rectangle_sum.hpp¶
#include "noya/rectangle_sum.hpp"
#ifndef NOYA_RECTANGLE_SUM_HPP
#define NOYA_RECTANGLE_SUM_HPP 1
#include "noya/point_add_range_sum.hpp"
#include <algorithm>
#include <array>
namespace noya {
/// @brief Offline rectangle sum. Points (x, y, weight), queries [l, r) x [d, u).
template <class T, class C = noya::fenwick<T>>
std::vector<T> rectangle_sum(std::vector<std::array<int, 3>> points,
std::vector<std::array<int, 4>> queries) {
std::vector<int> Xs;
std::vector<int> Ys;
for (auto &[x, y, z] : points) {
Xs.push_back(x);
Ys.push_back(y);
}
for (auto &[l, r, d, u] : queries) {
Xs.push_back(l);
Xs.push_back(r);
Ys.push_back(d);
Ys.push_back(u);
}
std::sort(Xs.begin(), Xs.end());
Xs.erase(std::unique(Xs.begin(), Xs.end()), Xs.end());
std::sort(Ys.begin(), Ys.end());
Ys.erase(std::unique(Ys.begin(), Ys.end()), Ys.end());
for (auto &[x, y, z] : points) {
x = std::lower_bound(Xs.begin(), Xs.end(), x) - Xs.begin();
y = std::lower_bound(Ys.begin(), Ys.end(), y) - Ys.begin();
}
for (auto &[l, r, d, u] : queries) {
l = std::lower_bound(Xs.begin(), Xs.end(), l) - Xs.begin();
r = std::lower_bound(Xs.begin(), Xs.end(), r) - Xs.begin();
d = std::lower_bound(Ys.begin(), Ys.end(), d) - Ys.begin();
u = std::lower_bound(Ys.begin(), Ys.end(), u) - Ys.begin();
}
int X = int(Xs.size());
int Y = int(Ys.size());
C F(Y);
std::vector<std::vector<std::array<int, 3>>> Q(X + 1);
for (int i = 0; i < int(queries.size()); i++) {
auto &[l, r, d, u] = queries[i];
Q[r].push_back({i, d, u});
Q[l].push_back({~i, d, u});
}
std::vector<std::vector<std::array<int, 2>>> A(X + 1);
for (auto &[x, y, z] : points) {
A[x].push_back({y, z});
}
std::vector<T> ans(queries.size());
for (int x = 0; x < X; x++) {
for (auto &[y, z] : A[x]) {
F.add(y, z);
}
for (auto &[i, d, u] : Q[x + 1]) {
if (i >= 0)
ans[i] += F.prod(d, u);
else
ans[~i] -= F.prod(d, u);
}
}
return ans;
}
} // namespace noya
#endif // NOYA_RECTANGLE_SUM_HPP
#include <algorithm>
#include <array>
#include <cassert>
#include <cmath>
#include <numeric>
#include <type_traits>
#include <vector>
namespace atcoder {
namespace internal {
#ifndef _MSC_VER
template <class T>
using is_signed_int128 =
typename std::conditional<std::is_same<T, __int128_t>::value ||
std::is_same<T, __int128>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int128 =
typename std::conditional<std::is_same<T, __uint128_t>::value ||
std::is_same<T, unsigned __int128>::value,
std::true_type,
std::false_type>::type;
template <class T>
using make_unsigned_int128 =
typename std::conditional<std::is_same<T, __int128_t>::value,
__uint128_t,
unsigned __int128>;
template <class T>
using is_integral = typename std::conditional<std::is_integral<T>::value ||
is_signed_int128<T>::value ||
is_unsigned_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_signed_int = typename std::conditional<(is_integral<T>::value &&
std::is_signed<T>::value) ||
is_signed_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int =
typename std::conditional<(is_integral<T>::value &&
std::is_unsigned<T>::value) ||
is_unsigned_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using to_unsigned = typename std::conditional<
is_signed_int128<T>::value,
make_unsigned_int128<T>,
typename std::conditional<std::is_signed<T>::value,
std::make_unsigned<T>,
std::common_type<T>>::type>::type;
#else
template <class T> using is_integral = typename std::is_integral<T>;
template <class T>
using is_signed_int =
typename std::conditional<is_integral<T>::value && std::is_signed<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int =
typename std::conditional<is_integral<T>::value &&
