#510293 (C++17) No.1112 冥界の音楽

• 問題: No.1112 冥界の音楽
• ユーザー: KoD
• 提出日時: 2020-07-10 23:24:03
• 言語: C++17 (gcc 12.3.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 12 ms / 2,000 ms
• コード長: 8,915 bytes
• コンパイル時間: 1,184 ms
• コンパイル使用メモリ: 89,016 KB
• 実行使用メモリ: 5,248 KB
• 最終ジャッジ日時: 2024-11-14 22:41:16
• 合計ジャッジ時間: 2,501 ms
• ジャッジサーバーID （参考情報）: judge3 / judge5

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	2 ms; 5,248 KB
testcase_01	AC	2 ms; 5,248 KB
testcase_02	AC	2 ms; 5,248 KB
testcase_03	AC	2 ms; 5,248 KB
testcase_04	AC	2 ms; 5,248 KB
testcase_05	AC	2 ms; 5,248 KB
testcase_06	AC	3 ms; 5,248 KB
testcase_07	AC	2 ms; 5,248 KB
testcase_08	AC	2 ms; 5,248 KB
testcase_09	AC	2 ms; 5,248 KB
testcase_10	AC	2 ms; 5,248 KB
testcase_11	AC	2 ms; 5,248 KB
testcase_12	AC	2 ms; 5,248 KB
testcase_13	AC	2 ms; 5,248 KB
testcase_14	AC	5 ms; 5,248 KB
testcase_15	AC	3 ms; 5,248 KB
testcase_16	AC	2 ms; 5,248 KB
testcase_17	AC	3 ms; 5,248 KB
testcase_18	AC	3 ms; 5,248 KB
testcase_19	AC	2 ms; 5,248 KB
testcase_20	AC	2 ms; 5,248 KB
testcase_21	AC	4 ms; 5,248 KB
testcase_22	AC	5 ms; 5,248 KB
testcase_23	AC	2 ms; 5,248 KB
testcase_24	AC	2 ms; 5,248 KB
testcase_25	AC	2 ms; 5,248 KB
testcase_26	AC	2 ms; 5,248 KB
testcase_27	AC	2 ms; 5,248 KB
testcase_28	AC	2 ms; 5,248 KB
testcase_29	AC	2 ms; 5,248 KB
testcase_30	AC	5 ms; 5,248 KB
testcase_31	AC	2 ms; 5,248 KB
testcase_32	AC	5 ms; 5,248 KB
testcase_33	AC	2 ms; 5,248 KB
testcase_34	AC	2 ms; 5,248 KB
testcase_35	AC	2 ms; 5,248 KB
testcase_36	AC	12 ms; 5,248 KB

ソースコード

#line 1 "main.cpp"

#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; }
};

template <class SemiRing>
class matrix {
public:
  using structure       = SemiRing;
  using value_structure = typename SemiRing::value_structure;
  using value_type      = typename SemiRing::value_structure::type;
  using size_type       = size_t;

private:
  std::vector<std::vector<value_type>> M_matrix;

public:
  matrix() = default;
  explicit matrix(size_type H, size_type W, 
    const value_type &value = value_structure::addition_identity()) { initialize(H, W, value); }
  explicit matrix(const std::vector<std::vector<value_type>> &cont) { construct(cont); }
  explicit matrix(const std::initializer_list<std::initializer_list<value_type>> &cont) { construct(cont); }

  void initialize(size_type H, size_type W, const value_type &value = value_structure::addition_identity()) {
    clear();
    M_matrix.assign(H, std::vector<value_type>(W, value));
  }
  void construct(const std::vector<std::vector<value_type>> &cont) {
    clear();
    M_matrix = cont;
  }
  void construct(const std::initializer_list<std::initializer_list<value_type>> &cont) {
    clear();
    if (cont.size() > 0) {
      M_matrix.reserve(cont.size());
      std::transform(cont.begin(), cont.end(), std::back_inserter(M_matrix), [](const auto &vec) {
        return std::vector<value_type>(vec.begin(), vec.end());
      });
    }
  }
  void fill(const value_type &value) {
    for (auto &vec: M_matrix) {
      std::fill(vec.begin(), vec.end(), value);
    }
  }

