verify/ds/range_query/offline_rectangle_add_rectangle_sum.test.cpp

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Last update: 2026-10-06 01:57:24+09:00
Problem: https://judge.yosupo.jp/problem/static_rectangle_add_rectangle_sum

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Code

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

#include "../../../ds/range_query/offline_rectangle_add_rectangle_sum.hpp"

#include <algorithm>
#include <cassert>
#include <cstdint>
#include <vector>

#include "../../../math/modint.hpp"
#include "../../../utilities/fast_io.hpp"

namespace {

struct Rectangle {
    int x_lower;
    int x_upper;
    int y_lower;
    int y_upper;
    long long value;
};

long long overlap_length(int first_lower, int first_upper, int second_lower, int second_upper) {
    return std::max(0, std::min(first_upper, second_upper) -
                           std::max(first_lower, second_lower));
}

long long naive_sum(
    const std::vector<Rectangle>& updates,
    int x_lower,
    int x_upper,
    int y_lower,
    int y_upper
) {
    long long result = 0;
    for (const Rectangle& update : updates) {
        const long long width = overlap_length(
            update.x_lower, update.x_upper, x_lower, x_upper
        );
        const long long height = overlap_length(
            update.y_lower, update.y_upper, y_lower, y_upper
        );
        result += width * height * update.value;
    }
    return result;
}

void test_randomized() {
    using Solver = m1une::ds::OfflineRectangleAddRectangleSum<long long, int>;

    Solver empty;
    assert(empty.empty());
    assert(empty.update_count() == 0);
    assert(empty.query_count() == 0);
    assert(empty.calculate().empty());

    int empty_query = empty.add_query(-5, 5, -5, 5);
    assert(empty_query == 0);
    assert(empty.calculate() == std::vector<long long>(1, 0));
    empty.clear();
    assert(empty.empty());

    Solver unordered_batch;
    int first_query = unordered_batch.add_query(1, 4, 1, 3);
    unordered_batch.add_rectangle(0, 3, 0, 2, 5);
    assert(unordered_batch.calculate()[first_query] == 10);

    std::uint64_t state = 987654321;
    auto random = [&state]() {
        state ^= state << 7;
        state ^= state >> 9;
        return state;
    };

    for (int trial = 0; trial < 400; trial++) {
        const int update_count = int(random() % 26);
        const int query_count = int(random() % 31);
        Solver solver;
        solver.reserve_updates(update_count);
        solver.reserve_queries(query_count);
        std::vector<Rectangle> updates;
        std::vector<long long> expected;

        for (int update_id = 0; update_id < update_count; update_id++) {
            int x_lower = int(random() % 21) - 10;
            int x_upper = int(random() % 21) - 10;
            int y_lower = int(random() % 21) - 10;
            int y_upper = int(random() % 21) - 10;
            if (x_upper < x_lower) std::swap(x_lower, x_upper);
            if (y_upper < y_lower) std::swap(y_lower, y_upper);
            long long value = static_cast<long long>(random() % 21) - 10;
            assert(
                solver.add_rectangle(x_lower, x_upper, y_lower, y_upper, value) ==
                update_id
            );
            updates.push_back(Rectangle{x_lower, x_upper, y_lower, y_upper, value});
        }

        for (int query_id = 0; query_id < query_count; query_id++) {
            int x_lower = int(random() % 25) - 12;
            int x_upper = int(random() % 25) - 12;
            int y_lower = int(random() % 25) - 12;
            int y_upper = int(random() % 25) - 12;
            if (x_upper < x_lower) std::swap(x_lower, x_upper);
            if (y_upper < y_lower) std::swap(y_lower, y_upper);
            assert(solver.add_query(x_lower, x_upper, y_lower, y_upper) == query_id);
            expected.push_back(
                naive_sum(updates, x_lower, x_upper, y_lower, y_upper)
            );
        }

        assert(solver.update_count() == update_count);
        assert(solver.query_count() == query_count);
        assert(solver.empty() == (update_count == 0 && query_count == 0));
        assert(solver.calculate() == expected);
        assert(solver.calculate() == expected);
    }
}

}  // namespace

int main() {
    m1une::utilities::FastInput fast_input;
    m1une::utilities::FastOutput fast_output;

    test_randomized();

    using Mint = m1une::math::modint998244353;
    using Solver = m1une::ds::OfflineRectangleAddRectangleSum<Mint>;

    int n, q;
    fast_input >> n >> q;
    Solver solver;
    solver.reserve_updates(n);
    solver.reserve_queries(q);
    for (int update = 0; update < n; update++) {
        long long left, lower, right, upper, value;
        fast_input >> left >> lower >> right >> upper >> value;
        solver.add_rectangle(left, right, lower, upper, Mint(value));
    }
    for (int query = 0; query < q; query++) {
        long long left, lower, right, upper;
        fast_input >> left >> lower >> right >> upper;
        solver.add_query(left, right, lower, upper);
    }

    for (const Mint& answer : solver.calculate()) {
        fast_output << answer << '\n';
    }
}

#line 1 "verify/ds/range_query/offline_rectangle_add_rectangle_sum.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/static_rectangle_add_rectangle_sum"

#line 1 "ds/range_query/offline_rectangle_add_rectangle_sum.hpp"



#include <algorithm>
#include <cassert>
#include <utility>
#include <vector>

#line 1 "ds/range_query/fenwick_tree.hpp"



#line 6 "ds/range_query/fenwick_tree.hpp"

namespace m1une {
namespace ds {

template <typename T>
struct FenwickTree {
   private:
    int _n;
    int _max_power;
    std::vector<T> _data;

    static int max_power_leq(int n) {
        int result = 1;
        while (result <= n / 2) result <<= 1;
        return result;
    }

