結果

問題 No.1302 Random Tree Score
ユーザー koba-e964
提出日時 2021-10-09 01:02:22
言語 Rust
(1.83.0 + proconio)
結果
AC  
実行時間 211 ms / 3,000 ms
コード長 15,292 bytes
コンパイル時間 12,845 ms
コンパイル使用メモリ 403,224 KB
実行使用メモリ 11,148 KB
最終ジャッジ日時 2024-07-23 09:56:47
合計ジャッジ時間 15,862 ms
ジャッジサーバーID
(参考情報)
judge3 / judge2
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 14
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ソースコード

diff #
プレゼンテーションモードにする

#[allow(unused_imports)]
use std::cmp::*;
#[allow(unused_imports)]
use std::collections::*;
use std::io::Read;
fn get_word() -> String {
let stdin = std::io::stdin();
let mut stdin=stdin.lock();
let mut u8b: [u8; 1] = [0];
loop {
let mut buf: Vec<u8> = Vec::with_capacity(16);
loop {
let res = stdin.read(&mut u8b);
if res.unwrap_or(0) == 0 || u8b[0] <= b' ' {
break;
} else {
buf.push(u8b[0]);
}
}
if buf.len() >= 1 {
let ret = String::from_utf8(buf).unwrap();
return ret;
}
}
}
#[allow(dead_code)]
fn get<T: std::str::FromStr>() -> T { get_word().parse().ok().unwrap() }
/// Verified by https://atcoder.jp/contests/abc198/submissions/21774342
mod mod_int {
use std::ops::*;
pub trait Mod: Copy { fn m() -> i64; }
#[derive(Copy, Clone, Hash, PartialEq, Eq, PartialOrd, Ord)]
pub struct ModInt<M> { pub x: i64, phantom: ::std::marker::PhantomData<M> }
impl<M: Mod> ModInt<M> {
// x >= 0
pub fn new(x: i64) -> Self { ModInt::new_internal(x % M::m()) }
fn new_internal(x: i64) -> Self {
ModInt { x: x, phantom: ::std::marker::PhantomData }
}
pub fn pow(self, mut e: i64) -> Self {
debug_assert!(e >= 0);
let mut sum = ModInt::new_internal(1);
let mut cur = self;
while e > 0 {
if e % 2 != 0 { sum *= cur; }
cur *= cur;
e /= 2;
}
sum
}
#[allow(dead_code)]
pub fn inv(self) -> Self { self.pow(M::m() - 2) }
}
impl<M: Mod, T: Into<ModInt<M>>> Add<T> for ModInt<M> {
type Output = Self;
fn add(self, other: T) -> Self {
let other = other.into();
let mut sum = self.x + other.x;
if sum >= M::m() { sum -= M::m(); }
ModInt::new_internal(sum)
}
}
impl<M: Mod, T: Into<ModInt<M>>> Sub<T> for ModInt<M> {
type Output = Self;
fn sub(self, other: T) -> Self {
let other = other.into();
let mut sum = self.x - other.x;
if sum < 0 { sum += M::m(); }
ModInt::new_internal(sum)
}
}
impl<M: Mod, T: Into<ModInt<M>>> Mul<T> for ModInt<M> {
type Output = Self;
fn mul(self, other: T) -> Self { ModInt::new(self.x * other.into().x % M::m()) }
}
impl<M: Mod, T: Into<ModInt<M>>> AddAssign<T> for ModInt<M> {
fn add_assign(&mut self, other: T) { *self = *self + other; }
}
impl<M: Mod, T: Into<ModInt<M>>> SubAssign<T> for ModInt<M> {
fn sub_assign(&mut self, other: T) { *self = *self - other; }
}
impl<M: Mod, T: Into<ModInt<M>>> MulAssign<T> for ModInt<M> {
fn mul_assign(&mut self, other: T) { *self = *self * other; }
}
impl<M: Mod> Neg for ModInt<M> {
type Output = Self;
fn neg(self) -> Self { ModInt::new(0) - self }
}
impl<M> ::std::fmt::Display for ModInt<M> {
fn fmt(&self, f: &mut ::std::fmt::Formatter) -> ::std::fmt::Result {
self.x.fmt(f)
}
}
impl<M: Mod> ::std::fmt::Debug for ModInt<M> {
fn fmt(&self, f: &mut ::std::fmt::Formatter) -> ::std::fmt::Result {
let (mut a, mut b, _) = red(self.x, M::m());
if b < 0 {
a = -a;
b = -b;
}
write!(f, "{}/{}", a, b)
}
}
impl<M: Mod> From<i64> for ModInt<M> {
fn from(x: i64) -> Self { Self::new(x) }
}
// Finds the simplest fraction x/y congruent to r mod p.
