結果

問題 No.1193 Penguin Sequence
ユーザー koba-e964koba-e964
提出日時 2021-10-09 17:41:16
言語 Rust
(1.77.0 + proconio)
結果
AC  
実行時間 117 ms / 2,000 ms
コード長 6,766 bytes
コンパイル時間 12,583 ms
コンパイル使用メモリ 405,804 KB
実行使用メモリ 12,848 KB
最終ジャッジ日時 2024-09-13 03:43:01
合計ジャッジ時間 16,939 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge5
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 67 ms
12,800 KB
testcase_01 AC 116 ms
12,792 KB
testcase_02 AC 117 ms
12,784 KB
testcase_03 AC 116 ms
12,848 KB
testcase_04 AC 115 ms
12,792 KB
testcase_05 AC 116 ms
12,784 KB
testcase_06 AC 116 ms
12,660 KB
testcase_07 AC 115 ms
12,788 KB
testcase_08 AC 117 ms
12,788 KB
testcase_09 AC 116 ms
12,788 KB
testcase_10 AC 116 ms
12,788 KB
testcase_11 AC 59 ms
8,016 KB
testcase_12 AC 61 ms
8,212 KB
testcase_13 AC 98 ms
11,288 KB
testcase_14 AC 89 ms
10,532 KB
testcase_15 AC 107 ms
12,028 KB
testcase_16 AC 32 ms
8,064 KB
testcase_17 AC 1 ms
6,944 KB
testcase_18 AC 8 ms
6,944 KB
testcase_19 AC 117 ms
12,816 KB
testcase_20 AC 87 ms
10,496 KB
testcase_21 AC 66 ms
8,932 KB
testcase_22 AC 10 ms
6,944 KB
testcase_23 AC 54 ms
7,508 KB
testcase_24 AC 46 ms
6,940 KB
testcase_25 AC 20 ms
6,940 KB
testcase_26 AC 5 ms
6,944 KB
testcase_27 AC 98 ms
11,032 KB
testcase_28 AC 61 ms
8,292 KB
testcase_29 AC 97 ms
11,264 KB
testcase_30 AC 28 ms
6,940 KB
testcase_31 AC 23 ms
6,944 KB
testcase_32 AC 73 ms
9,216 KB
testcase_33 AC 49 ms
7,076 KB
testcase_34 AC 38 ms
6,940 KB
testcase_35 AC 49 ms
7,124 KB
testcase_36 AC 36 ms
6,944 KB
testcase_37 AC 93 ms
10,904 KB
testcase_38 AC 1 ms
6,944 KB
testcase_39 AC 1 ms
6,944 KB
testcase_40 AC 1 ms
6,944 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, $t:ty) => ($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> From<i64> for ModInt<M> {
        fn from(x: i64) -> Self { Self::new(x) }
    }
} // 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)
}

/// Binary Indexed Tree (Fenwick Tree). Holds an array of type T.
/// T is a commutative monoid. Indices are 1 .. n.
/// Verified by yukicoder No.404 (http://yukicoder.me/submissions/155373)
struct BIT<T> {
    n: usize,
    ary: Vec<T>,
    e: T,
}

impl<T: Clone + std::ops::AddAssign<T>> BIT<T> {
    fn new(n: usize, e: T) -> Self {
        let n = n.next_power_of_two();
        BIT { n: n, ary: vec![e.clone(); n + 1], e: e }
    }
    /**
     * gets the sum in [1 .. idx]
     * @param idx
     * @return sum
     */
    fn accum(&self, mut idx: usize) -> T {
        let mut sum = self.e.clone();
        while idx > 0 {
            sum += self.ary[idx].clone();
            idx &= idx - 1;
        }
        sum
    }
    /**
     * performs data[idx] += val;
     */
    fn add<U: Clone>(&mut self, mut idx: usize, val: U)
        where T: std::ops::AddAssign<U> {
        assert!(idx > 0);
        let n = self.n;
        while idx <= n {
            self.ary[idx] += val.clone();
            idx += idx & idx.wrapping_neg();
        }
    }
    /// Make sure that 1 <= idx <= n.
    #[allow(unused)]
    fn single(&self, idx: usize) -> T
        where T: std::ops::Sub<Output = T> {
        self.accum(idx) - self.accum(idx - 1)
    }
}

fn main() {
    input! {
        n: usize,
        a: [i64; n],
    }
    let (fac, invfac) = fact_init(n + 1);
    let mut coo = a.clone();
    coo.sort(); coo.dedup();
    let m = coo.len();
    let mut tot = MInt::new(0);
    let mut f = vec![0; m];
    for &a in &a {
        let a = coo.binary_search(&a).unwrap();
        f[a] += 1;
    }
    let mut acc = vec![0; m + 1];
    for i in 0..m {
        acc[i + 1] = acc[i] + f[i];
    }
    let ninv2 = MInt::new(n as i64 * n as i64 * 2).inv();
    // inter
    let mut stairs = MInt::new(0);
    let mut sq = MInt::new(0);
    for i in 1..n + 1 {
        let i = i as i64;
        stairs += i;
        sq += i * i;
    }
    for i in 0..m {
        let count = acc[i] as i64 * f[i];
        tot += (stairs * stairs - sq) * ninv2 * count;
    }
    // self-contained
    let mut tmp = MInt::new(0);
    for i in 1..n + 1 {
        tmp += i as i64 * (i as i64 - 1);
    }
    tmp *= MInt::new(n as i64 * (n - 1) as i64).inv();
    let mut bit = BIT::new(m, 0);
    for i in 0..n {
        let a = coo.binary_search(&a[i]).unwrap();
        tot += tmp * (i as i64 - bit.accum(a + 1));
        bit.add(a + 1, 1);
    }
    for i in 1..n + 1 {
        tot *= fac[n] * invfac[i] * invfac[n - i];
    }
    println!("{}", tot);
}
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