結果
問題 | No.1302 Random Tree Score |
ユーザー |
|
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 |
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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)]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/21774342mod 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 >= 0pub 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_intmacro_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.rsfn 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 = 1let 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 FFTlet 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.rsfn 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/3153while 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.rsfn 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'/flet 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.rsfn 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/3153while 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^mlet 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^mtmp_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^mfor 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^mfft::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^mf[m..2 * m].copy_from_slice(&tmp[..m]);// 2.i': m *= 2m *= 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));}