#904561 (Rust) No.2471 Gemini Tree(Ver.Lapislazuli)

• 問題: No.2471 Gemini Tree(Ver.Lapislazuli)
• ユーザー: akakimidori
• 提出日時: 2023-08-17 18:55:56
• 言語: Rust (1.77.0 + proconio)
• 結果: AC
• 実行時間: 45 ms / 2,000 ms
• コード長: 10,085 bytes
• コンパイル時間: 13,193 ms
• コンパイル使用メモリ: 402,500 KB
• 実行使用メモリ: 18,548 KB
• 最終ジャッジ日時: 2024-11-26 18:15:41
• 合計ジャッジ時間: 14,012 ms
• ジャッジサーバーID （参考情報）: judge4 / judge1

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	1 ms; 5,248 KB
testcase_01	AC	1 ms; 5,248 KB
testcase_02	AC	0 ms; 5,248 KB
testcase_03	AC	0 ms; 5,248 KB
testcase_04	AC	1 ms; 5,248 KB
testcase_05	AC	1 ms; 5,248 KB
testcase_06	AC	1 ms; 5,248 KB
testcase_07	AC	1 ms; 5,248 KB
testcase_08	AC	1 ms; 5,248 KB
testcase_09	AC	1 ms; 5,248 KB
testcase_10	AC	2 ms; 5,248 KB
testcase_11	AC	2 ms; 5,248 KB
testcase_12	AC	1 ms; 5,248 KB
testcase_13	AC	1 ms; 5,248 KB
testcase_14	AC	1 ms; 5,248 KB
testcase_15	AC	1 ms; 5,248 KB
testcase_16	AC	1 ms; 5,248 KB
testcase_17	AC	1 ms; 5,248 KB
testcase_18	AC	1 ms; 5,248 KB
testcase_19	AC	1 ms; 5,248 KB
testcase_20	AC	1 ms; 5,248 KB
testcase_21	AC	1 ms; 5,248 KB
testcase_22	AC	1 ms; 5,248 KB
testcase_23	AC	42 ms; 16,128 KB
testcase_24	AC	41 ms; 16,256 KB
testcase_25	AC	45 ms; 16,128 KB
testcase_26	AC	42 ms; 16,256 KB
testcase_27	AC	42 ms; 16,128 KB
testcase_28	AC	41 ms; 16,000 KB
testcase_29	AC	40 ms; 16,128 KB
testcase_30	AC	41 ms; 16,128 KB
testcase_31	AC	41 ms; 16,256 KB
testcase_32	AC	29 ms; 18,548 KB
testcase_33	AC	27 ms; 17,744 KB
testcase_34	AC	27 ms; 17,596 KB
testcase_35	AC	27 ms; 17,720 KB
testcase_36	AC	29 ms; 17,400 KB
testcase_37	AC	34 ms; 17,920 KB

コンパイルメッセージ

warning: unused variable: `root`
  --> src/main.rs:10:9
   |
10 |     for root in 0..1 {
   |         ^^^^ help: if this is intentional, prefix it with an underscore: `_root`
   |
   = note: `#[warn(unused_variables)]` on by default

warning: function `rand_memory` is never used
   --> src/main.rs:377:4
    |
377 | fn rand_memory() -> usize {
    |    ^^^^^^^^^^^
    |
    = note: `#[warn(dead_code)]` on by default

warning: function `rand` is never used
   --> src/main.rs:381:4
    |
381 | fn rand() -> usize {
    |    ^^^^

warning: function `shuffle` is never used
   --> src/main.rs:394:4
    |
394 | fn shuffle<T>(a: &mut [T]) {
    |    ^^^^^^^

ソースコード

use std::collections::*;

type Map<K, V> = BTreeMap<K, V>;

fn run() {
    input! {
        n: usize,
        e: [(usize1, usize1); n - 1],
    }
    for root in 0..1 {
        let mut g = vec![vec![]; n];
        for &(a, b) in e.iter() {
            g[a].push(b);
            g[b].push(a);
        }
        let root = g.iter().position(|g| g.len() == 1).unwrap();
        let cl = g.iter().filter(|g| g.len() == 1).count();
        let mut topo = vec![root];
        let mut parent = vec![n; n];
        for i in 0..n {
            let v = topo[i];
            for u in g[v].clone() {
                g[u].retain(|p| *p != v);
                parent[u] = v;
                topo.push(u);
            }
        }
        let mut size = vec![1; n];
        let mut leaf = vec![0; n];
        let mut map = Map::new();
        for &v in topo.iter().rev() {
            for &u in g[v].iter() {
                size[v] += size[u];
                leaf[v] += leaf[u];
            }
            if g[v].is_empty() || (v == root && g[v].len() == 1) {
                leaf[v] += 1;
            }
            if v == root {
                break;
            }
            let s = size[v];
            if 2 * s <= n {
                let po = map.entry(s).or_insert((0, 0, false));
                po.0 += 1;
                po.1 += leaf[v];
                po.2 |= parent[v] != n && g[parent[v]].len() == 1;
            } else {
                let po = map.entry(n - s).or_insert((0, 0, false));
                po.0 += 1;
                po.1 += cl - leaf[v];
                po.2 |= g[v].len() <= 1;
            }
        }
        let mut ans = M::new(2);
        let pc = Precalc::new(n);
        for (&s, &(c, l, cond)) in map.iter() {
            if 2 * s == n {
                ans += pc.binom(n, s);
                continue;
            }
            let mut add = pc.binom(n, s);
            let mut elem = true;
            elem &= c == 1;
            elem &= s >= cl - l && n - s >= l;
            elem &= !cond;
            elem &= !map.contains_key(&(s - 1));
            if elem {
                add -= pc.binom(n - cl, s - (cl - l));
            }
            ans += M::new(2) * add;
        }
        println!("{}", ans);
    }
}

