#886523 (Rust) No.2369 Some Products

• 問題: No.2369 Some Products
• ユーザー: koba-e964
• 提出日時: 2023-07-01 11:37:51
• 言語: Rust (1.77.0)
• 結果: AC
• 実行時間: 670 ms / 2,500 ms
• コード長: 6,878 bytes
• コンパイル時間: 2,358 ms
• コンパイル使用メモリ: 163,804 KB
• 実行使用メモリ: 392,372 KB
• 最終ジャッジ日時: 2023-09-22 05:32:40
• 合計ジャッジ時間: 8,264 ms
• ジャッジサーバーID （参考情報）: judge15 / judge12

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	1 ms; 4,376 KB
testcase_01	AC	2 ms; 4,376 KB
testcase_02	AC	670 ms; 392,372 KB
testcase_03	AC	653 ms; 392,288 KB
testcase_04	AC	655 ms; 392,300 KB
testcase_05	AC	44 ms; 25,344 KB
testcase_06	AC	585 ms; 392,024 KB
testcase_07	AC	45 ms; 27,988 KB
testcase_08	AC	115 ms; 71,276 KB
testcase_09	AC	33 ms; 18,844 KB
testcase_10	AC	218 ms; 137,328 KB
testcase_11	AC	447 ms; 295,928 KB
testcase_12	AC	22 ms; 12,144 KB
testcase_13	AC	267 ms; 170,600 KB
testcase_14	AC	310 ms; 202,276 KB

ソースコード

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, usize1) => (read_value!($next, usize) - 1);
    ($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>;

// https://yukicoder.me/problems/no/2369 (3.5)
// f_i(x) = (1 + A[0]x)...(1 + A[i-1]x) として、 [x^K]f_R(x)/f_L(x)　が分かれば良い。
// f_i(x) も 1/f_i(x) (を x^N までで打ち切ったもの) も合計 O(N^2) 時間で計算できる。
// [x^K]f_R(x)/f_L(x) は 1 回　 O(N) 時間なので、合計 O(N^2 + QN) 時間である。
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();
}

fn solve() {
    let out = std::io::stdout();
    let mut out = BufWriter::new(out.lock());
    macro_rules! puts {($($format:tt)*) => (let _ = write!(out,$($format)*););}
    #[allow(unused)]
    macro_rules! putvec {
        ($v:expr) => {
            for i in 0..$v.len() {
                puts!("{}{}", $v[i], if i + 1 == $v.len() {"\n"} else {" "});
            }
        }
    }
    input! {
        n: usize,
        p: [i64; n],
        q: usize,
        abk: [(usize1, usize, usize); q],
    }
    let mut f = vec![vec![MInt::new(0); n + 1]; n + 1];
    let mut invf = vec![vec![MInt::new(0); n + 1]; n + 1];
    f[0][0] += 1;
    invf[0][0] += 1;
    for i in 0..n {
        let p = MInt::new(p[i] + 2 * MOD);
        for k in (0..n + 1).rev() {
            let mut me = f[i][k];
            if k > 0 {
                me += f[i][k - 1] * p;
            }
            f[i + 1][k] = me;
        }
        for k in 0..n + 1 {
            let mut me = invf[i][k];
            if k > 0 {
                me -= invf[i + 1][k - 1] * p;
            }
            invf[i + 1][k] = me;
        }
    }
    for (a, b, k) in abk {
        let mut ans = MInt::new(0);
        for i in 0..k + 1 {
            ans += f[b][i] * invf[a][k - i];
        }
        puts!("{}\n", ans);
    }
}