std::is_unsigned<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using to_unsigned = typename std::conditional<is_signed_int<T>::value,
std::make_unsigned<T>,
std::common_type<T>>::type;
#endif
template <class T>
using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;
template <class T>
using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;
template <class T> using to_unsigned_t = typename to_unsigned<T>::type;
} // namespace internal
} // namespace atcoder
namespace atcoder {
// Reference: https://en.wikipedia.org/wiki/Fenwick_tree
template <class T> struct fenwick_tree {
using U = internal::to_unsigned_t<T>;
public:
fenwick_tree() : _n(0) {}
explicit fenwick_tree(int n) : _n(n), data(n) {}
void add(int p, T x) {
assert(0 <= p && p < _n);
p++;
while (p <= _n) {
data[p - 1] += U(x);
p += p & -p;
}
}
T sum(int l, int r) {
assert(0 <= l && l <= r && r <= _n);
return sum(r) - sum(l);
}
private:
int _n;
std::vector<U> data;
U sum(int r) {
U s = 0;
while (r > 0) {
s += data[r - 1];
r -= r & -r;
}
return s;
}
};
} // namespace atcoder
namespace noya {
template <class T> struct block {
int V, sqrtV;
block() {}
block(const int &_V) {
if (_V > 0) {
build(_V);
}
}
std::vector<T> point, blo;
void build(const int &_V) {
V = _V;
sqrtV = sqrt(V);
point.assign(V, 0);
blo.assign(V / sqrtV + 1, 0);
}
void add(int x, T v) {
assert(0 <= x && x < V);
int bel = x / sqrtV;
blo[bel] += v;
point[x] += v;
}
T query(int x) const {
assert(0 <= x && x <= V);
T res = 0;
int bel = x / sqrtV;
for (int i = 0; i < bel; i++)
res += blo[i];
int start = bel * sqrtV;
int end = x;
for (int i = start; i < end; i++)
res += point[i];
return res;
}
/// @brief Sum of [l, r).
T prod(int l, int r) const {
assert(0 <= l && l <= r && r <= V);
return query(r) - query(l);
}
};
template <class T> struct fenwick : atcoder::fenwick_tree<T> {
using atcoder::fenwick_tree<T>::fenwick_tree;
using atcoder::fenwick_tree<T>::add;
T query(int x) { return this->sum(0, x); }
T prod(int l, int r) { return this->sum(l, r); }
};
} // namespace noya
namespace noya {
/// @brief Offline rectangle sum. Points (x, y, weight), queries [l, r) x [d, u).
template <class T, class C = noya::fenwick<T>>
std::vector<T> rectangle_sum(std::vector<std::array<int, 3>> points,
std::vector<std::array<int, 4>> queries) {
std::vector<int> Xs;
std::vector<int> Ys;
for (auto &[x, y, z] : points) {
Xs.push_back(x);
Ys.push_back(y);
}
for (auto &[l, r, d, u] : queries) {
Xs.push_back(l);
Xs.push_back(r);
Ys.push_back(d);
Ys.push_back(u);
}
std::sort(Xs.begin(), Xs.end());
Xs.erase(std::unique(Xs.begin(), Xs.end()), Xs.end());
std::sort(Ys.begin(), Ys.end());
Ys.erase(std::unique(Ys.begin(), Ys.end()), Ys.end());
for (auto &[x, y, z] : points) {
x = std::lower_bound(Xs.begin(), Xs.end(), x) - Xs.begin();
y = std::lower_bound(Ys.begin(), Ys.end(), y) - Ys.begin();
}
for (auto &[l, r, d, u] : queries) {
l = std::lower_bound(Xs.begin(), Xs.end(), l) - Xs.begin();
r = std::lower_bound(Xs.begin(), Xs.end(), r) - Xs.begin();
d = std::lower_bound(Ys.begin(), Ys.end(), d) - Ys.begin();
u = std::lower_bound(Ys.begin(), Ys.end(), u) - Ys.begin();
}
int X = int(Xs.size());
int Y = int(Ys.size());
C F(Y);
std::vector<std::vector<std::array<int, 3>>> Q(X + 1);
for (int i = 0; i < int(queries.size()); i++) {
auto &[l, r, d, u] = queries[i];
Q[r].push_back({i, d, u});
Q[l].push_back({~i, d, u});
}
std::vector<std::vector<std::array<int, 2>>> A(X + 1);
for (auto &[x, y, z] : points) {
A[x].push_back({y, z});
}
std::vector<T> ans(queries.size());
for (int x = 0; x < X; x++) {
for (auto &[y, z] : A[x]) {
F.add(y, z);
}
for (auto &[i, d, u] : Q[x + 1]) {
if (i >= 0)
ans[i] += F.prod(d, u);
else
ans[~i] -= F.prod(d, u);
}
}
return ans;
}
} // namespace noya