結果

問題 No.840 ほむほむほむら
ユーザー ngtkanangtkana
提出日時 2024-05-24 03:01:29
言語 Rust
(1.83.0 + proconio)
結果
AC  
実行時間 111 ms / 4,000 ms
コード長 20,194 bytes
コンパイル時間 13,765 ms
コンパイル使用メモリ 384,748 KB
実行使用メモリ 5,248 KB
最終ジャッジ日時 2024-12-20 19:12:51
合計ジャッジ時間 16,365 ms
ジャッジサーバーID
(参考情報)
judge3 / judge5
このコードへのチャレンジ
(要ログイン)
ファイルパターン 結果
sample AC * 3
other AC * 25
権限があれば一括ダウンロードができます
コンパイルメッセージ
warning: unused import: `factorial::Factorial`
   --> src/main.rs:385:13
    |
385 |     pub use factorial::Factorial;
    |             ^^^^^^^^^^^^^^^^^^^^
    |
    = note: `#[warn(unused_imports)]` on by default

warning: unused import: `fourier::any_mod_fps_mul`
   --> src/main.rs:386:13
    |
386 |     pub use fourier::any_mod_fps_mul;
    |             ^^^^^^^^^^^^^^^^^^^^^^^^

warning: unused import: `fourier::fft`
   --> src/main.rs:387:13
    |
387 |     pub use fourier::fft;
    |             ^^^^^^^^^^^^

warning: unused import: `fourier::fps_mul`
   --> src/main.rs:388:13
    |
388 |     pub use fourier::fps_mul;
    |             ^^^^^^^^^^^^^^^^

warning: unused import: `fourier::ifft`
   --> src/main.rs:389:13
    |
389 |     pub use fourier::ifft;
    |             ^^^^^^^^^^^^^

ソースコード

diff #
プレゼンテーションモードにする

type Fp = fp::Fp<998244353>;
const D: usize = 5;
const D3: usize = D * D * D;
fn main() {
let (e, d): (usize, usize) = io::input();
let encode = |i: usize, j: usize, k: usize| i * d * d + j * d + k;
let mut a = [[Fp::new(0); D3]; D3];
for i in 0..d {
for j in 0..d {
for k in 0..d {
let from = encode(i, j, k);
for to in [
encode((i + 1) % d, j, k),
encode(i, (j + i) % d, k),
encode(i, j, (k + j) % d),
] {
a[from][to] += Fp::new(1);
}
}
}
}
let mut x = [Fp::new(0); D3];
x[encode(0, 0, 0)] = Fp::new(1);
let x = pow_apply(a, x, e);
let ans = (0..d)
.map(|i| (0..d).map(|j| x[encode(i, j, 0)]).sum::<Fp>())
.sum::<Fp>();
println!("{}", ans);
}
fn pow_apply(mut a: [[Fp; D3]; D3], mut x: [Fp; D3], mut n: usize) -> [Fp; D3] {
assert_ne!(n, 0);
while n > 1 {
if n & 1 == 1 {
x = apply(&a, &x);
}
a = mul(&a, &a);
n >>= 1;
}
apply(&a, &x)
}
fn apply(a: &[[Fp; D3]; D3], x: &[Fp; D3]) -> [Fp; D3] {
let mut y = [Fp::new(0); D3];
for i in 0..D3 {
for j in 0..D3 {
y[i] += a[i][j] * x[j];
}
}
y
}
fn mul(a: &[[Fp; D3]; D3], b: &[[Fp; D3]; D3]) -> [[Fp; D3]; D3] {
let n = a.len();
let mut c = [[Fp::new(0); D3]; D3];
for i in 0..n {
for j in 0..n {
for k in 0..n {
c[i][j] += a[i][k] * b[k][j];
}
}
}
c
}
// io {{{
// https://ngtkana.github.io/ac-adapter-rs/io/index.html
#[allow(dead_code)]
mod io {
use std::cell::Cell;
use std::io::stdin;
use std::io::BufRead;
use std::io::BufReader;
use std::io::Lines;
use std::io::Stdin;
use std::sync::Mutex;
use std::sync::Once;
pub fn input<T: ParseLine>() -> T {
ParseLine::parse_line(&line())
}
pub trait ParseLine {
fn parse_line(s: &str) -> Self;
}
macro_rules! impl_parse_line {
($($t:ty),*) => {
$(impl ParseLine for $t {
fn parse_line(s: &str) -> Self {
s.parse().unwrap()
}
})*
};
}
