#736118 (C++17) No.1080 Strange Squared Score Sum

提出ソース
結果

問題	No.1080 Strange Squared Score Sum
ユーザー	tko919
提出日時	2022-02-02 01:51:54
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	799 ms / 5,000 ms
コード長	14,606 bytes
コンパイル時間	3,633 ms
コンパイル使用メモリ	243,176 KB
実行使用メモリ	24,212 KB
最終ジャッジ日時	2024-06-11 09:17:59
合計ジャッジ時間	13,901 ms
ジャッジサーバーID （参考情報）	judge1 / judge2
このコードへのチャレンジ
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テストケース

テストケース表示
入力	結果	実行時間実行使用メモリ
testcase_00	AC	11 ms 7,936 KB
testcase_01	AC	12 ms 7,936 KB
testcase_02	AC	390 ms 16,132 KB
testcase_03	AC	794 ms 23,904 KB
testcase_04	AC	188 ms 11,972 KB
testcase_05	AC	192 ms 12,012 KB
testcase_06	AC	51 ms 8,936 KB
testcase_07	AC	96 ms 10,136 KB
testcase_08	AC	388 ms 16,068 KB
testcase_09	AC	387 ms 15,912 KB
testcase_10	AC	52 ms 8,836 KB
testcase_11	AC	799 ms 23,876 KB
testcase_12	AC	386 ms 15,944 KB
testcase_13	AC	797 ms 23,932 KB
testcase_14	AC	385 ms 16,004 KB
testcase_15	AC	11 ms 7,936 KB
testcase_16	AC	795 ms 24,212 KB
testcase_17	AC	381 ms 16,420 KB
testcase_18	AC	386 ms 16,192 KB
testcase_19	AC	385 ms 16,168 KB
testcase_20	AC	791 ms 23,704 KB
testcase_21	AC	787 ms 23,660 KB
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ソースコード

raw source code
#line 1 "library/Template/template.hpp"
#include <bits/stdc++.h>
using namespace std;

#define rep(i,a,b) for(int i=(int)(a);i<(int)(b);i++)
#define ALL(v) (v).begin(),(v).end()
using ll=long long int;
const int inf = 0x3fffffff;
const ll INF = 0x1fffffffffffffff;
template<typename T>inline bool chmax(T& a,T b){if(a<b){a=b;return 1;}return 0;}
template<typename T>inline bool chmin(T& a,T b){if(a>b){a=b;return 1;}return 0;}
#line 2 "library/Utility/fastio.hpp"
#include <unistd.h>

class FastIO{
    static constexpr int L=1<<16;
    char rdbuf[L];
    int rdLeft=0,rdRight=0;
    inline void reload(){
        int len=rdRight-rdLeft;
        memmove(rdbuf,rdbuf+rdLeft,len);
        rdLeft=0,rdRight=len;
        rdRight+=fread(rdbuf+len,1,L-len,stdin);
    }
    inline bool skip(){
        for(;;){
            while(rdLeft!=rdRight and rdbuf[rdLeft]<=' ')rdLeft++;
            if(rdLeft==rdRight){
                reload();
                if(rdLeft==rdRight)return false;
            }
            else break;
        }
        return true;
    }
    template<typename T,enable_if_t<is_integral<T>::value,int> =0>inline bool _read(T& x){
        if(!skip())return false;
        if(rdLeft+20>=rdRight)reload();
        bool neg=false;
        if(rdbuf[rdLeft]=='-'){
            neg=true;
            rdLeft++;
        }
        x=0;
        while(rdbuf[rdLeft]>='0' and rdLeft<rdRight){
            x=x*10+(neg?-(rdbuf[rdLeft++]^48):(rdbuf[rdLeft++]^48));
        }
        return true;
    }
    template<typename T,enable_if_t<is_floating_point<T>::value,int> =0>inline bool _read(T& x){
        if(!skip())return false;
        if(rdLeft+20>=rdRight)reload();
        bool neg=false;
        if(rdbuf[rdLeft]=='-'){
            neg=true;
            rdLeft++;
        }
        x=0;
        while(rdbuf[rdLeft]>='0' and rdbuf[rdLeft]<='9' and rdLeft<rdRight){
            x=x*10+(rdbuf[rdLeft++]^48);
        }
        if(rdbuf[rdLeft]!='.')return true;
        rdLeft++;
        T base=.1;
        while(rdbuf[rdLeft]>='0' and rdbuf[rdLeft]<='9' and rdLeft<rdRight){
            x+=base*(rdbuf[rdLeft++]^48);
            base*=.1;
        }
        if(neg)x=-x;
        return true;
    }
    inline bool _read(char& x){
        if(!skip())return false;
        if(rdLeft+1>=rdRight)reload();
        x=rdbuf[rdLeft++];
        return true;
    }
    inline bool _read(string& x){
        if(!skip())return false;
        for(;;){
            int pos=rdLeft;
            while(pos<rdRight and rdbuf[pos]>' ')pos++;
            x.append(rdbuf+rdLeft,pos-rdLeft);
            if(rdLeft==pos)break;
            rdLeft=pos;
            if(rdLeft==rdRight)reload();
            else break;
        }
        return true;
    }
    template<typename T>inline bool _read(vector<T>& v){
        for(auto& x:v){
            if(!_read(x))return false;
        }
        return true;
    }