    T prefix_sum(int r) const {
        T result{};
        const T* data = _data.data();
        while (r > 0) {
            result += data[r];
            r -= r & -r;
        }
        return result;
    }

   public:
    FenwickTree() : _n(0), _max_power(0) {}

    explicit FenwickTree(int n)
        : _n(n), _max_power(max_power_leq(n > 0 ? n : 1)), _data(n + 1, T{}) {}

    explicit FenwickTree(const std::vector<T>& a)
        : _n(int(a.size())),
          _max_power(max_power_leq(_n > 0 ? _n : 1)),
          _data(a.size() + 1, T{}) {
        for (int i = 1; i <= _n; ++i) {
            _data[i] += a[i - 1];
            const int p = i + (i & -i);
            if (p <= _n) {
                _data[p] += _data[i];
            }
        }
    }

    int size() const {
        return _n;
    }

    bool empty() const {
        return _n == 0;
    }

    // Adds `x` to the element at zero-based index `p`.
    void add(int p, const T& x) {
        assert(0 <= p && p < _n);
        ++p;
        T* data = _data.data();
        while (p <= _n) {
            data[p] += x;
            p += p & -p;
        }
    }

    // Returns the sum of elements in the range [0, r).
    T sum(int r) const {
        assert(0 <= r && r <= _n);
        return prefix_sum(r);
    }

    // Returns the sum of elements in the range [l, r).
    T sum(int l, int r) const {
        assert(0 <= l && l <= r && r <= _n);
        return prefix_sum(r) - prefix_sum(l);
    }

    // Returns the minimum index `r` such that the sum of [0, r) >= w.
    // Requires all elements in the tree to be non-negative.
    int lower_bound(T w) const {
        if (w <= 0) return 0;
        int x = 0;
        const T* data = _data.data();
        for (int k = _max_power; k > 0; k >>= 1) {
            if (x + k <= _n && data[x + k] < w) {
                w -= data[x + k];
                x += k;
            }
        }
        return x + 1;
    }
};

}  // namespace ds
}  // namespace m1une


#line 10 "ds/range_query/offline_rectangle_add_rectangle_sum.hpp"

namespace m1une {
namespace ds {

// Records rectangle additions and rectangle-sum queries, then evaluates the
// complete static batch with an offline sweep.
template <class T, class X = long long, class Y = X>
class OfflineRectangleAddRectangleSum {
   public:
    using value_type = T;
    using x_type = X;
    using y_type = Y;

   private:
    struct Update {
        X x_lower;
        X x_upper;
        Y y_lower;
        Y y_upper;
        T value;
    };

    struct Query {
        X x_lower;
        X x_upper;
        Y y_lower;
        Y y_upper;
    };

    struct Coefficient {
        T xy{};
        T x{};
        T y{};
        T constant{};

        Coefficient& operator+=(const Coefficient& other) {
            xy += other.xy;
            x += other.x;
            y += other.y;
            constant += other.constant;
            return *this;
        }
    };

    struct PointEvent {
        X x;
        Y y;
        Coefficient coefficient;
    };

    struct PrefixEvent {
        X x;
        Y y;
        int query_id;
        bool subtract;
    };

    std::vector<Update> _updates;
    std::vector<Query> _queries;

    template <class Coordinate>
    static bool equivalent(const Coordinate& first, const Coordinate& second) {
        return !(first < second) && !(second < first);
    }

    static Coefficient make_coefficient(
        const X& x,
        const Y& y,
        const T& signed_value
    ) {
        const T converted_x(x);
        const T converted_y(y);
        return {
            signed_value,
            T{} - signed_value * converted_y,
            T{} - signed_value * converted_x,
            signed_value * converted_x * converted_y
        };
    }

    static T evaluate(
        const Coefficient& coefficient,
        const X& x,
        const Y& y
    ) {
        const T converted_x(x);
        const T converted_y(y);
        return coefficient.xy * converted_x * converted_y +
               coefficient.x * converted_x +
               coefficient.y * converted_y +
               coefficient.constant;
    }

   public:
    int update_count() const {
        return int(_updates.size());
    }

    int query_count() const {
        return int(_queries.size());
    }

    bool empty() const {
        return _updates.empty() && _queries.empty();
    }

    void reserve_updates(int capacity) {
        assert(0 <= capacity);
        _updates.reserve(capacity);
    }

    void reserve_queries(int capacity) {
        assert(0 <= capacity);
        _queries.reserve(capacity);
    }

    void clear() {
        _updates.clear();
        _queries.clear();
    }

    int add_rectangle(
        const X& x_lower,
        const X& x_upper,
        const Y& y_lower,
        const Y& y_upper,
        const T& value
    ) {
        assert(!(x_upper < x_lower));
        assert(!(y_upper < y_lower));
        const int id = update_count();
        _updates.push_back(Update{x_lower, x_upper, y_lower, y_upper, value});
        return id;
    }

    int add_query(
        const X& x_lower,
        const X& x_upper,
        const Y& y_lower,
        const Y& y_upper
    ) {
        assert(!(x_upper < x_lower));
        assert(!(y_upper < y_lower));
        const int id = query_count();
        _queries.push_back(Query{x_lower, x_upper, y_lower, y_upper});
        return id;
    }

    std::vector<T> calculate() const {
        std::vector<T> answers(_queries.size(), T{});
        if (_queries.empty() || _updates.empty()) return answers;

        std::vector<PointEvent> point_events;
        point_events.reserve(4 * _updates.size());
        std::vector<Y> y_coordinates;
        y_coordinates.reserve(2 * _updates.size());
        for (const Update& update : _updates) {
            if (equivalent(update.x_lower, update.x_upper) ||
                equivalent(update.y_lower, update.y_upper)) {
                continue;
            }
            const T negative_value = T{} - update.value;
            point_events.push_back(PointEvent{
                update.x_lower,
                update.y_lower,
                make_coefficient(update.x_lower, update.y_lower, update.value)
            });
            point_events.push_back(PointEvent{
                update.x_lower,
                update.y_upper,
                make_coefficient(update.x_lower, update.y_upper, negative_value)
            });
            point_events.push_back(PointEvent{
                update.x_upper,
                update.y_lower,
                make_coefficient(update.x_upper, update.y_lower, negative_value)
            });
            point_events.push_back(PointEvent{
                update.x_upper,
                update.y_upper,
                make_coefficient(update.x_upper, update.y_upper, update.value)
            });
            y_coordinates.push_back(update.y_lower);
            y_coordinates.push_back(update.y_upper);
        }
        if (point_events.empty()) return answers;

