Src/Algebra/Group/GroupConcept.hpp

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• Last update: 2025-04-17 19:44:48+09:00
• Include: #include "Src/Algebra/Group/GroupConcept.hpp"

Depends on

• Src/Algebra/Monoid/MonoidConcept.hpp
• Src/Algebra/Semigroup/SemigroupConcept.hpp

Required by

• Dual Fenwick Tree (Src/DataStructure/FenwickTree/DualFenwickTree.hpp)
• Fenwick Tree (Src/DataStructure/FenwickTree/FenwickTree.hpp)
• Fenwick Tree 2D (Offline Query) (Src/DataStructure/FenwickTree/OfflineFenwickTree2D.hpp)
• 昇順 $K$ 個の和を取れるpriority_queue (Src/DataStructure/Other/PriorityProductSet.hpp)

Verified with

• Test/AOJ/DSL_2_B.test.cpp
• Test/AtCoder/abc276_f.test.cpp
• Test/AtCoder/abc287_g.test.cpp
• Test/AtCoder/abc340_e.test.cpp
• Test/AtCoder/abc384_g.test.cpp
• Test/AtCoder/abc389_f.test.cpp
• Test/AtCoder/arc088_e.test.cpp
• Test/AtCoder/arc196_a.test.cpp
• Test/CF/EC2-E.test.cpp
• Test/LC/point_add_range_sum.test.cpp
• Test/LC/point_add_rectangle_sum/OfflineFenwickTree2D.test.cpp
• Test/LC/vertex_add_path_sum.test.cpp
• Test/LC/vertex_add_subtree_sum.test.cpp
• Test/yukicoder/649.test.cpp

Code

#pragma once

#include "../Monoid/MonoidConcept.hpp"

namespace zawa {

namespace concepts {

template <class T>
concept Inversible = requires {
    typename T::Element;
    { T::inverse(std::declval<typename T::Element>()) } -> std::same_as<typename T::Element>;
};

template <class T>
concept Group = Monoid<T> and Inversible<T>;

} // namespace Concept

} // namespace zawa

#line 2 "Src/Algebra/Group/GroupConcept.hpp"

#line 2 "Src/Algebra/Monoid/MonoidConcept.hpp"

#line 2 "Src/Algebra/Semigroup/SemigroupConcept.hpp"

#include <concepts>

namespace zawa {

namespace concepts {

template <class T>
concept Semigroup = requires {
    typename T::Element;
    { T::operation(std::declval<typename T::Element>(), std::declval<typename T::Element>()) } -> std::same_as<typename T::Element>;
};

} // namespace concepts

} // namespace zawa
#line 4 "Src/Algebra/Monoid/MonoidConcept.hpp"

#line 6 "Src/Algebra/Monoid/MonoidConcept.hpp"

namespace zawa {

namespace concepts {

template <class T>
concept Identitiable = requires {
    typename T::Element;
    { T::identity() } -> std::same_as<typename T::Element>;
};

template <class T>
concept Monoid = Semigroup<T> and Identitiable<T>;

} // namespace

} // namespace zawa
#line 4 "Src/Algebra/Group/GroupConcept.hpp"

namespace zawa {

namespace concepts {

template <class T>
concept Inversible = requires {
    typename T::Element;
    { T::inverse(std::declval<typename T::Element>()) } -> std::same_as<typename T::Element>;
};

template <class T>
concept Group = Monoid<T> and Inversible<T>;

} // namespace Concept

} // namespace zawa

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