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constexpr ll queryDefault = 0;
constexpr ll updateDefault = 0;
ll _modify(ll x, ll y) {
return x + y;
}
ll _query(ll x, ll y) {
return x + y;
}
ll _update(ll delta, int length) {
if (delta == updateDefault) return updateDefault;
//ll result = delta
//for (int i=1; i<length; i++) result = _query(result, delta);
return delta * length;
}
//generic:
ll joinValueDelta(ll value, ll delta) {
if (delta == updateDefault) return value;
return _modify(value, delta);
}
ll joinDeltas(ll delta1, ll delta2) {
if (delta1 == updateDefault) return delta2;
if (delta2 == updateDefault) return delta1;
return _modify(delta1, delta2);
}
struct LCT {
struct Node {
ll nodeValue, subTreeValue, delta;
bool revert;
int id, size;
Node *left, *right, *parent;
Node(int id = 0, int val = queryDefault) :
nodeValue(val), subTreeValue(val), delta(updateDefault),
revert(false), id(id), size(1),
left(nullptr), right(nullptr), parent(nullptr) {}
bool isRoot() {
return !parent || (parent->left != this &&
parent->right != this);
}
void push() {
if (revert) {
revert = false;
swap(left, right);
if (left) left->revert ^= 1;
if (right) right->revert ^= 1;
}
nodeValue = joinValueDelta(nodeValue, delta);
subTreeValue = joinValueDelta(subTreeValue,
_update(delta, size));
if (left) left->delta = joinDeltas(left->delta, delta);
if (right) right->delta = joinDeltas(right->delta, delta);
delta = updateDefault;
}
ll getSubtreeValue() {
return joinValueDelta(subTreeValue, _update(delta, size));
}
void update() {
subTreeValue = joinValueDelta(nodeValue, delta);
size = 1;
if (left) {
subTreeValue = _query(subTreeValue,
left->getSubtreeValue());
size += left->size;
}
if (right) {
subTreeValue = _query(subTreeValue,
right->getSubtreeValue());
size += right->size;
}}
};
vector<Node> nodes;
LCT(int n) : nodes(n) {
for (int i = 0; i < n; i++) nodes[i].id = i;
}
void connect(Node* ch, Node* p, int isLeftChild) {
if (ch) ch->parent = p;
if (isLeftChild >= 0) {
if (isLeftChild) p->left = ch;
else p->right = ch;
}}
void rotate(Node* x) {
Node* p = x->parent;
Node* g = p->parent;
bool isRootP = p->isRoot();
bool leftChildX = (x == p->left);
connect(leftChildX ? x->right : x->left, p, leftChildX);
connect(p, x, !leftChildX);
connect(x, g, isRootP ? -1 : p == g->left);
p->update();
}
void splay(Node* x) {
while (!x->isRoot()) {
Node* p = x->parent;
Node* g = p->parent;
if (!p->isRoot()) g->push();
p->push();
x->push();
if (!p->isRoot()) rotate((x == p->left) ==
(p == g->left) ? p : x);
rotate(x);
}
x->push();
x->update();
}
Node* expose(Node* x) {
Node* last = nullptr;
for (Node* y = x; y; y = y->parent) {
splay(y);
y->left = last;
last = y;
}
splay(x);
return last;
}
void makeRoot(Node* x) {
expose(x);
x->revert ^= 1;
}
bool connected(Node* x, Node* y) {
if (x == y) return true;
expose(x);
expose(y);
return x->parent;
}
void link(Node* x, Node* y) {
assert(!connected(x, y)); // not yet connected!
makeRoot(x);
x->parent = y;
}
void cut(Node* x, Node* y) {
makeRoot(x);
expose(y);
//must be a tree edge!
assert(!(y->right != x || x->left != nullptr));
y->right->parent = nullptr;
y->right = nullptr;
}
Node* lca(Node* x, Node* y) {
assert(connected(x, y));
expose(x);
return expose(y);
}
ll query(Node* from, Node* to) {
makeRoot(from);
expose(to);
if (to) return to->getSubtreeValue();
return queryDefault;
}
void modify(Node* from, Node* to, ll delta) {
makeRoot(from);
expose(to);
to->delta = joinDeltas(to->delta, delta);
}
};
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