結果

問題 No.1962 Not Divide
ユーザー koba-e964koba-e964
提出日時 2024-04-16 22:30:33
言語 Rust
(1.83.0 + proconio)
結果
AC  
実行時間 177 ms / 2,000 ms
コード長 11,190 bytes
コンパイル時間 17,840 ms
コンパイル使用メモリ 377,976 KB
実行使用メモリ 5,248 KB
最終ジャッジ日時 2024-10-08 04:09:48
合計ジャッジ時間 17,756 ms
ジャッジサーバーID
(参考情報)
judge4 / judge1
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 * 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)]
use std::cmp::*;
#[allow(unused_imports)]
use std::collections::*;
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;
}
}
}
#[allow(dead_code)]
fn get<T: std::str::FromStr>() -> T { get_word().parse().ok().unwrap() }
/// Verified by https://atcoder.jp/contests/abc198/submissions/21774342
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> 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> ::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 MInt = mod_int::ModInt<P>;
// FFT (in-place, verified as NTT only)
// R: Ring + Copy
// Verified by: https://judge.yosupo.jp/submission/53831
// Adopts the technique used in https://judge.yosupo.jp/submission/3153.
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 is bit-reversed.
pub fn fft<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 m = n;
let mut base = zeta;
unsafe {
while m > 2 {
m >>= 1;
let mut r = 0;
while r < n {
let mut w = one;
for s in r..r + m {
let &u = f.get_unchecked(s);
let d = *f.get_unchecked(s + m);
*f.get_unchecked_mut(s) = u + d;
*f.get_unchecked_mut(s + m) = w * (u - d);
w = w * base;
}
r += 2 * m;
}
base = base * base;
}
if m > 1 {
// m = 1
let mut r = 0;
while r < n {
let &u = f.get_unchecked(r);
let d = *f.get_unchecked(r + 1);
*f.get_unchecked_mut(r) = u + d;
*f.get_unchecked_mut(r + 1) = u - d;
r += 2;
}
}
}
}
pub fn inv_fft<R>(f: &mut [R], zeta_inv: 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 zeta = zeta_inv; // inverse FFT
let mut zetapow = Vec::with_capacity(20);
{
let mut m = 1;
let mut cur = zeta;
while m < n {
zetapow.push(cur);
cur = cur * cur;
m *= 2;
}
}
let mut m = 1;
unsafe {
if m < n {
zetapow.pop();
let mut r = 0;
while r < n {
let &u = f.get_unchecked(r);
let d = *f.get_unchecked(r + 1);
*f.get_unchecked_mut(r) = u + d;
*f.get_unchecked_mut(r + 1) = u - d;
r += 2;
}
m = 2;
}
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.get_unchecked(s);
let d = *f.get_unchecked(s + m) * w;
*f.get_unchecked_mut(s) = u + d;
*f.get_unchecked_mut(s + m) = u - d;
w = w * base;
}
r += 2 * m;
}
m *= 2;
}
}
}
}
// Depends on: fft.rs, MInt.rs
// Verified by: ABC269-Ex (https://atcoder.jp/contests/abc269/submissions/39116328)
pub struct FPSOps<M: mod_int::Mod> {
gen: mod_int::ModInt<M>,
}
impl<M: mod_int::Mod> FPSOps<M> {
pub fn new(gen: mod_int::ModInt<M>) -> Self {
FPSOps { gen: gen }
}
}
impl<M: mod_int::Mod> FPSOps<M> {
pub fn add(&self, mut a: Vec<mod_int::ModInt<M>>, mut b: Vec<mod_int::ModInt<M>>) -> Vec<mod_int::ModInt<M>> {
if a.len() < b.len() {
std::mem::swap(&mut a, &mut b);
}
for i in 0..b.len() {
a[i] += b[i];
}
a
}
pub fn mul(&self, a: Vec<mod_int::ModInt<M>>, b: Vec<mod_int::ModInt<M>>) -> Vec<mod_int::ModInt<M>> {
type MInt<M> = mod_int::ModInt<M>;
if a.is_empty() || b.is_empty() {
return vec![];
}
let n = a.len() - 1;
let m = b.len() - 1;
let mut p = 1;
while p <= n + m { p *= 2; }
let mut f = vec![MInt::new(0); p];
let mut g = vec![MInt::new(0); p];
for i in 0..n + 1 { f[i] = a[i]; }
for i in 0..m + 1 { g[i] = b[i]; }
let fac = MInt::new(p as i64).inv();
let zeta = self.gen.pow((M::m() - 1) / p as i64);
fft::fft(&mut f, zeta, 1.into());
fft::fft(&mut g, zeta, 1.into());
for i in 0..p { f[i] *= g[i] * fac; }
fft::inv_fft(&mut f, zeta.inv(), 1.into());
f.truncate(n + m + 1);
f
}
}
// Finds [x^n] p(x)/q(x)
// Ref: https://qiita.com/ryuhe1/items/da5acbcce4ac1911f47a
// Verified by: https://atcoder.jp/contests/tdpc/submissions/24583334
// Depends on: MInt.rs
fn bostan_mori(ops: &FPSOps<P>, p: &[MInt], q: &[MInt], mut n: i64) -> MInt {
if p.is_empty() {
return 0.into();
}
assert!(p.len() < q.len());
let mut p = p.to_vec();
let mut q = q.to_vec();
while n > 0 {
let mut qn = q.clone();
for i in 0..qn.len() {
if i % 2 == 1 {
qn[i] = -qn[i];
}
}
let num = ops.mul(p, qn.clone());
let den = ops.mul(q.clone(), qn);
let mut nxt_p = vec![MInt::new(0); q.len() - 1];
let mut nxt_q = vec![MInt::new(0); q.len()];
for i in 0..q.len() - 1 {
let to = 2 * i + (n % 2) as usize;
if to < num.len() {
nxt_p[i] = num[to];
}
}
for i in 0..q.len() {
nxt_q[i] = den[2 * i];
}
p = nxt_p;
q = nxt_q;
n /= 2;
}
p[0] * q[0].inv()
}
fn main() {
let n: i64 = get();
let m: usize = get();
let ops = FPSOps::new(MInt::new(3));
let mut num = vec![];
let mut den = vec![MInt::new(1)];
for i in 2..m + 1 {
// g += (x+...+x^{i-1}) / (1+...+x^{i-1}-x^i)
let mut num1 = vec![MInt::new(1); i];
num1[0] -= 1;
let mut den1 = vec![MInt::new(1); i + 1];
den1[i] -= 2;
let newnum = ops.mul(num.clone(), den1.clone());
let newnum = ops.add(newnum, ops.mul(den.clone(), num1.clone()));
let newden = ops.mul(den.clone(), den1);
num = newnum;
den = newden;
}
// g / (1 - g) = num / (den - num)
for i in 0..num.len() {
den[i] -= num[i];
}
let ans = bostan_mori(&ops, &num, &den, n);
println!("{}", ans);
}
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