test/src/datastructure/segment_tree/persistent_segment_tree/rectangle_sum.test.cpp

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• Last update: 2023-09-15 20:02:25+09:00
• Problem: https://judge.yosupo.jp/problem/rectangle_sum

Depends on

• 永続セグメント木 (library/datastructure/segment_tree/persistent_segment_tree.hpp)
• Type Traits (library/type_traits/type_traits.hpp)
• 座標圧縮 (library/util/coordinate_compressor.hpp)
• Object Pool (library/util/object_pool.hpp)

Code

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

#include <iostream>
#include <tuple>

#include "library/util/coordinate_compressor.hpp"
#include "library/datastructure/segment_tree/persistent_segment_tree.hpp"

long long op(long long x, long long y) {
    return x + y;
}
long long e() {
    return 0;
}

using suisen::CoordinateCompressorBuilder;
using suisen::PersistentSegmentTree;

using Tree = PersistentSegmentTree<long long, op, e>;

int main() {
    std::ios::sync_with_stdio(false);
    std::cin.tie(nullptr);

    int n, q;
    std::cin >> n >> q;

    std::vector<std::tuple<int, int, int>> points(n);
    CoordinateCompressorBuilder<int> bx, by;

    for (auto &[x, y, w] : points) {
        std::cin >> x >> y >> w;
        bx.push(x);
        by.push(y);
    }
    auto cmp_x = bx.build(), cmp_y = by.build();

    const int h = cmp_x.size(), w = cmp_y.size();

    std::vector<std::vector<std::pair<int, int>>> buckets(h);
    for (auto &[x, y, w] : points) {
        x = cmp_x[x];
        y = cmp_y[y];
        buckets[x].emplace_back(y, w);
    }

    Tree::init_pool(5000000);

    std::vector<Tree> fts(h + 1);
    fts[0] = Tree(w);

    for (int x = 0; x < h; ++x) {
        fts[x + 1] = fts[x];
        for (const auto yw : buckets[x]) {
            const int y = yw.first, w = yw.second;
            fts[x + 1] = fts[x + 1].apply(y, [w](long long e) { return e + w; });
        }
    }

    for (int query_id = 0; query_id < q; ++query_id) {
        int l, r, d, u;
        std::cin >> l >> d >> r >> u;

        l = cmp_x.min_geq_index(l);
        r = cmp_x.min_geq_index(r);
        d = cmp_y.min_geq_index(d);
        u = cmp_y.min_geq_index(u);

        std::cout << fts[r].prod(d, u) - fts[l].prod(d, u) << '\n';
    }

    return 0;
}

#line 1 "test/src/datastructure/segment_tree/persistent_segment_tree/rectangle_sum.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/rectangle_sum"

#include <iostream>
#include <tuple>

#line 1 "library/util/coordinate_compressor.hpp"



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

#line 1 "library/type_traits/type_traits.hpp"



#include <limits>
#line 6 "library/type_traits/type_traits.hpp"
#include <type_traits>

namespace suisen {
    template <typename ...Constraints> using constraints_t = std::enable_if_t<std::conjunction_v<Constraints...>, std::nullptr_t>;

    template <typename T, typename = std::nullptr_t> struct bitnum { static constexpr int value = 0; };
    template <typename T> struct bitnum<T, constraints_t<std::is_integral<T>>> { static constexpr int value = std::numeric_limits<std::make_unsigned_t<T>>::digits; };
    template <typename T> static constexpr int bitnum_v = bitnum<T>::value;
    template <typename T, size_t n> struct is_nbit { static constexpr bool value = bitnum_v<T> == n; };
    template <typename T, size_t n> static constexpr bool is_nbit_v = is_nbit<T, n>::value;

