data_structure/test/rectangle_sum.test.cpp

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Last update: 2022-08-25 19:52:54+09:00
Problem: https://judge.yosupo.jp/problem/rectangle_sum

Depends on

Code

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

#include "../../template/template.hpp"
#include "../../data_structure/range_tree.hpp"
#include "../../data_structure/operations.hpp"

int main() {
    i32 n, q;
    cin >> n >> q;
    Vec<tuple<i32, i32, i64>> pts(n);
    for (auto &[x, y, w] : pts) {
        cin >> x >> y >> w;
    }
    RangeTree<i32, Add<i64>> range_tree(pts);
    REP(qi, q) {
        i32 l, d, r, u;
        cin >> l >> d >> r >> u;
        cout << range_tree.sum(l, r, d, u) << '\n';
    }
}

#line 1 "data_structure/test/rectangle_sum.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/rectangle_sum"

#line 1 "template/template.hpp"
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cmath>
#include <iomanip>
#include <iostream>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <tuple>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

#define OVERRIDE(a, b, c, d, ...) d
#define REP2(i, n) for (i32 i = 0; i < (i32) (n); ++i)
#define REP3(i, m, n) for (i32 i = (i32) (m); i < (i32) (n); ++i)
#define REP(...) OVERRIDE(__VA_ARGS__, REP3, REP2)(__VA_ARGS__)
#define PER(i, n) for (i32 i = (i32) (n) - 1; i >= 0; --i)
#define ALL(x) begin(x), end(x)

using namespace std;

using u32 = unsigned int;
using u64 = unsigned long long;
using u128 = __uint128_t;
using i32 = signed int;
using i64 = signed long long;
using i128 = __int128_t;
using f64 = double;
using f80 = long double;

template <typename T>
using Vec = vector<T>;

template <typename T>
bool chmin(T &x, const T &y) {
    if (x > y) {
        x = y;
        return true;
    }
    return false;
}
template <typename T>
bool chmax(T &x, const T &y) {
    if (x < y) {
        x = y;
        return true;
    }
    return false;
}

istream &operator>>(istream &is, i128 &x) {
    i64 v;
    is >> v;
    x = v;
    return is;
}
ostream &operator<<(ostream &os, i128 x) {
    os << (i64) x;
    return os;
}
istream &operator>>(istream &is, u128 &x) {
    u64 v;
    is >> v;
    x = v;
    return is;
}
ostream &operator<<(ostream &os, u128 x) {
    os << (u64) x;
    return os;
}

[[maybe_unused]] constexpr i32 INF = 1000000100;
[[maybe_unused]] constexpr i64 INF64 = 3000000000000000100;
struct SetUpIO {
    SetUpIO() {
#ifdef FAST_IO
        ios::sync_with_stdio(false);
        cin.tie(nullptr);
#endif
        cout << fixed << setprecision(15);
    }
} set_up_io;
#line 2 "data_structure/range_tree.hpp"

#line 5 "data_structure/range_tree.hpp"

template <typename Coordinate, typename CommutativeGroup>
class RangeTree {
public:
    using Value = typename CommutativeGroup::Value;
    
private:
    struct Node {
        std::vector<Coordinate> ys;
        std::vector<Value> cum;
        
        Value sum(Coordinate yl, Coordinate yr) const {
            int yli = (int) (std::lower_bound(ys.begin(), ys.end(), yl) - ys.begin());
            int yri = (int) (std::lower_bound(ys.begin(), ys.end(), yr) - ys.begin());
            return CommutativeGroup::op(CommutativeGroup::inv(cum[yli]), cum[yri]);
        }
    };
    
    static void dedup(std::vector<Coordinate> &xs) {
        std::sort(xs.begin(), xs.end());
        xs.erase(std::unique(xs.begin(), xs.end()), xs.end());
    }
    static int index(const std::vector<Coordinate> &xs, int x) {
        return (int) (std::lower_bound(xs.begin(), xs.end(), x) - xs.begin());
    }
    
    std::vector<Node> nodes;
    std::vector<Coordinate> xs;
    
