結果

問題 No.1392 Don't be together
ユーザー koba-e964koba-e964
提出日時 2021-10-21 20:40:11
言語 Rust
(1.77.0)
結果
AC  
実行時間 324 ms / 2,000 ms
コード長 6,657 bytes
コンパイル時間 1,163 ms
コンパイル使用メモリ 184,740 KB
実行使用メモリ 4,348 KB
最終ジャッジ日時 2023-10-21 15:49:18
合計ジャッジ時間 5,473 ms
ジャッジサーバーID
（参考情報） 		judge15 / judge14
このコードへのチャレンジ
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 1 ms
4,348 KB
testcase_01 AC 1 ms
4,348 KB
testcase_02 AC 1 ms
4,348 KB
testcase_03 AC 1 ms
4,348 KB
testcase_04 AC 1 ms
4,348 KB
testcase_05 AC 1 ms
4,348 KB
testcase_06 AC 143 ms
4,348 KB
testcase_07 AC 227 ms
4,348 KB
testcase_08 AC 218 ms
4,348 KB
testcase_09 AC 324 ms
4,348 KB
testcase_10 AC 137 ms
4,348 KB
testcase_11 AC 215 ms
4,348 KB
testcase_12 AC 128 ms
4,348 KB
testcase_13 AC 180 ms
4,348 KB
testcase_14 AC 200 ms
4,348 KB
testcase_15 AC 135 ms
4,348 KB
testcase_16 AC 217 ms
4,348 KB
testcase_17 AC 144 ms
4,348 KB
testcase_18 AC 194 ms
4,348 KB
testcase_19 AC 173 ms
4,348 KB
testcase_20 AC 76 ms
4,348 KB
testcase_21 AC 28 ms
4,348 KB
testcase_22 AC 119 ms
4,348 KB
testcase_23 AC 80 ms
4,348 KB
testcase_24 AC 46 ms
4,348 KB
testcase_25 AC 88 ms
4,348 KB
testcase_26 AC 23 ms
4,348 KB
testcase_27 AC 34 ms
4,348 KB
testcase_28 AC 98 ms
4,348 KB
testcase_29 AC 50 ms
4,348 KB
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 # 

// 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 ; $len:expr ]) => {
        (0..$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, 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)
}

// [2, 4, 0, 1, 3, 7, 6] ==> [[0, 2], [1, 4, 3], [6, 7]]
// Verified by: https://atcoder.jp/contests/joisc2007/submissions/24248388
fn decompose_into_cycles(a: &[usize]) -> Vec<Vec<usize>> {
    let n = a.len();
    let mut vis = vec![false; n];
    let mut ans = vec![];
    for i in 0..n {
        if vis[i] { continue; }
        vis[i] = true;
        let mut cyc = vec![i];
        let mut v = a[i];
        while v != i {
            vis[v] = true;
            cyc.push(v);
            v = a[v];
        }
        ans.push(cyc)
    }
    ans
}

fn main() {
    input! {
        n: usize, m: usize,
        p: [usize1; n],
    }
    let (_fac, invfac) = fact_init(n + 1);
    let cycs = decompose_into_cycles(&p);
    let mut tot = MInt::new(0);
    for i in 1..m + 1 {
        let mut dp = vec![[MInt::new(0); 2]; n + 1];
        dp[1][1] = 1.into();
        for j in 2..n + 1 {
            let bef = dp[j - 1];
            dp[j][0] += bef[1];
            if i >= 2 {
                dp[j][0] += bef[0] * (i as i64 - 2);
            }
            dp[j][1] += bef[0] * (i as i64 - 1);
        }
        let mut tbl = vec![MInt::new(0); n + 1];
        for j in 1..n + 1 {
            tbl[j] = dp[j][0] * (i - 1) as i64 * i as i64;
        }
        let mut tmp = invfac[i] * invfac[m - i];
        for v in &cycs {
            tmp *= tbl[v.len()];
        }
        if (i + m) % 2 == 0 {
            tot += tmp;
        } else {
            tot -= tmp;
        }
    }
    println!("{}", tot);
}
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