    template <typename T, typename = std::nullptr_t> struct safely_multipliable { using type = T; };
    template <typename T> struct safely_multipliable<T, constraints_t<std::is_signed<T>, is_nbit<T, 32>>> { using type = long long; };
    template <typename T> struct safely_multipliable<T, constraints_t<std::is_signed<T>, is_nbit<T, 64>>> { using type = __int128_t; };
    template <typename T> struct safely_multipliable<T, constraints_t<std::is_unsigned<T>, is_nbit<T, 32>>> { using type = unsigned long long; };
    template <typename T> struct safely_multipliable<T, constraints_t<std::is_unsigned<T>, is_nbit<T, 64>>> { using type = __uint128_t; };
    template <typename T> using safely_multipliable_t = typename safely_multipliable<T>::type;

    template <typename T, typename = void> struct rec_value_type { using type = T; };
    template <typename T> struct rec_value_type<T, std::void_t<typename T::value_type>> {
        using type = typename rec_value_type<typename T::value_type>::type;
    };
    template <typename T> using rec_value_type_t = typename rec_value_type<T>::type;

    template <typename T> class is_iterable {
        template <typename T_> static auto test(T_ e) -> decltype(e.begin(), e.end(), std::true_type{});
        static std::false_type test(...);
    public:
        static constexpr bool value = decltype(test(std::declval<T>()))::value;
    };
    template <typename T> static constexpr bool is_iterable_v = is_iterable<T>::value;
    template <typename T> class is_writable {
        template <typename T_> static auto test(T_ e) -> decltype(std::declval<std::ostream&>() << e, std::true_type{});
        static std::false_type test(...);
    public:
        static constexpr bool value = decltype(test(std::declval<T>()))::value;
    };
    template <typename T> static constexpr bool is_writable_v = is_writable<T>::value;
    template <typename T> class is_readable {
        template <typename T_> static auto test(T_ e) -> decltype(std::declval<std::istream&>() >> e, std::true_type{});
        static std::false_type test(...);
    public:
        static constexpr bool value = decltype(test(std::declval<T>()))::value;
    };
    template <typename T> static constexpr bool is_readable_v = is_readable<T>::value;
} // namespace suisen

#line 9 "library/util/coordinate_compressor.hpp"

namespace suisen {
template <typename T>
class CoordinateCompressorBuilder {
    public:
        struct Compressor {
            public:
                static constexpr int absent = -1;

                // default constructor
                Compressor() : _xs(std::vector<T>{}) {}
                // Construct from strictly sorted vector
                Compressor(const std::vector<T> &xs) : _xs(xs) {
                    assert(is_strictly_sorted(xs));
                }

