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#include "data_structure/lazy_propagation_red_black_tree.hpp"
完全二分木上の遅延伝播セグメント木でできることに加え、$O(\log N)$ で次ができる:
#pragma once
#include <algorithm>
#include <cassert>
#include <memory>
#include <type_traits>
#include <vector>
/**
* @brief Lazy Propagation Segment Tree / 遅延伝播セグメント木 (monoids, 赤黒木)
* @docs data_structure/lazy_propagation_red_black_tree.md
* @tparam MonoidX is a monoid
* @tparam MonoidF is a monoid
* @tparam Action is a function phi : F * X -> X where the partial applied phi(f, -) : X -> X is a homomorphism on X
*/
template <class MonoidX, class MonoidF, class Action>
class lazy_propagation_red_black_tree {
static_assert (std::is_invocable_r<typename MonoidX::value_type, Action, typename MonoidF::value_type, typename MonoidX::value_type>::value, "");
typedef typename MonoidX::value_type value_type;
typedef typename MonoidF::value_type operator_type;
enum color_t { BLACK, RED };
struct node_t {
bool is_leaf;
value_type data;
operator_type lazy; // NOTE: this->lazy is already applied to this->data
bool reversed;
color_t color;
int rank;
int size;
node_t *left;
node_t *right;
node_t() = default;
node_t(value_type const & a_data)
: is_leaf(true)
, data(a_data)
, color(BLACK)
, rank(0)
, size(1) {
}
node_t(node_t *l, node_t *r, color_t c) // non-leaf node
: is_leaf(false)
, data(MonoidX().mult(l->data, r->data))
, lazy(MonoidF().unit())
, reversed(false)
, color(c)
, rank(std::max(l->rank + (l->color == BLACK),
r->rank + (r->color == BLACK)))
, size(l->size + r->size)
, left(l)
, right(r) {
}
};
struct node_deleter {
void operator () (node_t *t) const {
assert (t != nullptr);
if (not t->is_leaf) {
(*this)(t->right);
(*this)(t->left);
}
delete t;
}
};
static void propagate_only_operator(node_t *a) {
MonoidF mon_f;
Action act;
if (not a->is_leaf) {
if (a->lazy != mon_f.unit()) {
auto const & l = a->left;
auto const & r = a->right;
l->data = act(a->lazy, l->data);
r->data = act(a->lazy, r->data);
if (not l->is_leaf) l->lazy = mon_f.mult(a->lazy, l->lazy);
if (not r->is_leaf) r->lazy = mon_f.mult(a->lazy, r->lazy);
a->lazy = mon_f.unit();
}
}
}
static void propagate_only_reverse(node_t *a) {
if (not a->is_leaf) {
if (a->reversed) {
auto const & l = a->left;
auto const & r = a->right;
if (not l->is_leaf) l->reversed = not l->reversed;
if (not r->is_leaf) r->reversed = not r->reversed;
std::swap(a->left, a->right); // CAUTION: auto const & l, r are destroyed
a->reversed = false;
}
}
}
static void propagate(node_t *a) {
propagate_only_operator(a);
propagate_only_reverse(a);
}
/**
* @note trees a, b are consumed (at set_left()/set_right())
*/
static node_t *merge(node_t *a, node_t *b) {
if (a == nullptr) return b;
if (b == nullptr) return a;
node_t *c = merge_relax(a, b);
c->color = BLACK;
return c;
}
/*
* @note the root of returned tree may violates the color constraint
*/
static node_t *merge_relax(node_t *a, node_t *b) {
if ((a->rank) < b->rank) {
assert (not b->is_leaf);
propagate(b);
return set_left(b, merge_relax(a, b->left));
} else if (a->rank > b->rank) {
assert (not a->is_leaf);
propagate(a);
