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DataStructure/Fenwick/Fenwick2D.h
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- Last update: 2023-01-07 01:54:04+08:00
- Link: https://hitonanode.github.io/cplib-cpp/data_structure/rectangle_add_rectangle_sum.hpp
- Link: https://judge.yosupo.jp/problem/point_add_rectangle_sum
- Link: https://judge.yosupo.jp/problem/rectangle_sum
- Link: https://oj.vnoi.info/problem/kl11b
Depends on
Verified with
- DataStructure/test/fenwick_2d_pointaddrectsum.test.cpp
- DataStructure/test/fenwick_2d_rectsum.test.cpp
Code
// 2D Fenwick
// Note:
// - already included coordinate compression, so any `int` coordinates
// should work
// - For faster implementation which also supports Rectagle ADD, see:
// https://hitonanode.github.io/cplib-cpp/data_structure/rectangle_add_rectangle_sum.hpp
//
// If cannot use the struct directly (e.g. ICPC Vietnam national 2022 - G), do:
// 1. fakeUpdate
// 2. initNodes
// 3. Queries
//
// Tested:
// - https://judge.yosupo.jp/problem/rectangle_sum
// - https://judge.yosupo.jp/problem/point_add_rectangle_sum
// - https://oj.vnoi.info/problem/kl11b
#include "../../Misc/compress.h"
// Fenwick 2D {{{
const int INF = 2e9 + 11; // for coordinates
template<typename T>
struct Query {
static const int ADD = 0;
static const int QUERY = 1;
int typ; // ADD or QUERY
int x, y;
int x2, y2; // for QUERY: [x1, x2-1] * [y1, y2-1]
T weight;
};
template<typename T>
struct Fenwick2D {
vector<T> solve(vector<Query<T>> queries) {
// Get coordinates of ADD queries
CompressorBuilder<int> cx_builder, cy_builder;
cx_builder.add(INF);
cy_builder.add(INF);
for (const auto& query : queries) {
if (query.typ == Query<T>::ADD) {
cx_builder.add(query.x);
cy_builder.add(query.y);
}
}
auto cx = cx_builder.build();
auto cy = cy_builder.build();
sx = cx.size();
// Compress
for (auto& query : queries) {
query.x = cx.must_geq(query.x) + 1;
query.y = cy.must_geq(query.y) + 1;
if (query.typ == Query<T>::QUERY) {
query.x2 = cx.must_geq(query.x2) + 1;
query.y2 = cy.must_geq(query.y2) + 1;
}
}
// fake updates
nodes.resize(sx+1);
f.resize(sx+1);
for (const auto& query : queries) {
if (query.typ == Query<T>::ADD) {
fakeUpdate(query.x, query.y);
}
}
initNodes();
// answer queries
vector<T> res;
for (const auto& query : queries) {
if (query.typ == Query<T>::ADD) {
update(query.x, query.y, query.weight);
} else {
res.push_back(
+ get(query.x2 - 1, query.y2 - 1)
- get(query.x2 - 1, query.y - 1)
- get(query.x - 1, query.y2 - 1)
+ get(query.x - 1, query.y - 1)
);
}
}
return res;
}
// private:
// nodes[x] contains all relevant y coordinates
vector<vector<int>> nodes;
vector<vector<T>> f;
int sx;
void initNodes() {
for (int i = 1; i <= sx; i++) {
nodes[i].push_back(INF);
sort(nodes[i].begin(), nodes[i].end());
nodes[i].erase(unique(nodes[i].begin(), nodes[i].end()), nodes[i].end());
f[i].resize(nodes[i].size() + 1);
}
}
void fakeUpdate(int x, int y) {
for (; x <= sx; x += x & -x)
nodes[x].push_back(y);
}
// point (u, v) += val
void update(int u, int v, int val) {
for(int x = u; x <= sx; x += x & -x)
for(int y = lower_bound(nodes[x].begin(), nodes[x].end(), v) - nodes[x].begin() + 1; y <= (int) nodes[x].size(); y += y & -y)
f[x][y] += val;
}
// Get sum of point in rectangle with corners at (1, 1) and (u, v)
T get(int u, int v) {
T res = 0;
for(int x = u; x > 0; x -= x & -x)
for(int y = upper_bound(nodes[x].begin(), nodes[x].end(), v) - nodes[x].begin(); y > 0; y -= y & -y)
res += f[x][y];
return res;
}
};
// }}}#line 1 "DataStructure/Fenwick/Fenwick2D.h"
// 2D Fenwick
// Note:
// - already included coordinate compression, so any `int` coordinates
// should work
// - For faster implementation which also supports Rectagle ADD, see:
// https://hitonanode.github.io/cplib-cpp/data_structure/rectangle_add_rectangle_sum.hpp
//
// If cannot use the struct directly (e.g. ICPC Vietnam national 2022 - G), do:
// 1. fakeUpdate
// 2. initNodes
// 3. Queries
//
// Tested:
// - https://judge.yosupo.jp/problem/rectangle_sum
// - https://judge.yosupo.jp/problem/point_add_rectangle_sum
// - https://oj.vnoi.info/problem/kl11b
#line 1 "Misc/compress.h"
// Compressor {{{
/* Example usage:
auto compressor = CompressorBuilder<T>{vs}.build();
int x = compessor.must_eq(vs[0]);
compressor.compress_inplace(vs);
*/
// Based on https://suisen-cp.github.io/cp-library-cpp/library/util/coordinate_compressor.hpp
template<typename T>
struct CompressorBuilder {
// Do not use directly. Use builder.build()
struct Compressor {
// Number of unique keys
int size() const { return xs.size(); }
