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#include "structure/bbst/lazy-red-black-tree.hpp"
Lazy-Red-Black-Tree は Red-Black-Tree に遅延伝搬を実装したものである.
LazyRedBlackTree(n, f, g, h, M1, OM0)
: サイズ n
で初期化する. ここで f
は2つの区間の要素をマージする二項演算, g
は要素と作用素をマージする二項演算, h
は作用素同士をマージする二項演算, M1
はモノイドの単位元, OM0
は作用素の単位元である.split(t, k)
: 木 t
を $[0, k)[k, n)$ で分割する.split3(t, a, b)
: 木 t
を $[0, a)[a, b)[b, n)$ で分割する.merge(l, r)
: 木 l
と木 r
を併合する.build(v)
: 配列 v
をもとに木を構築する.dump(r)
: 木 r
の葉を通りがけ順に格納したものを返す.to_string(r)
: dump(r)
をスペース区切りで文字列として連結したものを返す.insert(t, k, v)
: 木 t
の位置 k
(0-indexed) にノード v
を挿入する.erase(t, k)
: 木 t
の位置 k
(0-indexed) のノードを削除する.query(t, l, r)
: 区間 $[l, r)$ の要素を二項演算した結果を返す.set_element(t, k, x)
: 木 t
の位置 k
(0-indexed) のノードを x
に変更する.set_propagate(t, a, b, pp)
: 木 t
の区間 $[a, b)$ の要素に作用素 pp
を適用する.push_front(t, v)
: 木 t
の先頭にノード v
を挿入する.push_back(t, v)
: 木 t
の末尾にノード v
を挿入する.pop_front(t)
: 木 t
の先頭要素を削除する.pop_back(t)
: 木 t
の末尾要素を削除する.build
と dump
は $O(n)$/**
* @brief Lazy-Red-Black-Tree(遅延伝搬赤黒木)
*
*/
template <typename Monoid, typename OperatorMonoid, typename F, typename G,
typename H>
struct LazyRedBlackTree {
public:
enum COLOR { BLACK, RED };
struct Node {
Node *l, *r;
COLOR color;
int level, cnt;
Monoid key, sum;
OperatorMonoid lazy;
Node() {}
Node(const Monoid &k, const OperatorMonoid &laz)
: key(k),
sum(k),
l(nullptr),
r(nullptr),
color(BLACK),
level(0),
cnt(1),
lazy(laz) {}
Node(Node *l, Node *r, const Monoid &k, const OperatorMonoid &laz)
: key(k), color(RED), l(l), r(r), lazy(laz) {}
bool is_leaf() const { return l == nullptr; }
};
private:
Node *propagate(Node *t) {
t = clone(t);
if (t->lazy != OM0) {
if (t->is_leaf()) {
t->key = g(t->key, t->lazy);
} else {
if (t->l) {
t->l = clone(t->l);
t->l->lazy = h(t->l->lazy, t->lazy);
t->l->sum = g(t->l->sum, t->lazy);
}
if (t->r) {
t->r = clone(t->r);
t->r->lazy = h(t->r->lazy, t->lazy);
t->r->sum = g(t->r->sum, t->lazy);
}
}
t->lazy = OM0;
}
return update(t);
}
inline Node *alloc(Node *l, Node *r) {
auto t = &(*pool.alloc() = Node(l, r, M1, OM0));
return update(t);
}
virtual Node *clone(Node *t) { return t; }
Node *rotate(Node *t, bool b) {
t = propagate(t);
Node *s;
if (b) {
s = propagate(t->l);
t->l = s->r;
s->r = t;
} else {
s = propagate(t->r);
t->r = s->l;
s->l = t;
}
update(t);
return update(s);
}
Node *submerge(Node *l, Node *r) {
if (l->level < r->level) {
r = propagate(r);
Node *c = (r->l = submerge(l, r->l));
if (r->color == BLACK && c->color == RED && c->l && c->l->color == RED) {
r->color = RED;
c->color = BLACK;
if (r->r->color == BLACK) return rotate(r, true);
r->r->color = BLACK;
}
return update(r);
}
if (l->level > r->level) {
l = propagate(l);
Node *c = (l->r = submerge(l->r, r));
if (l->color == BLACK && c->color == RED && c->r && c->r->color == RED) {
l->color = RED;
c->color = BLACK;
if (l->l->color == BLACK) return rotate(l, false);
l->l->color = BLACK;
}
return update(l);
}
return alloc(l, r);
}
Node *build(int l, int r, const vector<Monoid> &v) {
