Check whether T is a monoid (tools/is_monoid.hpp)

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• Last update: 2024-03-23 15:55:12+09:00
• Include: #include "tools/is_monoid.hpp"

template <typename M>
struct is_monoid {
  static constexpr bool value;
};

template <typename M>
inline constexpr bool is_monoid_v = is_monoid<M>::value;

If <M> satisfies the following conditions, tools::is_monoid<M>::value is true.

• typename M::T exists.
• The static member function typename M::T M::op(typename M::T, typename M::T) exists.
• The static member function typename M::T M::e() exists.

Otherwise, it is false.

Constraints

• None

Time Complexity

• Not applicable

License

• CC0

Author

• anqooqie

Required by

• $\left\lceil x^\frac{1}{k} \right\rceil$ (tools/ceil_kth_root.hpp)
• Two-dimensional circle (tools/circle_2d.hpp)
• tools/detail/geometry_2d.hpp
• tools/detail/rolling_hash.hpp
• Two-dimensional directed line segment (tools/directed_line_segment_2d.hpp)
• $\left\lfloor x^\frac{1}{k} \right\rfloor$ (tools/floor_kth_root.hpp)
• Two-dimensional half line (tools/half_line_2d.hpp)
• Precompute $n! \pmod{P}$ for $0 \leq n < P \approx 10^9$ (tools/large_fact_mod_cache.hpp)
• Two-dimensional line (tools/line_2d.hpp)
• $\mathbb{Z} / (2^{61} - 1) \mathbb{Z}$ (tools/modint_for_rolling_hash.hpp)
• Online cumulative sum (tools/online_cumsum.hpp)
• Online difference array (tools/online_imos.hpp)
• $\mathrm{ord}(x)$ for $x \in (\mathbb{Z}/p\mathbb{Z})^\times$ (tools/ord_mod.hpp)
• Two-dimensional polygon (tools/polygon_2d.hpp)
• $b^n$ under a given monoid, and std::pow(b, n) extended for my library (tools/pow.hpp)
• Quaternion (tools/quaternion.hpp)
• Rolling hash (tools/rolling_hash.hpp)
• Shift of sampling points of polynomial (tools/sample_point_shift.hpp)
• $x^2$ under a given monoid (tools/square.hpp)
• $x \uparrow\uparrow y \pmod{M}$ (tools/tetration_mod.hpp)
• Euler's totient function (tools/totient.hpp)
• Two-dimensional triangle (tools/triangle_2d.hpp)
• Twelvefold way (tools/twelvefold_way.hpp)

Verified with

• tests/ceil_kth_root.test.cpp
• tests/circle_2d/intersection_to_circle.test.cpp
• tests/circle_2d/intersection_to_line.test.cpp
• tests/circle_2d/where/with_radius.test.cpp
• tests/circle_2d/where/without_radius.test.cpp
• tests/directed_line_segment_2d/cross_point.test.cpp
• tests/directed_line_segment_2d/crosses.test.cpp
• tests/directed_line_segment_2d/intersection.test.cpp
• tests/directed_line_segment_2d/squared_distance.test.cpp
• tests/floor_kth_root.test.cpp
• tests/fps/exp_other_mods.test.cpp
• tests/fps/log_other_mods.test.cpp
• tests/fps/pow_other_mods.test.cpp
• tests/has_mod.test.cpp
• tests/is_monoid.test.cpp
• tests/large_fact_mod_cache/binomial.test.cpp
• tests/large_fact_mod_cache/fact.test.cpp
• tests/line_2d/is_parallel_to.test.cpp
• tests/line_2d/projection.test.cpp
• tests/online_cumsum.test.cpp
• tests/online_imos.test.cpp
• tests/ord_mod/count.test.cpp
• tests/ord_mod/query.test.cpp
• tests/permutation.test.cpp
• tests/polygon_2d/area.test.cpp
• tests/polygon_2d/minimum_bounding_circle.test.cpp
• tests/polygon_2d/where.test.cpp
• tests/quaternion/angle_axis.test.cpp
• tests/quaternion/dice_rotations.test.cpp
• tests/quaternion/look_rotation.test.cpp
• tests/quaternion/slerp.test.cpp
• tests/rolling_hash.test.cpp
• tests/sample_point_shift.test.cpp
• tests/tetration_mod.test.cpp
• tests/totient.test.cpp
• tests/triangle_2d/circumcircle.test.cpp
• tests/triangle_2d/incircle.test.cpp
• tests/twelvefold_way/labeled_ball_labeled_box_at_least_1.test.cpp
• tests/twelvefold_way/labeled_ball_labeled_box_at_most_1.test.cpp
• tests/twelvefold_way/labeled_ball_labeled_box_unrestricted.test.cpp
• tests/twelvefold_way/labeled_ball_unlabeled_box_at_least_1.test.cpp
• tests/twelvefold_way/labeled_ball_unlabeled_box_at_most_1.test.cpp
• tests/twelvefold_way/labeled_ball_unlabeled_box_unrestricted.test.cpp
• tests/twelvefold_way/unlabeled_ball_labeled_box_at_least_1.test.cpp
• tests/twelvefold_way/unlabeled_ball_labeled_box_at_most_1.test.cpp
• tests/twelvefold_way/unlabeled_ball_labeled_box_unrestricted.test.cpp
• tests/twelvefold_way/unlabeled_ball_unlabeled_box_at_least_1.test.cpp
• tests/twelvefold_way/unlabeled_ball_unlabeled_box_at_most_1.test.cpp
• tests/twelvefold_way/unlabeled_ball_unlabeled_box_unrestricted.test.cpp

Code

#ifndef TOOLS_IS_MONOID_HPP
#define TOOLS_IS_MONOID_HPP

#include <type_traits>
#include <utility>

namespace tools {

  template <typename M, typename = void>
  struct is_monoid : ::std::false_type {};

  template <typename M>
  struct is_monoid<M, ::std::enable_if_t<
    ::std::is_same_v<typename M::T, decltype(M::op(::std::declval<typename M::T>(), ::std::declval<typename M::T>()))> &&
    ::std::is_same_v<typename M::T, decltype(M::e())>
  , void>> : ::std::true_type {};

  template <typename M>
  inline constexpr bool is_monoid_v = ::tools::is_monoid<M>::value;
}

#endif

#line 1 "tools/is_monoid.hpp"



#include <type_traits>
#include <utility>

namespace tools {

  template <typename M, typename = void>
  struct is_monoid : ::std::false_type {};

  template <typename M>
  struct is_monoid<M, ::std::enable_if_t<
    ::std::is_same_v<typename M::T, decltype(M::op(::std::declval<typename M::T>(), ::std::declval<typename M::T>()))> &&
    ::std::is_same_v<typename M::T, decltype(M::e())>
  , void>> : ::std::true_type {};

  template <typename M>
  inline constexpr bool is_monoid_v = ::tools::is_monoid<M>::value;
}

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