impl_parse_line!(u8, u16, u32, u64, u128, usize, i8, i16, i32, i64, i128, isize, String, char);
macro_rules! impl_parse_line_tuple {
($($t:ident),*) => {
impl<$($t: ParseLine),*> ParseLine for ($($t,)*) {
fn parse_line(s: &str) -> Self {
let mut s = s.split_whitespace();
($($t::parse_line(s.next().unwrap()),)*)
}
}
};
}
impl_parse_line_tuple!(T0, T1);
impl_parse_line_tuple!(T0, T1, T2);
impl_parse_line_tuple!(T0, T1, T2, T3);
impl_parse_line_tuple!(T0, T1, T2, T3, T4);
impl_parse_line_tuple!(T0, T1, T2, T3, T4, T5);
impl_parse_line_tuple!(T0, T1, T2, T3, T4, T5, T6);
impl_parse_line_tuple!(T0, T1, T2, T3, T4, T5, T6, T7);
impl_parse_line_tuple!(T0, T1, T2, T3, T4, T5, T6, T7, T8);
impl_parse_line_tuple!(T0, T1, T2, T3, T4, T5, T6, T7, T8, T9);
impl<T: ParseLine> ParseLine for Vec<T> {
fn parse_line(s: &str) -> Self {
s.split_whitespace().map(T::parse_line).collect()
}
}
static ONCE: Once = Once::new();
type Server = Mutex<Lines<BufReader<Stdin>>>;
struct Lazy(Cell<Option<Server>>);
unsafe impl Sync for Lazy {}
fn line() -> String {
static SYNCER: Lazy = Lazy(Cell::new(None));
ONCE.call_once(|| {
SYNCER
.0
.set(Some(Mutex::new(BufReader::new(stdin()).lines())));
});
unsafe {
(*SYNCER.0.as_ptr())
.as_ref()
.unwrap()
.lock()
.unwrap()
.next()
.unwrap()
.unwrap()
}
}
}
// }}}
// fp {{{
// https://ngtkana.github.io/ac-adapter-rs/fp/index.html
#[allow(dead_code)]
mod fp {
mod ext_gcd {
pub(crate) fn mod_inv<const P: u64>(x: u64) -> u64 {
debug_assert!(P % 2 == 1);
debug_assert!(P < 1 << 31);
debug_assert!(x < P);
mod_inv_signed(x as i64, P as i64) as u64
}
fn mod_inv_signed(a: i64, m: i64) -> i64 {
debug_assert!(a > 0);
debug_assert!(m > 0);
if a == 1 {
return 1;
}
m + (1 - m * mod_inv_signed(m % a, a)) / a
}
}
mod factorial {
use super::Fp;
use std::ops::Index;
pub struct Factorial<const P: u64> {
fact: Vec<Fp<P>>,
inv_fact: Vec<Fp<P>>,
}
impl<const P: u64> Factorial<P> {
pub fn new(length: usize) -> Self {
let mut fact = vec![Fp::<P>::new(1); length + 1];
let mut inv_fact = vec![Fp::<P>::new(1); length + 1];
for i in 1..=length {
fact[i] = fact[i - 1] * Fp::<P>::new(i as u64);
}
inv_fact[length] = fact[length].inv();
for i in (1..=length).rev() {
inv_fact[i - 1] = inv_fact[i] * Fp::<P>::new(i as u64);
}
Self { fact, inv_fact }
}
pub fn fact(&self, n: usize) -> Fp<P> {
self.fact[n]
}
pub fn inv_fact(&self, n: usize) -> Fp<P> {
self.inv_fact[n]
}
pub fn perm(&self, n: usize, k: usize) -> Fp<P> {
self.fact[n] * self.inv_fact[n - k]
}
pub fn comb(&self, n: usize, k: usize) -> Fp<P> {
self.fact[n] * self.inv_fact[n - k] * self.inv_fact[k]
}
pub fn binom(&self, n: usize, k: usize) -> Fp<P> {
self.comb(n, k)
}
pub fn comb_or_zero(&self, n: usize, k: isize) -> Fp<P> {
if k < 0 || k as usize > n {
Fp::<P>::new(0)
} else {
self.comb(n, k as usize)
}
}
pub fn comb_with_reputation(&self, n: usize, k: usize) -> Fp<P> {
assert!(n > 0 || k > 0);
self.comb(n + k - 1, k)
}
}
impl<const P: u64> Index<usize> for Factorial<P> {
type Output = Fp<P>;
fn index(&self, index: usize) -> &Self::Output {
