Codeforces739E. Gosha is hunting

$n leq 2000$个东西要搬走，两个人分别能搬$a$和$b$件东西，给两个人搬走每种东西的概率，问最优决策下期望搬走多少东西。

一个人搬贡献：$p_i$，另一个人搬贡献：$q_i$，两人一起搬：$p_i+q_i-p_iq_i$。

$s$->两个人：流量分别$a,b$，费用0；两个人->每件东西：费用$p_i$或$q_i$，流量1；每件东西->$t$：两条边，一条流量1费用0，一条流量1费用$-p_iq_i$。跑最大费用流。

//#include<iostream>
#include<cstring>
#include<cstdio>
//#include<time.h>
//#include<complex>
//#include<set>
#include<queue>
#include<algorithm>
#include<stdlib.h>
using namespace std;

#define LL long long
int qread()
{
    char c; int s=0,f=1; while ((c=getchar())<'0' || c>'9') (c=='-') && (f=-1);
    do s=s*10+c-'0'; while ((c=getchar())>='0' && c<='9'); return s*f;
}

//Pay attention to '-' , LL and double of qread!!!!

int n,a,b;
#define maxn 6011
#define maxm 50011

struct Edge{int to,next,cap,flow; double cost;};
struct Network
{
    Edge edge[maxm<<1]; int first[maxn],le,n;
    void clear(int m) {le=2; n=m;}
    void in(int x,int y,int cap,double cost)
    {Edge &e=edge[le]; e.to=y; e.cap=cap; e.flow=0; e.cost=cost; e.next=first[x]; first[x]=le++;}
    void insert(int x,int y,int cap,double cost) {in(x,y,cap,cost); in(y,x,0,-cost);}
    double dis[maxn]; int que[maxn],head,tail,s,t,cur[maxn]; bool vis[maxn];
    bool spfa()
    {
        for (int i=1;i<=n;i++) dis[i]=1e18; dis[s]=0;
        vis[s]=1; head=tail=0; que[tail++]=s;
        while (head!=tail)
        {
            int x=que[head++]; if (head==maxn) head=0;
            vis[x]=0;
            for (int i=first[x];i;i=edge[i].next)
            {
                Edge &e=edge[i]; if (e.cap==e.flow) continue;
                if (dis[e.to]-(dis[x]+e.cost)>1e-9)
                {
                    dis[e.to]=dis[x]+e.cost;
                    if (!vis[e.to])
                    {
                        que[tail++]=e.to;
                        if (tail==maxn) tail=0;
                        vis[e.to]=1;
                    }
                }
            }
        }
        return dis[t]<1e17;
    }
    double cost;
    int dfs(int x,int a)
    {
        if (x==t || !a) {cost+=a*dis[t]; return a;}
        int flow=0,f;
        vis[x]=1;
        for (int &i=cur[x];i;i=edge[i].next)
        {
            Edge &e=edge[i];
            if (!vis[e.to] && fabs(dis[e.to]-(dis[x]+e.cost))<1e-9 && (f=dfs(e.to,min(e.cap-e.flow,a)))>0)
            {
                e.flow+=f; flow+=f;
                edge[i^1].flow-=f; a-=f;
                if (!a) break;
            }
        }
        vis[x]=0;
        return flow;
    }
    double Dinic(int S,int T)
    {
        s=S; t=T;
        cost=0;
        while (spfa())
        {
            for (int i=1;i<=n;i++) cur[i]=first[i];
            dfs(s,0x3f3f3f3f);
        }
        return cost;
    }
//    void test()
//    {
//        for (int i=1;i<=n;i++)
//            for (int j=first[i];j;j=edge[j].next)
//            {
//                Edge &e=edge[j];
//                cout<<i<<"->"<<e.to<<": cap"<<e.cap<<" flow"<<e.flow<<" cost"<<e.cost<<endl;
//            }
//        cout<<endl;
//    }
}g;

double p[maxn];
int main()
{
    n=qread(); a=qread(); b=qread();
    int A=n+1,B=A+1,s=B+1,t=s+1; g.clear(t);
    g.insert(s,A,a,0); g.insert(s,B,b,0);
    
    for (int i=1;i<=n;i++) scanf("%lf",&p[i]);
    double x;
    for (int i=1;i<=n;i++)
    {
        scanf("%lf",&x);
        g.insert(A,i,1,-p[i]); g.insert(B,i,1,-x);
        g.insert(i,t,1,0); g.insert(i,t,1,p[i]*x);
    }
//    g.test();
    printf("%.6f
",-g.Dinic(s,t));
//    g.test();
    return 0;
}