if (l + 1 >= r) return alloc(v[l]);
return merge(build(l, (l + r) >> 1, v), build((l + r) >> 1, r, v));
}
Node *update(Node *t) {
t->cnt = count(t->l) + count(t->r) + t->is_leaf();
t->level = t->is_leaf() ? 0 : t->l->level + (t->l->color == BLACK);
t->sum = f(f(sum(t->l), t->key), sum(t->r));
return t;
}
void dump(Node *r, typename vector<Monoid>::iterator &it,
OperatorMonoid lazy) {
if (r->lazy != OM0) lazy = h(lazy, r->lazy);
if (r->is_leaf()) {
*it++ = g(r->key, lazy);
return;
}
dump(r->l, it, lazy);
dump(r->r, it, lazy);
}
Node *merge(Node *l) { return l; }
public:
VectorPool<Node> pool;
const F f;
const G g;
const H h;
const OperatorMonoid OM0;
const Monoid M1;
LazyRedBlackTree(int sz, const F &f, const G &g, const H &h, const Monoid &M1,
const OperatorMonoid &OM0)
: pool(sz), M1(M1), OM0(OM0), f(f), g(g), h(h) {
pool.clear();
}
inline Node *alloc(const Monoid &key) {
return &(*pool.alloc() = Node(key, OM0));
}
inline int count(const Node *t) { return t ? t->cnt : 0; }
inline const Monoid &sum(const Node *t) { return t ? t->sum : M1; }
pair<Node *, Node *> split(Node *t, int k) {
if (!t) return {nullptr, nullptr};
t = propagate(t);
if (k == 0) return {nullptr, t};
if (k >= count(t)) return {t, nullptr};
Node *l = t->l, *r = t->r;
pool.free(t);
if (k < count(l)) {
auto pp = split(l, k);
return {pp.first, merge(pp.second, r)};
}
if (k > count(l)) {
auto pp = split(r, k - count(l));
return {merge(l, pp.first), pp.second};
}
return {l, r};
}
tuple<Node *, Node *, Node *> split3(Node *t, int a, int b) {
auto x = split(t, a);
auto y = split(x.second, b - a);
return make_tuple(x.first, y.first, y.second);
}
template <typename... Args>
Node *merge(Node *l, Args... rest) {
Node *r = merge(rest...);
if (!l || !r) return l ? l : r;
Node *c = submerge(l, r);
c->color = BLACK;
return c;
}
Node *build(const vector<Monoid> &v) { return build(0, (int)v.size(), v); }
vector<Monoid> dump(Node *r) {
vector<Monoid> v((size_t)count(r));
auto it = begin(v);
dump(r, it, OM0);
return v;
}
string to_string(Node *r) {
auto s = dump(r);
string ret;
for (int i = 0; i < s.size(); i++) {
ret += std::to_string(s[i]);
ret += ", ";
}
return ret;
}
void insert(Node *&t, int k, const Monoid &v) {
auto x = split(t, k);
t = merge(merge(x.first, alloc(v)), x.second);
}
Monoid erase(Node *&t, int k) {
auto x = split(t, k);
auto y = split(x.second, 1);
auto v = y.first->key;
pool.free(y.first);
t = merge(x.first, y.second);
return v;
}
Monoid query(Node *&t, int a, int b) {
auto x = split(t, a);
auto y = split(x.second, b - a);
Monoid ret = sum(y.first);
t = merge(x.first, y.first, y.second);
return ret;
}
void set_propagate(Node *&t, int a, int b, const OperatorMonoid &pp) {
auto x = split(t, a);
auto y = split(x.second, b - a);
y.first->lazy = h(y.first->lazy, pp);
t = merge(x.first, propagate(y.first), y.second);
}
void set_element(Node *&t, int k, const Monoid &x) {
t = propagate(t);
if (t->is_leaf()) {
t->key = t->sum = x;
