template/concepts.hpp

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• Last update: 2026-02-01 00:05:07+09:00
• Include: #include "template/concepts.hpp"

Required by

• Best Sum (Data_Structure/Best_Sum.hpp)
• Sliding Window Aggregation (Data_Structure/Sliding_Window_Aggregation.hpp)
• Monoid 重み付き Functional Graph (Functional_Graph/Monoid_Functional_Graph.hpp)
• 区間積 (Math/Interval_Product.hpp)
• Trie 木 (Sequence/Trie.hpp)
• 辺 xy を加える. これによって x, y が連結になった場合, 連結成分の色の更新を行う. (Union_Find/Coloring_Union_Find.hpp)
• 群作用 Union Find (Union_Find/Group_Action_Union_Find.hpp)

Verified with

• verify/yosupo_library_checker/data_structure/Deque_Operate_All_Composite.test.cpp
• verify/yosupo_library_checker/data_structure/Queue_Operate_All_Composite.test.cpp
• verify/yosupo_library_checker/data_structure/Static_Range_Sum-2.test.cpp

Code

#pragma once

// 単項演算子コンセプト
template <typename Op, typename X>
concept Unary_Operator_Concept = requires(Op op, const X &x) {
    { op(x) } -> std::convertible_to<X>;
};

// 二項演算子コンセプト
template <typename Op, typename X>
concept Binary_Operator_Concept = requires(Op op,const X &x, const X &y) {
    { op(x, y) } -> std::convertible_to<X>;
};

// モノイドコンセプト
// 二項演算 + 単位元
template <typename M, auto op, auto identity>
concept Monoid_Concept = 
    Binary_Operator_Concept<decltype(op), M>
    && std::convertible_to<decltype(identity), M>;

// 群コンセプト
// モノイド + 逆元
template <typename G, auto op, auto identity, auto inv>
concept Group_Concept = 
    Monoid_Concept<G, op, identity>
    && Unary_Operator_Concept<decltype(inv), G>;

// 順序群コンセプト
// 群 + 全順序
template <typename G, auto op, auto identity, auto inv>
concept Totally_Ordered_Group_Concept = 
    Group_Concept<G, op, identity, inv>
    && totally_ordered<G>;

// ハッシュ可能コンセプト
template<typename T>
concept Hashable = requires(T x) {
    { hash<T>{}(x) } -> convertible_to<size_t>;
};

#line 2 "template/concepts.hpp"

// 単項演算子コンセプト
template <typename Op, typename X>
concept Unary_Operator_Concept = requires(Op op, const X &x) {
    { op(x) } -> std::convertible_to<X>;
};

// 二項演算子コンセプト
template <typename Op, typename X>
concept Binary_Operator_Concept = requires(Op op,const X &x, const X &y) {
    { op(x, y) } -> std::convertible_to<X>;
};

// モノイドコンセプト
// 二項演算 + 単位元
template <typename M, auto op, auto identity>
concept Monoid_Concept = 
    Binary_Operator_Concept<decltype(op), M>
    && std::convertible_to<decltype(identity), M>;

// 群コンセプト
// モノイド + 逆元
template <typename G, auto op, auto identity, auto inv>
concept Group_Concept = 
    Monoid_Concept<G, op, identity>
    && Unary_Operator_Concept<decltype(inv), G>;

// 順序群コンセプト
// 群 + 全順序
template <typename G, auto op, auto identity, auto inv>
concept Totally_Ordered_Group_Concept = 
    Group_Concept<G, op, identity, inv>
    && totally_ordered<G>;

// ハッシュ可能コンセプト
template<typename T>
concept Hashable = requires(T x) {
    { hash<T>{}(x) } -> convertible_to<size_t>;
};

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