                // Return the number of distinct keys.
                int size() const {
                    return _xs.size();
                }
                // Check if the element is registered.
                bool has_key(const T &e) const {
                    return std::binary_search(_xs.begin(), _xs.end(), e);
                }
                // Compress the element. if not registered, returns `default_value`. (default: Compressor::absent)
                int comp(const T &e, int default_value = absent) const {
                    const int res = min_geq_index(e);
                    return res != size() and _xs[res] == e ? res : default_value;
                }
                // Restore the element from the index.
                T decomp(const int compressed_index) const {
                    return _xs[compressed_index];
                }
                // Compress the element. Equivalent to call `comp(e)`
                int operator[](const T &e) const {
                    return comp(e);
                }
                // Return the minimum registered value greater than `e`. if not exists, return `default_value`.
                T min_gt(const T &e, const T &default_value) const {
                    auto it = std::upper_bound(_xs.begin(), _xs.end(), e);
                    return it == _xs.end() ? default_value : *it;
                }
                // Return the minimum registered value greater than or equal to `e`. if not exists, return `default_value`.
                T min_geq(const T &e, const T &default_value) const {
                    auto it = std::lower_bound(_xs.begin(), _xs.end(), e);
                    return it == _xs.end() ? default_value : *it;
                }
                // Return the maximum registered value less than `e`. if not exists, return `default_value`
                T max_lt(const T &e, const T &default_value) const {
                    auto it = std::upper_bound(_xs.rbegin(), _xs.rend(), e, std::greater<T>());
                    return it == _xs.rend() ? default_value : *it;
                }
                // Return the maximum registered value less than or equal to `e`. if not exists, return `default_value`
                T max_leq(const T &e, const T &default_value) const {
                    auto it = std::lower_bound(_xs.rbegin(), _xs.rend(), e, std::greater<T>());
                    return it == _xs.rend() ? default_value : *it;
                }
                // Return the compressed index of the minimum registered value greater than `e`. if not exists, return `compressor.size()`.
                int min_gt_index(const T &e) const {
                    return std::upper_bound(_xs.begin(), _xs.end(), e) - _xs.begin();
                }
                // Return the compressed index of the minimum registered value greater than or equal to `e`. if not exists, return `compressor.size()`.
                int min_geq_index(const T &e) const {
                    return std::lower_bound(_xs.begin(), _xs.end(), e) - _xs.begin();
                }
                // Return the compressed index of the maximum registered value less than `e`. if not exists, return -1.
                int max_lt_index(const T &e) const {
                    return int(_xs.rend() - std::upper_bound(_xs.rbegin(), _xs.rend(), e, std::greater<T>())) - 1;
                }
                // Return the compressed index of the maximum registered value less than or equal to `e`. if not exists, return -1.
                int max_leq_index(const T &e) const {
                    return int(_xs.rend() - std::lower_bound(_xs.rbegin(), _xs.rend(), e, std::greater<T>())) - 1;
                }
            private:
                std::vector<T> _xs;
                static bool is_strictly_sorted(const std::vector<T> &v) {
                    return std::adjacent_find(v.begin(), v.end(), std::greater_equal<T>()) == v.end();
                }
        };
        CoordinateCompressorBuilder() : _xs(std::vector<T>{}) {}
        explicit CoordinateCompressorBuilder(const std::vector<T> &xs) : _xs(xs) {}
        explicit CoordinateCompressorBuilder(std::vector<T> &&xs) : _xs(std::move(xs)) {}
        template <typename Gen, constraints_t<std::is_invocable_r<T, Gen, int>> = nullptr>
        CoordinateCompressorBuilder(const int n, Gen generator) {
            reserve(n);
            for (int i = 0; i < n; ++i) push(generator(i));
        }
        // Attempt to preallocate enough memory for specified number of elements.
        void reserve(int n) {
            _xs.reserve(n);
        }
        // Add data.
        void push(const T &first) {
            _xs.push_back(first);
        }
        // Add data.
        void push(T &&first) {
            _xs.push_back(std::move(first));
        }
        // Add data in the range of [first, last). 
        template <typename Iterator>
        auto push(const Iterator &first, const Iterator &last) -> decltype(std::vector<T>{}.push_back(*first), void()) {
            for (auto it = first; it != last; ++it) _xs.push_back(*it);
        }
        // Add all data in the container. Equivalent to `push(iterable.begin(), iterable.end())`.
        template <typename Iterable>
        auto push(const Iterable &iterable) -> decltype(std::vector<T>{}.push_back(*iterable.begin()), void()) {
            push(iterable.begin(), iterable.end());
        }
        // Add data.
        template <typename ...Args>
        void emplace(Args &&...args) {
            _xs.emplace_back(std::forward<Args>(args)...);
        }
        // Build compressor.
        auto build() {
            std::sort(_xs.begin(), _xs.end()), _xs.erase(std::unique(_xs.begin(), _xs.end()), _xs.end());
            return Compressor {_xs};
        }
        // Build compressor from vector.
        static auto build(const std::vector<T> &xs) {
            return CoordinateCompressorBuilder(xs).build();
        }
        // Build compressor from vector.
        static auto build(std::vector<T> &&xs) {
            return CoordinateCompressorBuilder(std::move(xs)).build();
        }
        // Build compressor from generator.
        template <typename Gen, constraints_t<std::is_invocable_r<T, Gen, int>> = nullptr>
        static auto build(const int n, Gen generator) {
            return CoordinateCompressorBuilder<T>(n, generator).build();
        }
    private:
        std::vector<T> _xs;
};

