結果
| 問題 |
No.1614 Majority Painting on Tree
|
| コンテスト | |
| ユーザー |
 ngtkana
|
| 提出日時 | 2021-06-23 02:11:25 |
| 言語 | Rust (1.83.0 + proconio) |
| 結果 |
AC
|
| 実行時間 | 1,130 ms / 5,000 ms |
| コード長 | 19,968 bytes |
| コンパイル時間 | 14,012 ms |
| コンパイル使用メモリ | 378,596 KB |
| 実行使用メモリ | 5,376 KB |
| 最終ジャッジ日時 | 2024-07-17 15:40:29 |
| 合計ジャッジ時間 | 26,844 ms |
|
ジャッジサーバーID （参考情報） |
judge1 / judge2 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 4 |
| other | AC * 45 |
コンパイルメッセージ
warning: unused imports: `Leaf`, `Tuple`, `VecLen`
--> src/main.rs:364:27
|
364 | multi_token::{Leaf, Parser, ParserTuple, RawTuple, Tuple, VecLen},
| ^^^^ ^^^^^ ^^^^^^
|
= note: `#[warn(unused_imports)]` on by default
warning: unused import: `with_str`
--> src/main.rs:620:35
|
620 | pub use self::i::{with_stdin, with_str};
| ^^^^^^^^
warning: unused imports: `ParserTuple`, `Parser`, `RawTuple`, `Token`, `Usize1`
--> src/main.rs:623:28
|
623 | pub use super::i::{Parser, ParserTuple, RawTuple, Token, Usize1};
| ^^^^^^ ^^^^^^^^^^^ ^^^^^^^^ ^^^^^ ^^^^^^
ソースコード
use fp::F998244353 as Fp;
use std::iter::{once, repeat_with};
#[allow(unused_imports)]
#[cfg(feature = "dbg")]
use dbg::lg;
use crate::fp::fact_build;
fn main() {
let mut buf = ngtio::with_stdin();
let n = buf.usize();
let c = buf.usize();
let edges = repeat_with(|| [buf.usize() - 1, buf.usize() - 1])
.take(n - 1)
.collect::<Vec<_>>();
let mut degrees = vec![0; n];
for &[u, v] in &edges {
degrees[u] += 1;
degrees[v] += 1;
}
let [fact, finv] = fact_build(n + c + 1);
let cum = once(Fp::new(0))
.chain((1..=c).map(|c| {
degrees
.iter()
.map(|&d| cal(d, c, &fact, &finv))
.product::<Fp>()
* Fp::from(c)
}))
.collect::<Vec<_>>();
let ans = cum
.iter()
.enumerate()
.map(|(i, &x)| {
x * fact[c]
* finv[i]
* finv[c - i]
* match (c - i) % 2 {
0 => Fp::new(1),
1 => -Fp::new(1),
_ => unreachable!(),
}
})
.sum::<Fp>();
println!("{}", ans);
}
fn cal(d: usize, c: usize, fact: &[Fp], finv: &[Fp]) -> Fp {
Fp::from(c).pow((d - 1) as u32)
- (d / 2 + 1..=d)
.map(|i| Fp::from(c - 1).pow((d - i) as u32) * fact[d] * finv[i] * finv[d - i])
.sum::<Fp>()
+ Fp::from(1)
}
// fp {{{
#[allow(dead_code)]
mod fp {
use std::{
cmp::PartialEq,
fmt,
hash::{Hash, Hasher},
iter::{successors, Product, Sum},
marker::PhantomData,
mem::swap,
ops::{Add, AddAssign, Div, DivAssign, Mul, MulAssign, Neg, Sub, SubAssign},
};
pub trait Mod: Clone + Copy + Hash {
const P: u32;
const K: u32;
const R2: u32 = ((1_u128 << 64) % Self::P as u128) as _; // 2 ^ 64 mod P
}
fn reduce<M: Mod>(x: u64) -> u32 {
((x + u64::from(M::K.wrapping_mul(x as u32)) * u64::from(M::P)) >> 32) as u32
}
pub fn fact_iter<M: Mod>() -> impl Iterator<Item = Fp<M>> {
(1..).scan(Fp::new(1), |state, x| {
let ans = *state;
*state *= x;
Some(ans)
})
}
#[allow(clippy::missing_panics_doc)]
