結果
問題 | No.931 Multiplicative Convolution |
ユーザー |
|
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 |
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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::{Write, BufWriter};// https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8macro_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/3968098mod 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 { $modulo } }}}const MOD: i64 = 998_244_353;define_mod!(P, MOD);type ModInt = mod_int::ModInt<P>;/// FFT (in-place, verified as NTT only)/// R: Ring + Copy/// Verified by: https://codeforces.com/contest/1096/submission/47672373mod fft {use std::ops::*;/// n should be a power of 2. zeta is a primitive n-th root of unity./// one is unity/// Note that the result should be multiplied by 1/sqrt(n).pub fn transform<R>(f: &mut [R], zeta: R, one: R)where R: Copy +Add<Output = R> +Sub<Output = R> +Mul<Output = R> {let n = f.len();assert!(n.is_power_of_two());{let mut i = 0;for j in 1 .. n - 1 {let mut k = n >> 1;loop {i ^= k;if k <= i { break; }k >>= 1;}if j < i { f.swap(i, j); }}}let mut zetapow = Vec::new();{let mut m = 1;let mut cur = zeta;while m < n {zetapow.push(cur);cur = cur * cur;m *= 2;}}let mut m = 1;while m < n {let base = zetapow.pop().unwrap();let mut r = 0;while r < n {let mut w = one;for s in r .. r + m {let u = f[s];let d = f[s + m] * w;f[s] = u + d;f[s + m] = u - d;w = w * base;}r += 2 * m;}m *= 2;}}}fn solve() {let out = std::io::stdout();let mut out = BufWriter::new(out.lock());macro_rules! puts {($($format:tt)*) => (write!(out,$($format)*).unwrap());}input! {p: usize,a: [i64; p - 1],b: [i64; p - 1],}let pp = p as i64;// Find a generatorlet 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 MBlet thd = std::thread::Builder::new().stack_size(stack_size);thd.spawn(|| solve()).unwrap().join().unwrap();}