【二分答案】【最大流】bzoj3130 [Sdoi2013]费用流

二分最大的边的cap，记作Lim。

把所有的边的cap设为min(Lim,cap[i])。

Bob一定会把单位费用加到最大边上。

#include<cstdio>
#include<cstring>
#include<algorithm>
#include<queue>
#include<cmath>
using namespace std;
#define EPS 0.000001
#define N 101
#define INF 2147483647.0
#define M 1001
typedef double db;
int n,m,K,S,T;
int v[M<<1],next[M<<1],first[N],en;
db cap[M<<1];
void AddEdge(int U,int V,db Cap)
{
	v[en]=V; cap[en]=Cap; next[en]=first[U]; first[U]=en++;
	v[en]=U; cap[en]=0; next[en]=first[V]; first[V]=en++;
}
queue<int>q;
int d[N],cur[N];
bool bfs()
{
	memset(d,-1,sizeof(int)*(n+1));
	d[S]=0; q.push(S);
	while(!q.empty())
	  {
	  	int U=q.front(); q.pop();
	  	for(int i=first[U];i!=-1;i=next[i])
	  	  if(d[v[i]]==-1&&cap[i]>EPS)
	  	    {
	  	      d[v[i]]=d[U]+1;
	  	      q.push(v[i]);
	  	    }
	  }
	return d[T]!=-1;
}
db dfs(int U,db a)
{
	if(U==T||a<=EPS) return a;
	db Flow=0.0,f;
	for(int &i=cur[U];i!=-1;i=next[i])
	  if(d[v[i]]==d[U]+1&&(f=(dfs(v[i],min(a,cap[i]))))>EPS)
	    {
	      cap[i]-=f;
	      cap[i^1]+=f;
	      Flow+=f;
		  a-=f;
		  if(a<=EPS)
		    break;
	    }
	if(Flow<=EPS) d[U]=-1;
	return Flow;
}
db MaxFlow()
{
	db Flow=0.0,tmp;
	while(bfs())
	  {
	  	memcpy(cur,first,sizeof(int)*(n+1));
	  	while((tmp=dfs(S,INF))>EPS) Flow+=tmp;
	  }
	return Flow;
}
int xs[M],ys[M],zs[M];
int ChuShi;
bool check(db Lim)
{
	memset(first,-1,sizeof(int)*(n+1));
	en=0;
	for(int i=1;i<=m;++i)
	  AddEdge(xs[i],ys[i],min((db)zs[i],Lim));
	db t=MaxFlow();
	return fabs(t-(db)ChuShi)<=EPS?1:0;
}
int main()
{
//	freopen("bzoj3130.in","r",stdin);
	db r=0.0,l=0.0;
	scanf("%d%d%d",&n,&m,&K);
	S=1; T=n;
	memset(first,-1,sizeof(int)*(n+1));
	for(int i=1;i<=m;++i)
	  {
	  	scanf("%d%d%d",&xs[i],&ys[i],&zs[i]);
	  	AddEdge(xs[i],ys[i],(db)zs[i]);
	  	r=max(r,(db)zs[i]);
	  }
	ChuShi=(int)MaxFlow();
	while(r-l>EPS)
	  {
	  	db mid=(l+r)/2.0;
	  	if(check(mid)) r=mid-EPS;
	  	else l=mid+EPS;
	  }
	printf("%d
%.4lf
",ChuShi,l*(db)K);
	return 0;
}