FJ省队集训DAY4 T1
直接上题解
1 #include<cstdio> 2 #include<iostream> 3 #include<cmath> 4 #include<cstring> 5 #include<algorithm> 6 #define ll long long 7 const int Mod=1000000009,N=3000; 8 ll jc[N+10],jcny[N+10],jcnys[N+10],K[N+10],p[N+10],f[N+10]; 9 int read(){ 10 int t=0,f=1;char ch=getchar(); 11 while (ch<'0'||ch>'9'){if (ch=='-')f=-1;ch=getchar();} 12 while ('0'<=ch&&ch<='9'){t=t*10+ch-'0';ch=getchar();} 13 return t*f; 14 } 15 int Pow(int a,int n){ 16 int res=1; 17 while (n){ 18 if (n%2) res=((ll)res*a)%Mod; 19 a=((ll)a*a)%Mod; 20 n/=2; 21 } 22 return res; 23 } 24 int main(){ 25 jc[0]=1; 26 for (int i=1;i<=3000;i++) jc[i]=(ll)(jc[i-1]*i)%Mod; 27 jcny[3000]=Pow(jc[3000],Mod-2)%Mod; 28 for (int i=2999;i>=0;i--) jcny[i]=(ll)jcny[i+1]*(i+1)%Mod; 29 for (int i=0;i<=3000;i++) jcnys[i]=(ll)jcny[i]*jcny[i]%Mod; 30 for (int i=0;i<=3000;i++) 31 if ((i&1)&&jcny[i]) K[i]=Mod-jcny[i];else K[i]=jcny[i]; 32 int n=read(); 33 for (int i=1;i<=n;i++) { 34 int x=read();p[x]++; 35 } 36 f[0]=1; 37 for (int k=1,tot=0;k<=n;k++){ 38 if (p[k]==0) continue; 39 tot+=p[k]; 40 for (int i=tot;i>=0;i--){ 41 f[i]=(ll)f[i]*jcnys[p[k]]%Mod; 42 for (int j=1;j<=p[k]&&j<=i;j++) 43 f[i]=((ll)f[i-j]*K[j]%Mod*jcnys[p[k]-j]+f[i])%Mod; 44 } 45 } 46 ll ans=0; 47 for (int i=0;i<=n;i++) 48 ans=((ll)jc[n-i]*f[i]+ans)%Mod; 49 for (int i=1;i<=n;i++) 50 ans=(ll)ans*jc[p[i]]%Mod; 51 printf("%I64d\n",ans); 52 }
