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#include "structure/others/abstract-2d-binary-indexed-tree-compressed.hpp"
#include "abstract-binary-indexed-tree.hpp"
/**
* @brief Abstract 2D Binary Indexed Tree Compressed(抽象化2次元座圧BIT)
*/
template< typename T, typename F >
struct Abstract2DBinaryIndexedTreeCompressed {
private:
int n;
vector< AbstractBinaryIndexedTree< T, F > > data;
const F f;
const T e;
vector< int > hs;
vector< vector< int > > beet;
public:
Abstract2DBinaryIndexedTreeCompressed(const vector< int > &hs, const F f, const T &e) :
n((int) hs.size()), hs(hs), f(f), e(e) {
vector< int > ord(n);
iota(begin(ord), end(ord), 0);
sort(begin(ord), end(ord), [&](int a, int b) {
return hs[a] < hs[b];
});
beet.resize(n + 1);
for(auto &&i: ord) {
for(int k = i + 1; k <= n; k += k & -k) {
beet[k].emplace_back(hs[i]);
}
}
data.reserve(n + 1);
for(int k = 0; k <= n; k++) {
beet[k].erase(unique(begin(beet[k]), end(beet[k])), end(beet[k]));
data.emplace_back((int) beet[k].size(), f, e);
}
}
void apply(int k1, const T &x) {
int k2 = hs[k1];
for(++k1; k1 <= n; k1 += k1 & -k1) {
int p = lower_bound(begin(beet[k1]), end(beet[k1]), k2) - begin(beet[k1]);
data[k1].apply(p, x);
}
}
T prod(int r1, int r2) const {
T ret{e};
for(; r1 > 0; r1 -= r1 & -r1) {
int p = lower_bound(begin(beet[r1]), end(beet[r1]), r2) - begin(beet[r1]);
ret = f(ret, data[r1].prod(p));
}
return ret;
}
};
template< typename T, typename F >
Abstract2DBinaryIndexedTreeCompressed< T, F > get_abstract_2d_binary_indexed_tree_compressed(const vector< int > &hs, const F &f, const T &e) {
return Abstract2DBinaryIndexedTreeCompressed{hs, f, e};
}
#line 1 "structure/others/abstract-binary-indexed-tree.hpp"
/**
* @brief Abstract Binary Indexed Tree(抽象化BIT)
*/
template< typename T, typename F >
struct AbstractBinaryIndexedTree {
private:
int n;
vector< T > data;
const F f;
const T e;
public:
AbstractBinaryIndexedTree() = default;
explicit AbstractBinaryIndexedTree(int n, const F f, const T &e) : n(n), f(f), e(e) {
data.assign(n + 1, e);
}
explicit AbstractBinaryIndexedTree(const vector< T > &v, const F f, const T &e) :
AbstractBinaryIndexedTree((int) v.size(), f, e) {
build(v);
}
void build(const vector< T > &v) {
assert(n == (int) v.size());
for(int i = 1; i <= n; i++) data[i] = v[i - 1];
for(int i = 1; i <= n; i++) {
int j = i + (i & -i);
if(j <= n) data[j] = f(data[j], data[i]);
}
}
void apply(int k, const T &x) {
for(++k; k <= n; k += k & -k) data[k] = f(data[k], x);
}
T prod(int r) const {
T ret{e};
for(; r > 0; r -= r & -r) ret = f(ret, data[r]);
return ret;
}
};
template< typename T, typename F >
AbstractBinaryIndexedTree< T, F > get_abstract_binary_indexed_tree(int n, const F &f, const T &e) {
return AbstractBinaryIndexedTree{n, f, e};
}
template< typename T, typename F >
AbstractBinaryIndexedTree< T, F > get_abstract_binary_indexed_tree(const vector< T > &v, const F &f, const T &e) {
return AbstractBinaryIndexedTree{v, f, e};
}
#line 2 "structure/others/abstract-2d-binary-indexed-tree-compressed.hpp"
/**
* @brief Abstract 2D Binary Indexed Tree Compressed(抽象化2次元座圧BIT)
*/
template< typename T, typename F >
struct Abstract2DBinaryIndexedTreeCompressed {
private:
int n;
vector< AbstractBinaryIndexedTree< T, F > > data;
const F f;
const T e;
vector< int > hs;
vector< vector< int > > beet;
public:
Abstract2DBinaryIndexedTreeCompressed(const vector< int > &hs, const F f, const T &e) :
n((int) hs.size()), hs(hs), f(f), e(e) {
vector< int > ord(n);
iota(begin(ord), end(ord), 0);
sort(begin(ord), end(ord), [&](int a, int b) {
return hs[a] < hs[b];
});
beet.resize(n + 1);
for(auto &&i: ord) {
for(int k = i + 1; k <= n; k += k & -k) {
beet[k].emplace_back(hs[i]);
}
}
data.reserve(n + 1);
for(int k = 0; k <= n; k++) {
beet[k].erase(unique(begin(beet[k]), end(beet[k])), end(beet[k]));
data.emplace_back((int) beet[k].size(), f, e);
}
}
void apply(int k1, const T &x) {
int k2 = hs[k1];
for(++k1; k1 <= n; k1 += k1 & -k1) {
int p = lower_bound(begin(beet[k1]), end(beet[k1]), k2) - begin(beet[k1]);
data[k1].apply(p, x);
}
}
T prod(int r1, int r2) const {
T ret{e};
for(; r1 > 0; r1 -= r1 & -r1) {
int p = lower_bound(begin(beet[r1]), end(beet[r1]), r2) - begin(beet[r1]);
ret = f(ret, data[r1].prod(p));
}
return ret;
}
};
template< typename T, typename F >
Abstract2DBinaryIndexedTreeCompressed< T, F > get_abstract_2d_binary_indexed_tree_compressed(const vector< int > &hs, const F &f, const T &e) {
return Abstract2DBinaryIndexedTreeCompressed{hs, f, e};
}