Affine monoid
(Mylib/AlgebraicStructure/Monoid/affine.cpp)

• View this file on GitHub
• Last update: 2021-04-23 23:44:44+09:00
• Link: View error logs on GitHub Actions

Operations

• id()
  • 恒等関数 $f(x) = x$ を返す。
  • return (1, 0)
• op(a, b)
  • 合成した関数 $a \circ b$ を返す。

Requirements

Notes

Problems

• ARC 008 D - タコヤキオイシクナール
• Point Set Range Composite

References

Verified with

• test/yosupo-judge/point_set_range_composite/main.test.cpp
• test/yosupo-judge/queue_operate_all_composite/main.test.cpp
• test/yosupo-judge/range_affine_range_sum/main.test.cpp
• test/yosupo-judge/vertex_set_path_composite/main.test.cpp

Code

#pragma once
#include <utility>

namespace haar_lib {
  template <typename T>
  struct affine_monoid {
    using value_type = std::pair<T, T>;
    value_type operator()() const { return std::make_pair(1, 0); }
    value_type operator()(const value_type &a, const value_type &b) const {
      return std::make_pair(a.first * b.first, a.first * b.second + a.second);
    }
  };
}  // namespace haar_lib

#line 2 "Mylib/AlgebraicStructure/Monoid/affine.cpp"
#include <utility>

namespace haar_lib {
  template <typename T>
  struct affine_monoid {
    using value_type = std::pair<T, T>;
    value_type operator()() const { return std::make_pair(1, 0); }
    value_type operator()(const value_type &a, const value_type &b) const {
      return std::make_pair(a.first * b.first, a.first * b.second + a.second);
    }
  };
}  // namespace haar_lib

Back to top page