Fenwick tree (On Fenwick tree)
(Mylib/DataStructure/FenwickTree/fenwick_tree_on_fenwick_tree.cpp)
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Code
#pragma once
#include "Mylib/DataStructure/FenwickTree/fenwick_tree.cpp"
#include <algorithm>
#include <numeric>
#include <vector>
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/DataStructure/FenwickTree/fenwick_tree.cpp"
#include <cassert>
#include <vector>
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
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