    char wtbuf[L],tmp[50];
    int wtRight=0;
    inline void flush(){
        fwrite(wtbuf,1,wtRight,stdout);
        wtRight=0;
    }
    inline void _write(const char& x){
        if(wtRight>L-32)flush();
        wtbuf[wtRight++]=x;
    }
    inline void _write(const string& x){
        for(auto& c:x)_write(c);
    }
    template<typename T,enable_if_t<is_integral<T>::value,int> =0>inline void _write(T x){
        if(wtRight>L-32)flush();
        if(x==0){
            _write('0');
            return;
        }
        else if(x<0){
            _write('-');
            if (__builtin_expect(x == std::numeric_limits<T>::min(), 0)) {
                switch (sizeof(x)) {
                case 2: _write("32768"); return;
                case 4: _write("2147483648"); return;
                case 8: _write("9223372036854775808"); return;
                }
            }
            x=-x;
        }
        int pos=0;
        while(x!=0){
            tmp[pos++]=char((x%10)|48);
            x/=10;
        }
        rep(i,0,pos)wtbuf[wtRight+i]=tmp[pos-1-i];
        wtRight+=pos;
    }
    template<typename T>inline void _write(const vector<T>& v){
        rep(i,0,v.size()){
            if(i)_write(' ');
            _write(v[i]);
        }
    }
public:
    FastIO(){}
    ~FastIO(){flush();}
    inline void read(){}
    template <typename Head, typename... Tail>inline void read(Head& head,Tail&... tail){
        assert(_read(head));
        read(tail...); 
    }
    template<bool ln=true,bool space=false>inline void write(){if(ln)_write('\n');}
    template <bool ln=true,bool space=false,typename Head, typename... Tail>inline void write(const Head& head,const Tail&... tail){
        if(space)_write(' ');
        _write(head);
        write<ln,true>(tail...); 
    }
};

/**
 * @brief Fast IO
 */
#line 3 "sol.cpp"

#line 2 "library/Math/modint.hpp"

