#553321 (C++17) No.754 畳み込みの和

• 問題: No.754 畳み込みの和
• ユーザー: ate
• 提出日時: 2020-09-15 14:23:59
• 言語: C++17 (gcc 13.3.0 + boost 1.87.0)
• 結果: AC
• 実行時間: 314 ms / 5,000 ms
• コード長: 7,040 bytes
• コンパイル時間: 1,275 ms
• コンパイル使用メモリ: 94,796 KB
• 最終ジャッジ日時: 2025-01-14 15:01:40
• ジャッジサーバーID （参考情報）: judge3 / judge1

ファイルパターン	結果
other	AC * 3

ソースコード

#include<iostream>
#include<vector>
#include<cassert>
#include<tuple>

namespace ate{
  template<int64_t p>
  struct F_p{
    using value_type = int64_t;
    static constexpr inline value_type get_mod(){return p;}

    value_type value;

    constexpr F_p():value(value_type{}){}
    template<class T>constexpr F_p(T v):value(static_cast<value_type>(v<0?v%p+p:v%p)){}
    template<class T>constexpr operator T()const{return (T)value;}
  // operator +, -, *, /, ^ 
    constexpr F_p operator + (const F_p& other)const{
      return F_p(*this) += other;
    }
    constexpr F_p operator - (const F_p& other)const{
      return F_p(*this) -= other;
    }
    constexpr F_p operator * (const F_p& other)const{
      return F_p(*this) *= other;
    }
    constexpr F_p operator / (const F_p& other)const{
      return F_p(*this) /= other;
    }
    template<class T> constexpr F_p operator ^ (const T other)const{
      return F_p(*this) ^= other;
    }
    constexpr F_p &operator += (const F_p& other){
      value+=other.value;
      if(value>p)value-=p;
      return *this;
    }
    constexpr F_p &operator -= (const F_p& other){
      value-=other.value;
      if(value<0)value+=p;
      return *this;
    }
    constexpr F_p &operator *= (const F_p& other){
      value*=other.value;
      if(value>p)value%=p;
      return *this;
    }
    constexpr F_p &operator /= (const F_p& other){
      value*=other.inverse();
      if(value>p)value%=p;
      return *this;
    }
    template<class T>
    constexpr F_p &operator ^= (const T n){
      value = mpow(n).value;
      return *this;
    }
  // ext_gcd,inverse,mpow 
    static constexpr value_type ext_gcd(value_type a,value_type b,value_type& x,value_type& y){
      if(b==0){x=1,y=0;return a;}
      value_type d=ext_gcd(b,a%b,y,x);
      y-=a/b*x;return d;
    }
    constexpr value_type inverse()const{
      value_type x,y;
      ext_gcd(value,p,x,y);
      return x<0?x%p+p:x%p;
    }
    template<class T>
    static constexpr value_type inverse(T val){
      value_type x,y;
      ext_gcd(val,p,x,y);
      return x<0?x%p+p:x%p;
    }
    template<class T>
    constexpr F_p mpow(T n)const{
      F_p res(1),vn(*this);
      while(n){
        if(n&1)res*=vn;
        vn*=vn;
        n>>=1;
      }
      return res;
    }
    template<class T,class U>
    static constexpr T mpow(T a,U b){
      F_p x(a);
      return static_cast<T>(x.mpow(b).value);
    }
  // operator iostream 
    constexpr friend std::istream &operator >> (std::istream& is,F_p& fp){
      is>>fp.value;
      return is;
    }constexpr friend std::ostream &operator << (std::ostream& os,const F_p& fp){
      os<<fp.value;
      return os;
    }
  };
  template<int64_t MOD,int primitive_root>
  struct number_theoretic_transform{

    using value_type = F_p<MOD>;
    using vector_t = std::vector<value_type>;
    template<class T>
    static constexpr value_type pow(value_type v,T t){return v^t;}
    static constexpr int64_t get_mod(){return MOD;}

    number_theoretic_transform() = default;

