#1137263 (Rust) No.3376 Rectangle in Circle

• 問題: No.3376 Rectangle in Circle
• ユーザー: koba-e964
• 提出日時: 2025-11-30 17:35:43
• 言語: Rust (1.83.0 + proconio)
• 結果: AC
• 実行時間: 145 ms / 2,000 ms
• コード長: 5,782 bytes
• コンパイル時間: 11,148 ms
• コンパイル使用メモリ: 400,660 KB
• 実行使用メモリ: 8,220 KB
• 最終ジャッジ日時: 2025-11-30 17:36:01
• 合計ジャッジ時間: 15,886 ms
• ジャッジサーバーID （参考情報）: judge4 / judge3

ファイルパターン	結果
sample	AC * 1
other	AC * 20

ソースコード

fn getline() -> String {
    let mut ret = String::new();
    std::io::stdin().read_line(&mut ret).unwrap();
    ret
}

/// 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)]
        pub 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>;

fn calc(n: usize, diam: usize) -> MInt {
    if diam <= 1 {
        let mut sum = MInt::new(0);
        for i in 1..=n {
            sum += MInt::new(i as i64).inv();
        }
        return sum * n as i64
    }
    let mut dp = vec![vec![MInt::new(0); diam + 1]; 3];
    for i in (0..2).rev() {
        for j in (0..diam + 1).rev() {
            if j + 2 * i > 2 * diam {
                continue;
            }
            let mut me = MInt::new(1);
            if j > 0 {
                me += MInt::new((2 * diam) as i64).inv() * j as i64 * dp[i + 1][j - 1];
            }
            if j + i < diam {
                me += MInt::new((2 * diam) as i64).inv() * 2 * (diam - j - i) as i64 * dp[i][j + 1];
            }
            let f = MInt::new((2 * diam) as i64) * MInt::new((2 * diam - j - 2 * i) as i64).inv();
            dp[i][j] = me * f;
        }
    }
    dp[0][0] * MInt::new(n as i64) * MInt::new((2 * diam) as i64).inv()
}

// https://yukicoder.me/problems/no/3376 (3)
// solved with hints
fn main() {
    let t = getline().trim().parse::<i32>().unwrap();
    for _ in 0..t {
        let ints = getline().trim().split_whitespace()
            .map(|x| x.parse::<i64>().unwrap())
            .collect::<Vec<_>>();
        let l = ints[1];
        let a = getline().trim().split_whitespace()
            .map(|x| x.parse::<i64>().unwrap())
            .collect::<Vec<_>>();
        let n = a.len();
        let mut hs = std::collections::HashSet::new();
        for &a in &a {
            hs.insert(2 * a);
        }
        let mut diam = 0;
        for &a in &a {
            if hs.contains(&(2 * a + l)) {
                diam += 1;
            }
        }
        println!("{}", calc(n, diam));
        // eprintln!("{:?}", calc(n, diam));
    }
}