【BZOJ-4514】数字配对 最大费用最大流 + 质因数分解 + 二分图 + 贪心 + 线性筛

#include<iostream>
#include<cstdio>
#include<algorithm>
#include<cstring>
#include<cmath>
#include<queue>
using namespace std;
int read()
{
    int x=0,f=1; char ch=getchar();
    while (ch<‘0‘ || ch>‘9‘) {if (ch==‘-‘) f=-1; ch=getchar();}
    while (ch>=‘0‘ && ch<=‘9‘) {x=x*10+ch-‘0‘; ch=getchar();}
    return x*f;
}
#define maxn 1010
#define maxm 100010
int n,a[maxn],b[maxn];long long c[maxn]; bool f=0;
struct EdgeNode{int next,cap,to,from;long long cost;}edge[maxm];
int head[maxn],cnt=1;
void add(int u,int v,int w,long long c)
{
    cnt++;
    edge[cnt].to=v;edge[cnt].from=u;edge[cnt].cap=w;edge[cnt].cost=c;edge[cnt].next=head[u];head[u]=cnt;
}
void insert(int u,int v,int w,long long c) {add(u,v,w,c); add(v,u,0,-c);}
int from[maxn],S,T; long long dis[maxn]; bool mark[maxn];
#define inf 10000000000000LL
bool spfa()
{
    queue<int>q;
    for (int i=S; i<=T; i++) dis[i]=-inf; memset(from,0,sizeof(from));
    q.push(S); mark[S]=1; dis[S]=0;
    while (!q.empty())
        {
            int now=q.front(); q.pop(); mark[now]=0;
            for (int i=head[now]; i; i=edge[i].next)
                if (edge[i].cap && dis[edge[i].to]<dis[now]+edge[i].cost)
                    {
                        dis[edge[i].to]=dis[now]+edge[i].cost; from[edge[i].to]=i;
                        if (!mark[edge[i].to])
                            q.push(edge[i].to),mark[edge[i].to]=1;
                    }
        } 
    return dis[T]!=-inf;
}
long long Cost; int Flow;
void MaxCostFlow()
{
    int flow=inf;
    for (int i=from[T]; i; i=from[edge[i].from])
        flow=min(flow,edge[i].cap);
    
    if ((long long)Cost+flow*dis[T]>=0LL)
        {
            for (int i=from[T]; i; i=from[edge[i].from])
                edge[i].cap-=flow,edge[i^1].cap+=flow;
            Flow+=flow; Cost+=dis[T]*flow;
        
        }
    else 
        Flow+=abs(Cost/dis[T]),Cost-=(Cost/dis[T])*dis[T],f=1;
   // Flow+=flow;
    //printf("%d %I64d %I64d\n",Flow,Cost,dis[T]);
}
int prime[35001],tot; bool flag[35001]; 
void Prework()
{
    flag[1]=1;
    for (int i=2; i<=32000; i++)
        {
            if (!flag[i]) prime[++tot]=i;
            for (int j=1; j<=tot&&i*prime[j]<=32000; j++)
                flag[i*prime[j]]=1;
        }
}
int odd[maxn],even[maxn],ot,et;
bool check(int x,int y)
{
    if (x%y && y%x || !x || !y) return 0;
    int tmp=max(x/y,y/x);
    for (int i=1; i<=tot&&prime[i]<tmp; i++)
        if (tmp%prime[i]==0) return 0;
    return 1;
}    
void Build()
{
    Prework();
    S=0,T=n+1;
    for (int i=1,ct=0; i<=n; i++,ct=0)
        {
            for (int j=1,tmp=a[i]; j<=tot; j++,tmp=a[i])
                while (tmp%prime[j]==0) tmp/=prime[j],ct++;
                    //else if (prime[j]>tmp) break;
            if (ct&1) odd[++ot]=i; else even[++et]=i;
        }
    for (int i=1; i<=ot; i++)
        for (int j=1; j<=et; j++)
            if (check(a[odd[i]],a[even[j]]))
                insert(odd[i],even[j],inf,c[odd[i]]*c[even[j]])/*,printf("%d-->%d:%d/%I64d\n",odd[i],even[j],inf,c[odd[i]]*c[even[j]])*/;
    for (int i=1; i<=ot; i++) insert(S,odd[i],b[odd[i]],0LL)/*,printf("%d-->%d:%d/%I64d\n",S,odd[i],b[odd[i]],0LL)*/;
    for (int i=1; i<=et; i++) insert(even[i],T,b[even[i]],0LL)/*,printf("%d-->%d:%d/%I64d\n",even[i],T,b[even[i]],0LL)*/;
    //printf("%d %d %d\n",ot,et,cnt);
}
int main()
{
//    freopen("menci_pair.in","r",stdin);
//    freopen("menci_pair.out","w",stdout);
    n=read();
    for (int i=1; i<=n; i++) a[i]=read();
    for (int i=1; i<=n; i++) b[i]=read();
    for (int i=1; i<=n; i++) c[i]=(long long)read();
    Build();
    while (spfa() && !f) MaxCostFlow();
    printf("%d\n",Flow);
    return 0;
}