挿入/削除の可能な配列 (乱択二分探索木)
(binary-search-tree/rbst-array.hpp)
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#pragma once
#include "binary-search-tree/rbst-base.hpp"
template <typename T>
struct RBSTArrayNode {
typename RBSTBase<RBSTArrayNode>::Ptr l, r;
T key;
int cnt;
RBSTArrayNode(const T& t = T()) : l(), r(), key(t), cnt(1) {}
};
template <class T>
struct RBSTArray : RBSTBase<RBSTArrayNode<T>> {
using Node = RBSTArrayNode<T>;
using base = RBSTBase<Node>;
using base::merge;
using base::split;
using typename base::Ptr;
RBSTArray() = default;
T get(Ptr& t, int k) {
auto x = split(t, k);
auto y = split(x.second, 1);
T v = y.first->key;
t = merge(x.first, merge(y.first, y.second));
return v;
}
void set(Ptr& t, int k, T v) {
auto x = split(t, k);
auto y = split(x.second, 1);
y.first->key = v;
t = merge(x.first, merge(y.first, y.second));
}
protected:
Ptr update(Ptr t) override {
t->cnt = 1;
if (t->l) t->cnt += t->l->cnt;
if (t->r) t->cnt += t->r->cnt;
return t;
}
void push(Ptr t) override {}
};
/**
* @brief 挿入/削除の可能な配列 (乱択二分探索木)
*/
#line 2 "binary-search-tree/rbst-base.hpp"
template <class Node>
struct RBSTBase {
using Ptr = Node*;
template <typename... Args>
inline Ptr my_new(Args... args) {
return new Node(args...);
}
inline void my_del(Ptr t) { delete t; }
inline Ptr make_tree() const { return nullptr; }
int size(Ptr t) const { return count(t); }
Ptr merge(Ptr l, Ptr r) {
if (!l || !r) return l ? l : r;
if (int((rng() * (l->cnt + r->cnt)) >> 32) < l->cnt) {
push(l);
l->r = merge(l->r, r);
return update(l);
} else {
push(r);
r->l = merge(l, r->l);
return update(r);
}
}
pair<Ptr, Ptr> split(Ptr t, int k) {
if (!t) return {nullptr, nullptr};
push(t);
if (k <= count(t->l)) {
auto s = split(t->l, k);
t->l = s.second;
return {s.first, update(t)};
} else {
auto s = split(t->r, k - count(t->l) - 1);
t->r = s.first;
return {update(t), s.second};
}
}
Ptr build(int l, int r, const vector<decltype(Node::key)>& v) {
if (l + 1 == r) return my_new(v[l]);
int m = (l + r) >> 1;
Ptr pm = my_new(v[m]);
if (l < m) pm->l = build(l, m, v);
if (m + 1 < r) pm->r = build(m + 1, r, v);
return update(pm);
}
Ptr build(const vector<decltype(Node::key)>& v) {
return build(0, (int)v.size(), v);
}
template <typename... Args>
void insert(Ptr& t, int k, const Args&... args) {
auto x = split(t, k);
t = merge(merge(x.first, my_new(args...)), x.second);
}
void erase(Ptr& t, int k) {
auto x = split(t, k);
auto y = split(x.second, 1);
my_del(y.first);
t = merge(x.first, y.second);
}
protected:
static uint64_t rng() {
static uint64_t x_ = 123456789ull;
return x_ ^= x_ << 7, x_ ^= x_ >> 9, x_ & 0xFFFFFFFFull;
}
inline int count(const Ptr t) const { return t ? t->cnt : 0; }
virtual void push(Ptr) = 0;
virtual Ptr update(Ptr) = 0;
};
/**
* @brief Randomized Binary Search Tree (基底クラス)
* @docs docs/binary-search-tree/rbst-base.md
*/
#line 3 "binary-search-tree/rbst-array.hpp"
template <typename T>
struct RBSTArrayNode {
typename RBSTBase<RBSTArrayNode>::Ptr l, r;
T key;
int cnt;
RBSTArrayNode(const T& t = T()) : l(), r(), key(t), cnt(1) {}
};
template <class T>
struct RBSTArray : RBSTBase<RBSTArrayNode<T>> {
using Node = RBSTArrayNode<T>;
using base = RBSTBase<Node>;
using base::merge;
using base::split;
using typename base::Ptr;
RBSTArray() = default;
T get(Ptr& t, int k) {
auto x = split(t, k);
auto y = split(x.second, 1);
T v = y.first->key;
t = merge(x.first, merge(y.first, y.second));
return v;
}
void set(Ptr& t, int k, T v) {
auto x = split(t, k);
auto y = split(x.second, 1);
y.first->key = v;
t = merge(x.first, merge(y.first, y.second));
}
protected:
Ptr update(Ptr t) override {
t->cnt = 1;
if (t->l) t->cnt += t->l->cnt;
if (t->r) t->cnt += t->r->cnt;
return t;
}
void push(Ptr t) override {}
};
/**
* @brief 挿入/削除の可能な配列 (乱択二分探索木)
*/
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