結果
問題 | No.2514 Twelvefold Way Returns |
ユーザー |
|
提出日時 | 2023-12-15 18:06:12 |
言語 | Rust (1.83.0 + proconio) |
結果 |
AC
|
実行時間 | 18 ms / 3,000 ms |
コード長 | 5,664 bytes |
コンパイル時間 | 13,130 ms |
コンパイル使用メモリ | 395,600 KB |
実行使用メモリ | 5,376 KB |
最終ジャッジ日時 | 2024-09-27 06:29:17 |
合計ジャッジ時間 | 14,995 ms |
ジャッジサーバーID (参考情報) |
judge1 / judge4 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 38 |
ソースコード
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;}}}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> Default for ModInt<M> {fn default() -> Self { Self::new_internal(0) }}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> From<i64> for ModInt<M> {fn from(x: i64) -> Self { Self::new(x) }}} // mod mod_intmacro_rules! define_mod {($struct_name: ident, $modulo: expr) => {#[derive(Copy, Clone, PartialEq, Eq, PartialOrd, Ord, Hash)]pub 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)}fn mul((a, b): (MInt, MInt), (c, d): (MInt, MInt)) -> (MInt, MInt) {(a * c - b * d, a * d + b * c - b * d)}fn pow(a: (MInt, MInt), mut e: i64) -> (MInt, MInt) {let mut cur = a;let mut prod = (MInt::new(1), MInt::new(0));while e > 0 {if e % 2 != 0 {prod = mul(prod, cur);}cur = mul(cur, cur);e /= 2;}prod}// https://yukicoder.me/problems/no/2514 (4)// The author read the editorial before implementing this.// F(x) := \sum_i x^{3i+1}/(3i+1)! としたとき、答えは N! [x^N]F(x)^M である。// w := (-1 + sqrt(3))/2 とすると、F(x) = (exp(x)+w^2 exp(wx)+w exp(w^2x))/3 である。// F(x)^M = \sum_{i+j+k=M, i,j,k>=0} C(M,i,j,k) w^{2j+k} exp((i+wj+w^2k)x)/3^M// これの x^N の項は K[w] 上で計算できる。// 計算量は O(M^2 log N) である。// Tags: field-extensions, eisenstein-integersfn main() {let n: i64 = get();let m: usize = get();let (fac, invfac) = fact_init(m + 1);let mut tot = MInt::new(0);for i in 0..m + 1 {for j in 0..m - i + 1 {let k = m - i - j;let nth = pow((MInt::new(i as i64) - k as i64, MInt::new(j as i64) - k as i64), n);let mut tmp = mul(nth, (fac[m] * invfac[i] * invfac[j] * invfac[k], 0.into()));if (2 * j + k) % 3 == 1 {tmp = mul(tmp, (0.into(), 1.into()));} else if (2 * j + k) % 3 == 2 {tmp = mul(tmp, (-MInt::new(1), -MInt::new(1)));}tot += tmp.0;}}println!("{}", tot * MInt::new(3).inv().pow(m as i64));}