結果
問題 | No.1302 Random Tree Score |
ユーザー |
![]() |
提出日時 | 2020-12-09 18:49:03 |
言語 | Rust (1.83.0 + proconio) |
結果 |
AC
|
実行時間 | 571 ms / 3,000 ms |
コード長 | 19,860 bytes |
コンパイル時間 | 15,443 ms |
コンパイル使用メモリ | 378,656 KB |
実行使用メモリ | 5,480 KB |
最終ジャッジ日時 | 2024-09-19 01:41:36 |
合計ジャッジ時間 | 17,510 ms |
ジャッジサーバーID (参考情報) |
judge2 / judge3 |
(要ログイン)
ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 14 |
ソースコード
#![allow(unused_imports, unused_macros)]use kyoproio::*;use std::{collections::*,io::{self, prelude::*},iter,mem::{replace, swap},};fn run<I: Input, O: Write>(mut kin: I, out: O) {let mut out = KOutput::new(out);let n: usize = kin.input();let mut a = vec![mint(0); n - 1];let f = Fact::new(n);for i in 0..=n - 2 {a[i] = Mint::from(i + 1) * f.fact_inv(i);}a.resize((2 * a.len() - 1).next_power_of_two(), mint(0));let mut b = vec![mint(0); a.len()];b[0] = mint(1);let mut k = n;while k > 0 {dft(&mut a, false);if k & 1 == 1 {dft(&mut b, false);for i in 0..a.len() {b[i] *= a[i];}dft(&mut b, true);for i in n - 1..b.len() {b[i] = mint(0);}}for i in 0..a.len() {a[i] = a[i] * a[i];}dft(&mut a, true);for i in n - 1..a.len() {a[i] = mint(0);}k /= 2;}let ans = b[n - 2] * f.fact(n - 2) * Mint::from(n).inv().pow(n - 2);outln!(out, ans.get());}pub struct Fact<M> {f: Vec<ModInt<M>>,finv: Vec<ModInt<M>>,}impl<M: Modulo> Fact<M> {pub fn new(n: usize) -> Self {let mut f = vec![ModInt::new(0); n + 1];f[0] = ModInt::new(1);f[1] = ModInt::new(1);for i in 2..=n {f[i] = ModInt::new(i as u32) * f[i - 1];}let mut finv = vec![ModInt::new(0); n + 1];finv[n] = f[n].inv();for i in (0..n).rev() {finv[i] = finv[i + 1] * ModInt::new(i as u32 + 1);}Self { f, finv }}pub fn fact(&self, x: usize) -> ModInt<M> {self.f[x]}pub fn fact_inv(&self, x: usize) -> ModInt<M> {self.finv[x]}pub fn binom(&self, n: usize, k: usize) -> ModInt<M> {if n >= k {self.fact(n) * self.fact_inv(n - k) * self.fact_inv(k)} else {ModInt::new(0)}}pub fn perm(&self, n: usize, k: usize) -> ModInt<M> {if n >= k {self.fact(n) * self.fact_inv(n - k)} else {ModInt::new(0)}}}pub trait PrimitiveRoot: Modulo {fn primitive_root() -> u32;}impl PrimitiveRoot for Mod998244353 {fn primitive_root() -> u32 {3}}pub fn dft<M: PrimitiveRoot>(a: &mut [ModInt<M>], inv: bool) {assert!(a.len().is_power_of_two());let n = a.len();let shift = n.leading_zeros() + 1;for i in 0..n {let j = i.reverse_bits().wrapping_shr(shift);if i < j {a.swap(i, j);}}let pr = ModInt::new(M::primitive_root());let mut w = Vec::with_capacity(n / 2);w.push(ModInt::new(1));for m in (1..).map(|i| 1 << i).take_while(|m| *m <= n) {let neg1 = M::modulo() - 1;let s = neg1 / m as u32;let w1 = if inv { pr.pow(neg1 - s) } else { pr.pow(s) };w.resize(m / 2, ModInt::new(0));for i in (0..m / 4).rev() {w[2 * i] = w[i];w[2 * i + 1] = w1 * w[i];}for i in (0..n).step_by(m) {for j in 0..m / 2 {let t = w[j] * a[i + j + m / 2];a[i + j + m / 2] = a[i + j] - t;a[i + j] += t;}}}if inv {let d = ModInt::new(n as u32).inv();for a in a {*a *= d;}}}pub fn convolution<M: PrimitiveRoot, V: Into<Vec<ModInt<M>>>>(a: V, b: V) -> Vec<ModInt<M>> {let mut a = a.into();let mut b = b.into();let deg = a.len() + b.len() - 1;let n = deg.next_power_of_two();a.resize(n, ModInt::new(0));b.resize(n, ModInt::new(0));dft(&mut a, false);dft(&mut b, false);for (a, b) in a.iter_mut().zip(b.iter()) {*a *= *b;}dft(&mut a, true);a.truncate(deg);a}use std::{cmp, fmt, marker::PhantomData, ops};pub type Mint = ModInt<Mod998244353>;pub fn mint(x: u32) -> Mint {ModInt::new(x)}pub trait Modulo {fn modulo() -> u32;}macro_rules! modulo_impl {($($Type:ident $val:tt)*) => {$(pub struct $Type;impl Modulo for $Type {fn modulo() -> u32 {$val}})*};}modulo_impl!(Mod998244353 998244353 Mod1e9p7 1000000007);use std::sync::atomic;pub struct VarMod;static VAR_MOD: atomic::AtomicU32 = atomic::AtomicU32::new(0);pub fn set_var_mod(m: u32) {VAR_MOD.store(m, atomic::Ordering::Relaxed);}impl Modulo for VarMod {fn modulo() -> u32 {VAR_MOD.load(atomic::Ordering::Relaxed)}}pub struct ModInt<M>(u32, PhantomData<M>);impl<M: Modulo> ModInt<M> {pub fn new(x: u32) -> Self {debug_assert!(x < M::modulo());Self(x, PhantomData)}pub fn normalize(self) -> Self {if self.0 < M::modulo() {self} else {Self::new(self.0 % M::modulo())}}pub fn get(self) -> u32 {self.0}pub fn inv(self) -> Self {self.pow(M::modulo() - 2)}pub fn half(self) -> Self {Self::new(self.0 / 2 + self.0 % 2 * ((M::modulo() + 1) / 2))}pub fn modulo() -> u32 {M::modulo()}}impl<M: Modulo> ops::Neg for ModInt<M> {type Output = Self;fn neg(self) -> Self {Self::new(if self.0 == 0 { 0 } else { M::modulo() - self.0 })}}impl<M: Modulo> ops::Add for ModInt<M> {type Output = Self;fn add(self, rhs: Self) -> Self {let s = self.0 + rhs.0;Self::new(if s < M::modulo() { s } else { s - M::modulo() })}}impl<M: Modulo> ops::Sub for ModInt<M> {type Output = Self;fn sub(self, rhs: Self) -> Self {Self::new(if self.0 >= rhs.0 {self.0 - rhs.0} else {M::modulo() + self.0 - rhs.0})}}impl<M: Modulo> ops::Mul for ModInt<M> {type Output = Self;fn mul(self, rhs: Self) -> Self {Self::new((self.0 as u64 * rhs.0 as u64 % M::modulo() as u64) as u32)}}impl<M: Modulo> ops::Div for ModInt<M> {type Output = Self;fn div(self, rhs: Self) -> Self {assert_ne!(rhs.get(), 0);self * rhs.inv()}}macro_rules! op_impl {($($Op:ident $op:ident $OpAssign:ident $op_assign:ident)*) => {$(impl<M: Modulo> ops::$Op<&Self> for ModInt<M> {type Output = Self;fn $op(self, rhs: &Self) -> Self {self.$op(*rhs)}}impl<M: Modulo> ops::$Op<ModInt<M>> for &ModInt<M> {type Output = ModInt<M>;fn $op(self, rhs: ModInt<M>) -> ModInt<M> {(*self).$op(rhs)}}impl<M: Modulo> ops::$Op<&ModInt<M>> for &ModInt<M> {type Output = ModInt<M>;fn $op(self, rhs: &ModInt<M>) -> ModInt<M> {(*self).