結果

問題 No.1105 Many Triplets
コンテスト
ユーザー KoD
提出日時 2020-07-03 22:09:25
言語 C++17(gcc12)
(gcc 12.3.0 + boost 1.87.0)
結果
AC  
実行時間 3 ms / 2,000 ms
コード長 7,214 bytes
コンパイル時間 3,350 ms
コンパイル使用メモリ 119,676 KB
最終ジャッジ日時 2025-01-11 14:42:37
ジャッジサーバーID
（参考情報） 		judge4 / judge4
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ファイルパターン 結果
sample AC * 3
other AC * 25
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ソースコード

diff # 

#include <iostream>
#include <algorithm>
#include <utility>
#include <numeric>
#include <vector>
#include <array>

template <class T, class U>
inline bool chmin(T &lhs, const U &rhs) {
  if (lhs > rhs) { lhs = rhs; return true; }
  return false;
}

template <class T, class U>
inline bool chmax(T &lhs, const U &rhs) {
  if (lhs < rhs) { lhs = rhs; return true; }
  return false;
}

struct range {
  using itr = int64_t;
  struct iterator {
    itr i;
    constexpr iterator(itr i_) noexcept : i(i_) { }
    constexpr void operator ++ () noexcept { ++i; }
    constexpr itr operator * () const noexcept { return i; }
    constexpr bool operator != (iterator x) const noexcept { return i != x.i; }
  };
  const iterator l, r;
  constexpr range(itr l_, itr r_) noexcept : l(l_), r(std::max(l_, r_)) { }
  constexpr iterator begin() const noexcept { return l; }
  constexpr iterator end() const noexcept { return r; }
};

struct revrange {
  using itr = int64_t;
  struct iterator {
    itr i;
    constexpr iterator(itr i_) noexcept : i(i_) { }
    constexpr void operator ++ () noexcept { --i; }
    constexpr itr operator * () const noexcept { return i; }
    constexpr bool operator != (iterator x) const noexcept { return i != x.i; }
  };
  const iterator l, r;
  constexpr revrange(itr l_, itr r_) noexcept : l(l_ - 1), r(std::max(l_, r_) - 1) { }
  constexpr iterator begin() const noexcept { return r; }
  constexpr iterator end() const noexcept { return l; }
};

using i32 = int32_t;
using i64 = int64_t;
using u32 = uint32_t;
using u64 = uint64_t;

constexpr i32 inf32 = (i32(1) << 30) - 1;
constexpr i64 inf64 = (i64(1) << 62) - 1;

template <class T>
class matrix: public std::vector<std::vector<typename T::value_type>> {
public:
  using value_type = typename T::value_type;
  using addition = typename T::addition;
  using multiplication = typename T::multiplication;
 
private:
  addition add;
  multiplication mult;
 
public:
  int height, width;
 
  matrix(): add(addition()), mult(multiplication()) { }
  matrix(int height_, int width_, const value_type &initial_ = addition().identity):
    add(addition()), mult(multiplication()),
    height(height_), width(width_),
    std::vector<std::vector<value_type>>(height_, std::vector<value_type>(width_, initial_))
  { }
  matrix(const std::vector<std::vector<value_type>> &data_):
    add(addition()), mult(multiplication()),
    height(data_.size()), width(data_.front().size()),
    std::vector<std::vector<value_type>>(data_)
  { }
 
  matrix operator + (const matrix &rhs) const { return matrix(*this) += rhs; }
  matrix& operator += (const matrix &rhs) { 
    for (int i = 0; i < height; ++i) {
      for (int j = 0; j < width; ++j) {
        (*this)[i][j] = add((*this)[i][j], rhs[i][j]);
      }
    }
    return *this;
  }
 
  matrix& operator *= (const matrix &rhs) { *this = (*this) * rhs; return *this; }
  matrix operator * (const matrix &rhs) const {
    matrix res(height, rhs.width);
    for (int i = 0; i < height; ++i) {
      for (int j = 0; j < rhs.width; ++j) {
        for (int k = 0; k < width; ++k) {
          res[i][j] = add(res[i][j], mult((*this)[i][k], rhs[k][j]));
        }
      }
    }
    return res;
  }
 