public:
    RangeTree(const std::vector<std::tuple<Coordinate, Coordinate, Value>> &pts) : nodes(), xs() {
        xs.reserve(pts.size());
        for (const auto &[x, _y, _w] : pts) {
            xs.push_back(x);
        }
        dedup(xs);
        nodes.resize(xs.size());
        for (const auto &[x, y, _w] : pts) {
            int xi = index(xs, x);
            for (; xi < (int) xs.size(); xi |= xi + 1) {
                nodes[xi].ys.push_back(y);
            }
        }
        for (Node &node : nodes) {
            dedup(node.ys);
            node.cum.resize(node.ys.size() + 1, CommutativeGroup::id());
        }
        for (const auto &[x, y, w] : pts) {
            int xi = index(xs, x);
            for (; xi < (int) xs.size(); xi |= xi + 1) {
                int yi = index(nodes[xi].ys, y);
                nodes[xi].cum[yi + 1] = CommutativeGroup::op(nodes[xi].cum[yi + 1], w);
            }
        }
        for (Node &node : nodes) {
            for (int i = 1; i < (int) node.cum.size(); ++i) {
                node.cum[i] = CommutativeGroup::op(node.cum[i - 1], node.cum[i]);
            }
        }
    }
    
    Value sum(Coordinate xr, Coordinate yl, Coordinate yr) const {
        int xri = index(xs, xr);
        Value s = CommutativeGroup::id();
        for (; xri > 0; xri &= xri - 1) {
            s = CommutativeGroup::op(s, nodes[xri - 1].sum(yl, yr));
        }
        return s;
    }
    
    Value sum(Coordinate xl, Coordinate xr, Coordinate yl, Coordinate yr) const {
        Value l = sum(xl, yl, yr), r = sum(xr, yl, yr);
        return CommutativeGroup::op(r, CommutativeGroup::inv(l));
    }
};
#line 2 "data_structure/operations.hpp"

#include <limits>
#line 5 "data_structure/operations.hpp"

template <typename T>
struct Add {
    using Value = T;
    static Value id() {
        return T(0);
    }
    static Value op(const Value &lhs, const Value &rhs) {
        return lhs + rhs;
    }
    static Value inv(const Value &x) {
        return -x;
    }
};

template <typename T>
struct Mul {
    using Value = T;
    static Value id() {
        return Value(1);
    }
    static Value op(const Value &lhs, const Value &rhs) {
        return lhs * rhs;
    }
    static Value inv(const Value &x) {
        return Value(1) / x;
    }
};

template <typename T>
struct Min {
    using Value = T;
    static Value id() {
        return std::numeric_limits<T>::max();
    }
    static Value op(const Value &lhs, const Value &rhs) {
        return std::min(lhs, rhs);
    }
};

template <typename T>
struct Max {
    using Value = T;
    static Value id() {
        return std::numeric_limits<Value>::min();
    }
    static Value op(const Value &lhs, const Value &rhs) {
        return std::max(lhs, rhs);
    }
};

template <typename T>
struct Xor {
    using Value = T;
    static Value id() {
        return T(0);
    }
    static Value op(const Value &lhs, const Value &rhs) {
        return lhs ^ rhs;
    }
    static Value inv(const Value &x) {
        return x;
    }
};

template <typename Monoid>
struct Reversible {
    using Value = std::pair<typename Monoid::Value, typename Monoid::Value>;
    static Value id() {
        return Value(Monoid::id(), Monoid::id());
    }
    static Value op(const Value &v1, const Value &v2) {
        return Value(
            Monoid::op(v1.first, v2.first),
            Monoid::op(v2.second, v1.second));
    }
};

#line 6 "data_structure/test/rectangle_sum.test.cpp"

int main() {
    i32 n, q;
    cin >> n >> q;
    Vec<tuple<i32, i32, i64>> pts(n);
    for (auto &[x, y, w] : pts) {
        cin >> x >> y >> w;
    }
    RangeTree<i32, Add<i64>> range_tree(pts);
    REP(qi, q) {
        i32 l, d, r, u;
        cin >> l >> d >> r >> u;
        cout << range_tree.sum(l, r, d, u) << '\n';
    }
}