} // namespace suisen


#line 1 "library/datastructure/segment_tree/persistent_segment_tree.hpp"



#line 5 "library/datastructure/segment_tree/persistent_segment_tree.hpp"

#line 1 "library/util/object_pool.hpp"



#include <deque>
#line 6 "library/util/object_pool.hpp"

namespace suisen {
    template <typename T, bool auto_extend = false>
    struct ObjectPool {
        using value_type = T;
        using value_pointer_type = T*;

        template <typename U>
        using container_type = std::conditional_t<auto_extend, std::deque<U>, std::vector<U>>;

        container_type<value_type> pool;
        container_type<value_pointer_type> stock;
        decltype(stock.begin()) it;

        ObjectPool() : ObjectPool(0) {}
        ObjectPool(int siz) : pool(siz), stock(siz) {
            clear();
        }

        int capacity() const { return pool.size(); }
        int size() const { return it - stock.begin(); }

        value_pointer_type alloc() {
            if constexpr (auto_extend) ensure();
            return *it++;
        }

        void free(value_pointer_type t) {
            *--it = t;
        }

        void clear() {
            int siz = pool.size();
            it = stock.begin();
            for (int i = 0; i < siz; i++) stock[i] = &pool[i];
        }

        void ensure() {
            if (it != stock.end()) return;
            int siz = stock.size();
            for (int i = siz; i <= siz * 2; ++i) {
                stock.push_back(&pool.emplace_back());
            }
            it = stock.begin() + siz;
        }
    };
} // namespace suisen


#line 7 "library/datastructure/segment_tree/persistent_segment_tree.hpp"

namespace suisen {
    template <typename T, T(*op)(T, T), T(*e)()>
    struct PersistentSegmentTree {
        struct Node;

        using value_type = T;

        using node_type = Node;
        using node_pointer_type = node_type*;

        struct Node {
            static inline ObjectPool<node_type> _pool;

            node_pointer_type _ch[2]{ nullptr, nullptr };
            value_type _dat;

            Node() : _dat(e()) {}

            static node_pointer_type clone(node_pointer_type node) {
                return &(*_pool.alloc() = *node);
            }

            static void update(node_pointer_type node) {
                node->_dat = op(node->_ch[0]->_dat, node->_ch[1]->_dat);
            }

            static bool is_leaf(node_pointer_type node) {
                return not node->_ch[0];
            }

            static node_pointer_type build(const std::vector<value_type>& dat) {
                auto rec = [&](auto rec, int l, int r) -> node_pointer_type {
                    node_pointer_type res = _pool.alloc();
                    if (r - l == 1) {
                        res->_dat = dat[l];
                    } else {
                        int m = (l + r) >> 1;
                        res->_ch[0] = rec(rec, l, m), res->_ch[1] = rec(rec, m, r);
                        update(res);
                    }
                    return res;
                };
                return rec(rec, 0, dat.size());
            }

            static value_type prod_all(node_pointer_type node) {
                return node ? node->_dat : e();
            }
            static value_type prod(node_pointer_type node, int tl, int tr, int ql, int qr) {
                if (tr <= ql or qr <= tl) return e();
                if (ql <= tl and tr <= qr) return node->_dat;
                int tm = (tl + tr) >> 1;
                return op(prod(node->_ch[0], tl, tm, ql, qr), prod(node->_ch[1], tm, tr, ql, qr));
            }

            template <bool do_update, typename F>
            static auto search_node(node_pointer_type node, int siz, int i, F &&f) {
                static std::vector<node_pointer_type> path;

                node_pointer_type res = node;
                if constexpr (do_update) res = clone(res);
                node_pointer_type cur = res;

