#727208 (Rust) No.1510 Simple Integral

• 問題: No.1510 Simple Integral
• ユーザー: koba-e964
• 提出日時: 2021-12-30 17:20:59
• 言語: Rust (1.77.0 + proconio)
• 結果: WA
• 実行時間: -
• コード長: 7,501 bytes
• コンパイル時間: 15,701 ms
• コンパイル使用メモリ: 379,168 KB
• 実行使用メモリ: 5,248 KB
• 最終ジャッジ日時: 2024-10-06 11:54:48
• 合計ジャッジ時間: 16,118 ms
• ジャッジサーバーID （参考情報）: judge2 / judge5

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	1 ms; 5,248 KB
testcase_01	AC	1 ms; 5,248 KB
testcase_02	AC	1 ms; 5,248 KB
testcase_03	AC	1 ms; 5,248 KB
testcase_04	AC	1 ms; 5,248 KB
testcase_05	WA	-
testcase_06	AC	1 ms; 5,248 KB
testcase_07	AC	1 ms; 5,248 KB
testcase_08	AC	1 ms; 5,248 KB
testcase_09	AC	1 ms; 5,248 KB
testcase_10	AC	1 ms; 5,248 KB
testcase_11	AC	1 ms; 5,248 KB
testcase_12	AC	1 ms; 5,248 KB
testcase_13	WA	-
testcase_14	WA	-
testcase_15	WA	-
testcase_16	WA	-
testcase_17	WA	-
testcase_18	WA	-
testcase_19	WA	-
testcase_20	WA	-
testcase_21	WA	-
testcase_22	WA	-
testcase_23	AC	3 ms; 5,248 KB
testcase_24	AC	3 ms; 5,248 KB
testcase_25	AC	2 ms; 5,248 KB
testcase_26	AC	2 ms; 5,248 KB
testcase_27	AC	2 ms; 5,248 KB
testcase_28	AC	3 ms; 5,248 KB
testcase_29	AC	2 ms; 5,248 KB
testcase_30	AC	3 ms; 5,248 KB
testcase_31	AC	2 ms; 5,248 KB
testcase_32	AC	2 ms; 5,248 KB
testcase_33	WA	-
testcase_34	WA	-
testcase_35	WA	-
testcase_36	WA	-
testcase_37	WA	-
testcase_38	WA	-
testcase_39	WA	-
testcase_40	WA	-
testcase_41	WA	-
testcase_42	WA	-
testcase_43	AC	1 ms; 5,248 KB
testcase_44	AC	1 ms; 5,248 KB
testcase_45	WA	-

ソースコード

#[allow(unused_imports)]
use std::cmp::*;
// 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);
        read_value!($next, [$t; len])
    }};
    ($next:expr, $t:ty) => ($next().parse::<$t>().expect("Parse error"));
}

/// 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>;

// Depends on MInt.rs
fn 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-2*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 * 4 * coo[i] * ep[0] + frm[1]) * csinv;
                }
                for k in 2..a {
                    ep[k] = (im * 4 * coo[i] * ep[k - 1] + frm[k] - ep[k - 2]) * csinv;
                }
                frm = ep;
            }
        }
        // (1+x/(2*coo[i]*im))^a
        let 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;
        }
        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);
}