link-cut-tree.cpp

#include <bits/stdc++.h>
using namespace std;

//BeginCodeSnip{Link Cut Tree}
struct Node {
	int x;
	Node *l = 0;
	Node *r = 0;
	Node *p = 0;
	bool rev = false;

	Node() = default;

	Node(int v) {
		x = v;
	}

	void push() {
		if(rev) {
			rev = false;
			swap(l, r);
			if(l) l->rev ^= true;
			if(r) r->rev ^= true;
		}
	}

	bool is_root() {
		return p == 0 || (p->l != this && this != p->r);
	}
};

struct LCT {
	vector<Node> a;

	LCT(int n) {
		a.resize(n+1);
		for(int i = 1; i <= n; ++i)
		a[i].x = i;
	}

	void rot(Node* c) {
		auto p = c->p;
		auto g = p->p;

		if(!p->is_root())
			(g->r == p ? g->r : g->l) = c;

		p->push();
		c->push();

		if(p->l == c) { // rtr
			p->l = c->r;
			c->r = p;
			if(p->l) p->l->p = p;
		} else { // rtl
			p->r = c->l;
			c->l = p;
			if(p->r) p->r->p = p;
		}

		p->p = c;
		c->p = g;
	}

	void splay(Node* c) {
		while(!c->is_root()) {
			auto p = c->p;
			auto g = p->p;
			if(!p->is_root())
				rot((g->r == p) == (p->r == c) ? p : c);
			rot(c);
		}
		c->push();
	}

	Node* access(int v) {
		Node* last = 0;
		Node* c = &a[v];
		for(Node* p = c; p; p = p->p) {
			splay(p);
			p->r = last;
			last = p;
		}
		splay(c);
		return last;
	}

	void make_root(int v) {
		access(v);
		auto* c = &a[v];
		if(c->l)
			c->l->rev ^= true, c->l = 0;
	}

	void link(int u, int v) {
		make_root(v);
		Node* c = &a[v];
		c->p = &a[u];
	}

	void cut(int u, int v) {
		make_root(u);
		access(v);
		if(a[v].l) {
			a[v].l->p = 0;
			a[v].l = 0;
		}
	}

	bool connected(int u, int v) {
		access(u);
		access(v);
		return a[u].p;
	}
};
//EndCodeSnip

int N, M;

int main() {
	cin.tie(0)->sync_with_stdio(0);

	cin >> N >> M;

	LCT lc(N);

	while(M--) {
		string a; cin >> a;
		int b, c; cin >> b >> c;
		if(a == "add") {
			lc.link(b, c);
		}

		if(a == "rem") {
			lc.cut(b, c);
		}

		if(a == "conn") {
			cout << (lc.connected(b, c) ? "YES" : "NO") << "\n";
		}
	}
}