$op(*rhs)}}impl<M: Modulo> ops::$OpAssign for ModInt<M> {fn $op_assign(&mut self, rhs: Self) {*self = ops::$Op::$op(*self, rhs);}}impl<M: Modulo> ops::$OpAssign<&ModInt<M>> for ModInt<M> {fn $op_assign(&mut self, rhs: &ModInt<M>) {self.$op_assign(*rhs);}})*};}op_impl! {Add add AddAssign add_assignSub sub SubAssign sub_assignMul mul MulAssign mul_assignDiv div DivAssign div_assign}impl<M: Modulo> std::iter::Sum for ModInt<M> {fn sum<I: Iterator<Item = Self>>(iter: I) -> Self {iter.fold(ModInt::new(0), |x, y| x + y)}}impl<M: Modulo> std::iter::Product for ModInt<M> {fn product<I: Iterator<Item = Self>>(iter: I) -> Self {iter.fold(ModInt::new(1), |x, y| x * y)}}pub trait Pow<T> {fn pow(self, n: T) -> Self;}impl<M: Modulo> Pow<u32> for ModInt<M> {fn pow(mut self, mut n: u32) -> Self {let mut y = Self::new(1);while n > 0 {if n % 2 == 1 {y *= self;}self *= self;n /= 2;}y}}macro_rules! mod_int_pow_impl {($($T:ident)*) => {$(impl<M: Modulo> Pow<$T> for ModInt<M> {fn pow(self, n: $T) -> Self {self.pow(n.rem_euclid(M::modulo() as $T - 1) as u32)}})*};}mod_int_pow_impl!(isize i32 i64 usize u64);macro_rules! mod_int_from_impl {($($T:ident)*) => {$(impl<M: Modulo> From<$T> for ModInt<M> {#[allow(unused_comparisons)]fn from(x: $T) -> Self {if M::modulo() <= $T::max_value() as u32 {Self::new(x.rem_euclid(M::modulo() as $T) as u32)} else if x < 0 {Self::new((M::modulo() as i32 + x as i32) as u32)} else {Self::new(x as u32)}}})*}}mod_int_from_impl!(isize i8 i16 i32 i64 i128 usize u8 u16 u32 u64 u128);impl<M> Copy for ModInt<M> {}impl<M> Clone for ModInt<M> {fn clone(&self) -> Self {*self}}impl<M: Modulo> Default for ModInt<M> {fn default() -> Self {Self::new(0)}}impl<M> cmp::PartialEq for ModInt<M> {fn eq(&self, other: &Self) -> bool {self.0 == other.0}}impl<M> cmp::Eq for ModInt<M> {}impl<M> cmp::PartialOrd for ModInt<M> {fn partial_cmp(&self, other: &Self) -> Option<cmp::Ordering> {self.0.partial_cmp(&other.0)}}impl<M> cmp::Ord for ModInt<M> {fn cmp(&self, other: &Self) -> cmp::Ordering {self.0.cmp(&other.0)}}impl<M> std::hash::Hash for ModInt<M> {fn hash<H: std::hash::Hasher>(&self, state: &mut H) {self.0.hash(state);}}impl<M> fmt::Display for ModInt<M> {fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {self.0.fmt(f)}}impl<M> fmt::Debug for ModInt<M> {fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {f.pad("ModInt(")?;self.0.fmt(f)?;f.pad(")")}}// -----------------------------------------------------------------------------fn main() -> io::Result<()> {std::thread::Builder::new().stack_size(64 * 1024 * 1024).spawn(|| {run(KInput::new(io::stdin().lock()),io::BufWriter::new(io::stdout().lock()),)})?.join().unwrap();Ok(())}// -----------------------------------------------------------------------------pub mod kyoproio {use std::{io::prelude::*,iter::FromIterator,marker::PhantomData,mem::{self, MaybeUninit},ptr, slice, str,};pub trait Input {fn bytes(&mut self) -> &[u8];fn str(&mut