  matrix operator + (const matrix &rhs) const { return matrix(*this) += rhs; }
  matrix& operator += (const matrix &rhs) { 
    for (size_type i = 0; i < height(); ++i) {
      for (size_type j = 0; j < width(); ++j) {
        M_matrix[i][j] = value_structure::addition(M_matrix[i][j], rhs.M_matrix[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 (size_type i = 0; i < height(); ++i) {
      for (size_type k = 0; k < width(); ++k) {
        for (size_type j = 0; j < rhs.width(); ++j) {
          res.M_matrix[i][j] = value_structure::addition(res.M_matrix[i][j], 
            value_structure::multiplication(M_matrix[i][k], rhs.M_matrix[k][j]));
        }
      }
    }
    return res;
  }
 
  matrix operator * (const value_type &rhs) const { return matrix(*this) *= rhs; }
  matrix& operator *= (const value_type &rhs)  { 
    for (auto &vec: M_matrix) {
      for (auto &x: vec) {
        x = value_structure::multiplication(x, rhs);
      }
    }
    return *this;
  }
 
  matrix power(uint64_t exp) const {
    matrix res(height(), width()), use(*this);
    for (size_type i = 0; i < height(); ++i) {
      res[i][i] = value_structure::multiplication_identity();
    }
    while (exp > 0) {
      if (exp & 1) {
        res *= use;
      }
      use *= use;
      exp >>= 1;
    }
    return res;
  }

  std::vector<value_type>& operator [] (size_type index) {
    return M_matrix[index];
  }
  size_type height() const {
    return M_matrix.size();
  }
  size_type width() const {
    if (M_matrix.empty()) return 0;
    return M_matrix.front().size();
  }
  bool empty() const {
    return M_matrix.empty();
  }
  void clear() {
    M_matrix.clear();
    M_matrix.shrink_to_fit();
  }

};

#line 2 "/Users/kodamankod/Desktop/Programming/Library/algebraic/modular.cpp"

#include <cstdint>
#line 5 "/Users/kodamankod/Desktop/Programming/Library/algebraic/modular.cpp"

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

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

  constexpr value_type &extract() noexcept { return value; }
  constexpr modular inverse() const noexcept { return power(mod - 2); }
  constexpr modular power(max_type exp) const noexcept {
    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 noexcept { return modular(*this) += rhs; }
  constexpr modular& operator += (const modular &rhs) noexcept { 
    if ((value += rhs.value) >= mod) value -= mod; 
    return *this; 
  }

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

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

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

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

};

/**
 * @title Modint
 */
#line 162 "main.cpp"

using m32 = modular<1000000007>;

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;

struct semiring {
  struct value_structure {
    using type = m32;
    static type addition_identity() { return m32(0); }
    static type addition(const type& v1, const type& v2) { 
      return v1 + v2;
    }
    static type multiplication_identity() { return m32(1); }
    static type multiplication(const type& v1, const type& v2) { 
      return v1 * v2;
    }
  };
};

int main() {
  i32 K, M;
  std::cin >> K >> M;
  i64 N;
  std::cin >> N;
  using matrix_t = matrix<semiring>;
  matrix_t mult(K * K, K * K);
  for (auto i: range(0, M)) {
    i32 p, q, r;
    std::cin >> p >> q >> r;
    --p; --q; --r;
    mult[K * p + q][K * q + r] = m32(1);
  }
  matrix_t start(1, K * K);
  for (auto i: range(0, K)) {
    start[0][K * 0 + i] = m32(1);
  }
  matrix_t goal = start * mult.power(N - 2);
  m32 ans;
  for (auto i: range(0, K)) {
    ans += goal[0][K * i + 0];
  }
  std::cout << ans << '\n';
  return 0;
}