&self.fact[index]
}
}
}
mod fourier {
use super::mod_inv;
use super::Fp;
use super::PrimitiveRoot;
const P1: u64 = 924844033;
const P2: u64 = 998244353;
const P3: u64 = 1012924417;
type F1 = Fp<P1>;
type F2 = Fp<P2>;
type F3 = Fp<P3>;
pub fn fps_mul<const P: u64>(a: impl AsRef<[Fp<P>]>, b: impl AsRef<[Fp<P>]>) -> Vec<Fp<P>>
where
(): PrimitiveRoot<P>,
{
let a = a.as_ref();
let b = b.as_ref();
if a.is_empty() || b.is_empty() {
return vec![];
}
let mut a = a.to_vec();
let mut b = b.to_vec();
let n = a.len() + b.len() - 1;
let len = n.next_power_of_two();
a.resize(len, Fp::new(0));
b.resize(len, Fp::new(0));
fft(&mut a);
fft(&mut b);
for (a, b) in a.iter_mut().zip(b.iter()) {
*a *= *b;
}
ifft(&mut a);
a.truncate(n);
a
}
pub fn any_mod_fps_mul<const P: u64>(a: &[Fp<P>], b: &[Fp<P>]) -> Vec<Fp<P>> {
let v1 = fps_mul(
a.iter().map(|&x| F1::new(x.value())).collect::<Vec<_>>(),
b.iter().map(|&x| F1::new(x.value())).collect::<Vec<_>>(),
);
let v2 = fps_mul(
a.iter().map(|&x| F2::new(x.value())).collect::<Vec<_>>(),
b.iter().map(|&x| F2::new(x.value())).collect::<Vec<_>>(),
);
let v3 = fps_mul(
a.iter().map(|&x| F3::new(x.value())).collect::<Vec<_>>(),
b.iter().map(|&x| F3::new(x.value())).collect::<Vec<_>>(),
);
v1.into_iter()
.zip(v2)
.zip(v3)
.map(|((e1, e2), e3)| garner(e1, e2, e3))
.collect::<Vec<_>>()
}
pub fn fft<const P: u64>(f: &mut [Fp<P>])
where
(): PrimitiveRoot<P>,
{
let n = f.len();
assert!(n.is_power_of_two());
assert!((P - 1) % n as u64 == 0);
let mut root = <() as PrimitiveRoot<P>>::VALUE.pow((P - 1) / f.len() as u64);
let fourth = <() as PrimitiveRoot<P>>::VALUE.pow((P - 1) / 4);
let mut fft_len = n;
while 4 <= fft_len {
let quarter = fft_len / 4;
for f in f.chunks_mut(fft_len) {
let mut c = Fp::new(1);
for (((i, j), k), l) in (0..)
.zip(quarter..)
.zip(quarter * 2..)
.zip(quarter * 3..)
.take(quarter)
{
let c2 = c * c;
let x = f[i] + f[k];
let y = f[j] + f[l];
let z = f[i] - f[k];
let w = fourth * (f[j] - f[l]);
f[i] = x + y;
f[j] = c2 * (x - y);
f[k] = c * (z + w);
f[l] = c2 * c * (z - w);
c *= root;
}
}
root *= root;
root *= root;
fft_len = quarter;
}
if fft_len == 2 {
for f in f.chunks_mut(2) {
let x = f[0];
let y = f[1];
f[0] = x + y;
f[1] = x - y;
}
}
}
pub fn ifft<const P: u64>(f: &mut [Fp<P>])
where
(): PrimitiveRoot<P>,
{
let n = f.len();
assert!(n.is_power_of_two());
let root = <() as PrimitiveRoot<P>>::VALUE.pow((P - 1) / f.len() as u64);
let mut roots = std::iter::successors(Some(root.inv()), |x| Some(x * x))
.take(n.trailing_zeros() as usize + 1)
.collect::<Vec<_>>();
roots.reverse();
let fourth = <() as PrimitiveRoot<P>>::VALUE.pow((P - 1) / 4).inv();
let mut quarter = 1_usize;
if n.trailing_zeros() % 2 == 1 {
for f in f.chunks_mut(2) {
let x = f[0];
let y = f[1];
f[0] = x + y;
f[1] = x - y;
}
quarter = 2;
}
while quarter != n {
let fft_len = quarter * 4;
let root = roots[fft_len.trailing_zeros() as usize];
for f in f.chunks_mut(fft_len) {
let mut c = Fp::new(1);
for (((i, j), k), l) in (0..)
