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ID题目提交者结果用时内存语言文件大小提交时间测评时间
#450532#6349. Is This FFT?fireinceWA 7736ms551608kbC++144.4kb2024-06-22 15:13:252024-06-22 15:13:25

Judging History

你现在查看的是最新测评结果

  • [2024-06-22 15:13:25]
  • 评测
  • 测评结果:WA
  • 用时:7736ms
  • 内存:551608kb
  • [2024-06-22 15:13:25]
  • 提交

answer

#include<iostream>
#include<cstdio>
#include<algorithm>
#include<vector>
#include<cstring>
#include<array>
#define endl '\n'
using namespace std;
using ll = long long;
using pi2 = array<int,2>;
using pi3 = array<int,3>;
const int N=250,M=1<<17,FN=M;

struct FastMod{
	using ull=unsigned long long;
	using L=__int128;
	ull b,m;
    void set(ull b){
        this->b=b,this->m=ull((L(1)<<64)/b);
    }
	ull reduce(ull a) const{
		ull q=(ull)((L(m)*a)>>64),r=a-q*b;
		return r>=b?r-b:r;
	}
};
template<typename T>
T operator%(T x,const FastMod& Mod){
	return Mod.reduce(x);
}
template<typename T>
T& operator%=(T& x,const FastMod& Mod){
	return x=Mod.reduce(x);
}
FastMod P;
int P_;

int n;
ll fpow(ll a,ll b){
    return b==0?1:(b&1?a*fpow(a*a%P,b/2)%P:fpow(a*a%P,b/2));
}
ll fact[FN],inv_fact[FN];
void init_fact(int n){
    fact[0] = inv_fact[0] = 1;
    for (int i = 1; i <= n; i++)
        fact[i] = 1ll*fact[i - 1] * i % P;
    inv_fact[n] = fpow(fact[n], P_ - 2);
    for (int i = n - 1; i >= 1; i--)
        inv_fact[i] = 1ll*inv_fact[i + 1] * (i + 1) % P;
}
ll binom(ll n,ll k){
    if(n<k)return 0;
    return 1ll*fact[n]*inv_fact[k]%P*inv_fact[n-k]%P;
}
void mod(ll& x){
    if(x>=P_)x-=P_;
}
void mod(int& x){
    if(x>=P_)x-=P_;
}
int m;
ll res[N];
int root;

namespace NTT{
    void mod(int& x){
        if(x>=P_)x-=P_;
    }
    int W[M],IW[M];
    int G,IG;
    void init(int n){
        for(int l=2,mid=1;l<=n;l<<=1,mid<<=1)
            for(int i=0,wn=fpow(G,(P_-1)/l),iwn=fpow(IG,(P_-1)/l),w=1,iw=1;i<mid;i++)
                W[mid+i]=w,IW[mid+i]=iw,w=((ll)w*wn)%P,iw=((ll)iw*iwn)%P;
    }
    void dft(int* f,int n){
        for(int l=n,mid=l>>1;l>=2;l>>=1,mid>>=1)
            for(int p=0;p<n;p+=l)
                for(int i=0,x,y;i<mid;i++)
                    x=f[p+i],y=f[p+mid+i],mod(f[p+i]+=y),f[p+mid+i]=(ll)W[mid+i]*(P_+x-y)%P;
    }
    void idft(int* f,int n){
        for(int l=2,mid=1;l<=n;l<<=1,mid<<=1)
            for(int p=0;p<n;p+=l)
                for(int i=0,x,y;i<mid;i++)
                    x=f[p+i],y=(ll)f[p+mid+i]*IW[mid+i]%P,mod(f[p+i]+=y),mod(f[p+i+mid]=P_+x-y);
        for(int i=0,invn=fpow(n,P_-2);i<n;i++)f[i]=(ll)f[i]*invn%P;
    }
    int gt(int l){
        int n=1;
        while(n<l)n<<=1;
        return n;
    }
};

