#line 1 "test/yosupo-judge/rectangle_sum/main.segment_tree.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/rectangle_sum"
#include <iostream>
#include <vector>
#line 2 "Mylib/AlgebraicStructure/Monoid/sum.cpp"
namespace haar_lib {
template <typename T>
struct sum_monoid {
using value_type = T;
value_type operator()() const { return 0; }
value_type operator()(value_type a, value_type b) const { return a + b; }
};
} // namespace haar_lib
#line 2 "Mylib/DataStructure/SegmentTree/segment_tree.cpp"
#include <algorithm>
#include <cassert>
#include <functional>
#line 6 "Mylib/DataStructure/SegmentTree/segment_tree.cpp"
namespace haar_lib {
template <typename Monoid>
class segment_tree {
public:
using value_type = typename Monoid::value_type;
private:
Monoid M_;
int depth_, size_, hsize_;
std::vector<value_type> data_;
public:
segment_tree() {}
segment_tree(int n) : depth_(n > 1 ? 32 - __builtin_clz(n - 1) + 1 : 1),
size_(1 << depth_),
hsize_(size_ / 2),
data_(size_, M_()) {}
auto operator[](int i) const {
assert(0 <= i and i < hsize_);
return data_[hsize_ + i];
}
auto fold(int l, int r) const {
assert(0 <= l and l <= r and r <= hsize_);
value_type ret_left = M_();
value_type ret_right = M_();
int L = l + hsize_, R = r + hsize_;
while (L < R) {
if (R & 1) ret_right = M_(data_[--R], ret_right);
if (L & 1) ret_left = M_(ret_left, data_[L++]);
L >>= 1, R >>= 1;
}
return M_(ret_left, ret_right);
}
auto fold_all() const {
return data_[1];
}
void set(int i, const value_type &x) {
assert(0 <= i and i < hsize_);
i += hsize_;
data_[i] = x;
while (i > 1) i >>= 1, data_[i] = M_(data_[i << 1 | 0], data_[i << 1 | 1]);
}
void update(int i, const value_type &x) {
assert(0 <= i and i < hsize_);
i += hsize_;
data_[i] = M_(data_[i], x);
while (i > 1) i >>= 1, data_[i] = M_(data_[i << 1 | 0], data_[i << 1 | 1]);
}
template <typename T>
void init_with_vector(const std::vector<T> &val) {
data_.assign(size_, M_());
for (int i = 0; i < (int) val.size(); ++i) data_[hsize_ + i] = val[i];
for (int i = hsize_; --i >= 1;) data_[i] = M_(data_[i << 1 | 0], data_[i << 1 | 1]);
}
template <typename T>
void init(const T &val) {
init_with_vector(std::vector<value_type>(hsize_, val));
}
private:
template <bool Lower, typename F>
int bound(const int l, const int r, value_type x, F f) const {
std::vector<int> pl, pr;
int L = l + hsize_;
int R = r + hsize_;
while (L < R) {
if (R & 1) pr.push_back(--R);
if (L & 1) pl.push_back(L++);
L >>= 1, R >>= 1;
}
std::reverse(pr.begin(), pr.end());
pl.insert(pl.end(), pr.begin(), pr.end());
value_type a = M_();
for (int i : pl) {
auto b = M_(a, data_[i]);
if ((Lower and not f(b, x)) or (not Lower and f(x, b))) {
while (i < hsize_) {
const auto c = M_(a, data_[i << 1 | 0]);
if ((Lower and not f(c, x)) or (not Lower and f(x, c))) {
i = i << 1 | 0;
} else {
a = c;
i = i << 1 | 1;
}
}
return i - hsize_;
}
a = b;
}
return r;
}
public:
template <typename F = std::less<value_type>>
int lower_bound(int l, int r, value_type x, F f = F()) const {
return bound<true>(l, r, x, f);
}
template <typename F = std::less<value_type>>
int upper_bound(int l, int r, value_type x, F f = F()) const {
return bound<false>(l, r, x, f);
}
};
} // namespace haar_lib
#line 5 "Mylib/DataStructure/SegmentTree/segment_tree_on_segment_tree.cpp"
namespace haar_lib {
template <typename Monoid>
class segment_tree_on_segment_tree {
public:
using value_type = typename Monoid::value_type;
private:
Monoid M_;
int N_ = 0;
std::vector<int64_t> xs_, ys_;
std::vector<int> c_xs_;
std::vector<std::vector<int>> c_ys_;
int x_size_;
std::vector<segment_tree<Monoid>> segs_;
public:
segment_tree_on_segment_tree() {}
void add(int64_t x, int64_t y) {
xs_.push_back(x);
ys_.push_back(y);
++N_;
}
void build() {
c_xs_.insert(c_xs_.end(), xs_.begin(), xs_.end());
std::sort(c_xs_.begin(), c_xs_.end());
c_xs_.erase(std::unique(c_xs_.begin(), c_xs_.end()), c_xs_.end());
x_size_ = 1;
while (x_size_ < (int) c_xs_.size()) x_size_ *= 2;
x_size_ *= 2;
c_ys_.resize(x_size_);
segs_.resize(x_size_);
for (int i = 0; i < N_; ++i) {
int j = std::lower_bound(c_xs_.begin(), c_xs_.end(), xs_[i]) - c_xs_.begin();
c_ys_[j + x_size_ / 2].push_back(ys_[i]);
}
for (int i = 0; i < x_size_ / 2; ++i) {
auto &v = c_ys_[i + x_size_ / 2];
std::sort(v.begin(), v.end());
v.erase(std::unique(v.begin(), v.end()), v.end());
}
for (int i = x_size_ / 2 - 1; i >= 1; --i) {
