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#include "structure/lct/link-cut-tree-subtree.hpp"
template <typename SUM, typename KEY>
struct LinkCutTreeSubtree {
struct Node {
Node *l, *r, *p;
KEY key;
SUM sum;
bool rev;
int sz;
bool is_root() const { return !p || (p->l != this && p->r != this); }
Node(const KEY &key, const SUM &sum)
: key(key),
sum(sum),
rev(false),
sz(1),
l(nullptr),
r(nullptr),
p(nullptr) {}
};
const SUM ident;
LinkCutTreeSubtree(const SUM &ident) : ident(ident) {}
Node *make_node(const KEY &key) {
auto ret = new Node(key, ident);
update(ret);
return ret;
}
Node *set_key(Node *t, const KEY &key) {
expose(t);
t->key = key;
update(t);
return t;
}
void toggle(Node *t) {
swap(t->l, t->r);
t->sum.toggle();
t->rev ^= true;
}
void push(Node *t) {
if (t->rev) {
if (t->l) toggle(t->l);
if (t->r) toggle(t->r);
t->rev = false;
}
}
void update(Node *t) {
t->sz = 1;
if (t->l) t->sz += t->l->sz;
if (t->r) t->sz += t->r->sz;
t->sum.merge(t->key, t->l ? t->l->sum : ident, t->r ? t->r->sum : ident);
}
void rotr(Node *t) {
auto *x = t->p, *y = x->p;
if ((x->l = t->r)) t->r->p = x;
t->r = x, x->p = t;
update(x), update(t);
if ((t->p = y)) {
if (y->l == x) y->l = t;
if (y->r == x) y->r = t;
update(y);
}
}
void rotl(Node *t) {
auto *x = t->p, *y = x->p;
if ((x->r = t->l)) t->l->p = x;
t->l = x, x->p = t;
update(x), update(t);
if ((t->p = y)) {
if (y->l == x) y->l = t;
if (y->r == x) y->r = t;
update(y);
}
}
void splay(Node *t) {
push(t);
while (!t->is_root()) {
auto *q = t->p;
if (q->is_root()) {
push(q), push(t);
if (q->l == t)
rotr(t);
else
rotl(t);
} else {
auto *r = q->p;
push(r), push(q), push(t);
if (r->l == q) {
if (q->l == t)
rotr(q), rotr(t);
else
rotl(t), rotr(t);
} else {
if (q->r == t)
rotl(q), rotl(t);
else
rotr(t), rotl(t);
}
}
}
}
Node *expose(Node *t) {
Node *rp = nullptr;
for (auto *cur = t; cur; cur = cur->p) {
splay(cur);
if (cur->r) cur->sum.add(cur->r->sum);
cur->r = rp;
if (cur->r) cur->sum.erase(cur->r->sum);
update(cur);
rp = cur;
}
splay(t);
return rp;
}
void link(Node *child, Node *parent) {
expose(child);
expose(parent);
child->p = parent;
parent->r = child;
update(parent);
}
void cut(Node *child) {
expose(child);
auto *parent = child->l;
child->l = nullptr;
parent->p = nullptr;
update(child);
}
void evert(Node *t) {
expose(t);
toggle(t);
push(t);
}
Node *lca(Node *u, Node *v) {
if (get_root(u) != get_root(v)) return nullptr;
expose(u);
return expose(v);
}
Node *get_kth(Node *x, int k) {
expose(x);
while (x) {
push(x);
if (x->r && x->r->sz > k) {
x = x->r;
} else {
if (x->r) k -= x->r->sz;
if (k == 0) return x;
k -= 1;
x = x->l;
}
}
return nullptr;
}
Node *get_root(Node *x) {
expose(x);
while (x->l) {
push(x);
x = x->l;
}
return x;
}
SUM &query(Node *t) {
expose(t);
return t->sum;
}
};
#line 1 "structure/lct/link-cut-tree-subtree.hpp"
template <typename SUM, typename KEY>
struct LinkCutTreeSubtree {
struct Node {
Node *l, *r, *p;
KEY key;
SUM sum;
bool rev;
int sz;
bool is_root() const { return !p || (p->l != this && p->r != this); }
Node(const KEY &key, const SUM &sum)
: key(key),
sum(sum),
rev(false),
sz(1),
l(nullptr),
r(nullptr),
p(nullptr) {}
};
const SUM ident;
LinkCutTreeSubtree(const SUM &ident) : ident(ident) {}
Node *make_node(const KEY &key) {
auto ret = new Node(key, ident);
update(ret);
return ret;
}
Node *set_key(Node *t, const KEY &key) {
expose(t);
t->key = key;
update(t);
return t;
}
void toggle(Node *t) {
swap(t->l, t->r);
t->sum.toggle();
t->rev ^= true;
}
void push(Node *t) {
if (t->rev) {
if (t->l) toggle(t->l);
if (t->r) toggle(t->r);
t->rev = false;
}
}
void update(Node *t) {
t->sz = 1;
if (t->l) t->sz += t->l->sz;
if (t->r) t->sz += t->r->sz;
t->sum.merge(t->key, t->l ? t->l->sum : ident, t->r ? t->r->sum : ident);
}
void rotr(Node *t) {
auto *x = t->p, *y = x->p;
if ((x->l = t->r)) t->r->p = x;
t->r = x, x->p = t;
update(x), update(t);
if ((t->p = y)) {
if (y->l == x) y->l = t;
if (y->r == x) y->r = t;
update(y);
}
}
void rotl(Node *t) {
auto *x = t->p, *y = x->p;
if ((x->r = t->l)) t->l->p = x;
t->l = x, x->p = t;
update(x), update(t);
if ((t->p = y)) {
if (y->l == x) y->l = t;
if (y->r == x) y->r = t;
update(y);
}
}
void splay(Node *t) {
push(t);
while (!t->is_root()) {
auto *q = t->p;
if (q->is_root()) {
push(q), push(t);
if (q->l == t)
rotr(t);
else
rotl(t);
} else {
auto *r = q->p;
push(r), push(q), push(t);
if (r->l == q) {
if (q->l == t)
rotr(q), rotr(t);
else
rotl(t), rotr(t);
} else {
if (q->r == t)
rotl(q), rotl(t);
else
rotr(t), rotl(t);
}
}
}
}
Node *expose(Node *t) {
Node *rp = nullptr;
for (auto *cur = t; cur; cur = cur->p) {
splay(cur);
if (cur->r) cur->sum.add(cur->r->sum);
cur->r = rp;
if (cur->r) cur->sum.erase(cur->r->sum);
update(cur);
rp = cur;
}
splay(t);
return rp;
}
void link(Node *child, Node *parent) {
expose(child);
expose(parent);
child->p = parent;
parent->r = child;
update(parent);
}
void cut(Node *child) {
expose(child);
auto *parent = child->l;
child->l = nullptr;
parent->p = nullptr;
update(child);
}
void evert(Node *t) {
expose(t);
toggle(t);
push(t);
}
Node *lca(Node *u, Node *v) {
if (get_root(u) != get_root(v)) return nullptr;
expose(u);
return expose(v);
}
Node *get_kth(Node *x, int k) {
expose(x);
while (x) {
push(x);
if (x->r && x->r->sz > k) {
x = x->r;
} else {
if (x->r) k -= x->r->sz;
if (k == 0) return x;
k -= 1;
x = x->l;
}
}
return nullptr;
}
Node *get_root(Node *x) {
expose(x);
while (x->l) {
push(x);
x = x->l;
}
return x;
}
SUM &query(Node *t) {
expose(t);
return t->sum;
}
};