return set_right(a, merge_relax(a->right, b));
} else {
a->color = BLACK;
b->color = BLACK;
return new node_t(a, b, RED);
}
}
static node_t *set_left(node_t *b, node_t *c) {
if (b->color == BLACK and c->color == RED and c->left->color == RED) {
if (b->right->color == BLACK) {
*b = node_t(c->right, b->right, RED);
*c = node_t(c->left, b, BLACK);
std::swap(b, c);
} else {
b->right->color = BLACK;
c->color = BLACK;
*b = node_t(c, b->right, RED);
}
} else {
*b = node_t(c, b->right, b->color);
}
return b;
}
static node_t *set_right(node_t *a, node_t *c) {
if (a->color == BLACK and c->color == RED and c->right->color == RED) {
if (a->left->color == BLACK) {
*a = node_t(a->left, c->left, RED);
*c = node_t(a, c->right, BLACK);
std::swap(a, c);
} else {
a->left->color = BLACK;
c->color = BLACK;
*a = node_t(a->left, c, RED);
}
} else {
*a = node_t(a->left, c, a->color);
}
return a;
}
/**
* @note tree a is consumed (at explicit delete and merge())
*/
static std::pair<node_t *, node_t *> split(node_t *a, int k) {
if (k == 0) {
return std::make_pair( nullptr, a );
}
assert (a != nullptr);
if (k == a->size) {
return std::make_pair( a, nullptr );
}
assert (not a->is_leaf);
propagate(a);
node_t *a_left = a->left;
node_t *a_right = a->right;
delete a;
if (k < a_left->size) {
node_t *l, *r; tie(l, r) = split(a_left, k);
return std::make_pair( l, merge(r, a_right) );
} else if (k > a_left->size) {
node_t *l, *r; tie(l, r) = split(a_right, k - a_left->size);
return std::make_pair( merge(a_left, l), r );
} else {
return std::make_pair( a_left, a_right );
}
}
static void range_apply(node_t *a, int l, int r, const operator_type & func) {
MonoidX mon_x;
MonoidF mon_f;
Action act;
if (l == r) return;
if (l == 0 and r == a->size) {
a->data = act(func, a->data);
if (not a->is_leaf) a->lazy = mon_f.mult(func, a->lazy);
return;
}
assert (not a->is_leaf);
propagate(a);
int k = a->left->size;
if (r <= k) {
range_apply(a->left, l, r, func);
} else if (k <= l) {
range_apply(a->right, l - k, r - k, func);
} else {
range_apply(a->left, l, k, func);
range_apply(a->right, 0, r - k, func);
}
a->data = act(a->lazy, mon_x.mult(a->left->data, a->right->data));
}
static value_type range_get(node_t *a, int l, int r) {
MonoidX mon_x;
assert (l < r);
if (l == 0 and r == a->size) return a->data;
assert (not a->is_leaf);
propagate(a);
int k = a->left->size;
if (r <= k) {
return range_get(a->left, l, r);
} else if (k <= l) {
return range_get(a->right, l - k, r - k);
} else {
return mon_x.mult(
range_get(a->left, l, k),
range_get(a->right, 0, r - k));
}
}
static node_t *reverse(node_t *a, int l, int r) {
// TODO: find ways to do without split. there may be clever ways using recursion
if (l == r) return a;
node_t *bl, *br; tie(bl, br) = split(a, r);
node_t *bm; tie(bl, bm) = split(bl, l);
if (not bm->is_leaf) bm->reversed = not bm->reversed;
return merge(merge(bl, bm), br);
}
static void point_set(node_t *a, int i, const value_type & value) {
MonoidX mon_x;
Action act;
if (a->is_leaf) {
assert (i == 0);
a->data = value;
} else {
propagate_only_reverse(a); // should we do full propagation?