        std::sort(y_coordinates.begin(), y_coordinates.end());
        y_coordinates.erase(
            std::unique(
                y_coordinates.begin(),
                y_coordinates.end(),
                [](const Y& first, const Y& second) {
                    return equivalent(first, second);
                }
            ),
            y_coordinates.end()
        );
        std::sort(
            point_events.begin(),
            point_events.end(),
            [](const PointEvent& first, const PointEvent& second) {
                return first.x < second.x;
            }
        );

        std::vector<PrefixEvent> prefix_events;
        prefix_events.reserve(4 * _queries.size());
        for (int query_id = 0; query_id < query_count(); query_id++) {
            const Query& query = _queries[query_id];
            prefix_events.push_back(PrefixEvent{
                query.x_upper, query.y_upper, query_id, false
            });
            prefix_events.push_back(PrefixEvent{
                query.x_lower, query.y_upper, query_id, true
            });
            prefix_events.push_back(PrefixEvent{
                query.x_upper, query.y_lower, query_id, true
            });
            prefix_events.push_back(PrefixEvent{
                query.x_lower, query.y_lower, query_id, false
            });
        }
        std::sort(
            prefix_events.begin(),
            prefix_events.end(),
            [](const PrefixEvent& first, const PrefixEvent& second) {
                return first.x < second.x;
            }
        );

        FenwickTree<Coefficient> fenwick(int(y_coordinates.size()));
        int point_index = 0;
        for (const PrefixEvent& event : prefix_events) {
            while (
                point_index < int(point_events.size()) &&
                point_events[point_index].x < event.x
            ) {
                const PointEvent& point = point_events[point_index];
                const int y_index = int(
                    std::lower_bound(
                        y_coordinates.begin(), y_coordinates.end(), point.y
                    ) - y_coordinates.begin()
                );
                fenwick.add(y_index, point.coefficient);
                point_index++;
            }
            const int y_count = int(
                std::lower_bound(
                    y_coordinates.begin(), y_coordinates.end(), event.y
                ) - y_coordinates.begin()
            );
            const T value = evaluate(fenwick.sum(y_count), event.x, event.y);
            if (event.subtract) {
                answers[event.query_id] -= value;
            } else {
                answers[event.query_id] += value;
            }
        }
        return answers;
    }
};

}  // namespace ds
}  // namespace m1une


#line 4 "verify/ds/range_query/offline_rectangle_add_rectangle_sum.test.cpp"

#line 7 "verify/ds/range_query/offline_rectangle_add_rectangle_sum.test.cpp"
#include <cstdint>
#line 9 "verify/ds/range_query/offline_rectangle_add_rectangle_sum.test.cpp"

#line 1 "math/modint.hpp"



#line 6 "math/modint.hpp"
#include <iostream>
#include <type_traits>
#line 9 "math/modint.hpp"

namespace m1une {
namespace math {

template <uint32_t Modulus>
struct ModInt {
    static_assert(0 < Modulus, "Modulus must be positive");

   private:
    uint32_t _v;

   public:
    static constexpr uint32_t mod() {
        return Modulus;
    }

    static constexpr ModInt raw(uint32_t v) noexcept {
        ModInt x;
        x._v = v;
        return x;
    }

    constexpr ModInt() noexcept : _v(0) {}

    template <class Integer, std::enable_if_t<std::is_integral_v<Integer>, int> = 0>
    constexpr ModInt(Integer v) noexcept {
        if constexpr (std::is_signed_v<Integer>) {
            int64_t x = static_cast<int64_t>(v) % static_cast<int64_t>(Modulus);
            if (x < 0) x += Modulus;
            _v = static_cast<uint32_t>(x);
        } else {
            _v = static_cast<uint32_t>(static_cast<uint64_t>(v) % Modulus);
        }
    }

    constexpr uint32_t val() const noexcept {
        return _v;
    }

    constexpr ModInt& operator++() noexcept {
        _v++;
        if (_v == Modulus) _v = 0;
        return *this;
    }

    constexpr ModInt& operator--() noexcept {
        if (_v == 0) _v = Modulus;
        _v--;
        return *this;
    }

    constexpr ModInt operator++(int) noexcept {
        ModInt res = *this;
        ++*this;
        return res;
    }

    constexpr ModInt operator--(int) noexcept {
        ModInt res = *this;
        --*this;
        return res;
    }

    constexpr ModInt& operator+=(const ModInt& rhs) noexcept {
        _v += rhs._v;
        if (_v >= Modulus) _v -= Modulus;
        return *this;
    }

    constexpr ModInt& operator-=(const ModInt& rhs) noexcept {
        _v -= rhs._v;
        if (_v >= Modulus) _v += Modulus;
        return *this;
    }

    constexpr ModInt& operator*=(const ModInt& rhs) noexcept {
        uint64_t z = _v;
        z *= rhs._v;
        _v = static_cast<uint32_t>(z % Modulus);
        return *this;
    }

    constexpr ModInt& operator/=(const ModInt& rhs) noexcept {
        return *this *= rhs.inv();
    }

    constexpr ModInt operator+(const ModInt& rhs) const noexcept {
        return ModInt(*this) += rhs;
    }
    constexpr ModInt operator-(const ModInt& rhs) const noexcept {
        return ModInt(*this) -= rhs;
    }
    constexpr ModInt operator*(const ModInt& rhs) const noexcept {
        return ModInt(*this) *= rhs;
    }
    constexpr ModInt operator/(const ModInt& rhs) const noexcept {
        return ModInt(*this) /= rhs;
    }

    constexpr bool operator==(const ModInt& rhs) const noexcept {
        return _v == rhs._v;
    }
    constexpr bool operator!=(const ModInt& rhs) const noexcept {
        return _v != rhs._v;
    }