// The return value (x, y, z) satisfies x = y * r + z * p.
fn red(r: i64, p: i64) -> (i64, i64, i64) {
if r.abs() <= 10000 {
return (r, 1, 0);
}
let mut nxt_r = p % r;
let mut q = p / r;
if 2 * nxt_r >= r {
nxt_r -= r;
q += 1;
}
if 2 * nxt_r <= -r {
nxt_r += r;
q -= 1;
}
let (x, z, y) = red(nxt_r, r);
(x, y - q * z, z)
}
} // mod mod_int
macro_rules! define_mod {
($struct_name: ident, $modulo: expr) => {
#[derive(Copy, Clone, PartialEq, Eq, PartialOrd, Ord, Hash)]
struct $struct_name {}
impl mod_int::Mod for $struct_name { fn m() -> i64 { $modulo } }
}
}
const MOD: i64 = 998_244_353;
define_mod!(P, MOD);
type MInt = mod_int::ModInt<P>;
// Depends on MInt.rs
fn fact_init(w: usize) -> (Vec<MInt>, Vec<MInt>) {
let mut fac = vec![MInt::new(1); w];
let mut invfac = vec![0.into(); w];
for i in 1..w {
fac[i] = fac[i - 1] * i as i64;
}
invfac[w - 1] = fac[w - 1].inv();
for i in (0..w - 1).rev() {
invfac[i] = invfac[i + 1] * (i as i64 + 1);
}
(fac, invfac)
}
// FFT (in-place, verified as NTT only)
// R: Ring + Copy
// Verified by: https://judge.yosupo.jp/submission/53831
// Adopts the technique used in https://judge.yosupo.jp/submission/3153.
mod fft {
use std::ops::*;
// n should be a power of 2. zeta is a primitive n-th root of unity.
// one is unity
// Note that the result is bit-reversed.
pub fn fft<R>(f: &mut [R], zeta: R, one: R)
where R: Copy +
Add<Output = R> +
Sub<Output = R> +
Mul<Output = R> {
let n = f.len();
assert!(n.is_power_of_two());
let mut m = n;
let mut base = zeta;
unsafe {
while m > 2 {
m >>= 1;
let mut r = 0;
while r < n {
let mut w = one;
for s in r..r + m {
let &u = f.get_unchecked(s);
let d = *f.get_unchecked(s + m);
*f.get_unchecked_mut(s) = u + d;
*f.get_unchecked_mut(s + m) = w * (u - d);
w = w * base;
}
r += 2 * m;
}
base = base * base;
}
if m > 1 {
// m = 1
let mut r = 0;
while r < n {
let &u = f.get_unchecked(r);
let d = *f.get_unchecked(r + 1);
*f.get_unchecked_mut(r) = u + d;
*f.get_unchecked_mut(r + 1) = u - d;
r += 2;
}
}
}
}
pub fn inv_fft<R>(f: &mut [R], zeta_inv: R, one: R)
where R: Copy +
Add<Output = R> +
Sub<Output = R> +
Mul<Output = R> {
let n = f.len();
assert!(n.is_power_of_two());
let zeta = zeta_inv; // inverse FFT
let mut zetapow = Vec::with_capacity(20);
{
let mut m = 1;
let mut cur = zeta;
while m < n {
zetapow.push(cur);
cur = cur * cur;
m *= 2;
}
}
let mut m = 1;
unsafe {
if m < n {
zetapow.pop();
let mut r = 0;
while r < n {
let &u = f.get_unchecked(r);
let d = *f.get_unchecked(r + 1);
*f.get_unchecked_mut(r) = u + d;
*f.get_unchecked_mut(r + 1) = u - d;
r += 2;
}
m = 2;
}
while m < n {
let base = zetapow.pop().unwrap();
let mut r = 0;
while r < n {
let mut w = one;
for s in r..r + m {
let &u = f.get_unchecked(s);
let d = *f.get_unchecked(s + m) * w;
*f.get_unchecked_mut(s) = u + d;
*f.get_unchecked_mut(s + m) = u - d;
w = w * base;
}
r += 2 * m;
}
m *= 2;
}
}
}
}
// Computes f^{-1} mod x^{f.len()}.
