#define PROBLEM "https://judge.yosupo.jp/problem/rectangle_sum"
#include <iostream>
#include <vector>
#include "Mylib/AlgebraicStructure/Group/sum.cpp"
#include "Mylib/DataStructure/FenwickTree/fenwick_tree.cpp"
#include "Mylib/DataStructure/FenwickTree/fenwick_tree_on_fenwick_tree.cpp"
#include "Mylib/IO/input_tuple_vector.cpp"
#include "Mylib/IO/input_tuples.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::fenwick_tree_on_fenwick_tree<hl::sum_group<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;
}
#line 1 "test/yosupo-judge/rectangle_sum/main.fenwick_tree.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/rectangle_sum"
#include <iostream>
#include <vector>
#line 2 "Mylib/AlgebraicStructure/Group/sum.cpp"
namespace haar_lib {
template <typename T>
struct sum_group {
using value_type = T;
value_type operator()() const { return 0; }
value_type operator()(const value_type &a, const value_type &b) const { return a + b; }
value_type inv(const value_type &a) const { return -a; }
};
} // namespace haar_lib
#line 2 "Mylib/DataStructure/FenwickTree/fenwick_tree.cpp"
#include <cassert>
#line 4 "Mylib/DataStructure/FenwickTree/fenwick_tree.cpp"
namespace haar_lib {
template <typename AbelianGroup>
class fenwick_tree {
public:
using value_type = typename AbelianGroup::value_type;
private:
AbelianGroup G_;
int size_;
std::vector<value_type> data_;
public:
fenwick_tree() {}
fenwick_tree(int size) : size_(size), data_(size + 1, G_()) {}
void update(int i, const value_type &val) {
assert(0 <= i and i < size_);
i += 1; // 1-index
while (i <= size_) {
data_[i] = G_(data_[i], val);
i += i & (-i);
}
}
value_type fold(int i) const { // [0, i)
assert(0 <= i and i <= size_);
value_type ret = G_();
while (i > 0) {
ret = G_(ret, data_[i]);
i -= i & (-i);
}
return ret;
}
value_type fold(int l, int r) const { // [l, r)
assert(0 <= l and l <= r and r <= size_);
return G_(fold(r), G_.inv(fold(l)));
}
value_type operator[](int x) const {
return fold(x, x + 1);
}
};
} // namespace haar_lib
#line 3 "Mylib/DataStructure/FenwickTree/fenwick_tree_on_fenwick_tree.cpp"
#include <algorithm>
#include <numeric>
#line 6 "Mylib/DataStructure/FenwickTree/fenwick_tree_on_fenwick_tree.cpp"
namespace haar_lib {
template <typename AbelianGroup>
class fenwick_tree_on_fenwick_tree {
public:
using value_type = typename AbelianGroup::value_type;
private:
AbelianGroup G_;
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<fenwick_tree<AbelianGroup>> segs_;
public:
fenwick_tree_on_fenwick_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_ = c_xs_.size();
c_ys_.resize(x_size_ + 1);
segs_.resize(x_size_ + 1);
std::vector<int> ord(N_);
std::iota(ord.begin(), ord.end(), 0);
std::sort(ord.begin(), ord.end(), [&](int i, int j) { return ys_[i] < ys_[j]; });
for (auto i : ord) {
int x = std::lower_bound(c_xs_.begin(), c_xs_.end(), xs_[i]) - c_xs_.begin();
for (x += 1; x <= x_size_; x += x & (-x)) {
c_ys_[x].emplace_back(ys_[i]);
}
}
for (int i = 1; i <= x_size_; ++i) {
auto &a = c_ys_[i];
a.erase(std::unique(a.begin(), a.end()), a.end());
segs_[i] = fenwick_tree<AbelianGroup>(c_ys_[i].size());
}
}
void update(std::pair<int, int> 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();
for (i += 1; i <= x_size_; i += i & (-i)) {
int j = std::lower_bound(c_ys_[i].begin(), c_ys_[i].end(), y) - c_ys_[i].begin();
segs_[i].update(j, val);
}
}
private:
value_type get(int i, int64_t y1, int64_t y2) const {
value_type ret = G_();
for (; i > 0; i -= i & (-i)) {
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();
ret = G_(ret, segs_[i].fold(l, r));
}
return ret;
}
public:
// [x1, x2), [y1, y2)
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();
int r = std::lower_bound(c_xs_.begin(), c_xs_.end(), x2) - c_xs_.begin();
return G_(get(r, y1, y2), G_.inv(get(l, y1, y2)));
}
};
} // 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 10 "test/yosupo-judge/rectangle_sum/main.fenwick_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::fenwick_tree_on_fenwick_tree<hl::sum_group<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.fenwick_tree.test.cpp
Sum group
(Mylib/AlgebraicStructure/Group/sum.cpp)