結果

問題 No.1310 量子アニーリング
ユーザー cotton_fn_cotton_fn_
提出日時 2020-12-07 16:58:42
言語 Rust
(1.83.0 + proconio)
結果
AC  
実行時間 8 ms / 2,000 ms
コード長 17,856 bytes
コンパイル時間 13,153 ms
コンパイル使用メモリ 383,432 KB
実行使用メモリ 6,944 KB
最終ジャッジ日時 2024-09-17 13:56:51
合計ジャッジ時間 12,818 ms
ジャッジサーバーID
(参考情報)
judge2 / judge3
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 * 21
権限があれば一括ダウンロードができます

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, unused_macros)]
use kyoproio::*;
use std::{
collections::*,
io::{self, prelude::*},
iter,
mem::{replace, swap},
};
fn run<I: Input, O: Write>(mut kin: I, mut out: O) {
let n: usize = kin.input();
let f = Fact::<Mod998244353>::new(n - 1);
let mut ans = mint(0);
let mut bs = vec![mint(0); n + 1];
for i in 0..=n - 1 {
let b = f.binom(n - 1, i);
let j = (i + (i & 1)) as isize;
let k = (j - (n as isize - j)).abs() as usize;
bs[k] += b;
}
let mut two = mint(1);
for i in 0..bs.len() {
ans += bs[i] * two;
two = two + two;
}
ans *= mint(2);
outln!(out, ans.get());
}
pub fn mod_inv_table<M: Modulo>(n: usize) -> Vec<ModInt<M>> {
let mut inv = vec![ModInt::new(0); n + 1];
inv[1] = ModInt::new(1);
for x in 2..=n {
let div = M::modulo() as usize / x;
let rem = M::modulo() as usize % x;
inv[x] = inv[rem] * -ModInt::new(div as u32);
}
inv
}
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 inv = mod_inv_table(n);
let mut finv = vec![ModInt::new(0); n + 1];
finv[0] = ModInt::new(1);
finv[1] = ModInt::new(1);
for i in 2..=n {
finv[i] = inv[i] * finv[i - 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 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 {
$val
}
})*
};
}
modulo_impl!(Mod998244353 998244353 Mod1e9p7 1000000007);
use std::sync::atomic;
pub struct VarMod;
static VAR_MOD: atomic::AtomicU32 = atomic::AtomicU32::new(0);
pub fn set_var_mod(m: u32) {
VAR_MOD.store(m, atomic::Ordering::Relaxed);
}
impl Modulo for VarMod {
fn modulo() -> u32 {
VAR_MOD.load(atomic::Ordering::Relaxed)
}
}
use std::{fmt, marker::PhantomData, ops};
pub struct ModInt<M>(u32, PhantomData<M>);
impl<M: Modulo> ModInt<M> {
pub fn new(x: u32) -> Self {
debug_assert!(x < M::modulo());
Self(x, PhantomData)
}
pub fn normalize(self) -> Self {
if self.0 < M::modulo() {
self
} else {
Self::new(self.0 % M::modulo())
}
}
pub fn get(self) -> u32 {
self.0
}
pub fn inv(self) -> Self {
self.pow(M::modulo() - 2)
}
pub fn half(self) -> Self {
Self::new(self.0 / 2 + self.0 % 2 * ((M::modulo() + 1) / 2))
}
pub fn modulo() -> u32 {
M::modulo()
}
}
impl<M: Modulo> ops::Neg for ModInt<M> {
type Output = Self;
fn neg(self) -> Self {
Self::new(if self.0 == 0 { 0 } else { M::modulo() - self.0 })
}
}
impl<M: Modulo> ops::AddAssign for ModInt<M> {
fn add_assign(&mut self, rhs: Self) {
self.0 += rhs.0;
if self.0 >= M::modulo() {
self.0 -= M::modulo();
}
}
}
impl<M: Modulo> ops::SubAssign for ModInt<M> {
fn sub_assign(&mut self, rhs: Self) {
self.0 = if self.0 >= rhs.0 {
self.0 - rhs.0
} else {
M::modulo() - self.0 - rhs.0
}
}
}
impl<M: Modulo> ops::MulAssign for ModInt<M> {
fn mul_assign(&mut self, rhs: Self) {
self.0 = (self.0 as u64 * rhs.0 as u64 % M::modulo() as u64) as u32;
}
}
impl<M: Modulo> ops::DivAssign for ModInt<M> {
fn div_assign(&mut self, rhs: Self) {
assert_ne!(rhs.get(), 0);
*self *= rhs.inv();
}
}
macro_rules! op_impl {
($($Op:ident $op:ident $OpAssign:ident $op_assign:ident)*) => {