ll f[N][M],g[N][M];
int tmp[M],tmp2[M];
int gp[N][M];

ll WP[M];
int tr[M];
void init_butterfly(int n){
    int w=__lg(n);
    for(int i=0;i<n;i++)tr[i]=tr[i>>1]>>1|((i&1)<<w-1);
    ll wn=fpow(root,(P_-1)/n);
    WP[0]=1;
    for(int i=1;i<n;i++)WP[i]=WP[i-1]*wn%P;
}
void dp(){
    f[1][0]=g[1][0]=res[1]=1;
    int ml=NTT::gt(m);
    init_butterfly(ml);

    for(int j=0;j<=0;j++)gp[1][j]=g[1][j]*inv_fact[1*(1-1)/2-j]%P*inv_fact[j]%P;
    NTT::dft(gp[1],ml);

    for(int i=2;i<=n;i++){
        int im=i*(i-1)/2-(i-1);
        fill(tmp2,tmp2+ml,0);
        for(int k=1;k<i;k++){
            int x=k*(k-1)/2,y=(i-k)*(i-k-1)/2,z=k*(i-k)-1;
            
            ll bk=binom(i,k);
            for(int j=0;j<ml;j++)tmp[j]=(ll)gp[k][j]%P*gp[i-k][j]%P*bk%P;

            for(int j=0;j<ml;j++)tmp[j]=tmp[j]*WP[tr[j]*z%ml]%P;
            for(int j=0;j<ml;j++)
                mod(tmp2[j]+=tmp[j]);
        }
        NTT::idft(tmp2,ml);
        for(int j=0;j<=im;j++)
            f[i][j]=(ll)tmp2[j]*fact[i*(i-1)/2-1-j]%P*fact[j]%P;

        g[i][im]=f[i][im];
        for(int j=im-1;j>=0;j--)mod(g[i][j]=g[i][j+1]+f[i][j]);
        for(int j=0;j<=im;j++)gp[i][j]=g[i][j]*inv_fact[i*(i-1)/2-j]%P*inv_fact[j]%P;
        NTT::dft(gp[i],ml);
        for(int j=0;j<=im;j++)mod(res[i]+=f[i][j]);
        res[i]=res[i]*fpow(2,P_-2)%P;
    }
}

void findrt(){
    int t=P_-1;
    vector<int> vs;
    for(int i=2;i<=t&&i*i<=P_;i++){
        if(t%i==0){
            vs.push_back(i);
            while(t%i==0)t/=i;
        }
    }
    if(t!=1)vs.push_back(t);

    for(int i=2;i<=P_;i++){
        bool flag=true;
        for(int j:vs){
            if(fpow(i,(P_-1)/j)==1){
                flag=false;
                break;
            }
        }
        if(flag)return root=i,void();
    }
}

signed main(){
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    cin>>n>>P_;
    P.set(P_);
    findrt();
    NTT::G=root,NTT::IG=fpow(root,P_-2);
    m=n*(n-1)/2;
    init_fact(m);
    NTT::init(NTT::gt(m));
    dp();
    for(int i=2;i<=n;i++)cout<<res[i]*inv_fact[i*(i-1)/2]%P<<endl;
    return 0;
}

詳細信息

Test #1:

score: 100
Accepted
time: 0ms
memory: 38612kb

input:

10 998244353

output:

1
1
532396989
328786831
443364983
567813846
34567523
466373946
474334062

result:

ok 9 numbers

Test #2:

score: -100
Wrong Answer
time: 7736ms
memory: 551608kb

input:

250 998244353

output:

1
1
532396989
328786831
443364983
567813846
34567523
466373946
474334062
289137877
768923227
177538883
440227465
101981224
874960215
35275208
664066979
334444870
46651494
799130693
122319095
913072242
44703442
965640306
52873544
461938281
263838691
777326453
356621754
560569747
812581766
46147702
12...

result:

wrong answer 249th numbers differ - expected: '107476421', found: '299444202'