結果

問題 No.344 ある無理数の累乗
ユーザー ytqm3
提出日時 2023-07-18 00:24:33
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 46 ms / 2,000 ms
コード長 6,883 bytes
コンパイル時間 4,704 ms
コンパイル使用メモリ 264,476 KB
最終ジャッジ日時 2025-02-15 15:29:53
ジャッジサーバーID
（参考情報） 		judge1 / judge4
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ファイルパターン 結果
other AC * 30
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ソースコード

diff #
プレゼンテーションモードにする

#include <bits/stdc++.h>
#if __has_include(<atcoder/all>)
#include <atcoder/all>
#endif
namespace ttl{
using namespace std;
using f80=long double;
using i64=int64_t;
using u64=uint64_t;
template<int mod> struct mymodint{
  i64 vl;
  static constexpr i64 get_mod(){ return mod; }
  i64 val(){ return vl; }
  mymodint(i64 vl_=0):vl((vl_%mod+mod)%mod){}
  mymodint operator-(){ return (vl==0)?0:mod-vl; }
  mymodint operator+(mymodint rhs){ return mymodint(*this)+=rhs; }
  mymodint operator-(mymodint rhs){ return mymodint(*this)-=rhs; }
  mymodint operator*(mymodint rhs){ return mymodint(*this)*=rhs; }
  mymodint operator/(mymodint rhs){ return mymodint(*this)/=rhs; }
  mymodint pow(i64 rhs){
    mymodint res=1,now=(*this);
    while(rhs){
      res*=((rhs&1)?now:1),now*=now,rhs>>=1;
    }
    return res;
  }
  mymodint& operator+=(mymodint rhs){
    vl+=rhs.vl,vl-=((vl>=mod)?mod:0);
    return (*this);
  }
  mymodint& operator-=(mymodint rhs){
    vl+=((vl<rhs.vl)?mod:0),vl-=rhs.vl;
    return (*this);
  }
  mymodint& operator*=(mymodint rhs){
    vl=vl*rhs.vl%mod;
    return (*this);
  }
  mymodint& operator/=(mymodint rhs){ return (*this)*=rhs.pow(mod-2); }
  bool operator==(mymodint rhs){ return vl==rhs.vl; }
  bool operator!=(mymodint rhs){ return vl!=rhs.vl; }
};
template<u64 mod> using modint=mymodint<mod>;
template<int mod> std::ostream& operator<<(std::ostream& os,modint<mod> x){
  return os<<(x.val());
}
template<int mod> std::istream& operator>>(std::istream& is,modint<mod>& x){
  i64 t;
  is>>t,x=t;
  return is;
}
template<class T> void scn_(T& a){ cin>>a; }
template<class T,class U> void scn_(pair<T,U>& a){ scn_(a.first),scn_(a.second); }
template<class T> void scn_(vector<T>& a){
  for(auto& v:a){
    scn_(v);
  }
}
template<class T> void scn_(vector<vector<T>>& a){
  for(auto& v:a){
    for(auto& u:v){
      scn_(u);
    }
  }
}
void scn(){}
template<class T,class... Args> void scn(T& n,Args&... args){ scn_(n),scn(args...); }
template<class T> void prt_(T a){ cout<<a; }
template<class T,class U> void prt_(pair<T,U> a){ cout<<"{"<<a.first<<", "<<a.second<<"}"; }
void prt_(f80 a){ printf("%.15Lf",a); }
template<class T> void prt(vector<T> a){
  for(size_t i=0;i<a.size();++i){
    prt_(a[i]);
    cout<<" \n"[i==a.size()-1];
  }
}
template<class T> void prt(vector<vector<T>> a){
  for(auto& v:a){
    for(size_t i=0;i<v.size();++i){
      prt_(v[i]);
      cout<<" \n"[i==v.size()-1];
    }
  }
}
template<class T> void prt(T a){ prt_(a),cout<<"\n"; }
template<class T,class... Args> void prt(T a,Args... args){ prt_(a),cout<<" ",prt(args...); }
template<class Head,class... Tail> struct multi_dim_vector{ using type=vector<typename multi_dim_vector<Tail...>::type>; };
template<class T> struct multi_dim_vector<T>{ using type=T; };
template<class T,class Arg> vector<T> mvec(int n,Arg&& arg){ return vector<T>(n,arg); }
template<class T,class... Args> class multi_dim_vector<Args...,T>::type mvec(int n,Args&&... args){
  return typename multi_dim_vector<Args...,T>::type(n,mvec<T>(args...));
}
template<class T> void rev(T& a){ reverse(a.begin(),a.end());}
template<class T> void srt(T& a){ sort(a.begin(),a.end()); }
template<class T> void rsrt(T& a){ sort(a.rbegin(),a.rend()); }
template<class T> T revd(T a){
