BZOJ 3993 [SDOI2015]星际战争

题解:二分+网络流判定.

#include<iostream>
#include<cstdio>
#include<cstring>
#include<cstdlib>
#include<string>
#include<cmath>
#include<ctime>
#include<algorithm>
#include<map>
#include<set>
#include<queue>
#include<iomanip>
using namespace std;
#define ll long long
#define db double 
#define up(i,j,n) for(int i=j;i<=n;i++)
#define pii pair<int,int>
#define uint unsigned int
#define FILE "dealing"
#define eps 1e-4
int read(){
	int x=0,f=1,ch=getchar();
	while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}
	while(ch>='0'&&ch<='9'){x=(x<<1)+(x<<3)+ch-'0';ch=getchar();}
	return x*f;
}
template<class T> bool cmax(T& a,T b){return a<b?a=b,true:false;}
template<class T> bool cmin(T& a,T b){return a>b?a=b,true:false;}
const int maxn=60,limit=128,inf=1000000000,r=3,mod=1004535809;
int n,m,S,T;
int a[maxn][maxn];
int A[maxn],B[maxn];
db sum=0;
// 护甲    攻击
struct node{
	int y,next;
	db flow;
}e[maxn*maxn*maxn];
int len=1,linkk[maxn<<1];
inline void insert(int x,int y,db flow){
	e[++len].y=y;
	e[len].next=linkk[x];
	linkk[x]=len;
	e[len].flow=flow;
	e[++len].y=x;
	e[len].next=linkk[y];
	linkk[y]=len;
	e[len].flow=0;
}
inline int dcmp(db a){if(fabs(a)<eps)return 0;return a>0?1:-1;}
int d[maxn<<1],q[maxn<<1],tail,head=0;
bool makelevel(){
	memset(d,-1,sizeof(d));
	tail=head=0;
	q[++tail]=S;d[S]=1;
	while(++head<=tail){
		int x=q[head];
		for(int i=linkk[x];i;i=e[i].next){
			if(d[e[i].y]==-1&&e[i].flow>eps)
				q[++tail]=e[i].y,d[e[i].y]=d[x]+1;
		}
	}
	return d[T]!=-1;
}
inline db makeflow(int x,db flow){
	if(x==T||!dcmp(flow))return flow;
	db maxflow=0,dis=0;
	for(int i=linkk[x];i&&dcmp(flow-maxflow)>0;i=e[i].next){
		if(e[i].flow>eps&&d[e[i].y]==d[x]+1)
			if(dis=makeflow(e[i].y,min(e[i].flow,flow-maxflow))){
				e[i].flow-=dis;
				e[i^1].flow+=dis;
				maxflow+=dis;
			}
	}
	if(!dcmp(maxflow))d[x]=-1;
	return maxflow;
}
db dinic(){
	db ans=0,d;
	while(makelevel())
		while(dcmp(d=makeflow(S,1e9)))
			ans+=d;
	return ans;
}
bool check(db ti){
	memset(linkk,0,sizeof(linkk));
	len=1;
	up(i,1,m)insert(S,i,B[i]*ti);
	up(i,1,n)insert(i+m,T,A[i]);
	up(i,1,m)up(j,1,n)if(a[i][j])insert(i,m+j,1e9);
	db ans=dinic();
	if(!dcmp(sum-ans))return 1;
	else return 0;
}
int main(){
	freopen(FILE".in","r",stdin);
	freopen(FILE".out","w",stdout);
	n=read(),m=read();S=n+m+1,T=n+m+2;
	up(i,1,n)A[i]=read(),sum+=A[i];
	up(i,1,m)B[i]=read();
	up(i,1,m)up(j,1,n)
		a[i][j]=read();
	db left=0,right=1e8,mid;
	while(right-left>eps){
		mid=(left+right)/2;
		if(check(mid))right=mid;
		else left=mid;
	}
	printf("%.6lf\n",left);
	return 0;
}