【bzoj3993】星际战争

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二分答案+最大流验证

检验的条件是所有连向T的边满流

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#include<bits/stdc++.h>
#define FILE "read"
#define MAXN 510
#define eps 1e-6
#define INF 1e9
using namespace std;
struct node{int y,next,rel;double v;}e[MAXN*MAXN*2];
int n,m,S,T,len,sum,a[MAXN],b[MAXN],Map[MAXN][MAXN],level[MAXN],Link[MAXN];
queue<int>q;
inline int read(){
int x=0,f=1; char ch=getchar();
while(!isdigit(ch)) {if(ch=='-') f=-1; ch=getchar();}
while(isdigit(ch)) {x=x*10+ch-'0'; ch=getchar();}
return x*f;
}
void insert(int x,int y,double v){
e[++len].next=Link[x];Link[x]=len;e[len].y=y;e[len].v=v;e[len].rel=len+1;
e[++len].next=Link[y];Link[y]=len;e[len].y=x;e[len].v=0;e[len].rel=len-1;
}
bool bfs(){
memset(level,-1,sizeof(level));
q.push(S); level[S]=0;
while(!q.empty()){
int x=q.front(); q.pop();
for(int i=Link[x];i;i=e[i].next)
if(level[e[i].y]==-1&&e[i].v>eps){
q.push(e[i].y);
level[e[i].y]=level[x]+1;
}
}
return level[T]>=0;
}
double MAXFLOW(int x,double flow){
if(x==T) return flow;
double maxflow=0,d=0;
for(int i=Link[x];i&&maxflow-flow<eps;i=e[i].next)
if(level[e[i].y]==level[x]+1&&e[i].v>eps)
if((d=MAXFLOW(e[i].y,min(e[i].v,flow-maxflow)))>eps)
e[i].v-=d,e[e[i].rel].v+=d,maxflow+=d;
if(maxflow<eps) level[x]=-1;
return maxflow;
}
void pre(){len=0;memset(Link,0,sizeof(Link));}
bool check(double x){
S=0; T=n+m+1; pre();
for(int i=1;i<=n;++i) insert(i+m,T,(double)a[i]);
for(int i=1;i<=m;++i) insert(S,i,(double)x*b[i]);
for(int i=1;i<=m;++i)for(int j=1;j<=n;++j)if(Map[i][j]) insert(i,j+m,INF);
double d=0,ans=0;
while(bfs()) while((d=MAXFLOW(S,INF))>eps) ans+=d;
return fabs(sum-ans)<eps;
}
int main(){
freopen(FILE".in","r",stdin);
freopen(FILE".out","w",stdout);
n=read(); m=read();
for(int i=1;i<=n;++i) a[i]=read(),sum+=a[i];
for(int i=1;i<=m;++i) b[i]=read();
for(int i=1;i<=m;++i)for(int j=1;j<=n;++j)Map[i][j]=read();
double l=0,r=INF;
while(l+eps<r){
double mid=(l+r)/2;
if(check(mid)) r=mid;
else l=mid;
}
printf("%.6lf\n",check(l)?l:r);
return 0;
}
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