  reverse(a.begin(),a.end());
  return a;
}
template<class T> T srtd(T a){
  sort(a.begin(),a.end());
  return a;
}
template<class T> T rsrtd(T a){
  sort(a.rbegin(),a.rend());
  return a;
}
template<class T> void chmx(T& a,T b){ a=max(a,b); }
template<class T> void chmn(T& a,T b){ a=min(a,b); }
i64 pw(i64 a,i64 n){
  i64 res=1;
  while(n){
    if(n&1){ res*=a; }
    a*=a;
    n/=2;
  }
  return res;
}
template<class T> void zip(vector<T>& a){
  auto b=srtd(a);
  b.erase(unique(b.begin(),b.end()),b.end());
  map<T,int> mp;
  for(int i=0;i<b.size();++i){
    mp[b[i]]=i;
  }
  for(auto& v:a){
    v=mp[v];
  }
}
template<class T> auto runlng(T a) -> vector<pair<typename decltype(a)::value_type,i64>>{
  int n=a.size();
  vector<pair<typename decltype(a)::value_type,i64>> res;
  if(n==0){ return res; }
  typename decltype(a)::value_type now=a[0];
  i64 l=1;
  for(int i=1;i<n;++i){
    if(a[i-1]==a[i]){ l++; }
    else{
      res.emplace_back(now,l);
      now=a[i],l=1;
    }
  }
  res.emplace_back(now,l);
  return res;
}
template<class T> struct cmb{
  vector<T> fac,ifac;
  cmb(int mx=3000000):fac(mx+1,1),ifac(mx+1,1){
    for(int i=1;i<=mx;++i){ fac[i]=fac[i-1]*i; }
    ifac[mx]/=fac[mx];
    for(int i=mx;i>0;--i){ ifac[i-1]=ifac[i]*i; }
  }
  T operator()(i64 n,i64 k){
    if(n<0||k<0||n<k){ return 0; }
    return fac[n]*ifac[k]*ifac[n-k];
  }
  T f(i64 n){
    return n<0?T(0):fac[n];
  }
  T fi(i64 n){
    return n<0?T(0):ifac[n];
  }
};
}
using namespace ttl;
template<class T> T Identity(int n){
  T res(n,n);
  for(int i=0;i<n;++i){
    res[i][i]=1;
  }
  return res;
}
template<class T> struct Matrix{
  vector<vector<T>> val;
  int height,width;
  Matrix(int H,int W,T init=0):val(H,vector<T> (W,init)),height(H),width(W){}
  Matrix(vector<vector<T>> val_):val(val_),height(val_.size()),width(val_[0].size()){}
  vector<T> &operator[](int i){
    return val[i];
  }
  Matrix operator+(Matrix rhs){
    return Matrix(*this)+=rhs;
  }
  Matrix operator*(Matrix rhs){
    return Matrix(*this)*=rhs;
  }
  Matrix operator+=(Matrix rhs){
    for(int i=0;i<rhs.height;++i){
      for(int j=0;j<rhs.width;++j){
        (*this)[i][j]+=rhs[i][j];
      }
    }
    return (*this);
  }
  Matrix operator*=(Matrix rhs){
    Matrix<T> res(height,rhs.width,0);
    for(int i=0;i<this->height;++i){
      for(int j=0;j<rhs.width;++j){
        for(int k=0;k<this->width;++k){
          res[i][j]+=(*this)[i][k]*rhs[k][j];
        }
      }
    }
    return (*this)=res;
  }
  Matrix pow(i64 k){
    int n=(*this).height;
    Matrix res=Identity<Matrix<T>>(n),now=(*this);
    while(k>0){
      if(k%2==1){
        res*=now;
      }
      now*=now;
      k/=2;
    }
    return res;
  }
  T det(){
    int N=height;
    int rnk=0;
    T cff=1;
    for(int j=0;j<N;++j){
      if(rnk==N){
        break;
      }
      for(int i=rnk;i<N;++i){
        if(val[i][j]!=0){
          T C=val[i][j];
          cff*=C;
          for(auto& v:val[i]){
            v/=C;
          }
          swap(val[rnk],val[i]);
          if(i!=rnk){ cff*=-1; }
          break;
        }
      }
      if(val[rnk][j]==0){
        return T(0);
      }
      for(int i=0;i<N;++i){
        if(i!=rnk && val[i][j]!=0){
          T C=val[i][j]/val[rnk][j];
          for(int k=0;k<N;++k){
            val[i][k]-=val[rnk][k]*C;
          }
        }
      }
      rnk++;
    }
    return cff;
  }
};
int main(){
  constexpr int mod=1000;
  using mint=mymodint<mod>;
  cmb<mint> Cb;
  int N;
  scn(N);
  if(N==0){ prt(1); return 0; }
  Matrix<mint> M=vector<vector<mint>>{{1,1},{3,1}};
  M=M.pow(N);
  prt(M[0][0]*2+(N%2?0:-1));
}
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