template<int mod=1000000007>struct fp {
    int v; static int get_mod(){return mod;}
    int inv() const{
        int tmp,a=v,b=mod,x=1,y=0;
        while(b)tmp=a/b,a-=tmp*b,swap(a,b),x-=tmp*y,swap(x,y);
        if(x<0){x+=mod;} return x;
    }
    fp(ll x=0){init(x%mod+mod);}
    fp& init(int x){v=(x<mod?x:x-mod); return *this;}
    fp operator-()const{return fp()-*this;}
    fp pow(ll t){fp res=1,b=*this; while(t){if(t&1)res*=b;b*=b;t>>=1;} return res;}
    fp& operator+=(const fp& x){return init(v+x.v);}
    fp& operator-=(const fp& x){return init(v+mod-x.v);}
    fp& operator*=(const fp& x){v=ll(v)*x.v%mod; return *this;}
    fp& operator/=(const fp& x){v=ll(v)*x.inv()%mod; return *this;}
    fp operator+(const fp& x)const{return fp(*this)+=x;}
    fp operator-(const fp& x)const{return fp(*this)-=x;}
    fp operator*(const fp& x)const{return fp(*this)*=x;}
    fp operator/(const fp& x)const{return fp(*this)/=x;}
    bool operator==(const fp& x)const{return v==x.v;}
    bool operator!=(const fp& x)const{return v!=x.v;}
    friend istream& operator>>(istream& is,fp& x){return is>>x.v;}
    friend ostream& operator<<(ostream& os,const fp& x){return os<<x.v;}
};
template<typename T>struct factorial {
    vector<T> Fact,Finv,Inv;
    factorial(int maxx){
        Fact.resize(maxx); Finv.resize(maxx); Inv.resize(maxx);
        Fact[0]=Fact[1]=Finv[0]=Finv[1]=Inv[1]=1;
        rep(i,2,maxx){Fact[i]=Fact[i-1]*i;} Finv[maxx-1]=Fact[maxx-1].inv();
        for(int i=maxx-1;i>=2;i--){Finv[i-1]=Finv[i]*i; Inv[i]=Finv[i]*Fact[i-1];}
    }
    T fact(int n,bool inv=0){if(n<0)return 0; return (inv?Finv[n]:Fact[n]);}
    T inv(int n){if(n<0)return 0; return Inv[n];}
    T nPr(int n,int r,bool inv=0){if(n<0||n<r||r<0)return 0; return fact(n,inv)*fact(n-r,inv^1);}
    T nCr(int n,int r,bool inv=0){if(n<0||n<r||r<0)return 0; return fact(n,inv)*fact(r,inv^1)*fact(n-r,inv^1);}
    T nHr(int n,int r,bool inv=0){return nCr(n+r-1,r,inv);}
};

/**
 * @brief Modint
 */
#line 2 "library/Convolution/ntt.hpp"

template<typename T,unsigned p=3>struct NTT{
    vector<T> rt,irt;
    NTT(int lg=21){
        unsigned m=T::get_mod()-1; T prt=p;
        rt.resize(lg); irt.resize(lg);
        rep(k,0,lg){
            rt[k]=-prt.pow(m>>(k+2));
            irt[k]=rt[k].inv();
        }
    }
    void ntt(vector<T>& f,bool inv=0){
        int n=f.size();
        if(inv){
            for(int m=1;m<n;m<<=1){ T w=1;
                for(int s=0,t=0;s<n;s+=m*2){
                    for(int i=s,j=s+m;i<s+m;i++,j++){
                        auto x=f[i],y=f[j];
                        f[i]=x+y; f[j]=(x-y)*w;
                    } w*=irt[__builtin_ctz(++t)];
                }
             } T mul=T(n).inv(); rep(i,0,n)f[i]*=mul;
        }else{
            for(int m=n;m>>=1;){ T w=1;
                for(int s=0,t=0;s<n;s+=m*2){
                    for(int i=s,j=s+m;i<s+m;i++,j++){
                        auto x=f[i],y=f[j]*w;
                        f[i]=x+y; f[j]=x-y;
                    } w*=rt[__builtin_ctz(++t)];
                }
            }
         }
    }
    vector<T> mult(const vector<T>& a,const vector<T>& b,bool same=0){
        if(a.empty() or b.empty())return vector<T>();
        int n=a.size()+b.size()-1,m=1<<__lg(n*2-1);
        vector<T> res(m); rep(i,0,a.size()){res[i]=a[i];} ntt(res);
        if(same)rep(i,0,m)res[i]*=res[i];
        else{
            vector<T> c(m); rep(i,0,b.size())c[i]=b[i];
            ntt(c); rep(i,0,m)res[i]*=c[i];
        } ntt(res,1); res.resize(n); return res;
    }
};