$(impl<M: Modulo> ops::$Op for ModInt<M> {
type Output = Self;
fn $op(self, rhs: Self) -> Self {
let mut res = self;
ops::$OpAssign::$op_assign(&mut res, rhs);
res
}
}
impl<M: Modulo> ops::$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<&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> std::cmp::PartialEq for ModInt<M> {
fn eq(&self, other: &Self) -> bool {
self.0 == other.0
}
}
impl<M> std::cmp::Eq for ModInt<M> {}
impl<M> std::cmp::PartialOrd for ModInt<M> {
fn partial_cmp(&self, other: &Self) -> Option<std::cmp::Ordering> {
self.0.partial_cmp(&other.0)
}
}
impl<M> std::cmp::Ord for ModInt<M> {
fn cmp(&self, other: &Self) -> std::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 read = self.src.read(&mut self.buf[self.len..]).unwrap();
self.len += read;
read
}
}
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_impl {
{ $($T:ty)* } => {
$(impl InputItem for $T {
fn input<I: Input + ?Sized>(src: &mut I) -> Self {
src.str().parse::<$T>().unwrap()
}
})*
}
}
from_str_impl! { String char bool f32 f64 }
macro_rules! parse_int_impl {
{ $($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 $U)
}
})*
};
}
parse_int_impl! { isize:usize i8:u8 i16:u16 i32:u32 i64:u64 i128:u128 }
macro_rules! tuple_impl {
($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_impl!($($T)*);
};
() => {}
}
tuple_impl!(A B C D E F G);
macro_rules! array_impl {
{ $($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_impl! { 1 2 3 4 5 6 7 8 }
pub trait Output: Write + Sized {
fn bytes(&mut self, buf: &[u8]) {
self.write_all(buf).unwrap();
}
fn output<T: OutputItem>(&mut self, x: T) {
x.output(self);
}
fn byte(&mut self, b: u8) {
self.bytes(slice::from_ref(&b));
}
fn seq<T: OutputItem, I: IntoIterator<Item = T>>(&mut self, iter: I, delim: u8) {
let mut iter = iter.into_iter();
if let Some(x) = iter.next() {
self.output(x);
for x in iter {
self.byte(delim);
self.output(x);
}
}
}
fn flush_debug(&mut self) {
if cfg!(debug_assertions) {
self.flush().unwrap();
}
}
}
impl<W: Write + Sized> Output for W {}
pub trait OutputItem {
fn output<O: Output>(self, dest: &mut O);
}
impl OutputItem for &str {
fn output<O: Output>(self, dest: &mut O) {
dest.bytes(self.as_bytes());
}
}
impl OutputItem for char {
fn output<O: Output>(self, dest: &mut O) {
self.encode_utf8(&mut [0u8; 4]).output(dest);
}
}
impl OutputItem for () {
fn output<O: Output>(self, _dest: &mut O) {}
}
macro_rules! output_int_impl {
($conv:ident; $U:ty; $($T:ty)*) => {
$(impl OutputItem for $T {
fn output<O: Output>(self, dest: &mut O) {
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<O: Output>(self, dest: &mut O) {
(*self).output(dest);
}
})*
};
}
output_int_impl!(i64_to_bytes; i64; isize i8 i16 i32 i64);
output_int_impl!(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, $arg:expr) => {{
$out.output($arg);
}};
($out:expr, $first:expr, $($rest:expr),*) => {{
$out.output($first);
$out.byte(b' ');
out!($out, $($rest),*);
}}
}
#[macro_export]
macro_rules! outln {
($out:expr) => {{
$out.byte(b'\n');
$out.flush_debug();
}};
($out:expr, $($args:expr),*) => {{
out!($out, $($args),*);
outln!($out);
}}
}
#[macro_export]
macro_rules! kdbg {
($($v:expr),*) => {
if cfg!(debug_assertions) { dbg!($($v),*) } else { ($($v),*) }
}
}
}
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