// luogu-judger-enable-o2
#include<cstdio>
#include<queue>
#include<cstring>
#include<cstdlib>
#define INF 1e8+10
using namespace std;
const int MAXN=201;
const double eps=1e-7;
#define getchar() (p1==p2&&(p2=(p1=buf)+fread(buf,1,MAXN,stdin),p1==p2)?EOF:*p1++)
char buf[1<<20],*p1=buf,*p2=buf;
inline int read()
{
char c=getchar();int x=0,f=1;
while(c<'0'||c>'9'){if(c=='-')f=-1;c=getchar();}
while(c>='0'&&c<='9'){x=x*10+c-'0';c=getchar();}
return x*f;
}
struct node
{
int u,v,f,nxt;
double w;
}edge[MAXN*MAXN];
int head[MAXN],num=0;
int N,S,T;
int a[233][233],b[233][233];
double ans=0.0;
inline void add_edge(int x,int y,int z,double k)
{
edge[num].u=x;
edge[num].v=y;
edge[num].f=z;
edge[num].w=k;
edge[num].nxt=head[x];
head[x]=num++;
}
inline void AddEdge(int x,int y,int z,double k)
{
add_edge(x,y,z,k);
add_edge(y,x,0,-k);
}
int arrive[MAXN],vis[MAXN],pre[MAXN];
double dis[MAXN];
bool SPFA()
{
queue<int>q;
q.push(S);
for(register int i=S;i<=T;i++) dis[i]=-1e20,arrive[i]=0;
memset(vis,0,sizeof(vis));
dis[S]=0;vis[S]=1;
while(q.size()!=0)
{
int p=q.front();q.pop();
vis[p]=0;arrive[p]=1;
for(int i=head[p];i!=-1;i=edge[i].nxt)
{
if(edge[i].f&&dis[edge[i].v]<dis[p]+edge[i].w)
{
dis[edge[i].v]=dis[p]+edge[i].w;
pre[edge[i].v]=i;
if(!vis[edge[i].v])
q.push(edge[i].v),vis[edge[i].v]=1;
}
}
}
return arrive[T];
}
int dfs()
{
int mn=INF;
int now=T;
while(pre[now])
{
mn=min(mn,edge[pre[now]].f);
now=edge[pre[now]].u;
}
ans+=mn*dis[T];
now=T;
while(pre[now])
{
edge[pre[now]].f-=mn;
edge[pre[now]^1].f+=mn;
now=edge[pre[now]].u;
}
}
bool check(double val)
{
memset(pre,0,sizeof(pre));
memset(head,-1,sizeof(head));
num=2;
for(int i=1;i<=N;i++) AddEdge(S,i,1,0);
for(int i=1;i<=N;i++) AddEdge(i+N,T,1,0);
for(int i=1;i<=N;i++) for(int j=1;j<=N;j++) AddEdge(i,j+N,1,a[i][j]-1.0*val*b[i][j]);
ans=0.0;
while(SPFA())
dfs();
if (ans<=0) return 1;
else return 0;
}
int main()
{
#ifdef WIN32
freopen("a.in","r",stdin);
//freopen("c.out","w",stdout);
#else
#endif
N=read();
S=0,T=N*2|1;
for(int i=1;i<=N;i++)
for(int j=1;j<=N;j++)
a[i][j]=read();
for(int i=1;i<=N;i++)
for(int j=1;j<=N;j++)
b[i][j]=read();
double l=0,r=10000;
while(r-l>=eps)
{
double mid=(l+r)/2;
if(check(mid)) r=mid;
else l=mid;
}
printf("%.6lf",l);
return 0;
}
网友评论