                for (int l = 0, r = siz; r - l > 1;) {
                    if constexpr (do_update) path.push_back(cur);
                    int m = (l + r) >> 1;
                    if (i < m) {
                        if constexpr (do_update) cur->_ch[0] = clone(cur->_ch[0]);
                        cur = cur->_ch[0];
                        r = m;
                    } else {
                        if constexpr (do_update) cur->_ch[1] = clone(cur->_ch[1]);
                        cur = cur->_ch[1];
                        l = m;
                    }
                }
                f(cur);

                if constexpr (do_update) {
                    while (path.size()) update(path.back()), path.pop_back();
                    return res;
                } else {
                    return;
                }
            }

            static value_type get(node_pointer_type node, int siz, int i) {
                value_type res;
                search_node</* do_update = */false>(node, siz, i, [&](node_pointer_type i_th_node) { res = i_th_node->_dat; });
                return res;
            }
            template <typename F>
            static node_pointer_type apply(node_pointer_type node, int siz, int i, F&& f) {
                return search_node</* do_update = */true>(node, siz, i, [&](node_pointer_type i_th_node) { i_th_node->_dat = f(i_th_node->_dat); });
            }
            static node_pointer_type set(node_pointer_type node, int siz, int i, const value_type& dat) {
                return apply(node, siz, i, [&](const value_type&) { return dat; });
            }

            template <typename F>
            static int max_right(node_pointer_type node, int siz, int l, F&& f) {
                assert(f(e()));
                auto rec = [&](auto rec, node_pointer_type cur, int tl, int tr, value_type& sum) -> int {
                    if (tr <= l) return tr;
                    if (l <= tl) {
                        value_type nxt_sum = op(sum, cur->_dat);
                        if (f(nxt_sum)) {
                            sum = std::move(nxt_sum);
                            return tr;
                        }
                        if (tr - tl == 1) return tl;
                    }
                    int tm = (tl + tr) >> 1;
                    int res_l = rec(rec, cur->_ch[0], tl, tm, sum);
                    return res_l != tm ? res_l : rec(rec, cur->_ch[1], tm, tr, sum);
                };
                value_type sum = e();
                return rec(rec, node, 0, siz, sum);
            }
            template <typename F>
            static int min_left(node_pointer_type node, int siz, int r, F&& f) {
                assert(f(e()));
                auto rec = [&](auto rec, node_pointer_type cur, int tl, int tr, value_type& sum) -> int {
                    if (r <= tl) return tl;
                    if (tr <= r) {
                        value_type nxt_sum = op(cur->_dat, sum);
                        if (f(nxt_sum)) {
                            sum = std::move(nxt_sum);
                            return tl;
                        }
                        if (tr - tl == 1) return tr;
                    }
                    int tm = (tl + tr) >> 1;
                    int res_r = rec(rec, cur->_ch[1], tm, tr, sum);
                    return res_r != tm ? res_r : rec(rec, cur->_ch[0], tl, tm, sum);
                };
                value_type sum = e();
                return rec(rec, node, 0, siz, sum);
            }

            template <typename OutputIterator>
            static void dump(node_pointer_type node, OutputIterator it) {
                if (not node) return;
                auto rec = [&](auto rec, node_pointer_type cur) -> void {
                    if (is_leaf(cur)) {
                        *it++ = cur->_dat;
                    } else {
                        rec(rec, cur->_ch[0]), rec(rec, cur->_ch[1]);
                    }
                };
                rec(rec, node);
            }
            static std::vector<value_type> dump(node_pointer_type node) {
                std::vector<value_type> res;
                dump(node, std::back_inserter(res));
                return res;
            }
        };

