結果

問題 No.117 組み合わせの数
ユーザー KoD
提出日時 2020-07-05 00:22:22
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 278 ms / 5,000 ms
コード長 4,429 bytes
コンパイル時間 714 ms
コンパイル使用メモリ 68,984 KB
最終ジャッジ日時 2025-01-11 15:48:20
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
other AC * 1
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ソースコード

diff # 

#line 1 "main.cpp"

#define PROBLEM "https://yukicoder.me/problems/no/117"

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

#include <cstddef>
#include <array>

template <class T, size_t N>
class factorials {
public:
  using value_type = T;
  static constexpr size_t size = N;

public:
  std::array<value_type, size + 1> fact{};
  std::array<value_type, size + 1> fact_inv{};

  factorials() {
    fact.front() = value_type(1);
    for (size_t i = 1; i <= size; ++i) {
      fact[i] = fact[i - 1] * value_type(i);
    }
    fact_inv.back() = ~fact.back();
    for (size_t i = size; i > 0; --i) {
      fact_inv[i - 1] = fact_inv[i] * value_type(i);
    }
  }

  value_type operator () (size_t n, size_t r) const {
    return fact[n] * fact_inv[n - r] * fact_inv[r];
  }

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

#include <cstdint>
#include <iostream>

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;
  }

};
#line 6 "main.cpp"

#line 8 "main.cpp"

using m32 = modular<1000000007>;
factorials<m32, 2000000> fact;

m32 comb(size_t N, size_t K) {
  if (N < K) return m32(0);
  return fact(N, K);
}

m32 perm(size_t N, size_t K) {
  if (N < K) return m32(0);
  return fact.fact[N] * fact.fact_inv[N - K];
}

m32 homo(size_t N, size_t K) {
  if (N == 0 && K == 0) return m32(1);
  if (N == 0) return m32(0);
  return fact(N + K - 1, K);
}

int main() {
  size_t T;
  std::cin >> T;
  while (T--) {
    char type, dust;
    size_t N, K;
    std::cin >> type >> dust >> N >> dust >> K >> dust;
    if (type == 'C') std::cout << comb(N, K) << '\n';
    if (type == 'P') std::cout << perm(N, K) << '\n';
    if (type == 'H') std::cout << homo(N, K) << '\n';
  }
}
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