const auto &a = c_ys_[i << 1 | 0];
const auto &b = c_ys_[i << 1 | 1];
auto &c = c_ys_[i];
c.resize(a.size() + b.size());
std::merge(a.begin(), a.end(), b.begin(), b.end(), c.begin());
c.erase(std::unique(c.begin(), c.end()), c.end());
}
for (int i = 1; i < x_size_; ++i) {
segs_[i] = segment_tree<Monoid>(c_ys_[i].size());
}
}
void update(std::pair<int64_t, int64_t> p, const value_type &val) {
const auto [x, y] = p;
int i = std::lower_bound(c_xs_.begin(), c_xs_.end(), x) - c_xs_.begin() + x_size_ / 2;
while (i >= 1) {
int j = std::lower_bound(c_ys_[i].begin(), c_ys_[i].end(), y) - c_ys_[i].begin();
segs_[i].update(j, val);
i >>= 1;
}
}
private:
value_type get_sub(int i, int64_t y1, int64_t y2) const {
int l = std::lower_bound(c_ys_[i].begin(), c_ys_[i].end(), y1) - c_ys_[i].begin();
int r = std::lower_bound(c_ys_[i].begin(), c_ys_[i].end(), y2) - c_ys_[i].begin();
return segs_[i].fold(l, r);
}
public:
value_type fold(std::pair<int64_t, int64_t> p1, std::pair<int64_t, int64_t> p2) const {
const auto [x1, y1] = p1;
const auto [x2, y2] = p2;
int l = std::lower_bound(c_xs_.begin(), c_xs_.end(), x1) - c_xs_.begin() + x_size_ / 2;
int r = std::lower_bound(c_xs_.begin(), c_xs_.end(), x2) - c_xs_.begin() + x_size_ / 2;
value_type ret = M_();
while (l < r) {
if (r & 1) ret = M_(ret, get_sub(--r, y1, y2));
if (l & 1) ret = M_(ret, get_sub(l++, y1, y2));
l >>= 1;
r >>= 1;
}
return ret;
}
};
} // namespace haar_lib
#line 2 "Mylib/IO/input_tuple_vector.cpp"
#include <initializer_list>
#line 4 "Mylib/IO/input_tuple_vector.cpp"
#include <tuple>
#include <utility>
#line 7 "Mylib/IO/input_tuple_vector.cpp"
namespace haar_lib {
template <typename T, size_t... I>
void input_tuple_vector_init(T &val, int N, std::index_sequence<I...>) {
(void) std::initializer_list<int>{(void(std::get<I>(val).resize(N)), 0)...};
}
template <typename T, size_t... I>
void input_tuple_vector_helper(T &val, int i, std::index_sequence<I...>) {
(void) std::initializer_list<int>{(void(std::cin >> std::get<I>(val)[i]), 0)...};
}
template <typename... Args>
auto input_tuple_vector(int N) {
std::tuple<std::vector<Args>...> ret;
input_tuple_vector_init(ret, N, std::make_index_sequence<sizeof...(Args)>());
for (int i = 0; i < N; ++i) {
input_tuple_vector_helper(ret, i, std::make_index_sequence<sizeof...(Args)>());
}
return ret;
}
} // namespace haar_lib
#line 6 "Mylib/IO/input_tuple.cpp"
namespace haar_lib {
template <typename T, size_t... I>
static void input_tuple_helper(std::istream &s, T &val, std::index_sequence<I...>) {
(void) std::initializer_list<int>{(void(s >> std::get<I>(val)), 0)...};
}
template <typename T, typename U>
std::istream &operator>>(std::istream &s, std::pair<T, U> &value) {
s >> value.first >> value.second;
return s;
}
template <typename... Args>
std::istream &operator>>(std::istream &s, std::tuple<Args...> &value) {
input_tuple_helper(s, value, std::make_index_sequence<sizeof...(Args)>());
return s;
}
} // namespace haar_lib
#line 8 "Mylib/IO/input_tuples.cpp"
namespace haar_lib {
template <typename... Args>
class InputTuples {
struct iter {
using value_type = std::tuple<Args...>;
value_type value;
bool fetched = false;
int N, c = 0;
value_type operator*() {
if (not fetched) {
std::cin >> value;
}
return value;
}
void operator++() {
++c;
fetched = false;
}
bool operator!=(iter &) const {
return c < N;
}
iter(int N) : N(N) {}
};
int N;
public:
InputTuples(int N) : N(N) {}
iter begin() const { return iter(N); }
iter end() const { return iter(N); }
};
template <typename... Args>
auto input_tuples(int N) {
return InputTuples<Args...>(N);
}
} // namespace haar_lib
#line 9 "test/yosupo-judge/rectangle_sum/main.segment_tree.test.cpp"
namespace hl = haar_lib;
int main() {
std::cin.tie(0);
std::ios::sync_with_stdio(false);
int N, Q;
std::cin >> N >> Q;
auto [x, y, w] = hl::input_tuple_vector<int64_t, int64_t, int64_t>(N);
hl::segment_tree_on_segment_tree<hl::sum_monoid<int64_t>> seg;
for (int i = 0; i < N; ++i) {
seg.add(x[i], y[i]);
}
seg.build();
for (int i = 0; i < N; ++i) {
seg.update({x[i], y[i]}, w[i]);
}
for (auto [l, d, r, u] : hl::input_tuples<int64_t, int64_t, int64_t, int64_t>(Q)) {
auto ans = seg.fold({l, d}, {r, u});
std::cout << ans << std::endl;
}
return 0;
}
test/yosupo-judge/rectangle_sum/main.segment_tree.test.cpp
Sum monoid
(Mylib/AlgebraicStructure/Monoid/sum.cpp)