// Reference: https://codeforces.com/blog/entry/56422
// Complexity: O(n log n)
// Verified by: https://judge.yosupo.jp/submission/3219
// Depends on: MInt.rs, fft.rs
fn fps_inv<P: mod_int::Mod + PartialEq>(
f: &[mod_int::ModInt<P>],
gen: mod_int::ModInt<P>
) -> Vec<mod_int::ModInt<P>> {
let n = f.len();
assert!(n.is_power_of_two());
assert_eq!(f[0], 1.into());
let mut sz = 1;
let mut r = vec![mod_int::ModInt::new(0); n];
let mut tmp_f = vec![mod_int::ModInt::new(0); n];
let mut tmp_r = vec![mod_int::ModInt::new(0); n];
r[0] = 1.into();
// Adopts the technique used in https://judge.yosupo.jp/submission/3153
while sz < n {
let zeta = gen.pow((P::m() - 1) / sz as i64 / 2);
tmp_f[..2 * sz].copy_from_slice(&f[..2 * sz]);
tmp_r[..2 * sz].copy_from_slice(&r[..2 * sz]);
fft::fft(&mut tmp_r[..2 * sz], zeta, 1.into());
fft::fft(&mut tmp_f[..2 * sz], zeta, 1.into());
let fac = mod_int::ModInt::new(2 * sz as i64).inv().pow(2);
for i in 0..2 * sz {
tmp_f[i] *= tmp_r[i];
}
fft::inv_fft(&mut tmp_f[..2 * sz], zeta.inv(), 1.into());
for v in &mut tmp_f[..sz] {
*v = 0.into();
}
fft::fft(&mut tmp_f[..2 * sz], zeta, 1.into());
for i in 0..2 * sz {
tmp_f[i] = -tmp_f[i] * tmp_r[i] * fac;
}
fft::inv_fft(&mut tmp_f[..2 * sz], zeta.inv(), 1.into());
r[sz..2 * sz].copy_from_slice(&tmp_f[sz..2 * sz]);
sz *= 2;
}
r
}
// Computes ln f mod x^{f.len()}.
// Reference: https://codeforces.com/blog/entry/56422
// Complexity: O(n log n)
// Verified by: https://judge.yosupo.jp/submission/53708
// Depends on: MInt.rs, fact_init.rs, fft.rs, fps/fps_inv.rs
fn fps_ln<P: mod_int::Mod + PartialEq>(
f: &[mod_int::ModInt<P>],
gen: mod_int::ModInt<P>,
fac: &[mod_int::ModInt<P>],
invfac: &[mod_int::ModInt<P>],
) -> Vec<mod_int::ModInt<P>> {
let n = f.len();
assert!(n.is_power_of_two());
assert_eq!(f[0], 1.into());
let mut inv = fps_inv(&f, gen);
let mut der = vec![mod_int::ModInt::new(0); 2 * n];
for i in 1..n {
der[i - 1] = f[i] * i as i64;
}
inv.resize(2 * n, 0.into());
let zeta = gen.pow((P::m() - 1) / n as i64 / 2);
fft::fft(&mut der, zeta, 1.into());
fft::fft(&mut inv, zeta, 1.into());
let invlen = mod_int::ModInt::new(2 * n as i64).inv();
for i in 0..2 * n {
der[i] *= inv[i] * invlen;
}
fft::inv_fft(&mut der, zeta.inv(), 1.into());
// integral of f'/f
let mut ans = vec![mod_int::ModInt::new(0); n];
for i in 1..n {
ans[i] = der[i - 1] * invfac[i] * fac[i - 1];
}
ans
}
// Computes exp(f) mod x^{f.len()}.