    constexpr ModInt pow(long long n) const noexcept {
        ModInt res = raw(1 % Modulus);
        ModInt x = n < 0 ? inv() : *this;
        uint64_t exponent = n < 0 ? uint64_t(-(n + 1)) + 1 : uint64_t(n);
        while (exponent > 0) {
            if (exponent & 1) res *= x;
            x *= x;
            exponent >>= 1;
        }
        return res;
    }

    constexpr ModInt inv() const noexcept {
        int64_t a = _v, b = Modulus, u = 1, v = 0;
        while (b) {
            int64_t t = a / b;
            a -= t * b;
            std::swap(a, b);
            u -= t * v;
            std::swap(u, v);
        }
        assert(a == 1);
        u %= Modulus;
        if (u < 0) u += Modulus;
        return raw(static_cast<uint32_t>(u));
    }

    friend std::ostream& operator<<(std::ostream& os, const ModInt& rhs) {
        return os << rhs._v;
    }

    friend std::istream& operator>>(std::istream& is, ModInt& rhs) {
        long long v;
        is >> v;
        rhs = ModInt(v);
        return is;
    }
};

using modint998244353 = ModInt<998244353>;
using modint1000000007 = ModInt<1000000007>;

template <int Id = 0>
struct DynamicModInt {
   private:
    uint32_t _v;
    inline static uint32_t _mod = 1;

   public:
    static uint32_t mod() noexcept {
        return _mod;
    }

    static void set_mod(uint32_t modulus) noexcept {
        assert(modulus > 0);
        assert(modulus <= uint32_t(1) << 31);
        _mod = modulus;
    }

    static DynamicModInt raw(uint32_t v) noexcept {
        assert(v < _mod);
        DynamicModInt x;
        x._v = v;
        return x;
    }

    DynamicModInt() noexcept : _v(0) {}

    template <class Integer, std::enable_if_t<std::is_integral_v<Integer>, int> = 0>
    DynamicModInt(Integer v) noexcept {
        if constexpr (std::is_signed_v<Integer>) {
            int64_t x = static_cast<int64_t>(v) % static_cast<int64_t>(_mod);
            if (x < 0) x += _mod;
            _v = static_cast<uint32_t>(x);
        } else {
            _v = static_cast<uint32_t>(static_cast<uint64_t>(v) % _mod);
        }
    }

    uint32_t val() const noexcept {
        return _v;
    }

    DynamicModInt& operator++() noexcept {
        _v++;
        if (_v == _mod) _v = 0;
        return *this;
    }

    DynamicModInt& operator--() noexcept {
        if (_v == 0) _v = _mod;
        _v--;
        return *this;
    }

    DynamicModInt operator++(int) noexcept {
        DynamicModInt result = *this;
        ++*this;
        return result;
    }

    DynamicModInt operator--(int) noexcept {
        DynamicModInt result = *this;
        --*this;
        return result;
    }

    DynamicModInt& operator+=(const DynamicModInt& rhs) noexcept {
        _v += rhs._v;
        if (_v >= _mod) _v -= _mod;
        return *this;
    }

    DynamicModInt& operator-=(const DynamicModInt& rhs) noexcept {
        _v -= rhs._v;
        if (_v >= _mod) _v += _mod;
        return *this;
    }

    DynamicModInt& operator*=(const DynamicModInt& rhs) noexcept {
        _v = static_cast<uint32_t>(uint64_t(_v) * rhs._v % _mod);
        return *this;
    }

    DynamicModInt& operator/=(const DynamicModInt& rhs) noexcept {
        return *this *= rhs.inv();
    }

    DynamicModInt operator+(const DynamicModInt& rhs) const noexcept {
        return DynamicModInt(*this) += rhs;
    }

    DynamicModInt operator-(const DynamicModInt& rhs) const noexcept {
        return DynamicModInt(*this) -= rhs;
    }

    DynamicModInt operator*(const DynamicModInt& rhs) const noexcept {
        return DynamicModInt(*this) *= rhs;
    }

    DynamicModInt operator/(const DynamicModInt& rhs) const noexcept {
        return DynamicModInt(*this) /= rhs;
    }

    bool operator==(const DynamicModInt& rhs) const noexcept {
        return _v == rhs._v;
    }

    bool operator!=(const DynamicModInt& rhs) const noexcept {
        return _v != rhs._v;
    }

    DynamicModInt pow(long long exponent) const noexcept {
        DynamicModInt result = raw(1 % _mod);
        DynamicModInt base = exponent < 0 ? inv() : *this;
        uint64_t magnitude =
            exponent < 0 ? uint64_t(-(exponent + 1)) + 1 : uint64_t(exponent);
        while (magnitude > 0) {
            if (magnitude & 1) result *= base;
            base *= base;
            magnitude >>= 1;
        }
        return result;
    }

    DynamicModInt inv() const noexcept {
        int64_t a = _v, b = _mod, u = 1, v = 0;
        while (b) {
            int64_t quotient = a / b;
            a -= quotient * b;
            std::swap(a, b);
            u -= quotient * v;
            std::swap(u, v);
        }
        assert(a == 1);
        u %= _mod;
        if (u < 0) u += _mod;
        return raw(static_cast<uint32_t>(u));
    }

    friend std::ostream& operator<<(std::ostream& os, const DynamicModInt& rhs) {
        return os << rhs._v;
    }

    friend std::istream& operator>>(std::istream& is, DynamicModInt& rhs) {
        long long value;
        is >> value;
        rhs = DynamicModInt(value);
        return is;
    }
};

}  // namespace math
}  // namespace m1une


#line 1 "utilities/fast_io.hpp"



#line 5 "utilities/fast_io.hpp"
#include <array>
#include <cerrno>
#include <charconv>
#include <cstddef>
#include <cstdio>
#include <cstdlib>
#line 12 "utilities/fast_io.hpp"
#include <cstring>
#include <iterator>
#include <string>
#include <sys/stat.h>
#line 18 "utilities/fast_io.hpp"
#include <unistd.h>
#line 20 "utilities/fast_io.hpp"

namespace m1une {
namespace utilities {

struct FastOutput;

namespace internal {

// Shared with the convenience helpers in template.hpp.
inline FastOutput* standard_output_instance = nullptr;