fn main() {
    run();
}

// ---------- begin input macro ----------
// reference: https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8
#[macro_export]
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
    ($($r:tt)*) => {
        let s = {
            use std::io::Read;
            let mut s = String::new();
            std::io::stdin().read_to_string(&mut s).unwrap();
            s
        };
        let mut iter = s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
}

#[macro_export]
macro_rules! input_inner {
    ($iter:expr) => {};
    ($iter:expr, ) => {};
    ($iter:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($iter, $t);
        input_inner!{$iter $($r)*}
    };
}

#[macro_export]
macro_rules! read_value {
    ($iter:expr, ( $($t:tt),* )) => {
        ( $(read_value!($iter, $t)),* )
    };
    ($iter:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($iter, $t)).collect::<Vec<_>>()
    };
    ($iter:expr, chars) => {
        read_value!($iter, String).chars().collect::<Vec<char>>()
    };
    ($iter:expr, bytes) => {
        read_value!($iter, String).bytes().collect::<Vec<u8>>()
    };
    ($iter:expr, usize1) => {
        read_value!($iter, usize) - 1
    };
    ($iter:expr, $t:ty) => {
        $iter.next().unwrap().parse::<$t>().expect("Parse error")
    };
}
// ---------- end input macro ----------
// ---------- begin modint ----------
use std::marker::*;
use std::ops::*;

pub trait Modulo {
    fn modulo() -> u32;
}

pub struct ConstantModulo<const M: u32>;

impl<const M: u32> Modulo for ConstantModulo<{ M }> {
    fn modulo() -> u32 {
        M
    }
}

pub struct ModInt<T>(u32, PhantomData<T>);

impl<T> Clone for ModInt<T> {
    fn clone(&self) -> Self {
        Self::new_unchecked(self.0)
    }
}

impl<T> Copy for ModInt<T> {}

impl<T: Modulo> Add for ModInt<T> {
    type Output = ModInt<T>;
    fn add(self, rhs: Self) -> Self::Output {
        let mut v = self.0 + rhs.0;
        if v >= T::modulo() {
            v -= T::modulo();
        }
        Self::new_unchecked(v)
    }
}

impl<T: Modulo> AddAssign for ModInt<T> {
    fn add_assign(&mut self, rhs: Self) {
        *self = *self + rhs;
    }
}

impl<T: Modulo> Sub for ModInt<T> {
    type Output = ModInt<T>;
    fn sub(self, rhs: Self) -> Self::Output {
        let mut v = self.0 - rhs.0;
        if self.0 < rhs.0 {
            v += T::modulo();
        }
        Self::new_unchecked(v)
    }
}

impl<T: Modulo> SubAssign for ModInt<T> {
    fn sub_assign(&mut self, rhs: Self) {
        *self = *self - rhs;
    }
}

impl<T: Modulo> Mul for ModInt<T> {
    type Output = ModInt<T>;
    fn mul(self, rhs: Self) -> Self::Output {
        let v = self.0 as u64 * rhs.0 as u64 % T::modulo() as u64;
        Self::new_unchecked(v as u32)
    }
}

impl<T: Modulo> MulAssign for ModInt<T> {
    fn mul_assign(&mut self, rhs: Self) {
        *self = *self * rhs;
    }
}

impl<T: Modulo> Neg for ModInt<T> {
    type Output = ModInt<T>;
    fn neg(self) -> Self::Output {
        if self.is_zero() {
            Self::zero()
        } else {
            Self::new_unchecked(T::modulo() - self.0)
        }
    }
}

impl<T> std::fmt::Display for ModInt<T> {
    fn fmt<'a>(&self, f: &mut std::fmt::Formatter<'a>) -> std::fmt::Result {
        write!(f, "{}", self.0)
    }
}

impl<T> std::fmt::Debug for ModInt<T> {
    fn fmt<'a>(&self, f: &mut std::fmt::Formatter<'a>) -> std::fmt::Result {
        write!(f, "{}", self.0)
    }
}

impl<T> Default for ModInt<T> {
    fn default() -> Self {
        Self::zero()
    }
}

