結果

問題 No.1073 無限すごろく
ユーザー HaarHaar
提出日時 2020-06-05 21:45:16
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 4 ms / 2,000 ms
コード長 6,792 bytes
コンパイル時間 3,645 ms
コンパイル使用メモリ 196,316 KB
最終ジャッジ日時 2025-01-10 22:25:28
ジャッジサーバーID
（参考情報） 		judge4 / judge2
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ファイルパターン 結果
sample AC * 3
other AC * 30
権限があれば一括ダウンロードができます

ソースコード

diff # 

#include <bits/stdc++.h>


/**
 * @title modint
 * @docs mint.md
 */
template <uint32_t M> class ModInt{
public:
  constexpr static uint32_t MOD = M;
  uint64_t val;
  
  constexpr ModInt(): val(0){}
  constexpr ModInt(int64_t n){
    if(n >= M) val = n % M;
    else if(n < 0) val = n % M + M;
    else val = n;
  }
  
  inline constexpr auto operator+(const ModInt &a) const {return ModInt(val + a.val);}
  inline constexpr auto operator-(const ModInt &a) const {return ModInt(val - a.val);}
  inline constexpr auto operator*(const ModInt &a) const {return ModInt(val * a.val);}
  inline constexpr auto operator/(const ModInt &a) const {return ModInt(val * a.inv().val);}
  
  inline constexpr auto& operator=(const ModInt &a){val = a.val; return *this;}
  inline constexpr auto& operator+=(const ModInt &a){if((val += a.val) >= M) val -= M; return *this;}
  inline constexpr auto& operator-=(const ModInt &a){if(val < a.val) val += M; val -= a.val; return *this;}
  inline constexpr auto& operator*=(const ModInt &a){(val *= a.val) %= M; return *this;}
  inline constexpr auto& operator/=(const ModInt &a){(val *= a.inv().val) %= M; return *this;}
  
  inline constexpr bool operator==(const ModInt &a) const {return val == a.val;}
  inline constexpr bool operator!=(const ModInt &a) const {return val != a.val;}
  
  inline constexpr auto& operator++(){*this += 1; return *this;}
  inline constexpr auto& operator--(){*this -= 1; return *this;}
  
  inline constexpr auto operator++(int){auto t = *this; *this += 1; return t;}
  inline constexpr auto operator--(int){auto t = *this; *this -= 1; return t;}
  
  inline constexpr static ModInt power(int64_t n, int64_t p){
    if(p < 0) return power(n, -p).inv();
    
    int64_t ret = 1, e = n % M;
    for(; p; (e *= e) %= M, p >>= 1) if(p & 1) (ret *= e) %= M;
    return ret;
  }
  
  inline constexpr static ModInt inv(int64_t a){
    int64_t b = M, u = 1, v = 0;
    
    while(b){
      int64_t t = a / b;
      a -= t * b; std::swap(a,b);
      u -= t * v; std::swap(u,v);
    }
    
    u %= M;
    if(u < 0) u += M;
    
    return u;
  }
  
  inline constexpr static auto frac(int64_t a, int64_t b){return ModInt(a) / ModInt(b);}
  
  inline constexpr auto power(int64_t p) const {return power(val, p);}
  inline constexpr auto inv() const {return inv(val);}
  
  friend inline constexpr auto operator-(const ModInt &a){return ModInt(-a.val);}
  
  friend inline constexpr auto operator+(int64_t a, const ModInt &b){return ModInt(a) + b;}
  friend inline constexpr auto operator-(int64_t a, const ModInt &b){return ModInt(a) - b;}
  friend inline constexpr auto operator*(int64_t a, const ModInt &b){return ModInt(a) * b;}
  friend inline constexpr auto operator/(int64_t a, const ModInt &b){return ModInt(a) / b;}
  
  friend std::istream& operator>>(std::istream &s, ModInt<M> &a){s >> a.val; return s;}
  friend std::ostream& operator<<(std::ostream &s, const ModInt<M> &a){s << a.val; return s;}

  template <int N>
  inline static auto div(){
    static auto value = inv(N);
    return value;
  }

  explicit operator int32_t() const noexcept {return val;}
  explicit operator int64_t() const noexcept {return val;}
};

/**
 * @title 正方行列 (コンパイル時固定サイズ)
 * @docs square_matrix_const_size.md
 */
template <typename T, int N> struct SquareMatrixConst{
  using value_type = T;
  
  std::array<std::array<T,N>,N> matrix;

