#591263 (Rust) No.1302 Random Tree Score

• 問題: No.1302 Random Tree Score
• ユーザー: cotton_fn_
• 提出日時: 2020-12-09 18:49:03
• 言語: Rust (1.77.0 + 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

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	101 ms; 5,376 KB
testcase_03	AC	241 ms; 5,376 KB
testcase_04	AC	97 ms; 5,376 KB
testcase_05	AC	571 ms; 5,432 KB
testcase_06	AC	446 ms; 5,440 KB
testcase_07	AC	90 ms; 5,376 KB
testcase_08	AC	264 ms; 5,376 KB
testcase_09	AC	420 ms; 5,480 KB
testcase_10	AC	457 ms; 5,376 KB
testcase_11	AC	90 ms; 5,376 KB
testcase_12	AC	504 ms; 5,376 KB
testcase_13	AC	1 ms; 5,376 KB
testcase_14	AC	424 ms; 5,376 KB
testcase_15	AC	509 ms; 5,376 KB
testcase_16	AC	1 ms; 5,376 KB

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_assign
    Sub sub SubAssign sub_assign
    Mul mul MulAssign mul_assign
    Div 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),*) } }
    }
}