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d.rs
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d.rs
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use dsu::*;
use proconio::{input, marker::Usize1};
fn main() {
input! {
n: usize,
m: usize,
uv: [(Usize1, Usize1); m],
};
let mut edges = vec![vec![]; n];
let mut dsu = Dsu::new(n);
for (u, v) in uv.iter().copied() {
dsu.merge(u, v);
edges[u].push(v);
edges[v].push(u);
}
for group in dsu.groups() {
let count_v = group.len();
let mut count_e = 0_usize;
for g in group {
count_e += edges[g].len();
}
if count_v * 2 != count_e {
println!("No");
return;
}
}
println!("Yes");
}
//https://github.com/rust-lang-ja/ac-library-rs
pub mod dsu {
/// Implement (union by size) + (path compression)
/// Reference:
/// Zvi Galil and Giuseppe F. Italiano,
/// Data structures and algorithms for disjoint set union problems
pub struct Dsu {
n: usize,
// root node: -1 * component size
// otherwise: parent
parent_or_size: Vec<i32>,
}
impl Dsu {
// 0 <= size <= 10^8 is constrained.
pub fn new(size: usize) -> Self {
Self {
n: size,
parent_or_size: vec![-1; size],
}
}
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
}
pub fn same(&mut self, a: usize, b: usize) -> bool {
assert!(a < self.n);
assert!(b < self.n);
self.leader(a) == self.leader(b)
}
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
}
pub fn size(&mut self, a: usize) -> usize {
assert!(a < self.n);
let x = self.leader(a);
-self.parent_or_size[x] as usize
}
pub fn groups(&mut self) -> Vec<Vec<usize>> {
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::<Vec<Vec<usize>>>()
}
}
#[cfg(test)]
mod tests {
use super::*;
#[test]
fn dsu_works() {
let mut d = Dsu::new(4);
d.merge(0, 1);
assert_eq!(d.same(0, 1), true);
d.merge(1, 2);
assert_eq!(d.same(0, 2), true);
assert_eq!(d.size(0), 3);
assert_eq!(d.same(0, 3), false);
assert_eq!(d.groups(), vec![vec![0, 1, 2], vec![3]]);
}
}
}