.zip(quarter..)
.zip(quarter * 2..)
.zip(quarter * 3..)
.take(quarter)
{
let c2 = c * c;
let x = f[i] + c2 * f[j];
let y = f[i] - c2 * f[j];
let z = c * (f[k] + c2 * f[l]);
let w = fourth * c * (f[k] - c2 * f[l]);
f[i] = x + z;
f[j] = y + w;
f[k] = x - z;
f[l] = y - w;
c *= root;
}
}
quarter = fft_len;
}
let d = Fp::from(f.len()).inv();
f.iter_mut().for_each(|x| *x *= d);
}
fn garner<const P: u64>(x1: Fp<P1>, x2: Fp<P2>, x3: Fp<P3>) -> Fp<P> {
let (x1, x2, x3) = (x1.value(), x2.value(), x3.value());
let x2 = ((x2 + (P2 - x1)) * mod_inv::<P2>(P1)) % P2;
let x3 =
(((x3 + (P3 - x1)) * mod_inv::<P3>(P1) % P3 + (P3 - x2)) * mod_inv::<P3>(P2)) % P3;
Fp::new(x1 + P1 * (x2 + P2 * x3 % P))
}
}
use ext_gcd::mod_inv;
pub use factorial::Factorial;
pub use fourier::any_mod_fps_mul;
pub use fourier::fft;
pub use fourier::fps_mul;
pub use fourier::ifft;
use std::iter::Product;
use std::iter::Sum;
use std::mem::swap;
use std::ops::Add;
use std::ops::AddAssign;
use std::ops::Div;
use std::ops::DivAssign;
use std::ops::Mul;
use std::ops::MulAssign;
use std::ops::Neg;
use std::ops::Sub;
use std::ops::SubAssign;
#[macro_export]
macro_rules! fp {
($value:expr) => {
$crate::fp::Fp::from($value)
};
($value:expr; mod $p:expr) => {
$crate::fp::Fp::<$p>::from($value)
};
}
pub trait PrimitiveRoot<const P: u64> {
const VALUE: Fp<P>;
}
impl PrimitiveRoot<998244353> for () {
const VALUE: Fp<998244353> = Fp::new(3);
}
impl PrimitiveRoot<1012924417> for () {
const VALUE: Fp<1012924417> = Fp::new(5);
}
impl PrimitiveRoot<924844033> for () {
const VALUE: Fp<924844033> = Fp::new(5);
}
#[derive(Clone, Copy, PartialEq, Eq, Hash)]
pub struct Fp<const P: u64> {
value: u64,
}
impl<const P: u64> Fp<P> {
pub const fn new(value: u64) -> Self {
Self { value: value % P }
}
pub const fn value(self) -> u64 {
self.value
}
pub fn inv(self) -> Self {
Self {
value: mod_inv::<P>(self.value),
}
}
pub fn pow(self, mut exp: u64) -> Self {
let mut result = Self::new(1);
let mut base = self;
while exp > 0 {
if exp & 1 == 1 {
result *= base;
}
base *= base;
exp >>= 1;
}
result
}
pub fn sign(pow: usize) -> Self {
Self::new(if pow % 2 == 0 { 1 } else { P - 1 })
}
}
impl<const P: u64> std::fmt::Debug for Fp<P> {
fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
pub fn berlekamp_massey_fp(a: i64, p: i64) -> [i64; 2] {
let mut u0 = 0_i64;
let mut v0 = 1_i64;
let mut w0 = a * u0 + p * v0;
let mut u1 = 1_i64;
let mut v1 = 0_i64;
let mut w1 = a * u1 + p * v1;
while p <= w0 * w0 {
let q = w0 / w1;
u0 -= q * u1;
v0 -= q * v1;
w0 -= q * w1;
swap(&mut u0, &mut u1);
swap(&mut v0, &mut v1);
swap(&mut w0, &mut w1);
}
[w0, u0]
}
if self.value == 0 {
return write!(f, "0");
}
let [mut num, mut den] = berlekamp_massey_fp(self.value as i64, P as i64);
if den < 0 {
num = -num;
den = -den;
}
if den == 1 {
write!(f, "{}", num)
} else {
write!(f, "{}/{}", num, den)
}
}
}
impl<const P: u64> std::fmt::Display for Fp<P> {
fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
write!(f, "{}", self.value())
}
}
macro_rules! impl_from_signed {
($($t:ty),*) => {
$(
impl<const P: u64> From<$t> for Fp<P> {
fn from(x: $t) -> Self {
if x < 0 {
-Self::new((P as i64 - x as i64) as u64)
} else {
Self::new(x as u64)
}
}
}
)*
};
}
impl_from_signed!(i8, i16, i32, i64, i128, isize);
macro_rules! impl_from_unsigned {
($($t:ty),*) => {
$(
impl<const P: u64> From<$t> for Fp<P> {
fn from(x: $t) -> Self { Self::new(x as u64) }
}
)*
};
}
impl_from_unsigned!(u8, u16, u32, u64, u128, usize);
impl<const P: u64> AddAssign<Fp<P>> for Fp<P> {
fn add_assign(&mut self, rhs: Fp<P>) {
self.value += rhs.value;
if self.value >= P {
self.value -= P;
}
}
}
impl<const P: u64> SubAssign<Fp<P>> for Fp<P> {
fn sub_assign(&mut self, rhs: Fp<P>) {
if self.value < rhs.value {
self.value += P;
}
self.value -= rhs.value;
}
}
impl<const P: u64> MulAssign<Fp<P>> for Fp<P> {
fn mul_assign(&mut self, rhs: Fp<P>) {
self.value = self.value * rhs.value % P;
}
}
#[allow(clippy::suspicious_op_assign_impl)]
impl<const P: u64> DivAssign<Fp<P>> for Fp<P> {
fn div_assign(&mut self, rhs: Fp<P>) {
*self *= rhs.inv()
}
}
macro_rules! fp_forward_ops {
($(
$trait:ident,
$trait_assign:ident,
$fn:ident,
$fn_assign:ident,
)*) => {$(
impl<const P: u64> $trait_assign<&Fp<P>> for Fp<P> {
fn $fn_assign(&mut self, rhs: &Fp<P>) {
self.$fn_assign(*rhs);
}
}
impl<const P: u64, T: Into<Fp<P>>> $trait<T> for Fp<P> {
type Output = Fp<P>;
fn $fn(mut self, rhs: T) -> Self::Output {
self.$fn_assign(rhs.into());
self
}
}
impl<const P: u64> $trait<&Fp<P>> for Fp<P> {
type Output = Fp<P>;
fn $fn(self, rhs: &Fp<P>) -> Self::Output {
self.$fn(*rhs)
}
}
impl<const P: u64, T: Into<Fp<P>>> $trait<T> for &Fp<P> {
type Output = Fp<P>;
fn $fn(self, rhs: T) -> Self::Output {
(*self).$fn(rhs.into())
}
}
impl<const P: u64> $trait<&Fp<P>> for &Fp<P> {
type Output = Fp<P>;
fn $fn(self, rhs: &Fp<P>) -> Self::Output {
(*self).$fn(*rhs)
}
}
)*};
}
fp_forward_ops! {
Add, AddAssign, add, add_assign,
Sub, SubAssign, sub, sub_assign,
Mul, MulAssign, mul, mul_assign,
Div, DivAssign, div, div_assign,
}
impl<const P: u64> Neg for Fp<P> {
type Output = Fp<P>;
fn neg(mut self) -> Self::Output {
if self.value > 0 {
self.value = P - self.value;
}
self
}
}
impl<const P: u64> Sum for Fp<P> {
fn sum<I: Iterator<Item = Self>>(iter: I) -> Self {
iter.fold(Self::new(0), |acc, x| acc + x)
}
}
impl<'a, const P: u64> Sum<&'a Self> for Fp<P> {
fn sum<I: Iterator<Item = &'a Self>>(iter: I) -> Self {
iter.copied().sum()
}
}
impl<const P: u64> Product for Fp<P> {
fn product<I: Iterator<Item = Self>>(iter: I) -> Self {
iter.fold(Self::new(1), |acc, x| acc * x)
}
}
impl<'a, const P: u64> Product<&'a Self> for Fp<P> {
fn product<I: Iterator<Item = &'a Self>>(iter: I) -> Self {
iter.copied().product()
}
}
}
// }}}
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