codevs 5965 [SDOI2017]新生舞会

分数规划的裸题。

不会分数规划的OIer。百度：胡伯涛《最小割模型在信息学竞赛中的应用》

/*
TLE1:
last:add(i,j+n,1e9,(real)((real)a[i][j]-ans*(real)b[i][j]));
now :add(i,j+n,1,(real)((real)a[i][j]-ans*(real)b[i][j]));
TLE2:
last:real l=eps,r=(real)u/(real)v,mid,ans=0,now;
now :real l=0,r=(real)(u+v-1)/(real)v,mid,ans=0,now;
TLE3:
last:struct edge{int v,next;real cost,cap;}e[N<<1];
now :to[N],next[N],cap[N];real cost[N];(结构体跑得慢)
TLE4：
last:typedef long double real;
now :typedef double real;
*/
#include<cmath>
#include<cstdio>
#include<cstring>
#include<iostream>
#define set(x) freopen(#x".in","r",stdin);freopen(#x".out","w",stdout);
using namespace std;
const int N=1e5+;
const int Z=;
typedef long double real;
const real eps=1e-;
int n,m,S,T,a[Z][Z],b[Z][Z];
int to[N],next[N],cap[N];real cost[N];int tot=,head[N];
real dis[N];int q[N],pre[N];bool vis[N];
inline int read(){
    int x=,f=;char ch=getchar();
    while(ch<''||ch>''){if(ch=='-')f=-;ch=getchar();}
    while(ch>=''&&ch<=''){x=x*+ch-'';ch=getchar();}
    return x*f;
}
void add(int x,int y,int z,real Cost){
    to[++tot]=y;cap[tot]=z;cost[tot]=Cost;next[tot]=head[x];head[x]=tot;
    to[++tot]=x;cap[tot]=;cost[tot]=-Cost;next[tot]=head[y];head[y]=tot;
}
bool spfa(){
    memset(vis,,sizeof vis);
    for(int i=;i<=T+;i++) dis[i]=-1e9;
    unsigned short h=,t=;q[t]=S;dis[S]=;
    while(h!=t){
        int x=q[++h];vis[x]=;
        for(int i=head[x];i;i=next[i]){
            if(cap[i]>&&dis[to[i]]<dis[x]+cost[i]){
                dis[to[i]]=dis[x]+cost[i];
                pre[to[i]]=i;
                if(!vis[to[i]]){
                    vis[to[i]]=;
                    q[++t]=to[i];
                }
            }
        }
    }
    return dis[T]>-1e9;
}
real augment(){
//    int flow=1e9;
//    for(int i=T;i!=S;i=to[pre[i]^1]) flow=min(flow,cap[pre[i]]);
    int flow=;
    for(int i=T;i!=S;i=to[pre[i]^]){
        cap[pre[i]]-=flow;
        cap[pre[i]^]+=flow;
    }
    return dis[T]*flow;
}
real mapping(real ans){
    tot=;S=;T=n<<|;
    memset(head,,sizeof head);
    for(int i=;i<=n;i++) add(S,i,,),add(i+n,T,,);
    for(int i=;i<=n;i++){
        for(int j=;j<=n;j++){
            add(i,j+n,,(real)((real)a[i][j]-ans*(real)b[i][j]));
        }
    }
    real res=0.0;
    while(spfa()) res+=augment();
    return res;
}
int cmp(real x){
    if(fabs(x)<eps) return ;
    return x>?:-;
}
void work1(){
    tot=;S=;T=n<<|;
    memset(head,,sizeof head);
    for(int i=;i<=n;i++) add(S,i,,),add(i+n,T,,);
    for(int i=;i<=n;i++){
        for(int j=;j<=n;j++){
            add(i,j+n,,(real)a[i][j]);
        }
    }
    real res=0.0;
    while(spfa()) res+=augment();
    res/=1.0*n;
    printf("%.6lf\n",(double)res);
}
int main(){
    set(ball);
    n=read();
    int u=,v=;
    for(int i=,t;i<=n;i++){
        t=;
        for(int j=;j<=n;j++){
            a[i][j]=read();
            t=max(t,a[i][j]);
        }
        u+=t;
    }
    bool f=;
    for(int i=,t;i<=n;i++){
        t=1e9;
        for(int j=;j<=n;j++){
            b[i][j]=read();
            t=min(t,b[i][j]);
            if(b[i][j]!=) f=;
        }
        v+=t;
    }
    if(f){work1();return ;}
    real l=,r=(real)(u+v-)/(real)v,mid,ans=,now;
    while(l+eps<r){
        mid=(l+r)/2.0;
        now=mapping(mid);
        if(cmp(now)==){printf("%.6lf\n",(double)mid);return ;}
        if(cmp(now)>) l=mid;
        else r=mid;
    }
    printf("%.6lf\n",(double)l);
    fclose(stdin);
    fclose(stdout);
    return ;
}