// Detect std::begin(x), std::end(x).
template <class T, class = void>
struct is_range : std::false_type {};

template <class T>
struct is_range<T, std::void_t<
    decltype(std::begin(std::declval<T&>())),
    decltype(std::end(std::declval<T&>()))
>> : std::true_type {};

template <class T>
inline constexpr bool is_range_v = is_range<T>::value;

template <class T>
using range_reference_t = decltype(*std::begin(std::declval<T&>()));

template <class T>
using range_value_t = std::remove_cv_t<std::remove_reference_t<range_reference_t<T>>>;

template <class T, class = void>
struct range_stored_value {
    using type = range_value_t<T>;
};

template <class T>
struct range_stored_value<T, std::void_t<typename std::remove_cv_t<std::remove_reference_t<T>>::value_type>> {
    using type = typename std::remove_cv_t<std::remove_reference_t<T>>::value_type;
};

template <class T>
using range_stored_value_t = typename range_stored_value<T>::type;

// Treat strings and C strings as scalar output objects, not as ranges.
template <class T>
struct is_char_array : std::false_type {};

template <class T, std::size_t N>
struct is_char_array<T[N]>
    : std::bool_constant<std::is_same_v<std::remove_cv_t<T>, char>> {};

template <class T>
struct is_string_like
    : std::bool_constant<
          std::is_same_v<std::decay_t<T>, std::string>
          || std::is_same_v<std::decay_t<T>, const char*>
          || std::is_same_v<std::decay_t<T>, char*>
          || is_char_array<std::remove_reference_t<T>>::value
      > {};

template <class T>
inline constexpr bool is_string_like_v = is_string_like<T>::value;

// ModInt-like type: x.val() is printable, and x can be assigned from long long.
template <class T, class = void>
struct has_val_method : std::false_type {};

template <class T>
struct has_val_method<T, std::void_t<decltype(std::declval<const T&>().val())>>
    : std::true_type {};

template <class T>
inline constexpr bool has_val_method_v = has_val_method<T>::value;

template <class T, class = void>
struct has_static_mod_raw : std::false_type {};

template <class T>
struct has_static_mod_raw<
    T, std::void_t<decltype(T::mod()), decltype(T::raw(std::declval<uint32_t>()))>>
    : std::true_type {};

template <class T>
inline constexpr bool has_static_mod_raw_v = has_static_mod_raw<T>::value;

// libstdc++ before GCC 16 does not classify __int128 as an integral type in
// strict ISO modes such as -std=c++23. Keep the fast-I/O interface independent
// of that implementation detail.
template <class T>
inline constexpr bool is_integral_v =
    std::is_integral_v<T>
    || std::is_same_v<std::remove_cv_t<T>, __int128_t>
    || std::is_same_v<std::remove_cv_t<T>, __uint128_t>;

template <class T>
inline constexpr bool is_signed_v =
    std::is_signed_v<T>
    || std::is_same_v<std::remove_cv_t<T>, __int128_t>;

template <class T>
struct make_unsigned {
    using type = std::make_unsigned_t<T>;
};

template <>
struct make_unsigned<__int128_t> {
    using type = __uint128_t;
};

template <>
struct make_unsigned<__uint128_t> {
    using type = __uint128_t;
};

template <class T>
using make_unsigned_t = typename make_unsigned<std::remove_cv_t<T>>::type;

}  // namespace internal

struct FastInput {
    static constexpr int buffer_size = 1 << 20;

   private:
    std::FILE* _stream;
    char _buffer[buffer_size];
    int _position;
    int _length;
    int _file_descriptor;
    bool _streaming;

    bool refill() {
        _position = 0;
        if (_streaming) {
            ssize_t length;
            do {
                length = ::read(_file_descriptor, _buffer, buffer_size);
            } while (length < 0 && errno == EINTR);
            if (length <= 0) {
                _length = 0;
                return false;
            }
            _length = int(length);
        } else {
            _length = int(std::fread(_buffer, 1, buffer_size, _stream));
        }
        return _length != 0;
    }

    template <class T>
    bool read_integer_from_stream(T& value) {
        if (!skip_spaces()) return false;
        int c = read_char_raw();

        bool negative = false;
        if (c == '-') {
            negative = true;
            c = read_char_raw();
        }

        if constexpr (internal::is_signed_v<T>) {
            T result = 0;
            while ('0' <= c && c <= '9') {
                result = negative ? result * 10 - (c - '0')
                                  : result * 10 + (c - '0');
                c = read_char_raw();
            }
            value = result;
        } else {
            T result = 0;
            while ('0' <= c && c <= '9') {
                result = result * 10 + T(c - '0');
                c = read_char_raw();
            }
            value = negative ? T(0) - result : result;
        }
        return true;
    }

    bool prepare_number() {
        if (_length - _position >= 64) return true;
        const int remaining = _length - _position;
        if (remaining > 0) std::memmove(_buffer, _buffer + _position, remaining);
        const int added = int(std::fread(_buffer + remaining, 1, buffer_size - remaining, _stream));
        _position = 0;
        _length = remaining + added;
        if (_length < buffer_size) _buffer[_length] = '\0';
        return _length != 0;
    }

   public:
    explicit FastInput(std::FILE* stream = stdin)
        : _stream(stream),
          _position(0),
          _length(0),
          _file_descriptor(::fileno(stream)),
          _streaming([&] {
              struct stat status;
              return _file_descriptor >= 0
                     && ::fstat(_file_descriptor, &status) == 0
                     && !S_ISREG(status.st_mode);
          }()) {}