    static void ntt(vector_t& a,bool inv=false){
      const int n = std::size(a);
      for(int i=0,j=1;j+1<n;++j){
        for(int k=n>>1;k>(i^=k);k>>=1);
        if(i<j)std::swap(a[i],a[j]);
      }
      for(int t=2;t<=n;t<<=1){
        value_type bw = pow(primitive_root,(MOD-1)/t);
        if(inv)bw = bw.inverse();
        for(int i=0;i<n;i+=t){
          value_type w = 1;
          for(int j=0;j<t/2;++j){
            const value_type x = a[i+j];
            const value_type y = a[i+j+t/2]*w;
            a[i+j] = x+y;
            a[i+j+t/2] = x-y;
            w *= bw;
          }
        }
      }
      if(inv)for(auto& ai:a)ai/=n;
    }
    template<class T>
    static vector_t convolution(std::vector<T> const& a,std::vector<T> const& b){
      const int sz_a = std::size(a);
      const int sz_b = std::size(b);
      const int m = sz_a+sz_b-1;
      int n = 1;
      while(n<m)n<<=1;
      vector_t ntt_a(n),ntt_b(n),ntt_c(n);
      for(int i=0;i<sz_a;++i)ntt_a[i]=static_cast<value_type>(a[i]);
      for(int i=0;i<sz_b;++i)ntt_b[i]=static_cast<value_type>(b[i]);
      ntt(ntt_a);
      ntt(ntt_b);
      for(int i=0;i<n;++i)ntt_c[i]=ntt_a[i]*ntt_b[i];
      bool inverse = true;
      ntt(ntt_c,inverse);
      ntt_c.resize(m);
      return ntt_c;
    }
  };
  struct NTT{
    using NTT_1 = number_theoretic_transform<998244353,3>;
    using NTT_2 = number_theoretic_transform<754974721,11>;
    using NTT_3 = number_theoretic_transform<469762049,3>;
    using NTT_4 = number_theoretic_transform<167772161,3>;
    using NTT_5 = number_theoretic_transform<1224736769,3>;
    using NTT_6 = number_theoretic_transform<1012924417,5>;
    NTT(){}
    static std::tuple<int64_t,int64_t,int64_t> ext_gcd(int64_t a,int64_t b){
      if(b==0)return {a,1,0};auto[d,y,x]=ext_gcd(b,a%b);return {d,x,y-(a/b*x)};
    }
    static constexpr inline int64_t safe_mod(int64_t a,int64_t m){a%=m;return(a<0?a+m:a);}
    static int64_t mod_inv(int64_t a,int64_t m){
      auto[d,x,y]=ext_gcd(a,m);return(d!=1?-1:safe_mod(x,m));
    }
    static int64_t gerner (std::vector<int64_t> b,std::vector<int64_t> m,const int64_t MOD){
      const int n = std::size(b);
      m.emplace_back(MOD);
      std::vector<int64_t> coeffs(std::size(m),1);
      std::vector<int64_t> constants(std::size(m),0);
      for(int k=0;k<n;++k){
        const int64_t m_inv = mod_inv(coeffs[k],m[k]);
        const int64_t t = safe_mod((b[k]-constants[k])*m_inv,m[k]);
        for(int i=k+1;i<std::size(m);++i){
          (constants[i] += t*coeffs[i]) %= m[i];
          (coeffs[i] *= m[k]) %= m[i];
        }
      }
      return constants.back();
    }
    template<class T>
    static std::vector<int64_t> convolution(std::vector<T>const& a,std::vector<T>const& b,const int64_t MOD){
      const auto ntt1 = NTT_1::convolution(a,b);
      const auto ntt2 = NTT_2::convolution(a,b);
      const auto ntt3 = NTT_3::convolution(a,b);
      const int n = std::size(a)+std::size(b)-1;
      const int m = 3;
      const std::vector<int64_t> mods = {NTT_1::get_mod(),NTT_2::get_mod(),NTT_3::get_mod()};
      std::vector<int64_t> conv(n);
      for(int i=0;i<n;++i){
        const std::vector<int64_t> b = {ntt1[i],ntt2[i],ntt3[i]};
        conv[i] = gerner(b,mods,MOD);
      }
      return conv;
    }
  };
} //namespace ate

int main(){
  using namespace std;
  std::cin.tie(nullptr);
  std::ios_base::sync_with_stdio(false);
  constexpr char newl = '\n';

  int n;
  cin>>n;
  vector<int64_t> a(n+1),b(n+1);
  for(auto& ai:a)cin>>ai;
  for(auto& bi:b)cin>>bi;
  auto c = ate::NTT::convolution(a,b,1e9+7);
  ate::F_p<(int)1e9+7> ans = 0;
  for(int i=0;i<=n and i<size(c);++i)ans+=c[i];
  cout<<(ans)<<endl;
}

void solve_fft(){
  using namespace std;
  std::cin.tie(nullptr);
  std::ios_base::sync_with_stdio(false);
  constexpr char newl = '\n';

  int n;
  cin>>n;
  vector<int64_t> a(n),b(n);
  for(int i=0;i<n;++i)cin>>a[i]>>b[i];
  auto c = ate::NTT::NTT_1::convolution(a,b);
  cout<<0<<newl;
  for(auto ci:c)cout<<ci<<newl;
}