/**
 * @brief Number Theoretic Transform
 */
#line 4 "library/Convolution/arbitrary.hpp"

using M1=fp<1045430273>; using M2=fp<1051721729>; using M3=fp<1053818881>;
NTT<fp<1045430273>,3> N1; NTT<fp<1051721729>,6> N2; NTT<fp<1053818881>,7> N3;
template<typename T>vector<T> ArbitraryMult(const vector<T>& a,const vector<T>& b,bool same=0){
    if(a.empty() or b.empty())return vector<T>();
    int n=a.size()+b.size()-1; vector<T> res(n); vector<int> vals[3];
    vector<int> aa(a.size()),bb(b.size());
    rep(i,0,a.size())aa[i]=a[i].v; rep(i,0,b.size())bb[i]=b[i].v;
    vector<M1> a1(ALL(aa)),b1(ALL(bb)),c1=N1.mult(a1,b1,same);
    vector<M2> a2(ALL(aa)),b2(ALL(bb)),c2=N2.mult(a2,b2,same);
    vector<M3> a3(ALL(aa)),b3(ALL(bb)),c3=N3.mult(a3,b3,same);
    for(M1 x:c1)vals[0].push_back(x.v);
    for(M2 x:c2)vals[1].push_back(x.v);
    for(M3 x:c3)vals[2].push_back(x.v);
    M2 r_12=M2(M1::get_mod()).inv();
    M3 r_13=M3(M1::get_mod()).inv(),r_23=M3(M2::get_mod()).inv();
    M3 r_1323=r_13*r_23;
    T w1(M1::get_mod()),w2=w1*T(M2::get_mod());
    rep(i,0,n){
        ll p=vals[0][i];
        ll q=(vals[1][i]+M2::get_mod()-p)*r_12.v%M2::get_mod();
        ll r=((vals[2][i]+M3::get_mod()-p)*r_1323.v+
            (M3::get_mod()-q)*r_23.v)%M3::get_mod();
        res[i]=(p+q*w1.v+r*w2.v);
    } return res;
}

/**
 * @brief Arbitrary Mod Convolution
 */
#line 2 "library/FPS/arbitraryfps.hpp"

