//https://github.com/rust-lang-ja/ac-library-rs pub mod dsu { //! A Disjoint set union (DSU) with union by size and path compression. /// A Disjoint set union (DSU) with union by size and path compression. /// /// See: [Zvi Galil and Giuseppe F. Italiano, Data structures and algorithms for disjoint set union problems](https://core.ac.uk/download/pdf/161439519.pdf) /// /// In the following documentation, let $n$ be the size of the DSU. /// /// # Example /// /// ``` /// use ac_library_rs::Dsu; /// use proconio::{input, source::once::OnceSource}; /// /// input! { /// from OnceSource::from( /// "5\n\ /// 3\n\ /// 0 1\n\ /// 2 3\n\ /// 3 4\n", /// ), /// n: usize, /// abs: [(usize, usize)], /// } /// /// let mut dsu = Dsu::new(n); /// for (a, b) in abs { /// dsu.merge(a, b); /// } /// /// assert!(dsu.same(0, 1)); /// assert!(!dsu.same(1, 2)); /// assert!(dsu.same(2, 4)); /// /// assert_eq!( /// dsu.groups() /// .into_iter() /// .map(|mut group| { /// group.sort_unstable(); /// group /// }) /// .collect::>(), /// [&[0, 1][..], &[2, 3, 4][..]], /// ); /// ``` pub struct Dsu { n: usize, // root node: -1 * component size // otherwise: parent parent_or_size: Vec, } impl Dsu { /// Creates a new `Dsu`. /// /// # Constraints /// /// - $0 \leq n \leq 10^8$ /// /// # Complexity /// /// - $O(n)$ pub fn new(size: usize) -> Self { Self { n: size, parent_or_size: vec![-1; size], } } // `\textsc` does not work in KaTeX /// Performs the Uɴɪᴏɴ operation. /// /// # Constraints /// /// - $0 \leq a < n$ /// - $0 \leq b < n$ /// /// # Panics /// /// Panics if the above constraints are not satisfied. /// /// # Complexity /// /// - $O(\alpha(n))$ amortized pub fn merge(&mut self, a: usize, b: usize) -> usize { assert!(a < self.n); assert!(b < self.n); let (mut x, mut y) = (self.leader(a), self.leader(b)); if x == y { return x; } if -self.parent_or_size[x] < -self.parent_or_size[y] { std::mem::swap(&mut x, &mut y); } self.parent_or_size[x] += self.parent_or_size[y]; self.parent_or_size[y] = x as i32; x } /// Returns whether the vertices $a$ and $b$ are in the same connected component. /// /// # Constraints /// /// - $0 \leq a < n$ /// - $0 \leq b < n$ /// /// # Panics /// /// Panics if the above constraint is not satisfied. /// /// # Complexity /// /// - $O(\alpha(n))$ amortized pub fn same(&mut self, a: usize, b: usize) -> bool { assert!(a < self.n); assert!(b < self.n); self.leader(a) == self.leader(b) } /// Performs the Fɪɴᴅ operation. /// /// # Constraints /// /// - $0 \leq a < n$ /// /// # Panics /// /// Panics if the above constraint is not satisfied. /// /// # Complexity /// /// - $O(\alpha(n))$ amortized pub fn leader(&mut self, a: usize) -> usize { assert!(a < self.n); if self.parent_or_size[a] < 0 { return a; } self.parent_or_size[a] = self.leader(self.parent_or_size[a] as usize) as i32; self.parent_or_size[a] as usize } /// Returns the size of the connected component that contains the vertex $a$. /// /// # Constraints /// /// - $0 \leq a < n$ /// /// # Panics /// /// Panics if the above constraint is not satisfied. /// /// # Complexity /// /// - $O(\alpha(n))$ amortized pub fn size(&mut self, a: usize) -> usize { assert!(a < self.n); let x = self.leader(a); -self.parent_or_size[x] as usize } /// Divides the graph into connected components. /// /// The result may not be ordered. /// /// # Complexity /// /// - $O(n)$ pub fn groups(&mut self) -> Vec> { let mut leader_buf = vec![0; self.n]; let mut group_size = vec![0; self.n]; for i in 0..self.n { leader_buf[i] = self.leader(i); group_size[leader_buf[i]] += 1; } let mut result = vec![Vec::new(); self.n]; for i in 0..self.n { result[i].reserve(group_size[i]); } for i in 0..self.n { result[leader_buf[i]].push(i); } result .into_iter() .filter(|x| !x.is_empty()) .collect::>>() } } #[cfg(test)] mod tests { use super::*; #[test] fn dsu_works() { let mut d = Dsu::new(4); d.merge(0, 1); assert!(d.same(0, 1)); d.merge(1, 2); assert!(d.same(0, 2)); assert_eq!(d.size(0), 3); assert!(!d.same(0, 3)); assert_eq!(d.groups(), vec![vec![0, 1, 2], vec![3]]); } } } use dsu::*; fn solve(scanner: &mut Scanner) { let n: usize = scanner.next(); let q: usize = scanner.next(); let mut leaders = std::collections::BTreeSet::new(); for u in 0..n { leaders.insert(u); } let mut dsu = Dsu::new(n); for _ in 0..q { let t: usize = scanner.next(); if t == 1 { let u: usize = scanner.next(); let v: usize = scanner.next(); let u = u - 1; let v = v - 1; let lu = dsu.leader(u); let lv = dsu.leader(v); dsu.merge(u, v); let l = dsu.leader(u); for &k in [lu, lv].iter() { if k != l { leaders.remove(&k); } } } else { let v: usize = scanner.next(); let v = v - 1; let lv = dsu.leader(v); let mut ans: isize = -1; for &l in leaders.iter() { if l != lv { ans = (l + 1) as isize; break; } } println!("{}", ans); } } } fn main() { let mut scanner = Scanner::new(); let t: usize = 1; for _ in 0..t { solve(&mut scanner); } } pub struct Scanner { buf: Vec, } impl Scanner { fn new() -> Self { Self { buf: vec![] } } fn next(&mut self) -> T { loop { if let Some(x) = self.buf.pop() { return x.parse().ok().expect(""); } let mut source = String::new(); std::io::stdin().read_line(&mut source).expect(""); self.buf = Self::split(source); } } fn split(source: String) -> Vec { source .split_whitespace() .rev() .map(String::from) .collect::>() } }