return;
}
if (k < count(t->l))
set_element(t->l, k, x);
else
set_element(t->r, k - count(t->l), x);
t = update(t);
}
void push_front(Node *&t, const Monoid &v) { t = merge(alloc(v), t); }
void push_back(Node *&t, const Monoid &v) { t = merge(t, alloc(v)); }
Monoid pop_front(Node *&t) {
auto ret = split(t, 1);
t = ret.second;
return ret.first->key;
}
Monoid pop_back(Node *&t) {
auto ret = split(t, count(t) - 1);
t = ret.first;
return ret.second->key;
}
};
#line 1 "structure/bbst/lazy-red-black-tree.hpp"
/**
* @brief Lazy-Red-Black-Tree(遅延伝搬赤黒木)
*
*/
template <typename Monoid, typename OperatorMonoid, typename F, typename G,
typename H>
struct LazyRedBlackTree {
public:
enum COLOR { BLACK, RED };
struct Node {
Node *l, *r;
COLOR color;
int level, cnt;
Monoid key, sum;
OperatorMonoid lazy;
Node() {}
Node(const Monoid &k, const OperatorMonoid &laz)
: key(k),
sum(k),
l(nullptr),
r(nullptr),
color(BLACK),
level(0),
cnt(1),
lazy(laz) {}
Node(Node *l, Node *r, const Monoid &k, const OperatorMonoid &laz)
: key(k), color(RED), l(l), r(r), lazy(laz) {}
bool is_leaf() const { return l == nullptr; }
};
private:
Node *propagate(Node *t) {
t = clone(t);
if (t->lazy != OM0) {
if (t->is_leaf()) {
t->key = g(t->key, t->lazy);
} else {
if (t->l) {
t->l = clone(t->l);
t->l->lazy = h(t->l->lazy, t->lazy);
t->l->sum = g(t->l->sum, t->lazy);
}
if (t->r) {
t->r = clone(t->r);
t->r->lazy = h(t->r->lazy, t->lazy);
t->r->sum = g(t->r->sum, t->lazy);
}
}
t->lazy = OM0;
}
return update(t);
}
inline Node *alloc(Node *l, Node *r) {
auto t = &(*pool.alloc() = Node(l, r, M1, OM0));
return update(t);
}
virtual Node *clone(Node *t) { return t; }
Node *rotate(Node *t, bool b) {
t = propagate(t);
Node *s;
if (b) {
s = propagate(t->l);
t->l = s->r;
s->r = t;
} else {
s = propagate(t->r);
t->r = s->l;
s->l = t;
}
update(t);
return update(s);
}
Node *submerge(Node *l, Node *r) {
if (l->level < r->level) {
r = propagate(r);
Node *c = (r->l = submerge(l, r->l));
if (r->color == BLACK && c->color == RED && c->l && c->l->color == RED) {
r->color = RED;
c->color = BLACK;
if (r->r->color == BLACK) return rotate(r, true);
r->r->color = BLACK;
}
return update(r);
}
if (l->level > r->level) {
l = propagate(l);
Node *c = (l->r = submerge(l->r, r));
if (l->color == BLACK && c->color == RED && c->r && c->r->color == RED) {
l->color = RED;
c->color = BLACK;
if (l->l->color == BLACK) return rotate(l, false);
l->l->color = BLACK;
}
return update(l);
}
return alloc(l, r);
}
Node *build(int l, int r, const vector<Monoid> &v) {
if (l + 1 >= r) return alloc(v[l]);
return merge(build(l, (l + r) >> 1, v), build((l + r) >> 1, r, v));
}
Node *update(Node *t) {
t->cnt = count(t->l) + count(t->r) + t->is_leaf();
t->level = t->is_leaf() ? 0 : t->l->level + (t->l->color == BLACK);
t->sum = f(f(sum(t->l), t->key), sum(t->r));
return t;
}
void dump(Node *r, typename vector<Monoid>::iterator &it,
OperatorMonoid lazy) {
if (r->lazy != OM0) lazy = h(lazy, r->lazy);
if (r->is_leaf()) {
