BZOJ 4819：[Sdoi2017]新生舞会 01分数规划+费用流

题目

题目分析：

二分答案 mid

若C=(a’1+a’2+…+a’n)/(b’1+b’2+…+b’n)<=mid

则a1−mid∗b1+a2−mid∗b2+...+an−mid∗bn<=0a1−mid∗b1+a2−mid∗b2+...+an−mid∗bn<=0

实数二分，跑最大费用流即可。

不过我自己生成的数据咋T了(TAT

刚知道这玩意原来叫01分数规划

#include <cstdio>
#include <iostream>
#include <cstring>
#include <queue>
#define il inline
using namespace std;
const int inf=0x7fffffff;
const int maxm=205;
const double eps=1e-8;
int head[maxm],to[maxm*maxm],cap[maxm*maxm],net[maxm*maxm];
int a[600][600],b[600][600],n;
int cnt=1;
double min_cost,cost[maxm*maxm],dis[maxm];
il void add(int x,int y,int c,double z){cnt++,to[cnt]=y,cost[cnt]=z,cap[cnt]=c,net[cnt]=head[x],head[x]=cnt;}
int flow[maxm],pre[maxm],id[maxm],max_flow;
bool vis[maxm];
queue <int> dl;
il bool BFS(int s,int t)
{
while(!dl.empty()) dl.pop();
memset(pre,-1,sizeof(pre));
for(int i=1;i<=t;i++) dis[i]=-inf;
dis[s]=0,flow[s]=inf,pre[s]=0,vis[s]=1;
dl.push(s);
while(!dl.empty())
{
int x=dl.front();
dl.pop();
vis[x]=0;
for(int i=head[x];i;i=net[i])
{
int tmp=to[i];
if(cap[i]>0&&dis[tmp]<dis[x]+cost[i])
{
dis[tmp]=dis[x]+cost[i];
pre[tmp]=x;
id[tmp]=i;
flow[tmp]=min(flow[x],cap[i]);
if(!vis[tmp]) vis[tmp]=1,dl.push(tmp);
}
}
}
return pre[t]==-1?0:1;
}
il void change_cap(int s,int t,int x)
{
int now=t;
while(now!=s)
{
cap[id[now]]-=x,cap[id[now]^1]+=x;
now=pre[now];
}
}
void il get_ans(int s,int t)
{
max_flow=0,min_cost=0;
while(BFS(s,t))
{
max_flow+=flow[t],min_cost+=dis[t]*(double)flow[t];
change_cap(s,t,flow[t]);
}
}
il void adx(int x,int y,int cax,double c)
{
add(x,y,cax,c),add(y,x,0,-c);
}
il bool check(double mid)
{
memset(head,0,sizeof(head));
cnt=1;
int s=0,t=2*n+1;
for(int i=1;i<=n;i++)
{
adx(s,i,1,0.0),adx(i+n,t,1,0.0);
for(int j=1;j<=n;j++)
{
adx(i,j+n,1,(double)a[i][j]-mid*1.0*b[i][j]);
}

}
get_ans(s,t);
return min_cost<=0;
}
il double work()
{
double l=0,r=10000;
while(r-l>=eps)
{
double mid=(l+r)/2;
if(check(mid)) r=mid;
else l=mid;
}
return l;
}
int main()
{
scanf("%d",&n);
for(int i=1;i<=n;i++)
for(int j=1;j<=n;j++)
scanf("%d",&a[i][j]);
for(int i=1;i<=n;i++)
for(int j=1;j<=n;j++)
scanf("%d",&b[i][j]);
printf("%.6lf",work());
return 0;
}