// Reference: https://arxiv.org/pdf/1301.5804.pdf
// Complexity: O(n log n)
// Depends on: MInt.rs, fact_init.rs, fft.rs
fn fps_exp<P: mod_int::Mod + PartialEq>(
h: &[mod_int::ModInt<P>],
gen: mod_int::ModInt<P>,
fac: &[mod_int::ModInt<P>],
invfac: &[mod_int::ModInt<P>],
) -> Vec<mod_int::ModInt<P>> {
let n = h.len();
assert!(n.is_power_of_two());
assert_eq!(h[0], 0.into());
let mut m = 1;
let mut f = vec![mod_int::ModInt::new(0); n];
let mut g = vec![mod_int::ModInt::new(0); n];
let mut tmp_f = vec![mod_int::ModInt::new(0); n];
let mut tmp_g = vec![mod_int::ModInt::new(0); n];
let mut tmp = vec![mod_int::ModInt::new(0); n];
f[0] = 1.into();
g[0] = 1.into();
// Adopts the technique used in https://judge.yosupo.jp/submission/3153
while m < n {
// upheld invariants: f = exp(h) (mod x^m)
// g = exp(-h) (mod x^(m/2))
// Complexity: 4 * fft(2 * m) + 2 * fft(m) + 2 * inv_fft(2 * m) + 3 * inv_fft(m)
// ~= 8.5 * fft(2 * m)
let zeta2m = gen.pow((P::m() - 1) / m as i64 / 2);
let zeta = zeta2m * zeta2m;
// 2.a': g = 2g - fg^2 mod x^m
let factor2m = mod_int::ModInt::new(m as i64 * 2).inv();
let factor = factor2m * 2;
let factor2 = factor * factor;
// Here we only need FFT(f[..m]), but we use it later at 2.c'
tmp_f[..2 * m].copy_from_slice(&f[..2 * m]);
fft::fft(&mut tmp_f[..2 * m], zeta2m, 1.into());
if m > 1 {
// The following can be dropped because the actual
// computation was done in the previous iteration.
// tmp_g[..m].copy_from_slice(&g[..m]);
// fft::fft(&mut tmp_g[..m], zeta, 1.into());
for i in 0..m {
tmp[i] = tmp_f[i] * tmp_g[i];
}
fft::inv_fft(&mut tmp[..m], zeta.inv(), 1.into());
for v in &mut tmp[..m / 2] {
*v = 0.into();
}
fft::fft(&mut tmp[..m], zeta, 1.into());
for i in 0..m {
tmp[i] = -tmp[i] * tmp_g[i] * factor2;
}
fft::inv_fft(&mut tmp[..m], zeta.inv(), 1.into());
g[m / 2..m].copy_from_slice(&tmp[m / 2..m]);
}
// 2.b': q = h' mod x^(m-1)
for i in 0..m - 1 {
tmp[i] = h[i + 1] * (i + 1) as i64;
}
tmp[m - 1] = 0.into();
// 2.c': r = fq (mod x^m - 1)
fft::fft(&mut tmp[..m], zeta, 1.into());
// FFT(f[..2m])[..m] == FFT(f[..m])
// Note that the result of FFT is bit-reversed.
for i in 0..m {
tmp[i] *= tmp_f[i] * factor;
}
fft::inv_fft(&mut tmp[..m], zeta.inv(), 1.into());
// 2.d' s = x(f' - r) mod (x^m - 1)
for i in (0..m - 1).rev() {
tmp.swap(i, i + 1);
}
for i in 0..m {
tmp[i] = f[i] * i as i64 - tmp[i];
}
// 2.e': t = gs mod x^m
tmp_g[..2 * m].copy_from_slice(&g[..2 * m]);
fft::fft(&mut tmp_g[..2 * m], zeta2m, 1.into());
fft::fft(&mut tmp[..2 * m], zeta2m, 1.into());
for i in 0..2 * m {
tmp[i] *= tmp_g[i] * factor2m;
}
fft::inv_fft(&mut tmp[..2 * m], zeta2m.inv(), 1.into());
// 2.f': u = (h mod x^2m - \int tx^(m-1)) / x^m
for i in 0..m {
tmp[i] = h[i + m] - tmp[i] * fac[i + m - 1] * invfac[i + m];
}
for v in &mut tmp[m..2 * m] {
*v = 0.into();
}
// 2.g': v = fu mod x^m
fft::fft(&mut tmp[..2 * m], zeta2m, 1.into());
for i in 0..2 * m {
tmp[i] *= tmp_f[i] * factor2m;
}
fft::inv_fft(&mut tmp[..2 * m], zeta2m.inv(), 1.into());
// 2.h': f += vx^m
f[m..2 * m].copy_from_slice(&tmp[..m]);
// 2.i': m *= 2
m *= 2;
}
f
}
fn main() {
let n: usize = get();
let mut p = 1;
while p <= n {
p *= 2;
}
let (fac, invfac) = fact_init(p + 1);
let mut dp = vec![MInt::new(0); p];
for i in 0..p {
dp[i] = invfac[i] * (i as i64 + 1);
}
let mut tmp = fps_ln(&dp, 3.into(), &fac, &invfac);
for i in 0..tmp.len() {
tmp[i] *= n as i64;
}
let tmp = fps_exp(&tmp, 3.into(), &fac, &invfac);
println!("{}", tmp[n - 2] * fac[n - 2] * MInt::new(n as i64).pow(MOD - 1 - (n - 2) as i64));
}
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