cplib-cpp
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data_structure/rectangle_sum.hpp
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- Last update: 2022-01-08 20:23:44+09:00
- Include:
#include "data_structure/rectangle_sum.hpp" - Link: https://judge.yosupo.jp/submission/40312
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#pragma once
#include "../segmenttree/binary_indexed_tree.hpp"
#include <algorithm>
#include <tuple>
#include <vector>
// CUT begin
// Rectangle Sum: calculate sum of weights inside rectangles
// Sample: https://judge.yosupo.jp/submission/40312 (2e5 points, 2e5 rectangles, 566 ms)
// `add_point(x, y, weight)`: Add point at (x, y)
// `add_query(L, R, D, U)`: Add query rectangle [L, R) x [D, U)
template <typename Int, typename Weight> struct RectangleSum {
RectangleSum() = default;
struct Rectangle {
Int L, R, D, U;
};
std::vector<Rectangle> queries;
std::vector<std::tuple<Int, Int, Weight>> points;
void add_point(Int x, Int y, Weight weight) noexcept {
points.push_back({x + 1, y + 1, weight});
}
void add_query(Int L, Int R, Int D, Int U) noexcept { queries.push_back({L, R, D, U}); }
std::vector<Weight> solve() const {
std::vector<Int> xs, ys;
for (auto rect : queries) {
xs.push_back(rect.L);
xs.push_back(rect.R);
ys.push_back(rect.D);
ys.push_back(rect.U);
}
std::sort(xs.begin(), xs.end());
std::sort(ys.begin(), ys.end());
xs.erase(std::unique(xs.begin(), xs.end()), xs.end());
ys.erase(std::unique(ys.begin(), ys.end()), ys.end());
std::vector<std::vector<std::tuple<int, int, Weight>>> ops(ys.size()); // q, x, weight
for (auto p : points) {
int i = std::lower_bound(xs.begin(), xs.end(), std::get<0>(p)) - xs.begin();
int j = std::lower_bound(ys.begin(), ys.end(), std::get<1>(p)) - ys.begin();
if (j < int(ops.size())) ops[j].push_back({-1, i, std::get<2>(p)});
}
for (int q = 0; q < int(queries.size()); q++) {
int il = std::lower_bound(xs.begin(), xs.end(), queries[q].L) - xs.begin();
int ir = std::lower_bound(xs.begin(), xs.end(), queries[q].R) - xs.begin();
int jd = std::lower_bound(ys.begin(), ys.end(), queries[q].D) - ys.begin();
int ju = std::lower_bound(ys.begin(), ys.end(), queries[q].U) - ys.begin();
ops[jd].push_back({q, il, 1});
ops[jd].push_back({q, ir, -1});
ops[ju].push_back({q, il, -1});
ops[ju].push_back({q, ir, 1});
}
std::vector<Weight> ret(queries.size());
BIT<Weight> bit(xs.size());
for (auto &&op : ops) {
for (auto p : op) {
const auto q = std::get<0>(p), x = std::get<1>(p);
const auto w = std::get<2>(p);
if (q == -1) {
bit.add(x, w);
} else {
ret[q] += bit.sum(x + 1) * w;
}
}
}
return ret;
}
};#line 2 "segmenttree/binary_indexed_tree.hpp"
#include <algorithm>
#include <vector>
// CUT begin
// 0-indexed BIT (binary indexed tree / Fenwick tree) (i : [0, len))
template <class T> struct BIT {
int n;
std::vector<T> data;
BIT(int len = 0) : n(len), data(len) {}
void reset() { std::fill(data.begin(), data.end(), T(0)); }
void add(int pos, T v) { // a[pos] += v
pos++;
while (pos > 0 and pos <= n) data[pos - 1] += v, pos += pos & -pos;
}
T sum(int k) const { // a[0] + ... + a[k - 1]
T res = 0;
while (k > 0) res += data[k - 1], k -= k & -k;
return res;
}
T sum(int l, int r) const { return sum(r) - sum(l); } // a[l] + ... + a[r - 1]
template <class OStream> friend OStream &operator<<(OStream &os, const BIT &bit) {
T prv = 0;
os << '[';
for (int i = 1; i <= bit.n; i++) {
T now = bit.sum(i);
os << now - prv << ',', prv = now;
}
return os << ']';
}
};
#line 4 "data_structure/rectangle_sum.hpp"
#include <tuple>
#line 6 "data_structure/rectangle_sum.hpp"
// CUT begin
// Rectangle Sum: calculate sum of weights inside rectangles
// Sample: https://judge.yosupo.jp/submission/40312 (2e5 points, 2e5 rectangles, 566 ms)
// `add_point(x, y, weight)`: Add point at (x, y)
// `add_query(L, R, D, U)`: Add query rectangle [L, R) x [D, U)
template <typename Int, typename Weight> struct RectangleSum {
RectangleSum() = default;
struct Rectangle {
Int L, R, D, U;
};
std::vector<Rectangle> queries;
std::vector<std::tuple<Int, Int, Weight>> points;
void add_point(Int x, Int y, Weight weight) noexcept {
points.push_back({x + 1, y + 1, weight});
}
void add_query(Int L, Int R, Int D, Int U) noexcept { queries.push_back({L, R, D, U}); }
std::vector<Weight> solve() const {
std::vector<Int> xs, ys;
for (auto rect : queries) {
xs.push_back(rect.L);
xs.push_back(rect.R);
ys.push_back(rect.D);
ys.push_back(rect.U);
}
std::sort(xs.begin(), xs.end());
std::sort(ys.begin(), ys.end());
xs.erase(std::unique(xs.begin(), xs.end()), xs.end());
ys.erase(std::unique(ys.begin(), ys.end()), ys.end());
std::vector<std::vector<std::tuple<int, int, Weight>>> ops(ys.size()); // q, x, weight
for (auto p : points) {
int i = std::lower_bound(xs.begin(), xs.end(), std::get<0>(p)) - xs.begin();
int j = std::lower_bound(ys.begin(), ys.end(), std::get<1>(p)) - ys.begin();
if (j < int(ops.size())) ops[j].push_back({-1, i, std::get<2>(p)});
}
for (int q = 0; q < int(queries.size()); q++) {
int il = std::lower_bound(xs.begin(), xs.end(), queries[q].L) - xs.begin();
int ir = std::lower_bound(xs.begin(), xs.end(), queries[q].R) - xs.begin();
int jd = std::lower_bound(ys.begin(), ys.end(), queries[q].D) - ys.begin();
int ju = std::lower_bound(ys.begin(), ys.end(), queries[q].U) - ys.begin();
ops[jd].push_back({q, il, 1});
ops[jd].push_back({q, ir, -1});
ops[ju].push_back({q, il, -1});
ops[ju].push_back({q, ir, 1});
}
std::vector<Weight> ret(queries.size());
BIT<Weight> bit(xs.size());
for (auto &&op : ops) {
for (auto p : op) {
const auto q = std::get<0>(p), x = std::get<1>(p);
const auto w = std::get<2>(p);
if (q == -1) {
bit.add(x, w);
} else {
ret[q] += bit.sum(x + 1) * w;
}
}
}
return ret;
}
};