FJ省队集训DAY4 T1

 直接上题解

#include<cstdio>
#include<iostream>
#include<cmath>
#include<cstring>
#include<algorithm>
#define ll long long
const int Mod=1000000009,N=3000;
ll jc[N+10],jcny[N+10],jcnys[N+10],K[N+10],p[N+10],f[N+10];
int read(){
    int t=0,f=1;char ch=getchar();
    while (ch<'0'||ch>'9'){if (ch=='-')f=-1;ch=getchar();}
    while ('0'<=ch&&ch<='9'){t=t*10+ch-'0';ch=getchar();}
    return t*f;
}
int Pow(int a,int n){
    int res=1;
    while (n){
        if (n%2) res=((ll)res*a)%Mod;
        a=((ll)a*a)%Mod;
        n/=2;
    }
    return res;
}
int main(){
    jc[0]=1;
    for (int i=1;i<=3000;i++) jc[i]=(ll)(jc[i-1]*i)%Mod;
    jcny[3000]=Pow(jc[3000],Mod-2)%Mod;
    for (int i=2999;i>=0;i--) jcny[i]=(ll)jcny[i+1]*(i+1)%Mod;
    for (int i=0;i<=3000;i++) jcnys[i]=(ll)jcny[i]*jcny[i]%Mod;
    for (int i=0;i<=3000;i++)
     if ((i&1)&&jcny[i]) K[i]=Mod-jcny[i];else K[i]=jcny[i];
    int n=read();
    for (int i=1;i<=n;i++) {
        int x=read();p[x]++;
    } 
    f[0]=1;
    for (int k=1,tot=0;k<=n;k++){
        if (p[k]==0) continue;
        tot+=p[k];
        for (int i=tot;i>=0;i--){
            f[i]=(ll)f[i]*jcnys[p[k]]%Mod;
            for (int j=1;j<=p[k]&&j<=i;j++)
             f[i]=((ll)f[i-j]*K[j]%Mod*jcnys[p[k]-j]+f[i])%Mod;
        }
    }
    ll ans=0;
    for (int i=0;i<=n;i++)
     ans=((ll)jc[n-i]*f[i]+ans)%Mod;
    for (int i=1;i<=n;i++)
     ans=(ll)ans*jc[p[i]]%Mod;
    printf("%I64d
",ans); 
}