  SquareMatrixConst(){
    for(size_t i = 0; i < N; ++i) for(size_t j = 0; j < N; ++j) matrix[i][j] = 0;
  }
  SquareMatrixConst(const T &val){
    for(size_t i = 0; i < N; ++i) matrix[i].fill(val);
  }
  SquareMatrixConst(std::initializer_list<std::initializer_list<T>> list){
    int i = 0;
    for(auto it1 = list.begin(); it1 != list.end(); ++it1, ++i){
      int j = 0;
      for(auto it2 = it1->begin(); it2 != it1->end(); ++it2, ++j){
        matrix[i][j] = *it2;
      }
    }
  }

  bool operator==(const SquareMatrixConst &val) const {return matrix == val.matrix;}
  bool operator!=(const SquareMatrixConst &val) const {return !(*this == val);}

  auto& operator=(const SquareMatrixConst &val){
    this->matrix = val.matrix;
    return *this;
  }

  auto& operator+=(const SquareMatrixConst &val){
    for(int i = 0; i < N; ++i) for(int j = 0; j < N; ++j) matrix[i][j] = matrix[i][j] + val[i][j];
    return *this;
  }

  auto& operator-=(const SquareMatrixConst &val){
    for(int i = 0; i < N; ++i) for(int j = 0; j < N; ++j) matrix[i][j] = matrix[i][j] - val[i][j];
    return *this;
  }

  auto& operator*=(const SquareMatrixConst &val){
    std::array<std::array<T,N>,N> temp = {};
    for(int i = 0; i < N; ++i) for(int j = 0; j < N; ++j) for(int k = 0; k < N; ++k) temp[i][j] = temp[i][j] + matrix[i][k] * val[k][j];
    std::swap(matrix, temp);
    return *this;
  }

  inline const auto& operator[](size_t i) const {return matrix[i];}
  inline auto& operator[](size_t i){return matrix[i];}
  inline int size() const {return N;}
  
  static auto make_unit(){
    SquareMatrixConst ret;
    for(size_t i = 0; i < N; ++i) ret[i][i] = 1;
    return ret;
  }

  friend auto operator+(const SquareMatrixConst &a, const SquareMatrixConst &b){auto ret = a; ret += b; return ret;}
  friend auto operator-(const SquareMatrixConst &a, const SquareMatrixConst &b){auto ret = a; ret -= b; return ret;}
  friend auto operator*(const SquareMatrixConst &a, const SquareMatrixConst &b){auto ret = a; ret *= b; return ret;}
};

/**
 * @title 行列累乗
 * @docs power.md
 */
template <typename M, typename T = typename M::value_type>
M power(M a, uint64_t p){
  if(p == 0) return M::make_unit();
  if(p == 1) return a;

  M temp = power(a, p >> 1);
  auto ret = temp * temp;

  if(p & 1) ret *= a;  
  
  return ret;
}

/**
 * @docs show_matrix.md
 */
template <typename M, typename T = typename M::value_type>
void show_matrix(const M &m, int w = 10){
#ifdef DEBUG
  const int N = m.size();
  
  std::cerr << "⎛" << std::string((w+1)*N, ' ') << "⎞" << std::endl;
  for(int i = 0; i < N; ++i){
    std::cerr << "⎜";
    for(int j = 0; j < N; ++j) std::cerr << std::setw(w) << m[i][j] << " ";
    std::cerr << "⎟";
    std::cerr << std::endl;
  }
  std::cerr << "⎝" << std::string((w+1)*N, ' ') << "⎠" << std::endl;
#endif
}



using mint = ModInt<1000000007>;
using Mat = SquareMatrixConst<mint, 6>;

int main(){
  int64_t N;

  while(std::cin >> N){
    
    
    Mat m =
      {
       {mint::frac(1, 6), mint::frac(1, 6), mint::frac(1, 6), mint::frac(1, 6), mint::frac(1, 6), mint::frac(1, 6)},
       {1, 0, 0, 0, 0, 0},
       {0, 1, 0, 0, 0, 0},
       {0, 0, 1, 0, 0, 0},
       {0, 0, 0, 1, 0, 0},
       {0, 0, 0, 0, 1, 0}
      };

    m = power(m, N);
    
    //show_matrix(m);

    std::cout << m[0][0] << "\n";
    
    

    
  }

  return 0;
}
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