pub fn fact_build<M: Mod>(n: usize) -> [Vec<Fp<M>>; 2] {
if n == 0 {
[Vec::new(), Vec::new()]
} else {
let fact = fact_iter::<M>().take(n).collect::<Vec<_>>();
let mut fact_inv = vec![fact.last().unwrap().recip(); n];
(1..n).rev().for_each(|i| fact_inv[i - 1] = fact_inv[i] * i);
[fact, fact_inv]
}
}
pub fn binom_iter<M: Mod>() -> impl Iterator<Item = Vec<Fp<M>>> {
successors(Some(vec![Fp::new(1)]), |last| {
let mut crr = last.clone();
crr.push(Fp::new(0));
crr[1..].iter_mut().zip(last).for_each(|(x, &y)| *x += y);
Some(crr)
})
}
#[macro_export]
macro_rules! define_mod {
($(($Fp: ident, $Mod: ident, $mod: expr, $k: expr),)*) => {$(
#[derive(Clone, Debug, Default, Hash, Copy)]
pub struct $Mod {}
impl Mod for $Mod {
const P: u32 = $mod;
const K: u32 = $k;
}
pub type $Fp = Fp<$Mod>;
)*}
}
define_mod! {
(F998244353, Mod998244353, 998_244_353, 998_244_351),
(F1000000007, Mod1000000007, 1_000_000_007, 2_226_617_417),
(F1012924417, Mod1012924417, 1_012_924_417, 1_012_924_415),
(F924844033, Mod924844033, 924_844_033, 924_844_031),
}
#[derive(Clone, Default, Copy)]
pub struct Fp<M> {
value: u32,
__marker: PhantomData<M>,
}
impl<M: Mod> Fp<M> {
pub const P: u32 = M::P;
pub fn new(value: u32) -> Self {
Self::from_raw(reduce::<M>(u64::from(value) * u64::from(M::R2)))
}
pub fn value(self) -> u32 {
let x = reduce::<M>(u64::from(self.value));
if M::P <= x {
x - M::P
} else {
x
}
}
#[allow(clippy::many_single_char_names)]
pub fn recip(self) -> Self {
assert_ne!(self, Self::new(0), "0 はだめ。");
let mut x = M::P as i32;
let mut y = self.value() as i32;
let mut u = 0;
let mut v = 1;
while y != 0 {
let q = x / y;
x -= q * y;
u -= q * v;
swap(&mut x, &mut y);
swap(&mut u, &mut v);
}
debug_assert_eq!(x, 1);
if u < 0 {
debug_assert_eq!(v, M::P as i32);
u += v;
}
Self::new(u as u32)
}
pub fn pow<T: Into<u64>>(self, exp: T) -> Self {
let mut exp = exp.into();
if exp == 0 {
return Self::new(1);
}
let mut base = self;
let mut acc = Self::new(1);
while 1 < exp {
if exp & 1 == 1 {
acc *= base;
}
exp /= 2;
base *= base;
}
acc * base
}
fn from_raw(value: u32) -> Self {
Self {
value,
__marker: PhantomData,
}
}
}
fn simplify(value: i32, p: i32) -> (i32, i32, i32) {
if value.abs() < 10_000 {
(value, 1, 0)
} else {
let mut q = p.div_euclid(value);
let mut r = p.rem_euclid(value);
if value <= 2 * r {
q += 1;
r -= value;
}
let (num, pden, ppden) = simplify(r, value);
let den = ppden - q * pden;
(num, den, pden)
}
}
macro_rules! impl_from_large_int {
($($T: ty), *$(,)?) => {$(
impl<M: Mod> From<$T> for Fp<M> {
fn from(x: $T) -> Self {
Self::new(x.rem_euclid(M::P as _) as u32)
}
}
)*}
}
impl_from_large_int! {
u32, u64, u128, usize,
i32, i64, i128, isize,
}
macro_rules! impl_from_small_int {
($($T: ty), *$(,)?) => {$(
impl<M: Mod> From<$T> for Fp<M> {
fn from(x: $T) -> Self {
Self::new(x as u32)
}
}
)*}
}
