#705591 (C++17) No.1706 Many Bus Stops (hard)

提出ソース

結果

問題	No.1706 Many Bus Stops (hard)
ユーザー	jupiro
提出日時	2021-10-08 22:17:08
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	2 ms / 2,000 ms
コード長	5,185 bytes
コンパイル時間	2,386 ms
コンパイル使用メモリ	211,124 KB
実行使用メモリ	6,944 KB
最終ジャッジ日時	2024-07-23 04:45:37
合計ジャッジ時間	3,558 ms
ジャッジサーバーID （参考情報）	judge1 / judge5

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テストケース

テストケース表示

入力	結果	実行時間実行使用メモリ
testcase_00	AC	2 ms 6,812 KB
testcase_01	AC	2 ms 6,816 KB
testcase_02	AC	2 ms 6,940 KB
testcase_03	AC	2 ms 6,944 KB
testcase_04	AC	2 ms 6,940 KB
testcase_05	AC	2 ms 6,940 KB
testcase_06	AC	2 ms 6,944 KB
testcase_07	AC	2 ms 6,940 KB
testcase_08	AC	2 ms 6,944 KB
testcase_09	AC	2 ms 6,940 KB
testcase_10	AC	2 ms 6,940 KB
testcase_11	AC	2 ms 6,940 KB
testcase_12	AC	2 ms 6,944 KB
testcase_13	AC	2 ms 6,944 KB
testcase_14	AC	2 ms 6,940 KB
testcase_15	AC	1 ms 6,944 KB
testcase_16	AC	2 ms 6,940 KB
testcase_17	AC	2 ms 6,944 KB
testcase_18	AC	2 ms 6,944 KB
testcase_19	AC	2 ms 6,940 KB
testcase_20	AC	2 ms 6,940 KB
testcase_21	AC	2 ms 6,940 KB
testcase_22	AC	2 ms 6,944 KB
testcase_23	AC	2 ms 6,940 KB
testcase_24	AC	1 ms 6,940 KB
testcase_25	AC	1 ms 6,944 KB
testcase_26	AC	2 ms 6,940 KB
testcase_27	AC	2 ms 6,944 KB
testcase_28	AC	1 ms 6,944 KB
testcase_29	AC	1 ms 6,940 KB
testcase_30	AC	2 ms 6,944 KB
testcase_31	AC	2 ms 6,940 KB
testcase_32	AC	2 ms 6,940 KB
testcase_33	AC	2 ms 6,940 KB
testcase_34	AC	2 ms 6,940 KB
testcase_35	AC	2 ms 6,940 KB
testcase_36	AC	2 ms 6,944 KB
testcase_37	AC	2 ms 6,944 KB
testcase_38	AC	2 ms 6,940 KB
testcase_39	AC	2 ms 6,940 KB
testcase_40	AC	2 ms 6,944 KB
testcase_41	AC	2 ms 6,944 KB
testcase_42	AC	2 ms 6,940 KB

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ソースコード

raw source code

#include <bits/stdc++.h>
using ll = long long;
using std::cin;
using std::cout;
using std::endl;
std::mt19937 rnd(std::chrono::steady_clock::now().time_since_epoch().count());
template <class T>
inline bool chmax(T &a, T b)
{
  if (a < b)
  {
    a = b;
    return 1;
  }
  return 0;
}
template <class T>
inline bool chmin(T &a, T b)
{
  if (a > b)
  {
    a = b;
    return 1;
  }
  return 0;
}

const int inf = (int)1e9 + 7;
const long long INF = 1LL << 60;

template <int mod>
struct ModInt
{
  int x;

  ModInt() : x(0) {}

  ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}

  ModInt &operator+=(const ModInt &p)
  {
    if ((x += p.x) >= mod)
      x -= mod;
    return *this;
  }

  ModInt &operator-=(const ModInt &p)
  {
    if ((x += mod - p.x) >= mod)
      x -= mod;
    return *this;
  }

  ModInt &operator*=(const ModInt &p)
  {
    x = (int)(1LL * x * p.x % mod);
    return *this;
  }

  ModInt &operator/=(const ModInt &p)
  {
    *this *= p.inverse();
    return *this;
  }

  ModInt operator-() const { return ModInt(-x); }

  ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; }

  ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; }

  ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; }

  ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; }

  bool operator==(const ModInt &p) const { return x == p.x; }

  bool operator!=(const ModInt &p) const { return x != p.x; }

  ModInt inverse() const
  {
    int a = x, b = mod, u = 1, v = 0, t;
    while (b > 0)
    {
      t = a / b;
      std::swap(a -= t * b, b);
      std::swap(u -= t * v, v);
    }
    return ModInt(u);
  }

