use input::input; use input::input_array; use tree_fold::Ops; fn main() { let n = input::(); let mut g = vec![Vec::new(); n]; for _ in 0..n - 1 { let [i, j] = input_array::(); let i = i - 1; let j = j - 1; g[i].push(j); g[j].push(i); } let dp = O {}.two_way_tree_fold(0, &g); let ans = dp.iter().map(|value| value.black).min().unwrap(); println!("{ans}"); } #[derive(Clone, Copy)] struct Acc { pwhite: usize, pblack: usize, } impl std::fmt::Debug for Acc { fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result { f.debug_tuple("") .field(&self.pwhite) .field(&self.pblack) .finish() } } #[derive(Clone, Copy, Default)] struct Value { white: usize, black: usize, } impl std::fmt::Debug for Value { fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result { f.debug_tuple("") .field(&self.white) .field(&self.black) .finish() } } struct O {} impl tree_fold::Ops for O { type Acc = Acc; type Value = Value; fn identity(&self) -> Self::Acc { Acc { pwhite: 0, pblack: 0, } } fn proj(&self, value: Self::Value) -> Self::Acc { Acc { pwhite: value.white.max(value.black), pblack: value.white + 1, } } fn mul(&self, acc: Self::Acc, value: Self::Acc) -> Self::Acc { Acc { pwhite: acc.pwhite + value.pwhite, pblack: acc.pblack + value.pblack, } } fn finish(&self, acc: Self::Acc, _index: usize) -> Self::Value { Value { white: acc.pwhite, black: acc.pblack, } } } // tree_fold {{{ #[allow(dead_code)] mod tree_fold { use std::fmt::Debug; pub trait Ops: Sized { type Value: Clone + Debug + Default; type Acc: Clone + Debug; fn identity(&self) -> Self::Acc; fn proj(&self, value: Self::Value) -> Self::Acc; fn mul(&self, acc: Self::Acc, value: Self::Acc) -> Self::Acc; fn finish(&self, acc: Self::Acc, index: usize) -> Self::Value; fn tree_fold(&self, root: usize, g: &[Vec]) -> Vec { self.tree_fold_by_iter(root, g.len(), |x| g[x].iter().copied()) } fn tree_fold_by_iter( &self, root: usize, n: usize, g: impl Fn(usize) -> A, ) -> Vec where I: Iterator, A: IntoIterator, { let sort_tree = sort_tree(root, n, &g); fold_up(self, &sort_tree) } fn two_way_tree_fold(&self, root: usize, g: &[Vec]) -> Vec { self.two_way_tree_fold_by_iter(root, g.len(), |x| g[x].iter().copied()) } fn two_way_tree_fold_by_iter( &self, root: usize, n: usize, g: impl Fn(usize) -> A, ) -> Vec where I: Iterator, A: IntoIterator, { let sort_tree = sort_tree(root, n, &g); let dp = fold_up_without_finish(self, &sort_tree); fold_down(self, &sort_tree, &dp) } } fn fold_up(ops: &O, sort_tree: &SortedTree) -> Vec { let n = sort_tree.len(); let mut dp = vec![O::Value::default(); n]; for &x in sort_tree.ord.iter().rev() { dp[x] = ops.finish( sort_tree.child[x].iter().fold(ops.identity(), |acc, &y| { ops.mul(acc, ops.proj(dp[y].clone())) }), x, ); } dp } fn fold_up_without_finish(ops: &O, sort_tree: &SortedTree) -> Vec { let n = sort_tree.len(); let mut dp = vec![ops.identity(); n]; for &x in sort_tree.ord.iter().rev() { dp[x] = sort_tree.child[x].iter().fold(ops.identity(), |acc, &y| { ops.mul(acc, ops.proj(ops.finish(dp[y].clone(), y))) }) } dp } fn fold_down(ops: &O, sort_tree: &SortedTree, dp: &[O::Acc]) -> Vec { let n = sort_tree.len(); let mut ep = vec![ops.identity(); n]; let g = &sort_tree.child; for &x in &sort_tree.ord { if !g[x].is_empty() { let mut acc_rev = vec![ops.identity()]; for &y in g[x].iter().rev().take(g[x].len() - 1) { let aug = ops.mul( acc_rev.last().unwrap().clone(), ops.proj(ops.finish(dp[y].clone(), y)), ); acc_rev.push(aug); } let mut acc = ep[x].clone(); for (&y, acc_rev) in g[x].iter().zip(acc_rev.iter().rev().cloned()) { ep[y] = ops.proj(ops.finish(ops.mul(acc.clone(), acc_rev), y)); acc = ops.mul(acc.clone(), ops.proj(ops.finish(dp[y].clone(), y))); } } } dp.iter() .zip(&ep) .enumerate() .map(|(x, (dp_x, ep_x))| ops.finish(ops.mul(dp_x.clone(), ep_x.clone()), x)) .collect::>() } fn sort_tree(root: usize, n: usize, g: impl Fn(usize) -> A) -> SortedTree where I: Iterator, A: IntoIterator, { fn dfs( x: usize, p: usize, g: &impl Fn(usize) -> A, child: &mut [Vec], parent: &mut [usize], ord: &mut Vec, ) where I: Iterator, A: IntoIterator, { parent[x] = p; ord.push(x); child[x] = g(x) .into_iter() .filter(|&y| y != p) .inspect(|&y| dfs(y, x, g, child, parent, ord)) .collect::>() } let mut parent = vec![!0; n]; let mut child = vec![Vec::new(); n]; let mut ord = Vec::new(); dfs(root, root, &g, &mut child, &mut parent, &mut ord); SortedTree { child, parent, ord } } #[derive(Clone, Debug, Default, Hash, PartialEq)] struct SortedTree { child: Vec>, parent: Vec, ord: Vec, } impl SortedTree { fn len(&self) -> usize { self.child.len() } } } // }}} // input {{{ #[allow(dead_code)] mod input { use std::cell::Cell; use std::convert::TryFrom; use std::io::stdin; use std::io::BufRead; use std::io::BufReader; use std::io::Lines; use std::io::Stdin; use std::str::FromStr; use std::sync::Mutex; use std::sync::Once; type Server = Mutex>>; static ONCE: Once = Once::new(); pub struct Lazy(Cell>); unsafe impl Sync for Lazy {} fn line() -> String { static SYNCER: Lazy = Lazy(Cell::new(None)); ONCE.call_once(|| { SYNCER .0 .set(Some(Mutex::new(BufReader::new(stdin()).lines()))); }); unsafe { (*SYNCER.0.as_ptr()) .as_ref() .unwrap() .lock() .unwrap() .next() .unwrap() .unwrap() } } pub trait ForceFromStr: FromStr { fn force_from_str(s: &str) -> Self; } impl ForceFromStr for T where T: FromStr, E: std::fmt::Debug, { fn force_from_str(s: &str) -> Self { s.parse().unwrap() } } pub fn input_array() -> [T; N] where T: std::fmt::Debug, { <[_; N]>::try_from(input_vec()).unwrap() } pub fn input_vec() -> Vec { line() .split_whitespace() .map(T::force_from_str) .collect::>() } pub fn input() -> T { T::force_from_str(&line()) } } // }}}