    FastInput(const FastInput&) = delete;
    FastInput& operator=(const FastInput&) = delete;

    int read_char_raw() {
        if (_position == _length && !refill()) return EOF;
        return _buffer[_position++];
    }

    bool skip_spaces() {
        int c = read_char_raw();
        while (c != EOF && c <= ' ') c = read_char_raw();
        if (c == EOF) return false;
        --_position;
        return true;
    }

    bool read(char& value) {
        if (!skip_spaces()) return false;
        value = char(read_char_raw());
        return true;
    }

    bool read(std::string& value) {
        if (!skip_spaces()) return false;
        value.clear();
        while (true) {
            const int begin = _position;
            while (_position < _length &&
                   static_cast<unsigned char>(_buffer[_position]) > ' ') {
                ++_position;
            }
            value.append(_buffer + begin, _position - begin);
            if (_position < _length) {
                ++_position;
                return true;
            }
            if (!refill()) return true;
        }
    }

    bool read(bool& value) {
        int x;
        if (!read(x)) return false;
        value = x != 0;
        return true;
    }

    template <class T>
    std::enable_if_t<
        internal::is_integral_v<T>
            && !std::is_same_v<std::remove_cv_t<T>, bool>
            && !std::is_same_v<std::remove_cv_t<T>, char>,
        bool
    >
    read(T& value) {
        if (_streaming) return read_integer_from_stream(value);
        if (!prepare_number()) return false;
        int c = static_cast<unsigned char>(_buffer[_position++]);
        while (c <= ' ') c = static_cast<unsigned char>(_buffer[_position++]);

        bool negative = false;
        if (c == '-') {
            negative = true;
            c = static_cast<unsigned char>(_buffer[_position++]);
        }

        if constexpr (internal::is_signed_v<T>) {
            T result = 0;
            while ('0' <= c && c <= '9') {
                const int first = c - '0';
                const int second = static_cast<unsigned char>(_buffer[_position]) - '0';
                if (0 <= second && second <= 9) {
                    result = negative ? result * 100 - (first * 10 + second)
                                      : result * 100 + (first * 10 + second);
                    ++_position;
                } else {
                    result = negative ? result * 10 - first : result * 10 + first;
                }
                c = static_cast<unsigned char>(_buffer[_position++]);
            }
            value = result;
        } else {
            T result = 0;
            while ('0' <= c && c <= '9') {
                const unsigned first = unsigned(c - '0');
                const int second = static_cast<unsigned char>(_buffer[_position]) - '0';
                if (0 <= second && second <= 9) {
                    result = result * 100 + T(first * 10 + unsigned(second));
                    ++_position;
                } else {
                    result = result * 10 + T(first);
                }
                c = static_cast<unsigned char>(_buffer[_position++]);
            }
            value = negative ? T(0) - result : result;
        }
        if (_position > _length) _position = _length;
        return true;
    }

    template <class T>
    std::enable_if_t<std::is_floating_point_v<T>, bool>
    read(T& value) {
        if (!skip_spaces()) return false;
        int c = read_char_raw();
        bool negative = false;
        if (c == '-' || c == '+') {
            negative = c == '-';
            c = read_char_raw();
        }

        long double result = 0;
        while ('0' <= c && c <= '9') {
            result = result * 10 + (c - '0');
            c = read_char_raw();
        }
        if (c == '.') {
            long double place = 0.1L;
            c = read_char_raw();
            while ('0' <= c && c <= '9') {
                result += (c - '0') * place;
                place *= 0.1L;
                c = read_char_raw();
            }
        }
        if (c == 'e' || c == 'E') {
            c = read_char_raw();
            bool exponent_negative = false;
            if (c == '-' || c == '+') {
                exponent_negative = c == '-';
                c = read_char_raw();
            }
            int exponent = 0;
            while ('0' <= c && c <= '9') {
                exponent = exponent * 10 + (c - '0');
                c = read_char_raw();
            }
            long double scale = 1;
            long double power = 10;
            while (exponent > 0) {
                if (exponent & 1) scale *= power;
                power *= power;
                exponent >>= 1;
            }
            result = exponent_negative ? result / scale : result * scale;
        }
        value = static_cast<T>(negative ? -result : result);
        return true;
    }

    template <class T>
    std::enable_if_t<
        internal::has_val_method_v<T>
            && !internal::is_integral_v<T>
            && !internal::is_range_v<T>,
        bool
    >
    read(T& value) {
        long long x;
        if (!read(x)) return false;
        if constexpr (internal::has_static_mod_raw_v<T>) {
            if (x >= 0 && uint64_t(x) < uint64_t(T::mod())) {
                value = T::raw(uint32_t(x));
            } else {
                value = T(x);
            }
        } else {
            value = T(x);
        }
        return true;
    }

    template <class First, class Second>
    bool read(std::pair<First, Second>& value) {
        if (!read(value.first)) return false;
        return read(value.second);
    }

    template <class Range>
    std::enable_if_t<
        internal::is_range_v<Range>
            && !internal::is_string_like_v<Range>,
        bool
    >
    read(Range& range) {
        using StoredValue = internal::range_stored_value_t<Range>;
        constexpr bool nested = internal::is_range_v<StoredValue>
                                && !internal::is_string_like_v<StoredValue>;

        for (auto&& value : range) {
            if constexpr (std::is_same_v<StoredValue, bool> && !nested) {
                bool x;
                if (!read(x)) return false;
                value = x;
            } else {
                if (!read(value)) return false;
            }
        }
        return true;
    }

    template <class First, class Second, class... Rest>
    bool read(First& first, Second& second, Rest&... rest) {
        if (!read(first)) return false;
        return read(second, rest...);
    }

    template <class T>
    FastInput& operator>>(T& value) {
        if (!read(value)) std::abort();
        return *this;
    }
};

struct FastOutput {
    static constexpr int buffer_size = 1 << 20;

   private:
    inline static const auto digit_quads = [] {
        std::array<char, 40000> result{};
        for (int i = 0; i < 10000; i++) {
            int value = i;
            for (int j = 3; j >= 0; j--) {
                result[4 * i + j] = char('0' + value % 10);
                value /= 10;
            }
        }
        return result;
    }();

    std::FILE* _stream;
    char _buffer[buffer_size];
    int _position;
    int _precision;
    std::chars_format _float_format;
    char _range_separator;
    std::string* _capture = nullptr;