impl_from_small_int! {
u8, u16,
i8, i16,
}
impl<M: Mod> PartialEq for Fp<M> {
fn eq(&self, other: &Self) -> bool {
fn value<M: Mod>(fp: Fp<M>) -> u32 {
if fp.value >= M::P {
fp.value - M::P
} else {
fp.value
}
}
value(*self) == value(*other)
}
}
impl<M: Mod> Eq for Fp<M> {}
impl<M: Mod> Hash for Fp<M> {
fn hash<H: Hasher>(&self, state: &mut H) {
self.value().hash(state);
}
}
impl<M: Mod, T: Into<Self>> AddAssign<T> for Fp<M> {
fn add_assign(&mut self, rhs: T) {
self.value += rhs.into().value;
if M::P * 2 <= self.value {
self.value -= M::P * 2;
}
}
}
impl<M: Mod, T: Into<Self>> SubAssign<T> for Fp<M> {
fn sub_assign(&mut self, rhs: T) {
let rhs = rhs.into();
if self.value < rhs.value {
self.value += M::P * 2;
}
self.value -= rhs.value;
}
}
impl<M: Mod, T: Into<Self>> MulAssign<T> for Fp<M> {
fn mul_assign(&mut self, rhs: T) {
self.value = reduce::<M>(u64::from(self.value) * u64::from(rhs.into().value));
}
}
#[allow(clippy::suspicious_op_assign_impl)]
impl<M: Mod, T: Into<Self>> DivAssign<T> for Fp<M> {
fn div_assign(&mut self, rhs: T) {
*self *= rhs.into().recip();
}
}
impl<'a, M: Mod> From<&'a Self> for Fp<M> {
fn from(x: &Self) -> Self {
*x
}
}
macro_rules! forward_ops {
($(($trait:ident, $method_assign:ident, $method:ident),)*) => {$(
impl<M: Mod, T: Into<Fp<M>>> $trait<T> for Fp<M> {
type Output = Self;
fn $method(mut self, rhs: T) -> Self {
self.$method_assign(rhs);
self
}
}
impl<'a, M: Mod, T: Into<Fp<M>>> $trait<T> for &'a Fp<M> {
type Output = Fp<M>;
fn $method(self, other: T) -> Self::Output {
$trait::$method(*self, other)
}
}
)*};
}
forward_ops! {
(Add, add_assign, add),
(Sub, sub_assign, sub),
(Mul, mul_assign, mul),
(Div, div_assign, div),
}
impl<M: Mod> Neg for Fp<M> {
type Output = Self;
fn neg(self) -> Self {
Self::from_raw(M::P * 2 - self.value)
}
}
impl<M: Mod> Sum for Fp<M> {
fn sum<I: Iterator<Item = Self>>(iter: I) -> Self {
iter.fold(Self::new(0), |b, x| b + x)
}
}
impl<M: Mod> Product for Fp<M> {
fn product<I: Iterator<Item = Self>>(iter: I) -> Self {
iter.fold(Self::new(1), |b, x| b * x)
}
}
impl<'a, M: Mod> Sum<&'a Self> for Fp<M> {
fn sum<I: Iterator<Item = &'a Self>>(iter: I) -> Self {
iter.fold(Self::new(0), |b, x| b + x)
}
}
impl<'a, M: Mod> Product<&'a Self> for Fp<M> {
fn product<I: Iterator<Item = &'a Self>>(iter: I) -> Self {
iter.fold(Self::new(1), |b, x| b * x)
}
}
impl<M: Mod> fmt::Debug for Fp<M> {
fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> Result<(), std::fmt::Error> {
let (num, den, _) = simplify(self.value() as i32, M::P as i32);
let (num, den) = match den.signum() {
1 => (num, den),
-1 => (-num, -den),
_ => unreachable!(),
};
if den == 1 {
write!(f, "{}", num)
} else {
write!(f, "{}/{}", num, den)
}
}
}
impl<M: Mod> fmt::Display for Fp<M> {
fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
