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:heavy_check_mark: Test/AOJ/3111.test.cpp

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Code

#define PROBLEM "https://onlinejudge.u-aizu.ac.jp/problems/3111"

#include "../../Src/Algebra/Monoid/SubarraySumMaxMonoid.hpp"
#include "../../Src/DataStructure/SegmentTree/SegmentTree.hpp"

#include <iostream>
#include <vector>

using namespace std;
using namespace zawa;
using M = SubarraySumMaxMonoid<long long>;
int main() {
    cin.tie(0);
    cout.tie(0);
    ios::sync_with_stdio(0);
    int N, Q;
    cin >> N >> Q;
    vector<M::Element> A(N);
    for (int i = 0 ; i < N ; i++) {
        int a;
        cin >> a;
        A[i] = M::convert(a);
    }
    SegmentTree<M> seg{A};
    auto prod = [&]() -> long long {
        auto pd = seg.product(0, N);
        return pd ? max(pd->ans(), 0LL) : 0LL;
    };
    cout << prod() << '\n';
    while (Q--) {
        int k, x;
        cin >> k >> x;
        k--;
        seg.assign(k, M::convert(x));
        cout << prod() << '\n';
    }
}
#line 1 "Test/AOJ/3111.test.cpp"
#define PROBLEM "https://onlinejudge.u-aizu.ac.jp/problems/3111"

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

#include <algorithm>
#include <concepts>
#include <optional>

namespace zawa {

template <std::totally_ordered T>
class SubarraySumMax {
public:

    SubarraySumMax() = default;

    explicit SubarraySumMax(T v) : m_ans{v}, m_sum{v}, m_pref{v}, m_suf{v}, m_entire{true} {}

    SubarraySumMax(T ans, T sum, T pref, T suf, bool entire) : m_ans{ans}, m_sum{sum}, m_pref{pref}, m_suf{suf}, m_entire{entire} {}

    inline T ans() const {
        return m_ans;
    }

    inline T sum() const {
        return m_sum;
    }

    inline T pref() const {
        return m_pref;
    }

    inline T suf() const {
        return m_suf;
    }

    inline bool entire() const {
        return m_entire;
    }

    static SubarraySumMax<T> merge(const SubarraySumMax<T>& lhs, const SubarraySumMax<T>& rhs) {
        T sum = lhs.sum() + rhs.sum();
        T pref = std::max(lhs.pref(), lhs.sum() + rhs.pref());
        T suf = std::max(rhs.suf(), lhs.suf() + rhs.sum());
        T ans = std::max({lhs.ans(), rhs.ans(), lhs.suf() + rhs.pref(), sum});
        bool entire = (ans == sum);
        return {ans, sum, pref, suf, entire};
    }

private:

    T m_ans{}, m_sum{}, m_pref{}, m_suf{};

    bool m_entire{};
};

template <std::totally_ordered T>
struct SubarraySumMaxMonoid {

    using Element = std::optional<SubarraySumMax<T>>;

    static Element identity() {
        return std::nullopt;
    }

    static Element operation(const Element& L, const Element& R) {
        if (!L) return R;
        if (!R) return L;
        return Element::value_type::merge(L.value(), R.value());
    }

    static Element convert(T v) {
        return Element{v};
    }
};

} // namespace zawa
#line 2 "Src/DataStructure/SegmentTree/SegmentTree.hpp"

#line 2 "Src/Template/TypeAlias.hpp"

#include <cstdint>
#include <cstddef>

namespace zawa {

using i16 = std::int16_t;
using i32 = std::int32_t;
using i64 = std::int64_t;
using i128 = __int128_t;

using u8 = std::uint8_t;
using u16 = std::uint16_t;
using u32 = std::uint32_t;
using u64 = std::uint64_t;

using usize = std::size_t;

} // namespace zawa
#line 2 "Src/Algebra/Monoid/MonoidConcept.hpp"

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

#line 4 "Src/Algebra/Semigroup/SemigroupConcept.hpp"

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 5 "Src/DataStructure/SegmentTree/SegmentTree.hpp"

#include <vector>
#include <cassert>
#include <functional>
#include <type_traits>
#include <ostream>

namespace zawa {

template <concepts::Monoid Monoid>
class SegmentTree {
public:

    using VM = Monoid;

    using V = typename VM::Element;

    using OM = Monoid;

    using O = typename OM::Element;

    SegmentTree() = default;

    explicit SegmentTree(usize n) : m_n{ n }, m_dat(n << 1, VM::identity()) {}

    explicit SegmentTree(const std::vector<V>& dat) : m_n{ dat.size() }, m_dat(dat.size() << 1, VM::identity()) {
        for (usize i{} ; i < m_n ; i++) {
            m_dat[i + m_n] = dat[i];
        }
        for (usize i{m_n} ; i-- ; ) {
            m_dat[i] = VM::operation(m_dat[left(i)], m_dat[right(i)]);
        }
    }