    template <class T>
    std::string format_cell(const T& value) {
        std::string result;
        struct CaptureGuard {
            std::string*& target;
            std::string* previous;
            ~CaptureGuard() { target = previous; }
        } guard{_capture, _capture};
        _capture = &result;
        write(value);
        return result;
    }

    template <class Matrix>
    void write_aligned_matrix(const Matrix& matrix) {
        std::vector<std::vector<std::string>> rows;
        std::vector<std::size_t> widths;
        for (const auto& row : matrix) {
            auto& cells = rows.emplace_back();
            std::size_t column = 0;
            for (const auto& value : row) {
                cells.push_back(format_cell(value));
                if (column == widths.size()) widths.push_back(0);
                widths[column] = std::max(widths[column], cells.back().size());
                ++column;
            }
        }
        bool first = true;
        for (const auto& row : rows) {
            if (!first) write_char('\n');
            first = false;
            for (std::size_t column = 0; column < row.size(); ++column) {
                if (column != 0) write_char(_range_separator);
                for (std::size_t padding = row[column].size();
                     padding < widths[column]; ++padding) {
                    write_char(' ');
                }
                write(row[column]);
            }
        }
    }

   public:
    explicit FastOutput(std::FILE* stream = stdout)
        : _stream(stream),
          _position(0),
          _precision(6),
          _float_format(std::chars_format::general),
          _range_separator(' ') {
        if (_stream == stdout
            && internal::standard_output_instance == nullptr) {
            internal::standard_output_instance = this;
        }
    }

    FastOutput(const FastOutput&) = delete;
    FastOutput& operator=(const FastOutput&) = delete;

    ~FastOutput() {
        flush();
        if (internal::standard_output_instance == this) {
            internal::standard_output_instance = nullptr;
        }
    }

    void flush() {
        if (_position != 0) {
            std::fwrite(_buffer, 1, _position, _stream);
            _position = 0;
        }
        std::fflush(_stream);
    }

    void write_char(char c) {
        if (_capture != nullptr) {
            _capture->push_back(c);
            return;
        }
        if (_position == buffer_size) flush();
        _buffer[_position++] = c;
    }

    void write(const char* s) {
        while (*s != '\0') write_char(*s++);
    }

    void write(const std::string& s) {
        if (_capture != nullptr) {
            _capture->append(s);
            return;
        }
        std::size_t position = 0;
        while (position < s.size()) {
            if (_position == buffer_size) flush();
            const std::size_t copied =
                std::min<std::size_t>(buffer_size - _position, s.size() - position);
            std::memcpy(_buffer + _position, s.data() + position, copied);
            _position += int(copied);
            position += copied;
        }
    }

    void write(char c) {
        write_char(c);
    }

    void write(bool value) {
        write_char(value ? '1' : '0');
    }

    template <class T>
    std::enable_if_t<std::is_floating_point_v<T>>
    write(T value) {
        char digits[128];
        auto [end, error] = std::to_chars(
            digits,
            digits + sizeof(digits),
            value,
            _float_format,
            _precision
        );
        if (error != std::errc()) std::abort();
        for (const char* pointer = digits; pointer != end; pointer++) {
            write_char(*pointer);
        }
    }

    template <class T>
    std::enable_if_t<
        internal::is_integral_v<T>
            && !std::is_same_v<std::remove_cv_t<T>, bool>
            && !std::is_same_v<std::remove_cv_t<T>, char>
    >
    write(T value) {
        using Raw = std::remove_cv_t<T>;
        using Unsigned = internal::make_unsigned_t<Raw>;

        Unsigned magnitude;
        if constexpr (internal::is_signed_v<Raw>) {
            if (value < 0) {
                write_char('-');
                magnitude = Unsigned(0) - Unsigned(value);
            } else {
                magnitude = Unsigned(value);
            }
        } else {
            magnitude = value;
        }

        if (magnitude == 0) {
            write_char('0');
            return;
        }

        unsigned chunks[16];
        int count = 0;
        while (magnitude >= 10000) {
            const Unsigned quotient = magnitude / 10000;
            chunks[count++] = unsigned(magnitude - quotient * 10000);
            magnitude = quotient;
        }
        if (_capture == nullptr && _position > buffer_size - 64) flush();
        char captured[64];
        char* const begin = _capture != nullptr ? captured : _buffer + _position;
        char* destination = begin;
        const unsigned leading = unsigned(magnitude);
        const char* first = digit_quads.data() + 4 * leading;
        int skip = leading < 10 ? 3 : leading < 100 ? 2 : leading < 1000 ? 1 : 0;
        for (; skip < 4; skip++) *destination++ = first[skip];
        while (count--) {
            const char* digits = digit_quads.data() + 4 * chunks[count];
            std::memcpy(destination, digits, 4);
            destination += 4;
        }
        if (_capture != nullptr) {
            _capture->append(begin, destination - begin);
        } else {
            _position += int(destination - begin);
        }
    }

    template <class T>
    std::enable_if_t<
        internal::has_val_method_v<T>
            && !internal::is_integral_v<T>
            && !internal::is_range_v<T>
    >
    write(const T& value) {
        write(value.val());
    }

    template <class First, class Second>
    void write(const std::pair<First, Second>& value) {
        write(value.first);
        write_char(' ');
        write(value.second);
    }

    template <class Range>
    std::enable_if_t<
        internal::is_range_v<Range>
            && !internal::is_string_like_v<Range>
    >
    write(const Range& range) {
        using StoredValue = internal::range_stored_value_t<const Range>;
        constexpr bool nested = internal::is_range_v<StoredValue>
                                && !internal::is_string_like_v<StoredValue>;

        bool first = true;
        for (const auto& value : range) {
            if (!first) write_char(nested ? '\n' : _range_separator);
            first = false;
            if constexpr (std::is_same_v<StoredValue, bool> && !nested) {
                write(static_cast<bool>(value));
            } else {
                write(value);
            }
        }
    }

    template <class First, class... Rest>
    void print(const First& first, const Rest&... rest) {
        write(first);
        ((write_char(' '), write(rest)), ...);
    }

