p5339 [TJOI2019]唱、跳、rap和篮球

分析

 代码

#include<bits/stdc++.h>
using namespace std;
#define int long long
const int mod = ;
const int g = ;
int p[],inv[],G,cc[][],a[],b[],c[],d[],r[];
inline int pw(int x,int p){
    int res=;
    while(p){
      if(p&)res=1ll*res*x%mod;
      x=1ll*x*x%mod;
      p>>=;
    }
    return res;
}
inline void ntt(int a[],int n,int f){
    int i,j,k,now;
    for(i=;i<n;i++)if(i<r[i])swap(a[i],a[r[i]]);
    for(k=;k<n;k<<=){
      if(f==)now=g;
        else now=G;
      int wn=pw(now,(mod-)/(k<<));
      for(i=;i<n;i+=(k<<)){
          int w=,p,q;
          for(j=;j<k;j++,w=1ll*w*wn%mod){
            p=a[i+j],q=1ll*a[i+j+k]*w%mod;
            a[i+j]=(p+q)%mod;
            a[i+j+k]=(p-q+mod)%mod;
        }
      }
    }
}
inline int get_sum(int n,int A,int B,int C,int D){
    int i,j,k,m=,len=;
    if(n>A+B+C+D||n<)return ;
    while(m<((A+B+C+D)<<))m<<=,len++;
    for(i=;i<m;i++)r[i]=((r[i>>]>>)|((i&)<<(len-)));
    for(i=;i<m;i++)a[i]=(i<=A)?inv[i]:;
    for(i=;i<m;i++)b[i]=(i<=B)?inv[i]:;
    for(i=;i<m;i++)c[i]=(i<=C)?inv[i]:;
    for(i=;i<m;i++)d[i]=(i<=D)?inv[i]:;
    ntt(a,m,),ntt(b,m,),ntt(c,m,),ntt(d,m,);
    for(i=;i<m;i++)a[i]=1ll*a[i]*b[i]%mod*c[i]%mod*d[i]%mod;
    ntt(a,m,-);
    return 1ll*p[n]*a[n]%mod*pw(m,mod-)%mod;
}
signed main(){
    int n,A,B,C,D,i,j,k;
    G=pw(g,mod-);
    p[]=;
    for(i=;i<=;i++)p[i]=1ll*p[i-]*i%mod;
    inv[]=pw(p[],mod-);
    for(i=;i>=;i--)inv[i]=1ll*inv[i+]*(i+)%mod;
    for(i=;i<=;i++)cc[i][]=cc[i][i]=;
    for(i=;i<=;i++)
      for(j=;j<i;j++)cc[i][j]=(cc[i-][j]+cc[i-][j-])%mod;
    scanf("%lld%lld%lld%lld%lld",&n,&A,&B,&C,&D);
    int Ans=;
    for(i=;i<=n/;i++){
      int res=(i&)?-:;
      res*=cc[n-*i][i];
      res=1ll*res*get_sum(n-*i,A-i,B-i,C-i,D-i)%mod;
      Ans=(Ans+res+mod)%mod;
    }
    printf("%lld\n",Ans);
    return ;
}