self) -> &str {str::from_utf8(self.bytes()).unwrap()}fn input<T: InputItem>(&mut self) -> T {T::input(self)}fn iter<T: InputItem>(&mut self) -> Iter<T, Self> {Iter(self, PhantomData)}fn seq<T: InputItem, B: FromIterator<T>>(&mut self, n: usize) -> B {self.iter().take(n).collect()}}pub struct KInput<R> {src: R,buf: Vec<u8>,pos: usize,len: usize,}impl<R: Read> KInput<R> {pub fn new(src: R) -> Self {Self {src,buf: vec![0; 1 << 16],pos: 0,len: 0,}}fn read(&mut self) -> usize {if self.pos > 0 {self.buf.copy_within(self.pos..self.len, 0);self.len -= self.pos;self.pos = 0;} else if self.len >= self.buf.len() {self.buf.resize(2 * self.buf.len(), 0);}let n = self.src.read(&mut self.buf[self.len..]).unwrap();self.len += n;n}}impl<R: Read> Input for KInput<R> {fn bytes(&mut self) -> &[u8] {loop {while let Some(d) = self.buf[self.pos..self.len].iter().position(u8::is_ascii_whitespace){let p = self.pos;self.pos += d + 1;if d > 0 {return &self.buf[p..p + d];}}if self.read() == 0 {return &self.buf[mem::replace(&mut self.pos, self.len)..self.len];}}}}pub struct Iter<'a, T, I: ?Sized>(&'a mut I, PhantomData<*const T>);impl<'a, T: InputItem, I: Input + ?Sized> Iterator for Iter<'a, T, I> {type Item = T;fn next(&mut self) -> Option<T> {Some(self.0.input())}fn size_hint(&self) -> (usize, Option<usize>) {(!0, None)}}pub trait InputItem: Sized {fn input<I: Input + ?Sized>(src: &mut I) -> Self;}impl InputItem for Vec<u8> {fn input<I: Input + ?Sized>(src: &mut I) -> Self {src.bytes().to_owned()}}macro_rules! from_str {($($T:ty)*) => {$(impl InputItem for $T {fn input<I: Input + ?Sized>(src: &mut I) -> Self {src.str().parse::<$T>().unwrap()}})*}}from_str!(String char bool f32 f64);macro_rules! parse_int {($($I:ty: $U:ty)*) => {$(impl InputItem for $I {fn input<I: Input + ?Sized>(src: &mut I) -> Self {let f = |s: &[u8]| s.iter().fold(0, |x, b| 10 * x + (b & 0xf) as $I);let s = src.bytes();if let Some((&b'-', t)) = s.split_first() { -f(t) } else { f(s) }}}impl InputItem for $U {fn input<I: Input + ?Sized>(src: &mut I) -> Self {src.bytes().iter().fold(0, |x, b| 10 * x + (b & 0xf) as $U)}})*};}parse_int!(isize:usize i8:u8 i16:u16 i32:u32 i64:u64 i128:u128);macro_rules! tuple {($H:ident $($T:ident)*) => {impl<$H: InputItem, $($T: InputItem),*> InputItem for ($H, $($T),*) {fn input<I: Input + ?Sized>(src: &mut I) -> Self {($H::input(src), $($T::input(src)),*)}}tuple!($($T)*);};() => {}}tuple!(A B C D E F G);macro_rules! array {($($N:literal)*) => {$(impl<T: InputItem> InputItem for [T; $N] {fn input<I: Input + ?Sized>(src: &mut I) -> Self {let mut arr = MaybeUninit::uninit();let ptr = arr.as_mut_ptr() as *mut T;unsafe {for i in 0..$N {ptr.add(i).write(src.input());}arr.assume_init()}}})*};}array!