  ModInt pow(int64_t n) const
  {
    ModInt ret(1), mul(x);
    while (n > 0)
    {
      if (n & 1)
        ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }

  friend std::ostream &operator<<(std::ostream &os, const ModInt &p)
  {
    return os << p.x;
  }

  friend std::istream &operator>>(std::istream &is, ModInt &a)
  {
    int64_t t;
    is >> t;
    a = ModInt<mod>(t);
    return (is);
  }

  static int get_mod() { return mod; }
};

constexpr int mod = (int)1e9 + 7;
using mint = ModInt<mod>;
template <class T>
struct Matrix
{
  std::vector<std::vector<T>> A;

  Matrix() {}

  Matrix(int n, int m) : A(n, std::vector<T>(m, 0)) {}

  Matrix(int n) : A(n, std::vector<T>(n, 0)){};

  int height() const
  {
    return (A.size());
  }

  int width() const
  {
    return (A[0].size());
  }

  inline const std::vector<T> &operator[](int k) const
  {
    return (A.at(k));
  }

  inline std::vector<T> &operator[](int k)
  {
    return (A.at(k));
  }

  static Matrix I(int n)
  {
    Matrix mat(n);
    for (int i = 0; i < n; i++)
      mat[i][i] = 1;
    return (mat);
  }

  Matrix &operator+=(const Matrix &B)
  {
    int n = height(), m = width();
    assert(n == B.height() && m == B.width());
    for (int i = 0; i < n; i++)
      for (int j = 0; j < m; j++)
        (*this)[i][j] += B[i][j];
    return (*this);
  }

  Matrix &operator-=(const Matrix &B)
  {
    int n = height(), m = width();
    assert(n == B.height() && m == B.width());
    for (int i = 0; i < n; i++)
      for (int j = 0; j < m; j++)
        (*this)[i][j] -= B[i][j];
    return (*this);
  }

  Matrix &operator*=(const Matrix &B)
  {
    int n = height(), m = B.width(), p = width();
    assert(p == B.height());
    std::vector<std::vector<T>> C(n, std::vector<T>(m, 0));
    for (int i = 0; i < n; i++)
      for (int j = 0; j < m; j++)
        for (int k = 0; k < p; k++)
          C[i][j] = (C[i][j] + (*this)[i][k] * B[k][j]);
    A.swap(C);
    return (*this);
  }

  Matrix &operator^=(long long k)
  {
    Matrix B = Matrix::I(height());
    while (k > 0)
    {
      if (k & 1)
        B *= *this;
      *this *= *this;
      k >>= 1LL;
    }
    A.swap(B.A);
    return (*this);
  }

  Matrix operator+(const Matrix &B) const
  {
    return (Matrix(*this) += B);
  }

  Matrix operator-(const Matrix &B) const
  {
    return (Matrix(*this) -= B);
  }

  Matrix operator*(const Matrix &B) const
  {
    return (Matrix(*this) *= B);
  }

  Matrix operator^(const long long k) const
  {
    return (Matrix(*this) ^= k);
  }

  friend std::ostream &operator<<(std::ostream &os, Matrix &p)
  {
    int n = p.height(), m = p.width();
    for (int i = 0; i < n; i++)
    {
      os << "[";
      for (int j = 0; j < m; j++)
      {
        os << p[i][j] << (j + 1 == m ? "]\n" : ",");
      }
    }
    return (os);
  }
};
void solve([[maybe_unused]] int CASE)
{
  int C, N, M;
  cin >> C >> N >> M;
  Matrix<mint> mat(4, 4);
  const mint cinv = mint(1) / mint(C);
  mat[0][0] = cinv;
  mat[0][1] = 1;
  mat[1][3] = cinv;
  mat[2][0] = cinv * (C - 1);
  mat[2][3] = cinv * (C - 2);
  mat[3][2] = 1;
  mat[3][3] = cinv;
  mat ^= N;
  Matrix<mint> ini(4, 1);
  ini[0][0] = 1;
  mat *= ini;
  mint exist = mat[0][0];
  mint ret = mint(1) - mint(mint(1) - exist).pow(M);
  cout << ret << "\n";
}

int main()
{
  std::cin.tie(nullptr);
  std::ios::sync_with_stdio(false);

  int kkt = 1;
  // cin >> kkt;
  for (int jupi = 1; jupi <= kkt; jupi++)
    solve(jupi);
  return 0;
}

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結果

テストケース

ソースコード