        PersistentSegmentTree() : _n(0), _root(nullptr) {}
        explicit PersistentSegmentTree(int n) : PersistentSegmentTree(std::vector<value_type>(n, e())) {}
        PersistentSegmentTree(const std::vector<value_type>& dat) : _n(dat.size()), _root(node_type::build(dat)) {}

        static void init_pool(int siz) {
            node_type::_pool = ObjectPool<node_type>(siz);
        }
        static void clear_pool() {
            node_type::_pool.clear();
        }

        value_type prod_all() {
            return node_type::prod_all(_root);
        }
        value_type prod(int l, int r) {
            assert(0 <= l and l <= r and r <= _n);
            return node_type::prod(_root, 0, _n, l, r);
        }
        value_type operator()(int l, int r) {
            return prod(l, r);
        }

        value_type get(int i) {
            assert(0 <= i and i < _n);
            return node_type::get(_root, _n, i);
        }
        value_type operator[](int i) {
            return get(i);
        }

        template <typename F>
        PersistentSegmentTree apply(int i, F&& f) {
            assert(0 <= i and i < _n);
            return PersistentSegmentTree(_n, node_type::apply(_root, _n, i, std::forward<F>(f)));
        }
        PersistentSegmentTree set(int i, const value_type& v) {
            assert(0 <= i and i < _n);
            return PersistentSegmentTree(_n, node_type::set(_root, _n, i, v));
        }

        template <typename F>
        int max_right(int l, F&& f) {
            assert(0 <= l and l <= _n);
            return node_type::max_right(_root, _n, l, std::forward<F>(f));
        }
        template <bool(*pred)(value_type)>
        static int max_right(int l) {
            return max_right(l, pred);
        }
        template <typename F>
        int min_left(int r, F&& f) {
            assert(0 <= r and r <= _n);
            return node_type::min_left(_root, _n, r, std::forward<F>(f));
        }
        template <bool(*pred)(value_type)>
        static int min_left(int r) {
            return min_left(r, pred);
        }

        template <typename OutputIterator>
        void dump(OutputIterator it) {
            node_type::dump(_root, it);
        }
        std::vector<value_type> dump() {
            return node_type::dump(_root);
        }

    private:
        int _n;
        node_pointer_type _root;
        PersistentSegmentTree(int n, node_pointer_type root) : _n(n), _root(root) {}
    };
}


#line 8 "test/src/datastructure/segment_tree/persistent_segment_tree/rectangle_sum.test.cpp"

long long op(long long x, long long y) {
    return x + y;
}
long long e() {
    return 0;
}

using suisen::CoordinateCompressorBuilder;
using suisen::PersistentSegmentTree;

using Tree = PersistentSegmentTree<long long, op, e>;

int main() {
    std::ios::sync_with_stdio(false);
    std::cin.tie(nullptr);

    int n, q;
    std::cin >> n >> q;

    std::vector<std::tuple<int, int, int>> points(n);
    CoordinateCompressorBuilder<int> bx, by;

    for (auto &[x, y, w] : points) {
        std::cin >> x >> y >> w;
        bx.push(x);
        by.push(y);
    }
    auto cmp_x = bx.build(), cmp_y = by.build();

    const int h = cmp_x.size(), w = cmp_y.size();

    std::vector<std::vector<std::pair<int, int>>> buckets(h);
    for (auto &[x, y, w] : points) {
        x = cmp_x[x];
        y = cmp_y[y];
        buckets[x].emplace_back(y, w);
    }

    Tree::init_pool(5000000);

    std::vector<Tree> fts(h + 1);
    fts[0] = Tree(w);

    for (int x = 0; x < h; ++x) {
        fts[x + 1] = fts[x];
        for (const auto yw : buckets[x]) {
            const int y = yw.first, w = yw.second;
            fts[x + 1] = fts[x + 1].apply(y, [w](long long e) { return e + w; });
        }
    }

    for (int query_id = 0; query_id < q; ++query_id) {
        int l, r, d, u;
        std::cin >> l >> d >> r >> u;

        l = cmp_x.min_geq_index(l);
        r = cmp_x.min_geq_index(r);
        d = cmp_y.min_geq_index(d);
        u = cmp_y.min_geq_index(u);

        std::cout << fts[r].prod(d, u) - fts[l].prod(d, u) << '\n';
    }

    return 0;
}

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