  matrix operator * (const value_type &rhs) const { return matrix(*this) *= rhs; }
  matrix& operator *= (const value_type &rhs)  { 
    for (int i = 0; i < height; ++i) {
      for (int j = 0; j < width; ++j) {
        (*this)[i][j] = mult((*this)[i][j], rhs);
      }
    }
    return *this;
  }
 
  matrix power(unsigned long long pow) const {
    matrix res(height, width), use(*this);
    for (int i = 0; i < height; ++i) {
      res[i][i] = mult.identity;
    }
    while (pow > 0) {
      if (pow & 1) {
        res *= use;
      }
      use *= use;
      pow >>= 1;
    }
    return res;
  }
 
};
 
template <class T>
struct number {
  using value_type = T;
  struct addition {
    value_type identity = value_type(0);
    value_type operator () (const value_type &x, const value_type &y) const {
      return x + y;
    }
  };
  struct multiplication {
    value_type identity = value_type(1);
    value_type operator () (const value_type &x, const value_type &y) const {
      return x * y;
    }
  };
};

template <uint32_t Modulus>
class modular {
public:
  using value_type = uint32_t;
  using max_type = uint64_t;

  static constexpr value_type mod = Modulus;
  static constexpr value_type get_mod() { return mod; }
  static_assert(mod >= 2, "invalid mod :: smaller than 2");
  static_assert(mod < (value_type(1) << 31), "invalid mod :: over 2^31");

  template <class T>
  static constexpr value_type normalize(T value_) {
    if (value_ < 0) {
      value_ = -value_;
      value_ %= mod;
      if (value_ == 0) return 0;
      return mod - value_;
    }
    return value_ % mod;
  }

private:
  value_type value;

public:
  constexpr modular(): value(0) { }
  template <class T>
  explicit constexpr modular(T value_): value(normalize(value_)) { }
  template <class T>
  explicit constexpr operator T() { return static_cast<T>(value); }

  constexpr value_type get() const { return value; }
  constexpr modular operator - () const { return modular(mod - value); }
  constexpr modular operator ~ () const { return inverse(); }

  constexpr value_type &extract() { return value; }
  constexpr modular inverse() const { return power(mod - 2); }
  constexpr modular power(max_type exp) const {
    modular res(1), mult(*this);
    while (exp > 0) {
      if (exp & 1) res *= mult;
      mult *= mult;
      exp >>= 1;
    }
    return res;
  }

  constexpr modular operator + (const modular &rhs) const { return modular(*this) += rhs; }
  constexpr modular& operator += (const modular &rhs) { 
    if ((value += rhs.value) >= mod) value -= mod; 
    return *this; 
  }

  constexpr modular operator - (const modular &rhs) const { return modular(*this) -= rhs; }
  constexpr modular& operator -= (const modular &rhs) { 
    if ((value += mod - rhs.value) >= mod) value -= mod; 
    return *this; 
  }

  constexpr modular operator * (const modular &rhs) const { return modular(*this) *= rhs; }
  constexpr modular& operator *= (const modular &rhs) { 
    value = (max_type) value * rhs.value % mod;
    return *this;
  }

  constexpr modular operator / (const modular &rhs) const { return modular(*this) /= rhs; }
  constexpr modular& operator /= (const modular &rhs) { return (*this) *= rhs.inverse(); }

  constexpr bool zero() const { return value == 0; }
  constexpr bool operator == (const modular &rhs) const { return value == rhs.value; }
  constexpr bool operator != (const modular &rhs) const { return value != rhs.value; }
  friend std::ostream& operator << (std::ostream &stream, const modular &rhs) {
    return stream << rhs.value;
  }

};

using m32 = modular<1000000007>;

int main() {
  i64 N;
  std::cin >> N;
  i32 a, b, c;
  std::cin >> a >> b >> c;
  using mat = matrix<number<m32>>;
  mat mult({ 
    { m32(1), m32(0), m32(-1) },
    { m32(-1), m32(1), m32(0) },
    { m32(0), m32(-1), m32(1) },
  });
  mat start({
    { m32(a), m32(b), m32(c) }
  });
  start *= mult.power(N - 1);
  std::cout << start[0][0] << ' ' << start[0][1] << ' ' << start[0][2] << '\n';
  return 0;
}
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