Test/LC/point_add_range_sum.test.cpp

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• Last update: 2025-06-24 20:48:55+09:00
• Problem: https://judge.yosupo.jp/problem/point_add_range_sum

Depends on

• 加法群 (Src/Algebra/Group/AdditiveGroup.hpp)
• Src/Algebra/Group/GroupConcept.hpp
• Src/Algebra/Monoid/MonoidConcept.hpp
• Src/Algebra/Semigroup/SemigroupConcept.hpp
• Fenwick Tree (Src/DataStructure/FenwickTree/FenwickTree.hpp)
• ioまわりの設定 (Src/Template/IOSetting.hpp)
• 標準データ型のエイリアス (Src/Template/TypeAlias.hpp)
• std::vectorの入出力 (Src/Template/VectorIO.hpp)

Code

#define PROBLEM "https://judge.yosupo.jp/problem/point_add_range_sum"

#include "../../Src/Template/TypeAlias.hpp"
#include "../../Src/Template/IOSetting.hpp"
#include "../../Src/Template/VectorIO.hpp"
#include "../../Src/Algebra/Group/AdditiveGroup.hpp"
#include "../../Src/DataStructure/FenwickTree/FenwickTree.hpp"

#include <iostream>
#include <vector>
#include <cassert>

using namespace zawa;

int main() {
    SetFastIO();
    usize N, Q; std::cin >> N >> Q;
    std::vector<i64> A(N); std::cin >> A;

    FenwickTree<AdditiveGroup<i64>> ft(A);

    for (u32 _{} ; _ < Q ; _++) {
        u32 t; std::cin >> t;
        if (t == 0) {
            u32 p; std::cin >> p;
            i64 x; std::cin >> x;
            ft.operation(p, x);
        }
        else if (t == 1) {
            u32 l, r; std::cin >> l >> r;
            std::cout << ft.product(l, r) << '\n';
        }
        else {
            assert(!"input fail");
        }
    }
}

#line 1 "Test/LC/point_add_range_sum.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/point_add_range_sum"

#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/Template/IOSetting.hpp"

#line 4 "Src/Template/IOSetting.hpp"

#include <iostream>
#include <iomanip>

namespace zawa {

void SetFastIO() {
    std::cin.tie(nullptr)->sync_with_stdio(false);
}

void SetPrecision(u32 dig) {
    std::cout << std::fixed << std::setprecision(dig);
}

} // namespace zawa
#line 2 "Src/Template/VectorIO.hpp"

#line 4 "Src/Template/VectorIO.hpp"

#line 6 "Src/Template/VectorIO.hpp"
#include <vector>

namespace zawa {

template <class T>
std::istream &operator>>(std::istream& is, std::vector<T>& A) {
    for (T& a : A) {
        is >> a;
    }
    return is;
}

template <class T>
std::ostream &operator<<(std::ostream& os, const std::vector<T>& A) {
    for (u32 i{} ; i < A.size() ; i++) {
        os << A[i] << (i + 1 == A.size() ? "" : " ");
    }
    return os;
}

} // namespace zawa
#line 2 "Src/Algebra/Group/AdditiveGroup.hpp"

namespace zawa {

template <class T>
class AdditiveGroup {
public:
    using Element = T;
    static constexpr T identity() noexcept {
        return T{};
    }
    static constexpr T operation(const T& l, const T& r) noexcept {
        return l + r;
    }
    static constexpr T inverse(const T& v) noexcept {
        return -v;
    }
};

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

#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
#line 5 "Src/DataStructure/FenwickTree/FenwickTree.hpp"

#line 7 "Src/DataStructure/FenwickTree/FenwickTree.hpp"
#include <cassert>
#include <ostream>
#include <functional>
#include <type_traits>

namespace zawa {

template <concepts::Group Group>
class FenwickTree {
public:

    using VM = Group;
    
    using V = typename VM::Element;

    FenwickTree() = default;

    explicit FenwickTree(usize n) : m_n{ n }, m_bitwidth{ std::__lg(n) + 1 }, m_a(n), m_dat(n + 1, VM::identity()) {
        m_dat.shrink_to_fit();
        m_a.shrink_to_fit();
    }

    explicit FenwickTree(const std::vector<V>& a) : m_n{ a.size() }, m_bitwidth{ std::__lg(a.size()) + 1 }, m_a(a), m_dat(a.size() + 1, VM::identity()) {
        m_dat.shrink_to_fit();  
        m_a.shrink_to_fit();
        for (i32 i{} ; i < static_cast<i32>(m_n) ; i++) {
            addDat(i, a[i]);
        }
    }