(1 2 3 4 5 6 7 8);pub struct KOutput<W: Write> {dest: W,delim: bool,}impl<W: Write> KOutput<W> {pub fn new(dest: W) -> Self {Self { dest, delim: false }}pub fn bytes(&mut self, s: &[u8]) {self.dest.write_all(s).unwrap();}pub fn byte(&mut self, b: u8) {self.bytes(slice::from_ref(&b));}pub fn output<T: OutputItem>(&mut self, x: T) {if self.delim {self.byte(b' ');}self.delim = true;x.output(self);}pub fn ln(&mut self) {self.delim = false;self.byte(b'\n');self.flush_debug();}pub fn inner(&mut self) -> &mut W {&mut self.dest}pub fn seq<T: OutputItem, I: IntoIterator<Item = T>>(&mut self, iter: I) {for x in iter.into_iter() {self.output(x);}}pub fn flush(&mut self) {self.dest.flush().unwrap();}pub fn flush_debug(&mut self) {if cfg!(debug_assertions) {self.flush();}}}pub trait OutputItem {fn output<W: Write>(self, dest: &mut KOutput<W>);}impl OutputItem for &str {fn output<W: Write>(self, dest: &mut KOutput<W>) {dest.bytes(self.as_bytes());}}impl OutputItem for char {fn output<W: Write>(self, dest: &mut KOutput<W>) {self.encode_utf8(&mut [0; 4]).output(dest);}}macro_rules! output_fmt {($($T:ty)*) => {$(impl OutputItem for $T {fn output<W: Write>(self, dest: &mut KOutput<W>) {write!(dest.inner(), "{}", self).unwrap();}})*}}output_fmt!(f32 f64);macro_rules! output_int {($conv:ident; $U:ty; $($T:ty)*) => {$(impl OutputItem for $T {fn output<W: Write>(self, dest: &mut KOutput<W>) {let mut buf = MaybeUninit::<[u8; 20]>::uninit();unsafe {let ptr = buf.as_mut_ptr() as *mut u8;let ofs = $conv(self as $U, ptr, 20);dest.bytes(slice::from_raw_parts(ptr.add(ofs), 20 - ofs));}}}impl OutputItem for &$T {fn output<W: Write>(self, dest: &mut KOutput<W>) {(*self).output(dest);}})*};}output_int!(i64_to_bytes; i64; isize i8 i16 i32 i64);output_int!(u64_to_bytes; u64; usize u8 u16 u32 u64);static DIGITS_LUT: &[u8; 200] = b"0001020304050607080910111213141516171819\2021222324252627282930313233343536373839\4041424344454647484950515253545556575859\6061626364656667686970717273747576777879\8081828384858687888990919293949596979899";unsafe fn i64_to_bytes(x: i64, buf: *mut u8, len: usize) -> usize {let (neg, x) = if x < 0 { (true, -x) } else { (false, x) };let mut i = u64_to_bytes(x as u64, buf, len);if neg {i -= 1;*buf.add(i) = b'-';}i}unsafe fn u64_to_bytes(mut x: u64, buf: *mut u8, len: usize) -> usize {let lut = DIGITS_LUT.as_ptr();let mut i = len;let mut two = |x| {i -= 2;ptr::copy_nonoverlapping(lut.add(2 * x), buf.add(i), 2);};while x >= 10000 {let rem = (x % 10000) as usize;two(rem % 100);two(rem / 100);x /= 10000;}let mut x = x as usize;if x >= 100 {two(x % 100);x /= 100;}if x >= 10 {two(x);} else {i -= 1;*buf.add(i) = x as u8 + b'0';}i}#[macro_export]macro_rules! out {($out:expr, $($args:expr),*) => {{ $($out.output($args);)* }};}#[macro_export]macro_rules! outln {($out:expr) => { $out.ln(); };($out:expr, $($args:expr),*) => {{out!($out, $($args),*);outln!($out);}}}#[macro_export]macro_rules! kdbg {($($v:expr),*) => { if cfg!(debug_assertions) { dbg!($($v),*) } else { ($($v),*) } }}}