*it++ = g(r->key, lazy);
return;
}
dump(r->l, it, lazy);
dump(r->r, it, lazy);
}
Node *merge(Node *l) { return l; }
public:
VectorPool<Node> pool;
const F f;
const G g;
const H h;
const OperatorMonoid OM0;
const Monoid M1;
LazyRedBlackTree(int sz, const F &f, const G &g, const H &h, const Monoid &M1,
const OperatorMonoid &OM0)
: pool(sz), M1(M1), OM0(OM0), f(f), g(g), h(h) {
pool.clear();
}
inline Node *alloc(const Monoid &key) {
return &(*pool.alloc() = Node(key, OM0));
}
inline int count(const Node *t) { return t ? t->cnt : 0; }
inline const Monoid &sum(const Node *t) { return t ? t->sum : M1; }
pair<Node *, Node *> split(Node *t, int k) {
if (!t) return {nullptr, nullptr};
t = propagate(t);
if (k == 0) return {nullptr, t};
if (k >= count(t)) return {t, nullptr};
Node *l = t->l, *r = t->r;
pool.free(t);
if (k < count(l)) {
auto pp = split(l, k);
return {pp.first, merge(pp.second, r)};
}
if (k > count(l)) {
auto pp = split(r, k - count(l));
return {merge(l, pp.first), pp.second};
}
return {l, r};
}
tuple<Node *, Node *, Node *> split3(Node *t, int a, int b) {
auto x = split(t, a);
auto y = split(x.second, b - a);
return make_tuple(x.first, y.first, y.second);
}
template <typename... Args>
Node *merge(Node *l, Args... rest) {
Node *r = merge(rest...);
if (!l || !r) return l ? l : r;
Node *c = submerge(l, r);
c->color = BLACK;
return c;
}
Node *build(const vector<Monoid> &v) { return build(0, (int)v.size(), v); }
vector<Monoid> dump(Node *r) {
vector<Monoid> v((size_t)count(r));
auto it = begin(v);
dump(r, it, OM0);
return v;
}
string to_string(Node *r) {
auto s = dump(r);
string ret;
for (int i = 0; i < s.size(); i++) {
ret += std::to_string(s[i]);
ret += ", ";
}
return ret;
}
void insert(Node *&t, int k, const Monoid &v) {
auto x = split(t, k);
t = merge(merge(x.first, alloc(v)), x.second);
}
Monoid erase(Node *&t, int k) {
auto x = split(t, k);
auto y = split(x.second, 1);
auto v = y.first->key;
pool.free(y.first);
t = merge(x.first, y.second);
return v;
}
Monoid query(Node *&t, int a, int b) {
auto x = split(t, a);
auto y = split(x.second, b - a);
Monoid ret = sum(y.first);
t = merge(x.first, y.first, y.second);
return ret;
}
void set_propagate(Node *&t, int a, int b, const OperatorMonoid &pp) {
auto x = split(t, a);
auto y = split(x.second, b - a);
y.first->lazy = h(y.first->lazy, pp);
t = merge(x.first, propagate(y.first), y.second);
}
void set_element(Node *&t, int k, const Monoid &x) {
t = propagate(t);
if (t->is_leaf()) {
t->key = t->sum = x;
return;
}
if (k < count(t->l))
set_element(t->l, k, x);
else
set_element(t->r, k - count(t->l), x);
t = update(t);
}
void push_front(Node *&t, const Monoid &v) { t = merge(alloc(v), t); }
void push_back(Node *&t, const Monoid &v) { t = merge(t, alloc(v)); }
Monoid pop_front(Node *&t) {
auto ret = split(t, 1);
t = ret.second;
return ret.first->key;
}
Monoid pop_back(Node *&t) {
auto ret = split(t, count(t) - 1);
t = ret.first;
return ret.second->key;
}
};