#706567 (Rust) No.1193 Penguin Sequence

• 問題: No.1193 Penguin Sequence
• ユーザー: koba-e964
• 提出日時: 2021-10-09 17:40:45
• 言語: Rust (1.83.0 + proconio)
• 結果: AC
• 実行時間: 122 ms / 2,000 ms
• コード長: 7,779 bytes
• コンパイル時間: 15,802 ms
• コンパイル使用メモリ: 404,308 KB
• 実行使用メモリ: 12,800 KB
• 最終ジャッジ日時: 2024-09-13 03:42:16
• 合計ジャッジ時間: 21,023 ms
• ジャッジサーバーID （参考情報）: judge3 / judge1

ファイルパターン	結果
sample	AC * 3
other	AC * 38

ソースコード

#[allow(unused_imports)]
use std::cmp::*;
#[allow(unused_imports)]
use std::collections::*;
// 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> ::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)
}

/// 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;
    }
    eprintln!("{:?}", tot);
    // 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();
    eprintln!("tmp = {:?}", tmp);
    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);
}