algebra/acted_monoid/acted_monoid_inversion01_flip.hpp

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• Last update: 2026-04-11 00:41:57+09:00
• Include: #include "algebra/acted_monoid/acted_monoid_inversion01_flip.hpp"
• Link: https://atcoder.jp/contests/practice2/tasks/practice2_l

Depends on

• algebra/monoid/monoid_xor.hpp

Verified with

• segment_tree/test/lazy_segment_tree_inversion01_flip.test.cpp

Code

#pragma once

#include "../monoid/monoid_xor.hpp"

// https://atcoder.jp/contests/practice2/tasks/practice2_l
template <class T> struct Inversion01 {
    // c0: 0 の個数, c1: 1 の個数, c10: 転倒数
    T c0, c1, c10;
};

template <class T> struct MonoidInversion01 {
    using value_type = Inversion01<T>;
    static constexpr value_type operation(const value_type& a,
                                          const value_type& b) {
        return {a.c0 + b.c0, a.c1 + b.c1, a.c10 + b.c10 + a.c1 * b.c0};
    }
    static constexpr value_type identity() { return {T(0), T(0), T(0)}; }
};

template <class T> struct ActedMonoidInversion01Flip {
    using MS = MonoidInversion01<T>;
    using MF = MonoidXor<int>;
    using S = typename MS::value_type;
    using F = typename MF::value_type;
    static constexpr S mapping(const F f, S x, const int size) {
        if (f == MF::identity()) {
            return x;
        }
        return {x.c1, x.c0, x.c0 * x.c1 - x.c10};
    }
};

#line 2 "algebra/acted_monoid/acted_monoid_inversion01_flip.hpp"

#line 2 "algebra/monoid/monoid_xor.hpp"

template <class T> struct MonoidXor {
    using value_type = T;
    static constexpr T operation(const T& a, const T& b) noexcept {
        return a ^ b;
    }
    static constexpr T identity() noexcept { return T(0); }
    static constexpr T inverse(const T& a) noexcept { return a; }
    static constexpr bool commutative = true;
};
#line 4 "algebra/acted_monoid/acted_monoid_inversion01_flip.hpp"

// https://atcoder.jp/contests/practice2/tasks/practice2_l
template <class T> struct Inversion01 {
    // c0: 0 の個数, c1: 1 の個数, c10: 転倒数
    T c0, c1, c10;
};

template <class T> struct MonoidInversion01 {
    using value_type = Inversion01<T>;
    static constexpr value_type operation(const value_type& a,
                                          const value_type& b) {
        return {a.c0 + b.c0, a.c1 + b.c1, a.c10 + b.c10 + a.c1 * b.c0};
    }
    static constexpr value_type identity() { return {T(0), T(0), T(0)}; }
};

template <class T> struct ActedMonoidInversion01Flip {
    using MS = MonoidInversion01<T>;
    using MF = MonoidXor<int>;
    using S = typename MS::value_type;
    using F = typename MF::value_type;
    static constexpr S mapping(const F f, S x, const int size) {
        if (f == MF::identity()) {
            return x;
        }
        return {x.c1, x.c0, x.c0 * x.c1 - x.c10};
    }
};

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