結果
問題 | No.1510 Simple Integral |
ユーザー |
|
提出日時 | 2021-12-30 17:44:48 |
言語 | Rust (1.83.0 + proconio) |
結果 |
AC
|
実行時間 | 3 ms / 2,000 ms |
コード長 | 7,596 bytes |
コンパイル時間 | 15,472 ms |
コンパイル使用メモリ | 377,724 KB |
実行使用メモリ | 5,248 KB |
最終ジャッジ日時 | 2024-10-06 12:44:47 |
合計ジャッジ時間 | 14,230 ms |
ジャッジサーバーID (参考情報) |
judge2 / judge4 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 43 |
ソースコード
#[allow(unused_imports)]use std::cmp::*;// 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);read_value!($next, [$t; len])}};($next:expr, $t:ty) => ($next().parse::<$t>().expect("Parse error"));}/// Verified by https://atcoder.jp/contests/abc198/submissions/21774342mod 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> 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_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 MInt = mod_int::ModInt<P>;// Depends on MInt.rsfn fact_init(w: usize) -> (Vec<MInt>, Vec<MInt>) {let mut fac = vec![MInt::new(1); w];let mut invfac = vec![0.into(); w];for i in 1..w {fac[i] = fac[i - 1] * i as i64;}invfac[w - 1] = fac[w - 1].inv();for i in (0..w - 1).rev() {invfac[i] = invfac[i + 1] * (i as i64 + 1);}(fac, invfac)}trait Change { fn chmax(&mut self, x: Self); fn chmin(&mut self, x: Self); }impl<T: PartialOrd> Change for T {fn chmax(&mut self, x: T) { if *self < x { *self = x; } }fn chmin(&mut self, x: T) { if *self > x { *self = x; } }}fn main() {input! {n: usize,a: [i64; n],}let im = MInt::new(3).pow((MOD - 1) / 4);let mut coo = a.clone();coo.sort(); coo.dedup();let m = coo.len();let mut f = vec![0; m];for &a in &a {f[coo.binary_search(&a).unwrap()] += 1;}let (fac, invfac) = fact_init(2 * n);let mut tot = MInt::new(0);for i in 0..m {let a = f[i];// \prod 1/((x+coo[i]*im)^2 + coo[j])^f[j]let mut frm = vec![MInt::new(0); a];frm[0] = 1.into();for j in 0..m {if i == j { continue; }let cs = MInt::new(coo[j]).pow(2) - coo[i] * coo[i];let csinv = cs.inv();for _ in 0..f[j] {let mut ep = vec![MInt::new(0); a];ep[0] = frm[0] * csinv;if a > 1 {ep[1] = (-im * 2 * coo[i] * ep[0] + frm[1]) * csinv;}for k in 2..a {ep[k] = (-im * 2 * coo[i] * ep[k - 1] + frm[k] - ep[k - 2]) * csinv;}frm = ep;}// eprintln!("{} {} frm = {:?}", i, j, frm);}// (1+x/(2*coo[i]*im))^alet mut lat = vec![MInt::new(0); a];let mut cur = MInt::new(1);let inv = (im * 2 * coo[i]).inv();for i in 0..a {lat[i] = fac[i + a - 1] * invfac[i] * invfac[a - 1] * cur;cur *= -inv;}// eprintln!("lat = {:?}", lat);let mut tmp = MInt::new(0);for j in 0..a {tmp += frm[a - 1 - j] * lat[j];}let tmp = tmp * inv.pow(a as i64) * 2 * im;tot += tmp;}println!("{}", tot);eprintln!("{:?}", tot);}