    [[nodiscard]] inline usize size() const noexcept {
        return m_n;
    }

    [[nodiscard]] V get(usize i) const {
        assert(i < size());
        return m_dat[i + m_n];
    }

    [[nodiscard]] V operator[](usize i) const {
        assert(i < size());
        return m_dat[i + m_n];
    }

    void operation(usize i, const O& value) {
        assert(i < size());
        i += size();
        m_dat[i] = OM::operation(m_dat[i], value);
        while (i = parent(i), i) {
            m_dat[i] = VM::operation(m_dat[left(i)], m_dat[right(i)]);
        }
    }

    void assign(usize i, const V& value) {
        assert(i < size());
        i += size();
        m_dat[i] = value;
        while (i = parent(i), i) {
            m_dat[i] = VM::operation(m_dat[left(i)], m_dat[right(i)]);
        }
    }

    [[nodiscard]] V product(u32 l, u32 r) const {
        assert(l <= r and r <= size());
        V L{ VM::identity() }, R{ VM::identity() };
        for (l += size(), r += size() ; l < r ; l = parent(l), r = parent(r)) {
            if (l & 1) {
                L = VM::operation(L, m_dat[l++]);
            }
            if (r & 1) {
                R = VM::operation(m_dat[--r], R);
            }
        }
        return VM::operation(L, R);
    }

    template <class F>
    requires std::predicate<F, V>
    [[nodiscard]] usize maxRight(usize l, const F& f) {
        assert(l < size());
        static_assert(std::is_convertible_v<decltype(f), std::function<bool(V)>>, "maxRight's argument f must be function bool(T)");
        assert(f(VM::identity()));
        usize res{l}, width{1};
        V prod{ VM::identity() };
        // 現在の見ている頂点の幅をwidthで持つ
        // 境界がある頂点を含む部分木の根を探す
        // (折り返す時は必要以上の幅を持つ根になるが、widthを持っているのでオーバーしない)
        for (l += size() ; res + width <= size() ; l = parent(l), width <<= 1) if (l & 1) {
            if (not f(VM::operation(prod, m_dat[l]))) break; 
            res += width;
            prod = VM::operation(prod, m_dat[l++]);
        }
        // 根から下って、境界を発見する
        while (l = left(l), width >>= 1) {
            if (res + width <= size() and f(VM::operation(prod, m_dat[l]))) {
                res += width;
                prod = VM::operation(prod, m_dat[l++]);
            } 
        }
        return res;
    }

    template <class F>
    requires std::predicate<F, V>
    [[nodiscard]] usize minLeft(usize r, const F& f) const {
        assert(r <= size());
        static_assert(std::is_convertible_v<decltype(f), std::function<bool(V)>>, "minLeft's argument f must be function bool(T)");
        assert(f(VM::identity()));
        usize res{r}, width{1};
        V prod{ VM::identity() };
        for (r += size() ; res >= width ; r = parent(r), width <<= 1) if (r & 1) {
            if (not f(VM::operation(m_dat[r - 1], prod))) break;
            res -= width;
            prod = VM::operation(prod, m_dat[--r]);
        }
        while (r = left(r), width >>= 1) {
            if (res >= width and f(VM::operation(m_dat[r - 1], prod))) {
                res -= width;
                prod = VM::operation(m_dat[--r], prod);
            }
        }
        return res;
    }

    friend std::ostream& operator<<(std::ostream& os, const SegmentTree& st) {
        for (usize i{1} ; i < 2 * st.size() ; i++) {
            os << st.m_dat[i] << (i + 1 == 2 * st.size() ? "" : " ");
        }
        return os;
    }

private:

    constexpr u32 left(u32 v) const {
        return v << 1;
    }

    constexpr u32 right(u32 v) const {
        return v << 1 | 1;
    }

    constexpr u32 parent(u32 v) const {
        return v >> 1;
    }

    usize m_n;

    std::vector<V> m_dat;
};

} // namespace zawa
#line 5 "Test/AOJ/3111.test.cpp"

#include <iostream>
#line 8 "Test/AOJ/3111.test.cpp"

using namespace std;
using namespace zawa;
using M = SubarraySumMaxMonoid<long long>;
int main() {
    cin.tie(0);
    cout.tie(0);
    ios::sync_with_stdio(0);
    int N, Q;
    cin >> N >> Q;
    vector<M::Element> A(N);
    for (int i = 0 ; i < N ; i++) {
        int a;
        cin >> a;
        A[i] = M::convert(a);
    }
    SegmentTree<M> seg{A};
    auto prod = [&]() -> long long {
        auto pd = seg.product(0, N);
        return pd ? max(pd->ans(), 0LL) : 0LL;
    };
    cout << prod() << '\n';
    while (Q--) {
        int k, x;
        cin >> k >> x;
        k--;
        seg.assign(k, M::convert(x));
        cout << prod() << '\n';
    }
}
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