self.value().fmt(f)
}
}
}
// }}}
// template {{{
#[cfg(not(feature = "dbg"))]
#[allow(unused_macros)]
#[macro_export]
macro_rules! lg {
($($expr:expr),*) => {};
}
#[allow(dead_code)]
mod ngtio {
mod i {
use std::{
io::{self, BufRead},
iter,
};
pub use self::{
multi_token::{Leaf, Parser, ParserTuple, RawTuple, Tuple, VecLen},
token::{Token, Usize1},
};
pub fn with_stdin() -> Tokenizer<io::BufReader<io::Stdin>> {
io::BufReader::new(io::stdin()).tokenizer()
}
pub fn with_str(src: &str) -> Tokenizer<&[u8]> {
src.as_bytes().tokenizer()
}
pub struct Tokenizer<S: BufRead> {
queue: Vec<String>, // FIXME: String のみにすると速そうです。
scanner: S,
}
macro_rules! prim_method {
($name:ident: $T:ty) => {
pub fn $name(&mut self) -> $T {
<$T>::leaf().parse(self)
}
};
($name:ident) => {
prim_method!($name: $name);
};
}
macro_rules! prim_methods {
($name:ident: $T:ty; $($rest:tt)*) => {
prim_method!($name:$T);
prim_methods!($($rest)*);
};
($name:ident; $($rest:tt)*) => {
prim_method!($name);
prim_methods!($($rest)*);
};
() => ()
}
impl<S: BufRead> Tokenizer<S> {
pub fn token(&mut self) -> String {
self.load();
self.queue.pop().expect("入力が終了したのですが。")
}
pub fn new(scanner: S) -> Self {
Self {
queue: Vec::new(),
scanner,
}
}
fn load(&mut self) {
while self.queue.is_empty() {
let mut s = String::new();
let length = self.scanner.read_line(&mut s).unwrap(); // 入力が UTF-8 でないときにエラーだそうです。
if length == 0 {
break;
}
self.queue = s.split_whitespace().rev().map(str::to_owned).collect();
}
}
pub fn skip_line(&mut self) {
assert!(
self.queue.is_empty(),
"行の途中で呼ばないでいただきたいです。現在のトークンキュー: {:?}",
&self.queue
);
self.load();
}
pub fn end(&mut self) {
self.load();
assert!(self.queue.is_empty(), "入力はまだあります！");
}
pub fn parse<T: Token>(&mut self) -> T::Output {
T::parse(&self.token())
}
pub fn parse_collect<T: Token, B>(&mut self, n: usize) -> B
where
B: iter::FromIterator<T::Output>,
{
iter::repeat_with(|| self.parse::<T>()).take(n).collect()
}
pub fn tuple<T: RawTuple>(&mut self) -> <T::LeafTuple as Parser>::Output {
T::leaf_tuple().parse(self)
}
pub fn vec<T: Token>(&mut self, len: usize) -> Vec<T::Output> {
T::leaf().vec(len).parse(self)
}
pub fn vec_tuple<T: RawTuple>(
&mut self,
len: usize,
) -> Vec<<T::LeafTuple as Parser>::Output> {
T::leaf_tuple().vec(len).parse(self)
}
pub fn vec2<T: Token>(&mut self, height: usize, width: usize) -> Vec<Vec<T::Output>> {
T::leaf().vec(width).vec(height).parse(self)
}
pub fn vec2_tuple<T>(
&mut self,
height: usize,
width: usize,
) -> Vec<Vec<<T::LeafTuple as Parser>::Output>>
where
T: RawTuple,
{
T::leaf_tuple().vec(width).vec(height).parse(self)
}
prim_methods! {
u8; u16; u32; u64; u128; usize;
i8; i16; i32; i64; i128; isize;
f32; f64;
char; string: String;
}
}
mod token {
use super::multi_token::Leaf;
use std::{any, fmt, marker, str};