if (i < a->left->size) {
point_set(a->left, i, value);
} else {
point_set(a->right, i - a->left->size, value);
}
a->data = act(a->lazy,
mon_x.mult(a->left->data, a->right->data));
}
}
static value_type & point_get(node_t *a, int i) {
if (a->is_leaf) {
assert (i == 0);
return a->data;
} else {
propagate(a);
if (i < a->left->size) {
return point_get(a->left, i);
} else {
return point_get(a->right, i - a->left->size);
}
}
}
private:
std::unique_ptr<node_t, node_deleter> root;
public:
lazy_propagation_red_black_tree() = default;
lazy_propagation_red_black_tree(node_t *a_root)
: root(a_root) {
}
template <class InputIterator>
lazy_propagation_red_black_tree(InputIterator first, InputIterator last)
: root(nullptr) {
for (; first != last; ++ first) {
this->push_back(*first);
}
}
static lazy_propagation_red_black_tree merge(lazy_propagation_red_black_tree & l, lazy_propagation_red_black_tree & r) {
node_t *a = l.root.release();
node_t *b = r.root.release();
if (a == nullptr) return lazy_propagation_red_black_tree(b);
if (b == nullptr) return lazy_propagation_red_black_tree(a);
return lazy_propagation_red_black_tree(merge(a, b));
}
std::pair<lazy_propagation_red_black_tree, lazy_propagation_red_black_tree> split(int k) {
assert (0 <= k and k <= size());
node_t *l, *r; tie(l, r) = split(root.release(), k);
return std::make_pair( lazy_propagation_red_black_tree(l), lazy_propagation_red_black_tree(r) );
}
void insert(int i, const value_type & data) {
assert (0 <= i and i <= size());
if (empty()) {
root.reset(new node_t(data));
return;
} else {
node_t *l, *r; tie(l, r) = split(root.release(), i);
root.reset( merge(merge(l, new node_t(data)), r) );
}
}
void erase(int i) {
assert (0 <= i and i < size());
node_t *l, *r; tie(l, r) = split(root.release(), i + 1);
node_t *m; tie(l, m) = split(l, i);
node_deleter()(m);
root.reset( merge(l, r) );
}
void point_set(int i, const value_type & value) {
assert (0 <= i and i < size());
point_set(root.get(), i, value);
}
value_type const & point_get(int i) const {
assert (0 <= i and i < size());
return point_get(const_cast<node_t *>(root.get()), i);
}
void range_apply(int l, int r, const operator_type & func) {
assert (0 <= l and l <= r and r <= size());
if (l == r) return;
range_apply(root.get(), l, r, func);
}
value_type const range_get(int l, int r) const {
assert (0 <= l and l <= r and r <= size());
if (l == r) return MonoidX().unit();
return range_get(const_cast<node_t *>(root.get()), l, r);
}
void reverse(int l, int r) {
assert (0 <= l and l <= r and r <= size());
if (not root) return;
root.reset( reverse(root.release(), l, r) );
}
void push_back(const value_type & data) {
root.reset( merge(root.release(), new node_t(data)) );
}
void push_front(const value_type & data) {
root.reset( merge(new node_t(data), root.release()) );
}
void pop_back() {
int k = size() - 1;
auto lr = split(root.release(), k);
root.reset(lr.first);
node_deleter()(lr.second);
}
void pop_front() {
auto lr = split(root.release(), 1);
node_deleter()(lr.first);
root.reset(lr.second);
}
int size() const {
return root ? root.get()->size : 0;
}
bool empty() const {
return not root;
}
void clear() {
root = nullptr;
}
};
#line 2 "data_structure/lazy_propagation_red_black_tree.hpp"
#include <algorithm>
#include <cassert>
#include <memory>
#include <type_traits>
#include <vector>
/**
* @brief Lazy Propagation Segment Tree / 遅延伝播セグメント木 (monoids, 赤黒木)
* @docs data_structure/lazy_propagation_red_black_tree.md
* @tparam MonoidX is a monoid
* @tparam MonoidF is a monoid
* @tparam Action is a function phi : F * X -> X where the partial applied phi(f, -) : X -> X is a homomorphism on X
*/
template <class MonoidX, class MonoidF, class Action>
class lazy_propagation_red_black_tree {
static_assert (std::is_invocable_r<typename MonoidX::value_type, Action, typename MonoidF::value_type, typename MonoidX::value_type>::value, "");
typedef typename MonoidX::value_type value_type;
typedef typename MonoidF::value_type operator_type;
enum color_t { BLACK, RED };
struct node_t {
bool is_leaf;
value_type data;
operator_type lazy; // NOTE: this->lazy is already applied to this->data
bool reversed;
color_t color;
int rank;
int size;
node_t *left;
node_t *right;
node_t() = default;
node_t(value_type const & a_data)
: is_leaf(true)
, data(a_data)
, color(BLACK)
, rank(0)
, size(1) {
}
node_t(node_t *l, node_t *r, color_t c) // non-leaf node
: is_leaf(false)
, data(MonoidX().mult(l->data, r->data))
, lazy(MonoidF().unit())
, reversed(false)
, color(c)
, rank(std::max(l->rank + (l->color == BLACK),
r->rank + (r->color == BLACK)))
, size(l->size + r->size)
, left(l)
, right(r) {
}
