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 = 998244353;
const int g = 3;
int p[40010],inv[40010],G,cc[2100][2100],a[40010],b[40010],c[40010],d[40010],r[40010];
inline int pw(int x,int p){
    int res=1;
    while(p){
      if(p&1)res=1ll*res*x%mod;
      x=1ll*x*x%mod;
      p>>=1;
    }
    return res;
}
inline void ntt(int a[],int n,int f){
    int i,j,k,now;
    for(i=0;i<n;i++)if(i<r[i])swap(a[i],a[r[i]]);
    for(k=1;k<n;k<<=1){
      if(f==1)now=g;
        else now=G;
      int wn=pw(now,(mod-1)/(k<<1));
      for(i=0;i<n;i+=(k<<1)){
          int w=1,p,q;
          for(j=0;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=1,len=0;
    if(n>A+B+C+D||n<0)return 0;
    while(m<((A+B+C+D)<<1))m<<=1,len++;
    for(i=0;i<m;i++)r[i]=((r[i>>1]>>1)|((i&1)<<(len-1)));
    for(i=0;i<m;i++)a[i]=(i<=A)?inv[i]:0;
    for(i=0;i<m;i++)b[i]=(i<=B)?inv[i]:0;
    for(i=0;i<m;i++)c[i]=(i<=C)?inv[i]:0;
    for(i=0;i<m;i++)d[i]=(i<=D)?inv[i]:0;
    ntt(a,m,1),ntt(b,m,1),ntt(c,m,1),ntt(d,m,1);
    for(i=0;i<m;i++)a[i]=1ll*a[i]*b[i]%mod*c[i]%mod*d[i]%mod;
    ntt(a,m,-1);
    return 1ll*p[n]*a[n]%mod*pw(m,mod-2)%mod;
}
signed main(){
    int n,A,B,C,D,i,j,k;
    G=pw(g,mod-2);
    p[0]=1;
    for(i=1;i<=2000;i++)p[i]=1ll*p[i-1]*i%mod;
    inv[2000]=pw(p[2000],mod-2);
    for(i=1999;i>=0;i--)inv[i]=1ll*inv[i+1]*(i+1)%mod;
    for(i=0;i<=2000;i++)cc[i][0]=cc[i][i]=1;
    for(i=1;i<=2000;i++)
      for(j=1;j<i;j++)cc[i][j]=(cc[i-1][j]+cc[i-1][j-1])%mod;
    scanf("%lld%lld%lld%lld%lld",&n,&A,&B,&C,&D);
    int Ans=0;
    for(i=0;i<=n/4;i++){
      int res=(i&1)?-1:1;
      res*=cc[n-3*i][i];
      res=1ll*res*get_sum(n-4*i,A-i,B-i,C-i,D-i)%mod;
      Ans=(Ans+res+mod)%mod;
    }
    printf("%lld\n",Ans);
    return 0;
}