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| #include <bits/stdc++.h>
template <typename T, typename Comp = std::less<T>>
class splay_tree {
using size_type = int;
Comp comp_;
struct node {
node *children[2]{nullptr, nullptr}, *parent = nullptr;
size_type size = 1;
T key;
node(auto&& key) : key(std::forward<decltype(key)>(key)) {}
~node() { delete children[0], delete children[1]; }
};
node* copy_node(node* x) {
if (x == nullptr) return nullptr;
node* ret = new node(x->key);
ret->size = x->size;
for (int i = 0; i < 2; ++i) {
ret->children[i] = copy_node(x->children[i]);
if (ret->children[i] != nullptr) ret->children[i]->parent = ret;
}
return ret;
}
node* root = nullptr;
static void maintain_size(node* x) {
x->size = 1;
if (x->children[0] != nullptr) x->size += x->children[0]->size;
if (x->children[1] != nullptr) x->size += x->children[1]->size;
}
static void rotate_up(node* x) {
node *y = x->parent, *z = y->parent;
int chk = x == y->children[1];
y->children[chk] = x->children[chk ^ 1];
if (x->children[chk ^ 1] != nullptr) x->children[chk ^ 1]->parent = y;
x->children[chk ^ 1] = y;
y->parent = x;
x->parent = z;
if (z != nullptr) z->children[y == z->children[1]] = x;
maintain_size(y);
maintain_size(x);
}
static node* splay(node* x) {
for (node* f; (f = x->parent) != nullptr; rotate_up(x))
if (f->parent != nullptr) rotate_up((x == f->children[1]) == (f == f->parent->children[1]) ? f : x);
return x;
}
public:
explicit splay_tree(Comp comp = Comp()) : comp_(comp){};
~splay_tree() { delete root; }
splay_tree(splay_tree&& other) noexcept : comp_(std::move(other.comp_)), root(other.root) { other.root = nullptr; }
splay_tree& operator=(splay_tree&& other) noexcept {
delete root;
comp_ = std::move(other.comp_);
root = other.root;
other.root = nullptr;
return *this;
}
splay_tree(const splay_tree& other) : comp_(other.comp_) { root = copy_node(other.root); }
splay_tree& operator=(const splay_tree& other) {
delete root;
comp_ = other.comp_;
root = copy_node(other.root);
return *this;
}
size_type size() const noexcept { return root == nullptr ? 0 : root->size; }
bool empty() const noexcept { return root == nullptr; }
const T& top() const {
assert(!empty());
return root->key;
}
size_type rank() const {
assert(!empty());
return root->children[0] == nullptr ? 0 : root->children[0]->size;
}
void insert(auto&& key) {
if (empty()) {
root = new node(std::forward<decltype(key)>(key));
return;
}
node *x = root, *y = nullptr;
while (x != nullptr) y = x, x = x->children[comp_(x->key, key)];
x = new node(std::forward<decltype(key)>(key));
x->parent = y;
y->children[comp_(y->key, key)] = x;
root = splay(x);
}
bool prev() {
if (empty() || root->children[0] == nullptr) return false;
node* x = root->children[0];
while (x->children[1] != nullptr) x = x->children[1];
root = splay(x);
return true;
}
bool next() {
if (empty() || root->children[1] == nullptr) return false;
node* x = root->children[1];
while (x->children[0] != nullptr) x = x->children[0];
root = splay(x);
return true;
}
bool upper_bound(auto&& key) {
if (empty()) return false;
node *x = root, *y = nullptr, *ret = nullptr;
while (x != nullptr) {
y = x;
bool chk = comp_(key, x->key);
if (chk) ret = x;
x = x->children[!chk];
}
root = splay(ret == nullptr ? y : ret);
return ret != nullptr;
}
bool lower_bound(auto&& key) {
if (empty()) return false;
node *x = root, *y = nullptr, *ret = nullptr;
while (x != nullptr) {
y = x;
bool chk = comp_(x->key, key);
if (!chk) ret = x;
x = x->children[chk];
}
root = splay(ret == nullptr ? y : ret);
return ret != nullptr;
}
bool at(size_type k) {
if (size() <= k) return false;
node* x = root;
for (;;) {
size_type left_size = x->children[0] == nullptr ? 0 : x->children[0]->size;
if (left_size == k) {
root = splay(x);
return true;
}
if (left_size > k)
x = x->children[0];
else
k -= left_size + 1, x = x->children[1];
}
}
void pop() {
assert(!empty());
std::unique_ptr<node> old_root(root);
root = nullptr;
if (old_root->children[0] == nullptr && old_root->children[1] == nullptr) return;
for (int k = 0; k < 2; ++k) {
if (old_root->children[k ^ 1] == nullptr) {
root = old_root->children[k];
old_root->children[k] = nullptr;
root->parent = nullptr;
return;
}
}
node *x = old_root->children[0], *y = old_root->children[1];
old_root->children[0] = old_root->children[1] = nullptr;
x->parent = y->parent = nullptr;
while (x->children[1] != nullptr) x = x->children[1];
root = splay(x);
root->children[1] = y;
root->size += y->size;
y->parent = root;
}
splay_tree split_right() {
assert(!empty());
splay_tree ret;
if (root->children[1] == nullptr) return ret;
ret.root = root->children[1];
root->children[1] = nullptr;
ret.root->parent = nullptr;
root->size -= ret.root->size;
return ret;
}
splay_tree split_left() {
assert(!empty());
splay_tree ret;
if (root->children[0] == nullptr) return ret;
ret.root = root->children[0];
root->children[0] = nullptr;
ret.root->parent = nullptr;
ret.root->size = root->size - ret.root->size;
return ret;
}
void for_each(auto&& f) const {
auto dfs = [&](auto&& dfs, node* x) -> void {
if (x == nullptr) return;
dfs(dfs, x->children[0]);
f(x->key);
dfs(dfs, x->children[1]);
};
dfs(dfs, root);
}
friend std::ostream& operator<<(std::ostream& os, const splay_tree& s) {
size_type i = 0;
s.for_each([&](auto&& key) { os << (i++ ? ", " : "[") << key; });
if (!i) os << '[';
return os << ']';
}
};
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