};
struct node_deleter {
void operator () (node_t *t) const {
assert (t != nullptr);
if (not t->is_leaf) {
(*this)(t->right);
(*this)(t->left);
}
delete t;
}
};
static void propagate_only_operator(node_t *a) {
MonoidF mon_f;
Action act;
if (not a->is_leaf) {
if (a->lazy != mon_f.unit()) {
auto const & l = a->left;
auto const & r = a->right;
l->data = act(a->lazy, l->data);
r->data = act(a->lazy, r->data);
if (not l->is_leaf) l->lazy = mon_f.mult(a->lazy, l->lazy);
if (not r->is_leaf) r->lazy = mon_f.mult(a->lazy, r->lazy);
a->lazy = mon_f.unit();
}
}
}
static void propagate_only_reverse(node_t *a) {
if (not a->is_leaf) {
if (a->reversed) {
auto const & l = a->left;
auto const & r = a->right;
if (not l->is_leaf) l->reversed = not l->reversed;
if (not r->is_leaf) r->reversed = not r->reversed;
std::swap(a->left, a->right); // CAUTION: auto const & l, r are destroyed
a->reversed = false;
}
}
}
static void propagate(node_t *a) {
propagate_only_operator(a);
propagate_only_reverse(a);
}
/**
* @note trees a, b are consumed (at set_left()/set_right())
*/
static node_t *merge(node_t *a, node_t *b) {
if (a == nullptr) return b;
if (b == nullptr) return a;
node_t *c = merge_relax(a, b);
c->color = BLACK;
return c;
}
/*
* @note the root of returned tree may violates the color constraint
*/
static node_t *merge_relax(node_t *a, node_t *b) {
if ((a->rank) < b->rank) {
assert (not b->is_leaf);
propagate(b);
return set_left(b, merge_relax(a, b->left));
} else if (a->rank > b->rank) {
assert (not a->is_leaf);
propagate(a);
return set_right(a, merge_relax(a->right, b));
} else {
a->color = BLACK;
b->color = BLACK;
return new node_t(a, b, RED);
}
}
static node_t *set_left(node_t *b, node_t *c) {
if (b->color == BLACK and c->color == RED and c->left->color == RED) {
if (b->right->color == BLACK) {
*b = node_t(c->right, b->right, RED);
*c = node_t(c->left, b, BLACK);
std::swap(b, c);
} else {
b->right->color = BLACK;
c->color = BLACK;
*b = node_t(c, b->right, RED);
}
} else {
*b = node_t(c, b->right, b->color);
}
return b;
}
static node_t *set_right(node_t *a, node_t *c) {
if (a->color == BLACK and c->color == RED and c->right->color == RED) {
if (a->left->color == BLACK) {
*a = node_t(a->left, c->left, RED);
*c = node_t(a, c->right, BLACK);
std::swap(a, c);
} else {
a->left->color = BLACK;
c->color = BLACK;
*a = node_t(a->left, c, RED);
}
} else {
*a = node_t(a->left, c, a->color);
}
return a;
}
/**
* @note tree a is consumed (at explicit delete and merge())
*/
static std::pair<node_t *, node_t *> split(node_t *a, int k) {
if (k == 0) {
return std::make_pair( nullptr, a );
}
assert (a != nullptr);
if (k == a->size) {
return std::make_pair( a, nullptr );
}
assert (not a->is_leaf);
propagate(a);
node_t *a_left = a->left;
node_t *a_right = a->right;
delete a;
if (k < a_left->size) {
node_t *l, *r; tie(l, r) = split(a_left, k);
return std::make_pair( l, merge(r, a_right) );
} else if (k > a_left->size) {
node_t *l, *r; tie(l, r) = split(a_right, k - a_left->size);
return std::make_pair( merge(a_left, l), r );
} else {
return std::make_pair( a_left, a_right );
}
}
static void range_apply(node_t *a, int l, int r, const operator_type & func) {
MonoidX mon_x;
MonoidF mon_f;
Action act;
if (l == r) return;
if (l == 0 and r == a->size) {
a->data = act(func, a->data);
if (not a->is_leaf) a->lazy = mon_f.mult(func, a->lazy);
return;
}
assert (not a->is_leaf);
propagate(a);
int k = a->left->size;
if (r <= k) {
range_apply(a->left, l, r, func);
} else if (k <= l) {
range_apply(a->right, l - k, r - k, func);
} else {
range_apply(a->left, l, k, func);
range_apply(a->right, 0, r - k, func);
}
a->data = act(a->lazy, mon_x.mult(a->left->data, a->right->data));
}
static value_type range_get(node_t *a, int l, int r) {
MonoidX mon_x;
assert (l < r);
if (l == 0 and r == a->size) return a->data;
assert (not a->is_leaf);
propagate(a);
int k = a->left->size;
if (r <= k) {
return range_get(a->left, l, r);
} else if (k <= l) {
return range_get(a->right, l - k, r - k);
} else {
return mon_x.mult(
range_get(a->left, l, k),
range_get(a->right, 0, r - k));
}
}
static node_t *reverse(node_t *a, int l, int r) {
// TODO: find ways to do without split. there may be clever ways using recursion
if (l == r) return a;
node_t *bl, *br; tie(bl, br) = split(a, r);
node_t *bm; tie(bl, bm) = split(bl, l);
if (not bm->is_leaf) bm->reversed = not bm->reversed;
return merge(merge(bl, bm), br);
}
static void point_set(node_t *a, int i, const value_type & value) {
MonoidX mon_x;
Action act;
if (a->is_leaf) {
assert (i == 0);
a->data = value;
} else {
propagate_only_reverse(a); // should we do full propagation?