impl<T: Modulo> std::str::FromStr for ModInt<T> {
    type Err = std::num::ParseIntError;
    fn from_str(s: &str) -> Result<Self, Self::Err> {
        let val = s.parse::<u32>()?;
        Ok(ModInt::new(val))
    }
}

impl<T: Modulo> From<usize> for ModInt<T> {
    fn from(val: usize) -> ModInt<T> {
        ModInt::new_unchecked((val % T::modulo() as usize) as u32)
    }
}

impl<T: Modulo> From<u64> for ModInt<T> {
    fn from(val: u64) -> ModInt<T> {
        ModInt::new_unchecked((val % T::modulo() as u64) as u32)
    }
}

impl<T: Modulo> From<i64> for ModInt<T> {
    fn from(val: i64) -> ModInt<T> {
        let mut v = ((val % T::modulo() as i64) + T::modulo() as i64) as u32;
        if v >= T::modulo() {
            v -= T::modulo();
        }
        ModInt::new_unchecked(v)
    }
}

impl<T> ModInt<T> {
    pub fn new_unchecked(n: u32) -> Self {
        ModInt(n, PhantomData)
    }
    pub fn zero() -> Self {
        ModInt::new_unchecked(0)
    }
    pub fn one() -> Self {
        ModInt::new_unchecked(1)
    }
    pub fn is_zero(&self) -> bool {
        self.0 == 0
    }
}

impl<T: Modulo> ModInt<T> {
    pub fn new(d: u32) -> Self {
        ModInt::new_unchecked(d % T::modulo())
    }
    pub fn pow(&self, mut n: u64) -> Self {
        let mut t = Self::one();
        let mut s = *self;
        while n > 0 {
            if n & 1 == 1 {
                t *= s;
            }
            s *= s;
            n >>= 1;
        }
        t
    }
    pub fn inv(&self) -> Self {
        assert!(!self.is_zero());
        self.pow(T::modulo() as u64 - 2)
    }
    pub fn fact(n: usize) -> Self {
        (1..=n).fold(Self::one(), |s, a| s * Self::from(a))
    }
    pub fn perm(n: usize, k: usize) -> Self {
        if k > n {
            return Self::zero();
        }
        ((n - k + 1)..=n).fold(Self::one(), |s, a| s * Self::from(a))
    }
    pub fn binom(n: usize, k: usize) -> Self {
        if k > n {
            return Self::zero();
        }
        let k = k.min(n - k);
        let mut nu = Self::one();
        let mut de = Self::one();
        for i in 0..k {
            nu *= Self::from(n - i);
            de *= Self::from(i + 1);
        }
        nu * de.inv()
    }
}
// ---------- end modint ----------
// ---------- begin precalc ----------
pub struct Precalc<T> {
    fact: Vec<ModInt<T>>,
    ifact: Vec<ModInt<T>>,
    inv: Vec<ModInt<T>>,
}

impl<T: Modulo> Precalc<T> {
    pub fn new(n: usize) -> Precalc<T> {
        let mut inv = vec![ModInt::one(); n + 1];
        let mut fact = vec![ModInt::one(); n + 1];
        let mut ifact = vec![ModInt::one(); n + 1];
        for i in 2..=n {
            fact[i] = fact[i - 1] * ModInt::new_unchecked(i as u32);
        }
        ifact[n] = fact[n].inv();
        if n > 0 {
            inv[n] = ifact[n] * fact[n - 1];
        }
        for i in (1..n).rev() {
            ifact[i] = ifact[i + 1] * ModInt::new_unchecked((i + 1) as u32);
            inv[i] = ifact[i] * fact[i - 1];
        }
        Precalc { fact, ifact, inv }
    }
    pub fn inv(&self, n: usize) -> ModInt<T> {
        assert!(n > 0);
        self.inv[n]
    }
    pub fn fact(&self, n: usize) -> ModInt<T> {
        self.fact[n]
    }
    pub fn ifact(&self, n: usize) -> ModInt<T> {
        self.ifact[n]
    }
    pub fn perm(&self, n: usize, k: usize) -> ModInt<T> {
        if k > n {
            return ModInt::zero();
        }
        self.fact[n] * self.ifact[n - k]
    }
    pub fn binom(&self, n: usize, k: usize) -> ModInt<T> {
        if k > n {
            return ModInt::zero();
        }
        self.fact[n] * self.ifact[k] * self.ifact[n - k]
    }
}
// ---------- end precalc ----------

type M = ModInt<ConstantModulo<998_244_353>>;

fn rand_memory() -> usize {
    Box::into_raw(Box::new("I hope this is a random number")) as usize
}

fn rand() -> usize {
    static mut X: usize = 0;
    unsafe {
        if X == 0 {
            X = rand_memory();
        }
        X ^= X << 13;
        X ^= X >> 17;
        X ^= X << 5;
        X
    }
}

fn shuffle<T>(a: &mut [T]) {
    for i in 1..a.len() {
        let p = rand() % (i + 1);
        a.swap(i, p);
    }
}