    void println() {
        write_char('\n');
    }

    void set_precision(int precision) {
        _precision = precision;
    }

    void set_fixed(int precision = 6) {
        _float_format = std::chars_format::fixed;
        _precision = precision;
    }

    void set_general(int precision = 6) {
        _float_format = std::chars_format::general;
        _precision = precision;
    }

    void set_range_separator(char separator) {
        _range_separator = separator;
    }

    template <class Matrix>
    void write_aligned(const Matrix& matrix) {
        using Row = internal::range_stored_value_t<const Matrix>;
        using Cell = internal::range_stored_value_t<const Row>;
        static_assert(internal::is_range_v<Row> && !internal::is_string_like_v<Row>,
                      "write_aligned requires a two-dimensional range");
        static_assert(!internal::is_range_v<Cell> || internal::is_string_like_v<Cell>,
                      "write_aligned requires scalar cells");
        write_aligned_matrix(matrix);
    }

    template <class Matrix>
    void println_aligned(const Matrix& matrix) {
        write_aligned(matrix);
        write_char('\n');
    }

    template <class... Args>
    void println(const Args&... args) {
        print(args...);
        write_char('\n');
    }

    template <class T>
    FastOutput& operator<<(const T& value) {
        write(value);
        return *this;
    }
};

}  // namespace utilities
}  // namespace m1une


#line 12 "verify/ds/range_query/offline_rectangle_add_rectangle_sum.test.cpp"

namespace {

struct Rectangle {
    int x_lower;
    int x_upper;
    int y_lower;
    int y_upper;
    long long value;
};

long long overlap_length(int first_lower, int first_upper, int second_lower, int second_upper) {
    return std::max(0, std::min(first_upper, second_upper) -
                           std::max(first_lower, second_lower));
}

long long naive_sum(
    const std::vector<Rectangle>& updates,
    int x_lower,
    int x_upper,
    int y_lower,
    int y_upper
) {
    long long result = 0;
    for (const Rectangle& update : updates) {
        const long long width = overlap_length(
            update.x_lower, update.x_upper, x_lower, x_upper
        );
        const long long height = overlap_length(
            update.y_lower, update.y_upper, y_lower, y_upper
        );
        result += width * height * update.value;
    }
    return result;
}

void test_randomized() {
    using Solver = m1une::ds::OfflineRectangleAddRectangleSum<long long, int>;

    Solver empty;
    assert(empty.empty());
    assert(empty.update_count() == 0);
    assert(empty.query_count() == 0);
    assert(empty.calculate().empty());

    int empty_query = empty.add_query(-5, 5, -5, 5);
    assert(empty_query == 0);
    assert(empty.calculate() == std::vector<long long>(1, 0));
    empty.clear();
    assert(empty.empty());

    Solver unordered_batch;
    int first_query = unordered_batch.add_query(1, 4, 1, 3);
    unordered_batch.add_rectangle(0, 3, 0, 2, 5);
    assert(unordered_batch.calculate()[first_query] == 10);

    std::uint64_t state = 987654321;
    auto random = [&state]() {
        state ^= state << 7;
        state ^= state >> 9;
        return state;
    };

    for (int trial = 0; trial < 400; trial++) {
        const int update_count = int(random() % 26);
        const int query_count = int(random() % 31);
        Solver solver;
        solver.reserve_updates(update_count);
        solver.reserve_queries(query_count);
        std::vector<Rectangle> updates;
        std::vector<long long> expected;

        for (int update_id = 0; update_id < update_count; update_id++) {
            int x_lower = int(random() % 21) - 10;
            int x_upper = int(random() % 21) - 10;
            int y_lower = int(random() % 21) - 10;
            int y_upper = int(random() % 21) - 10;
            if (x_upper < x_lower) std::swap(x_lower, x_upper);
            if (y_upper < y_lower) std::swap(y_lower, y_upper);
            long long value = static_cast<long long>(random() % 21) - 10;
            assert(
                solver.add_rectangle(x_lower, x_upper, y_lower, y_upper, value) ==
                update_id
            );
            updates.push_back(Rectangle{x_lower, x_upper, y_lower, y_upper, value});
        }

        for (int query_id = 0; query_id < query_count; query_id++) {
            int x_lower = int(random() % 25) - 12;
            int x_upper = int(random() % 25) - 12;
            int y_lower = int(random() % 25) - 12;
            int y_upper = int(random() % 25) - 12;
            if (x_upper < x_lower) std::swap(x_lower, x_upper);
            if (y_upper < y_lower) std::swap(y_lower, y_upper);
            assert(solver.add_query(x_lower, x_upper, y_lower, y_upper) == query_id);
            expected.push_back(
                naive_sum(updates, x_lower, x_upper, y_lower, y_upper)
            );
        }

        assert(solver.update_count() == update_count);
        assert(solver.query_count() == query_count);
        assert(solver.empty() == (update_count == 0 && query_count == 0));
        assert(solver.calculate() == expected);
        assert(solver.calculate() == expected);
    }
}

}  // namespace

int main() {
    m1une::utilities::FastInput fast_input;
    m1une::utilities::FastOutput fast_output;

    test_randomized();

    using Mint = m1une::math::modint998244353;
    using Solver = m1une::ds::OfflineRectangleAddRectangleSum<Mint>;

    int n, q;
    fast_input >> n >> q;
    Solver solver;
    solver.reserve_updates(n);
    solver.reserve_queries(q);
    for (int update = 0; update < n; update++) {
        long long left, lower, right, upper, value;
        fast_input >> left >> lower >> right >> upper >> value;
        solver.add_rectangle(left, right, lower, upper, Mint(value));
    }
    for (int query = 0; query < q; query++) {
        long long left, lower, right, upper;
        fast_input >> left >> lower >> right >> upper;
        solver.add_query(left, right, lower, upper);
    }

    for (const Mint& answer : solver.calculate()) {
        fast_output << answer << '\n';
    }
}

m1une's library

This documentation is automatically generated by online-judge-tools/verification-helper

verify/ds/range_query/offline_rectangle_add_rectangle_sum.test.cpp

Depends on

Code