if (i < a->left->size) {
point_set(a->left, i, value);
} else {
point_set(a->right, i - a->left->size, value);
}
a->data = act(a->lazy,
mon_x.mult(a->left->data, a->right->data));
}
}
static value_type & point_get(node_t *a, int i) {
if (a->is_leaf) {
assert (i == 0);
return a->data;
} else {
propagate(a);
if (i < a->left->size) {
return point_get(a->left, i);
} else {
return point_get(a->right, i - a->left->size);
}
}
}
private:
std::unique_ptr<node_t, node_deleter> root;
public:
lazy_propagation_red_black_tree() = default;
lazy_propagation_red_black_tree(node_t *a_root)
: root(a_root) {
}
template <class InputIterator>
lazy_propagation_red_black_tree(InputIterator first, InputIterator last)
: root(nullptr) {
for (; first != last; ++ first) {
this->push_back(*first);
}
}
static lazy_propagation_red_black_tree merge(lazy_propagation_red_black_tree & l, lazy_propagation_red_black_tree & r) {
node_t *a = l.root.release();
node_t *b = r.root.release();
if (a == nullptr) return lazy_propagation_red_black_tree(b);
if (b == nullptr) return lazy_propagation_red_black_tree(a);
return lazy_propagation_red_black_tree(merge(a, b));
}
std::pair<lazy_propagation_red_black_tree, lazy_propagation_red_black_tree> split(int k) {
assert (0 <= k and k <= size());
node_t *l, *r; tie(l, r) = split(root.release(), k);
return std::make_pair( lazy_propagation_red_black_tree(l), lazy_propagation_red_black_tree(r) );
}
void insert(int i, const value_type & data) {
assert (0 <= i and i <= size());
if (empty()) {
root.reset(new node_t(data));
return;
} else {
node_t *l, *r; tie(l, r) = split(root.release(), i);
root.reset( merge(merge(l, new node_t(data)), r) );
}
}
void erase(int i) {
assert (0 <= i and i < size());
node_t *l, *r; tie(l, r) = split(root.release(), i + 1);
node_t *m; tie(l, m) = split(l, i);
node_deleter()(m);
root.reset( merge(l, r) );
}
void point_set(int i, const value_type & value) {
assert (0 <= i and i < size());
point_set(root.get(), i, value);
}
value_type const & point_get(int i) const {
assert (0 <= i and i < size());
return point_get(const_cast<node_t *>(root.get()), i);
}
void range_apply(int l, int r, const operator_type & func) {
assert (0 <= l and l <= r and r <= size());
if (l == r) return;
range_apply(root.get(), l, r, func);
}
value_type const range_get(int l, int r) const {
assert (0 <= l and l <= r and r <= size());
if (l == r) return MonoidX().unit();
return range_get(const_cast<node_t *>(root.get()), l, r);
}
void reverse(int l, int r) {
assert (0 <= l and l <= r and r <= size());
if (not root) return;
root.reset( reverse(root.release(), l, r) );
}
void push_back(const value_type & data) {
root.reset( merge(root.release(), new node_t(data)) );
}
void push_front(const value_type & data) {
root.reset( merge(new node_t(data), root.release()) );
}
void pop_back() {
int k = size() - 1;
auto lr = split(root.release(), k);
root.reset(lr.first);
node_deleter()(lr.second);
}
void pop_front() {
auto lr = split(root.release(), 1);
node_deleter()(lr.first);
root.reset(lr.second);
}
int size() const {
return root ? root.get()->size : 0;
}
bool empty() const {
return not root;
}
void clear() {
root = nullptr;
}
};