template<typename T>struct Poly:vector<T>{
    Poly(int n=0){this->assign(n,T());}
    Poly(const vector<T>& f){this->assign(ALL(f));}
    T eval(const T& x){
        T res;
        for(int i=this->size()-1;i>=0;i--)res*=x,res+=this->at(i);
        return res;
    }
    Poly rev()const{Poly res=*this; reverse(ALL(res)); return res;}
    void shrink(){while(!this->empty() and this->back()==0)this->pop_back();}
    Poly inv()const{
        assert(this->front()!=0); const int n=this->size();
        Poly res(1); res.front()=T(1)/this->front();
        for(int k=1;k<n;k<<=1){
            Poly g=res,h=*this; h.resize(k*2); res.resize(k*2);
            g=(g.square()*h); g.resize(k*2);
            rep(i,k,min(k*2,n))res[i]-=g[i];
        }
        res.resize(n); return res;
    }
    Poly square()const{return Poly(mult(*this,*this,1));}
    Poly operator+(const Poly& g)const{return Poly(*this)+=g;}
    Poly operator+(const T& g)const{return Poly(*this)+=g;}
    Poly operator-(const Poly& g)const{return Poly(*this)-=g;}
    Poly operator-(const T& g)const{return Poly(*this)-=g;}
    Poly operator*(const Poly& g)const{return Poly(*this)*=g;}
    Poly operator*(const T& g)const{return Poly(*this)*=g;}
    Poly operator/(const Poly& g)const{return Poly(*this)/=g;}
    Poly operator%(const Poly& g)const{return Poly(*this)%=g;}
    Poly& operator+=(const Poly& g){
        if(g.size()>this->size())this->resize(g.size());
        rep(i,0,g.size()){(*this)[i]+=g[i];} return *this;
    }
    Poly& operator+=(const T& g){
        if(this->empty())this->push_back(0);
        (*this)[0]+=g; return *this;
    }
    Poly& operator-=(const Poly& g){
        if(g.size()>this->size())this->resize(g.size());
        rep(i,0,g.size()){(*this)[i]-=g[i];} return *this;
    }
    Poly& operator-=(const T& g){
        if(this->empty())this->push_back(0);
        (*this)[0]-=g; return *this;
    }
    Poly& operator*=(const Poly& g){
        *this=mult(*this,g,0);
        return *this;
    }
    Poly& operator*=(const T& g){
        rep(i,0,this->size())(*this)[i]*=g;
        return *this;
    }
    Poly& operator/=(const Poly& g){
        if(g.size()>this->size()){
            this->clear(); return *this;
        }
        Poly g2=g;
        reverse(ALL(*this));
        reverse(ALL(g2));
        int n=this->size()-g2.size()+1;
        this->resize(n); g2.resize(n);
        *this*=g2.inv(); this->resize(n); 
        reverse(ALL(*this));
        shrink();
        return *this;
    }
    Poly& operator%=(const Poly& g){*this-=*this/g*g; shrink(); return *this;}
    Poly diff()const{
        Poly res(this->size()-1);
        rep(i,0,res.size())res[i]=(*this)[i+1]*(i+1);
        return res;
    }
    Poly inte()const{
        Poly res(this->size()+1);
        for(int i=res.size()-1;i;i--)res[i]=(*this)[i-1]/i;
        return res;
    }
    Poly log()const{
        assert(this->front()==1); const int n=this->size();
        Poly res=diff()*inv(); res=res.inte(); 
        res.resize(n); return res;
    }
    Poly exp()const{
        assert(this->front()==0); const int n=this->size();
        Poly res(1),g(1); res.front()=g.front()=1;
        for(int k=1;k<n;k<<=1){
            g=(g+g-g.square()*res); g.resize(k);
            Poly q=*this; q.resize(k); q=q.diff();
            Poly w=(q+g*(res.diff()-res*q)),t=*this;
            w.resize(k*2-1); t.resize(k*2);
            res=(res+res*(t-w.inte())); res.resize(k*2);
        } res.resize(n); return res;
    }
    Poly shift(const int& c)const{
        const int n=this->size();
        Poly res=*this,g(n); g[0]=1; rep(i,1,n)g[i]=g[i-1]*c/i;
        vector<T> fact(n,1);
        rep(i,0,n){
            if(i)fact[i]=fact[i-1]*i;
            res[i]*=fact[i];
        }
        res=res.rev();
        res*=g;
        res.resize(n);
        res=res.rev();
        rep(i,0,n)res[i]/=fact[i];
        return res;
    }
    Poly pow(ll t){
        int n=this->size(),k=0; while(k<n and (*this)[k]==0)k++;
        Poly res(n); if(t*k>=n)return res;
        n-=t*k; Poly g(n); T c=(*this)[k],ic=T(1)/c;
        rep(i,0,n)g[i]=(*this)[i+k]*ic;
        g=g.log(); for(auto& x:g)x*=t; g=g.exp(); 
        c=c.pow(t); rep(i,0,n)res[i+t*k]=g[i]*c; return res;
    }
    vector<T> mult(const vector<T>& a,const vector<T>& b,bool same)const;
};

/**
 * @brief Formal Power Series (Arbitrary mod)
 */
#line 7 "sol.cpp"
using Fp=fp<1000000009>;
template<>vector<Fp> Poly<Fp>::mult(const vector<Fp>& a,const vector<Fp>& b,bool same)const{
    return ArbitraryMult(a,b,same);
}

constexpr int I=430477711;
factorial<Fp> fact(402020);

FastIO io;
int main(){
    int n;
    io.read(n);
    Poly<Fp> f(n+1);
    rep(i,1,n+1)f[i]=Fp(i+1)*(i+1)*I;
    auto s=f.exp(),t=s.inv();
    Fp c1=Fp(I*2).inv(),c2=Fp(2).inv();
    rep(i,1,n+1){
        Fp ret=(s[i]-t[i])*c1+(s[i]+t[i])*c2;
        ret*=fact.fact(n);
        io.write(ret.v);
    }
    return 0;
}
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結果

テストケース

ソースコード