void compress_inplace(std::vector<T>& vals) {
for (int& val : vals) {
val = must_eq(val);
}
}
[[nodiscard]] std::vector<T> compress(const std::vector<T>& vals) {
std::vector<T> res(vals.size());
for (int i = 0; i < static_cast<int> (res.size()); ++i) {
res[i] = must_eq(vals[i]);
}
return res;
}
bool has_key(const T& key) const {
return std::binary_search(xs.begin(), xs.end(), key);
}
#define LB(key) std::lower_bound(xs.begin(), xs.end(), key)
#define UB(key) std::upper_bound(xs.begin(), xs.end(), key)
std::optional<int> eq(const T& key) {
auto it = LB(key);
return it == xs.end() ? std::nullopt : std::optional<int>{it - xs.begin()};
}
std::optional<int> geq(const T& key) {
auto it = LB(key);
return it == xs.end() ? std::nullopt : std::optional<int>{it - xs.begin()};
}
std::optional<int> gt(const T& key) {
auto it = UB(key);
return it == xs.end() ? std::nullopt : std::optional<int>{it - xs.begin()};
}
std::optional<int> leq(const T& key) {
auto it = UB(key);
return it == xs.begin() ? std::nullopt : std::optional<int>{it - xs.begin() - 1};
}
std::optional<int> lt(const T& key) {
auto it = LB(key);
return it == xs.begin() ? std::nullopt : std::optional<int>{it - xs.begin() - 1};
}
// throw exception if no such key is found
int must_eq(const T& key) {
auto it = LB(key);
assert(it != xs.end());
return it - xs.begin();
}
// throw exception if no such key is found
int must_geq(const T& key) {
auto it = LB(key);
assert(it != xs.end());
return it - xs.begin();
}
// throw exception if no such key is found
int must_gt(const T& key) {
auto it = UB(key);
assert(it != xs.end());
return it - xs.begin();
}
// throw exception if no such key is found
int must_leq(const T& key) {
auto it = UB(key);
assert(it != xs.begin());
return it - xs.begin() - 1;
}
// throw exception if no such key is found
int must_lt(const T& key) {
auto it = LB(key);
assert(it != xs.begin());
return it - xs.begin() - 1;
}
#undef LB
#undef UB
std::vector<T> xs;
};
auto build() {
std::sort(xs.begin(), xs.end());
xs.erase(std::unique(xs.begin(), xs.end()), xs.end());
return Compressor{xs};
}
void add(const T& key) { xs.push_back(key); }
void add(T&& key) { xs.push_back(std::move(key)); }
std::vector<T> xs;
};
// }}}
#line 19 "DataStructure/Fenwick/Fenwick2D.h"
// Fenwick 2D {{{
const int INF = 2e9 + 11; // for coordinates
template<typename T>
struct Query {
static const int ADD = 0;
static const int QUERY = 1;
int typ; // ADD or QUERY
int x, y;
int x2, y2; // for QUERY: [x1, x2-1] * [y1, y2-1]
T weight;
};
template<typename T>
struct Fenwick2D {
vector<T> solve(vector<Query<T>> queries) {
// Get coordinates of ADD queries
CompressorBuilder<int> cx_builder, cy_builder;
cx_builder.add(INF);
cy_builder.add(INF);
for (const auto& query : queries) {
if (query.typ == Query<T>::ADD) {
cx_builder.add(query.x);
cy_builder.add(query.y);
}
}
auto cx = cx_builder.build();
auto cy = cy_builder.build();
sx = cx.size();
// Compress
for (auto& query : queries) {
query.x = cx.must_geq(query.x) + 1;
query.y = cy.must_geq(query.y) + 1;
if (query.typ == Query<T>::QUERY) {
query.x2 = cx.must_geq(query.x2) + 1;
query.y2 = cy.must_geq(query.y2) + 1;
}
}
// fake updates
nodes.resize(sx+1);
f.resize(sx+1);
for (const auto& query : queries) {
if (query.typ == Query<T>::ADD) {
fakeUpdate(query.x, query.y);
}
}
initNodes();
// answer queries
vector<T> res;
for (const auto& query : queries) {
if (query.typ == Query<T>::ADD) {
update(query.x, query.y, query.weight);
} else {
res.push_back(
+ get(query.x2 - 1, query.y2 - 1)
- get(query.x2 - 1, query.y - 1)
- get(query.x - 1, query.y2 - 1)
+ get(query.x - 1, query.y - 1)
);
}
}
return res;
}
// private:
// nodes[x] contains all relevant y coordinates
vector<vector<int>> nodes;
vector<vector<T>> f;
int sx;
void initNodes() {
for (int i = 1; i <= sx; i++) {
nodes[i].push_back(INF);
sort(nodes[i].begin(), nodes[i].end());
nodes[i].erase(unique(nodes[i].begin(), nodes[i].end()), nodes[i].end());
f[i].resize(nodes[i].size() + 1);
}
}
void fakeUpdate(int x, int y) {
for (; x <= sx; x += x & -x)
nodes[x].push_back(y);
}
// point (u, v) += val
void update(int u, int v, int val) {
for(int x = u; x <= sx; x += x & -x)
for(int y = lower_bound(nodes[x].begin(), nodes[x].end(), v) - nodes[x].begin() + 1; y <= (int) nodes[x].size(); y += y & -y)
f[x][y] += val;
}
// Get sum of point in rectangle with corners at (1, 1) and (u, v)
T get(int u, int v) {
T res = 0;
for(int x = u; x > 0; x -= x & -x)
for(int y = upper_bound(nodes[x].begin(), nodes[x].end(), v) - nodes[x].begin(); y > 0; y -= y & -y)
res += f[x][y];
return res;
}
};
// }}}