結果

問題 No.931 Multiplicative Convolution
ユーザー koba-e964
提出日時 2020-01-01 14:35:27
言語 Rust
(1.83.0 + proconio)
結果
AC  
実行時間 103 ms / 2,000 ms
コード長 9,032 bytes
コンパイル時間 12,981 ms
コンパイル使用メモリ 401,136 KB
実行使用メモリ 9,088 KB
最終ジャッジ日時 2024-11-22 04:08:32
合計ジャッジ時間 15,724 ms
ジャッジサーバーID
(参考情報)
judge3 / judge4
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::{Write, BufWriter};
// https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8
macro_rules! input {
($($r:tt)*) => {
let stdin = std::io::stdin();
let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock()));
let mut next = move || -> String{
bytes
.by_ref()
.map(|r|r.unwrap() as char)
.skip_while(|c|c.is_whitespace())
.take_while(|c|!c.is_whitespace())
.collect()
};
input_inner!{next, $($r)*}
};
}
macro_rules! input_inner {
($next:expr) => {};
($next:expr, ) => {};
($next:expr, $var:ident : $t:tt $($r:tt)*) => {
let $var = read_value!($next, $t);
input_inner!{$next $($r)*}
};
}
macro_rules! read_value {
($next:expr, ( $($t:tt),* )) => {
( $(read_value!($next, $t)),* )
};
($next:expr, [ $t:tt ; $len:expr ]) => {
(0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
};
($next:expr, chars) => {
read_value!($next, String).chars().collect::<Vec<char>>()
};
($next:expr, usize1) => {
read_value!($next, usize) - 1
};
($next:expr, [ $t:tt ]) => {{
let len = read_value!($next, usize);
(0..len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
}};
($next:expr, $t:ty) => {
$next().parse::<$t>().expect("Parse error")
};
}
#[allow(unused)]
macro_rules! debug {
($($format:tt)*) => (write!(std::io::stderr(), $($format)*).unwrap());
}
#[allow(unused)]
macro_rules! debugln {
($($format:tt)*) => (writeln!(std::io::stderr(), $($format)*).unwrap());
}
/// Verified by https://atcoder.jp/contests/arc093/submissions/3968098
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 { $modulo } }
}
}
const MOD: i64 = 998_244_353;
define_mod!(P, MOD);
type ModInt = mod_int::ModInt<P>;
/// FFT (in-place, verified as NTT only)
/// R: Ring + Copy
/// Verified by: https://codeforces.com/contest/1096/submission/47672373
mod fft {
use std::ops::*;
/// n should be a power of 2. zeta is a primitive n-th root of unity.
/// one is unity
/// Note that the result should be multiplied by 1/sqrt(n).
pub fn transform<R>(f: &mut [R], zeta: R, one: R)
where R: Copy +
Add<Output = R> +
Sub<Output = R> +
Mul<Output = R> {
let n = f.len();
assert!(n.is_power_of_two());
{
let mut i = 0;
for j in 1 .. n - 1 {
let mut k = n >> 1;
loop {
i ^= k;
if k <= i { break; }
k >>= 1;
}
if j < i { f.swap(i, j); }
}
}
let mut zetapow = Vec::new();
{
let mut m = 1;
let mut cur = zeta;
while m < n {
zetapow.push(cur);
cur = cur * cur;
m *= 2;
}
}
let mut m = 1;
while m < n {
let base = zetapow.pop().unwrap();
let mut r = 0;
while r < n {
let mut w = one;
for s in r .. r + m {
let u = f[s];
let d = f[s + m] * w;
f[s] = u + d;
f[s + m] = u - d;
w = w * base;
}
r += 2 * m;
}
m *= 2;
}
}
}
fn solve() {
let out = std::io::stdout();
let mut out = BufWriter::new(out.lock());
macro_rules! puts {
($($format:tt)*) => (write!(out,$($format)*).unwrap());
}
input! {
p: usize,
a: [i64; p - 1],
b: [i64; p - 1],
}
let pp = p as i64;
// Find a generator
let mut g: i64 = 2;
if p == 2 {
g = 1;
} else {
loop {
let mut ok = true;
let mut cur = 1;
for _ in 0..pp - 2 {
cur *= g;
cur %= pp;
if cur == 1 {
ok = false;
break;
}
}
if ok { break; }
g += 1;
}
}
debugln!("g = {}", g);
let mut fwd = vec![0; p - 1];
let mut rev = vec![0; p];
let mut cur = 1;
for i in 0..p - 1 {
fwd[i] = cur;
rev[cur] = i;
cur = cur * (g as usize) % p;
}
const W: usize = 1 << 18;
let mut x = vec![ModInt::new(0); W];
let mut y = vec![ModInt::new(0); W];
for i in 0..p - 1 {
let idx = rev[i + 1];
x[idx] += a[i];
y[idx] += b[i];
}
let zeta = ModInt::new(3).pow((MOD - 1) / W as i64);
fft::transform(&mut x, zeta, 1.into());
fft::transform(&mut y, zeta, 1.into());
let fac = ModInt::new(W as i64).inv();
for i in 0..W {
x[i] *= y[i] * fac;
}
fft::transform(&mut x, zeta.inv(), 1.into());
for i in 0..p - 1 {
let idx = rev[i + 1];
puts!("{}{}", x[idx] + x[idx + p - 1], if i + 1 == p - 1 { "\n" } else { " " });
}
}
fn main() {
// In order to avoid potential stack overflow, spawn a new thread.
let stack_size = 104_857_600; // 100 MB
let thd = std::thread::Builder::new().stack_size(stack_size);
thd.spawn(|| solve()).unwrap().join().unwrap();
}
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