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

    // return a[i]
    const V& get(usize i) const noexcept {
        assert(i < size());
        return m_a[i];
    }

    // return a[i]
    const V& operator[](usize i) const noexcept {
        assert(i < size());
        return m_a[i];
    }

    // a[i] <- a[i] + v
    void operation(usize i, const V& v) {
        assert(i < size());
        addDat(i, v);
        m_a[i] = VM::operation(m_a[i], v);
    }

    // a[i] <- v
    void assign(usize i, const V& v) {
        assert(i < size());
        addDat(i, VM::operation(VM::inverse(m_a[i]), v));
        m_a[i] = v;
    }

    // return a[0] + a[1] + ... + a[r - 1]
    V prefixProduct(usize r) const {
        assert(r <= size());
        return product(r);
    }

    // return a[l] + a[l + 1] ... + a[r - 1]
    V product(usize l, usize r) const {
        assert(l <= r and r <= size());
        return VM::operation(VM::inverse(product(l)), product(r));
    }

    template <class Function>
    usize maxRight(usize l, const Function& f) const {
        static_assert(std::is_convertible_v<decltype(f), std::function<bool(V)>>, "maxRight's argument f must be function bool(T)");
        assert(l < size());
        V sum{ VM::inverse(product(l)) }; 
        usize r{};
        for (usize bit{ m_bitwidth } ; bit ; ) {
            bit--;
            usize nxt{ r | (1u << bit) };
            if (nxt < m_dat.size() and f(VM::operation(sum, m_dat[nxt]))) {
                sum = VM::operation(sum, m_dat[nxt]);
                r = std::move(nxt);
            }
        }
        assert(l <= r);
        return r;
    }

    template <class Function>
    usize minLeft(usize r, const Function& f) const {
        static_assert(std::is_convertible_v<decltype(f), std::function<bool(V)>>, "minLeft's argument f must be function bool(T)");
        assert(r <= size());
        V sum{ product(r) };
        usize l{};
        for (usize bit{ m_bitwidth } ; bit ; ) {
            bit--;
            usize nxt{ l | (1u << bit) };
            if (nxt <= r and not f(VM::operation(VM::inverse(m_dat[nxt]), sum))) {
                sum = VM::operation(VM::inverse(m_dat[nxt]), sum);
                l = std::move(nxt);
            }
        }
        assert(l <= r);
        return l;
    }

    // debug print
    friend std::ostream& operator<<(std::ostream& os, const FenwickTree& ft) {
        for (usize i{} ; i <= ft.size() ; i++) {
            os << ft.prefixProduct(i) << (i == ft.size() ? "" : " ");
        }
        return os;
    }

private:

    usize m_n{};

    usize m_bitwidth{};

    std::vector<V> m_a, m_dat;

    constexpr i32 lsb(i32 x) const noexcept {
        return x & -x;
    }
    
    // a[i] <- a[i] + v
    void addDat(i32 i, const V& v) {
        assert(0 <= i and i < static_cast<i32>(m_n));
        for ( i++ ; i < static_cast<i32>(m_dat.size()) ; i += lsb(i)) {
            m_dat[i] = VM::operation(m_dat[i], v);
        }
    }

    // return a[0] + a[1] + .. + a[i - 1]
    V product(i32 i) const {
        assert(0 <= i and i <= static_cast<i32>(m_n));
        V res{ VM::identity() };
        for ( ; i > 0 ; i -= lsb(i)) {
            res = VM::operation(res, m_dat[i]);
        }
        return res;
    }

};

} // namespace zawa
#line 8 "Test/LC/point_add_range_sum.test.cpp"

#line 12 "Test/LC/point_add_range_sum.test.cpp"

using namespace zawa;

int main() {
    SetFastIO();
    usize N, Q; std::cin >> N >> Q;
    std::vector<i64> A(N); std::cin >> A;

    FenwickTree<AdditiveGroup<i64>> ft(A);

    for (u32 _{} ; _ < Q ; _++) {
        u32 t; std::cin >> t;
        if (t == 0) {
            u32 p; std::cin >> p;
            i64 x; std::cin >> x;
            ft.operation(p, x);
        }
        else if (t == 1) {
            u32 l, r; std::cin >> l >> r;
            std::cout << ft.product(l, r) << '\n';
        }
        else {
            assert(!"input fail");
        }
    }
}

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