pub trait Token: Sized {
type Output;
fn parse(s: &str) -> Self::Output;
fn leaf() -> Leaf<Self> {
Leaf(marker::PhantomData)
}
}
impl<T> Token for T
where
T: str::FromStr,
<T as str::FromStr>::Err: fmt::Debug,
{
type Output = T;
fn parse(s: &str) -> Self::Output {
s.parse().unwrap_or_else(|_| {
panic!("Parse error!: ({}: {})", s, any::type_name::<T>(),)
})
}
}
pub struct Usize1 {}
impl Token for Usize1 {
type Output = usize;
fn parse(s: &str) -> Self::Output {
usize::parse(s)
.checked_sub(1)
.expect("Parse error! (Zero substruction error of Usize1)")
}
}
}
mod multi_token {
use super::{Token, Tokenizer};
use std::{io::BufRead, iter, marker};
pub trait Parser: Sized {
type Output;
fn parse<S: BufRead>(&self, server: &mut Tokenizer<S>) -> Self::Output;
fn vec(self, len: usize) -> VecLen<Self> {
VecLen { len, elem: self }
}
}
pub struct Leaf<T>(pub(super) marker::PhantomData<T>);
impl<T: Token> Parser for Leaf<T> {
type Output = T::Output;
fn parse<S: BufRead>(&self, server: &mut Tokenizer<S>) -> T::Output {
server.parse::<T>()
}
}
pub struct VecLen<T> {
pub len: usize,
pub elem: T,
}
impl<T: Parser> Parser for VecLen<T> {
type Output = Vec<T::Output>;
fn parse<S: BufRead>(&self, server: &mut Tokenizer<S>) -> Self::Output {
iter::repeat_with(|| self.elem.parse(server))
.take(self.len)
.collect()
}
}
pub trait RawTuple {
type LeafTuple: Parser;
fn leaf_tuple() -> Self::LeafTuple;
}
pub trait ParserTuple {
type Tuple: Parser;
fn tuple(self) -> Self::Tuple;
}
pub struct Tuple<T>(pub T);
macro_rules! impl_tuple {
($($t:ident: $T:ident),*) => {
impl<$($T),*> Parser for Tuple<($($T,)*)>
where
$($T: Parser,)*
{
type Output = ($($T::Output,)*);
#[allow(unused_variables)]
fn parse<S: BufRead >(&self, server: &mut Tokenizer<S>) -> Self::Output {
match self {
Tuple(($($t,)*)) => {
($($t.parse(server),)*)
}
}
}
}
impl<$($T: Token),*> RawTuple for ($($T,)*) {
type LeafTuple = Tuple<($(Leaf<$T>,)*)>;
fn leaf_tuple() -> Self::LeafTuple {
Tuple(($($T::leaf(),)*))
}
}
impl<$($T: Parser),*> ParserTuple for ($($T,)*) {
type Tuple = Tuple<($($T,)*)>;
fn tuple(self) -> Self::Tuple {
Tuple(self)
}
}
};
}
impl_tuple!();
impl_tuple!(t1: T1);
impl_tuple!(t1: T1, t2: T2);
impl_tuple!(t1: T1, t2: T2, t3: T3);
impl_tuple!(t1: T1, t2: T2, t3: T3, t4: T4);
impl_tuple!(t1: T1, t2: T2, t3: T3, t4: T4, t5: T5);
impl_tuple!(t1: T1, t2: T2, t3: T3, t4: T4, t5: T5, t6: T6);
impl_tuple!(t1: T1, t2: T2, t3: T3, t4: T4, t5: T5, t6: T6, t7: T7);
impl_tuple!(
t1: T1,
t2: T2,
t3: T3,
t4: T4,
t5: T5,
t6: T6,
t7: T7,
t8: T8
);
}
trait Scanner: BufRead + Sized {
fn tokenizer(self) -> Tokenizer<Self> {
Tokenizer::new(self)
}
}
impl<R: BufRead> Scanner for R {}
}
pub use self::i::{with_stdin, with_str};
pub mod prelude {
pub use super::i::{Parser, ParserTuple, RawTuple, Token, Usize1};
}
}
// }}}