeof(cur));
flow+=DFS(s,INF);
}
return flow;
}
};
Dinic g;
Node a[maxm];
int tot,n,ENDT,m;
int main()
{
#ifdef debug
freopen("in.in","r",stdin);
#endif // debug
ios::sync_with_stdio(0);
while(cin>>n)
{
string st,ed;
cin>>st>>ed>>ENDT>>m;
g.init(2*m+1);
for(int i=1; i<=m; i++)
{
cin>>a[i].x>>a[i].y>>a[i].c>>a[i].Tst>>a[i].Ted;
if(a[i].x==st) g.addedge(0,i,INF);
if(a[i].y==ed&&a[i].Ted<=ENDT) g.addedge(i+m,2*m+1,INF);
g.addedge(i,i+m,a[i].c);
}
for(int i=1; i<=m; i++)
{
if(a[i].Ted>=ENDT) continue;
for(int j=1; j<=m; j++)
{
if(i==j) continue;
int tmp1=(a[i].Ted%100);
int tmp2=(a[i].Ted/100);
tmp2+=(tmp1+30>=60)?1:0;
tmp1=(tmp1+30)%60;
if(tmp1+tmp2*100<=a[j].Tst&&a[j].Ted<=ENDT)
{
if(a[i].y==a[j].x) g.addedge(i+m,j,INF);
}
}
}
cout<<g.Maxflow(0,2*m+1)<<endl;
}
return 0;
}