#713088 (Rust) No.1608 Yet Another Ants Problem

• 問題: No.1608 Yet Another Ants Problem
• ユーザー: koba-e964
• 提出日時: 2021-11-05 20:54:24
• 言語: Rust (1.77.0)
• 結果: AC
• 実行時間: 505 ms / 2,000 ms
• コード長: 7,649 bytes
• コンパイル時間: 1,523 ms
• コンパイル使用メモリ: 172,288 KB
• 実行使用メモリ: 72,576 KB
• 最終ジャッジ日時: 2024-04-24 04:46:12
• 合計ジャッジ時間: 9,580 ms
• ジャッジサーバーID （参考情報）: judge1 / judge2

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	1 ms; 5,248 KB
testcase_01	AC	1 ms; 5,376 KB
testcase_02	AC	1 ms; 5,376 KB
testcase_03	AC	1 ms; 5,376 KB
testcase_04	AC	1 ms; 5,376 KB
testcase_05	AC	1 ms; 5,376 KB
testcase_06	AC	1 ms; 5,376 KB
testcase_07	AC	1 ms; 5,376 KB
testcase_08	AC	1 ms; 5,376 KB
testcase_09	AC	1 ms; 5,376 KB
testcase_10	AC	1 ms; 5,376 KB
testcase_11	AC	1 ms; 5,376 KB
testcase_12	AC	1 ms; 5,376 KB
testcase_13	AC	1 ms; 5,376 KB
testcase_14	AC	461 ms; 72,448 KB
testcase_15	AC	463 ms; 72,448 KB
testcase_16	AC	468 ms; 72,448 KB
testcase_17	AC	459 ms; 72,576 KB
testcase_18	AC	468 ms; 72,576 KB
testcase_19	AC	30 ms; 7,552 KB
testcase_20	AC	187 ms; 31,872 KB
testcase_21	AC	182 ms; 30,976 KB
testcase_22	AC	114 ms; 20,736 KB
testcase_23	AC	448 ms; 69,632 KB
testcase_24	AC	505 ms; 72,576 KB
testcase_25	AC	321 ms; 72,448 KB
testcase_26	AC	316 ms; 72,448 KB
testcase_27	AC	311 ms; 72,448 KB
testcase_28	AC	314 ms; 72,320 KB
testcase_29	AC	315 ms; 72,448 KB
testcase_30	AC	295 ms; 72,448 KB
testcase_31	AC	295 ms; 72,448 KB
testcase_32	AC	289 ms; 72,448 KB
testcase_33	AC	292 ms; 72,448 KB
testcase_34	AC	293 ms; 72,448 KB

ソースコード

#[allow(unused_imports)]
use std::cmp::*;
#[allow(unused_imports)]
use std::collections::*;
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 ; $len:expr ]) => {
        (0..$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)
}

trait Bisect<T> {
    fn lower_bound(&self, val: &T) -> usize;
    fn upper_bound(&self, val: &T) -> usize;
}

impl<T: Ord> Bisect<T> for [T] {
    fn lower_bound(&self, val: &T) -> usize {
        let mut pass = self.len() + 1;
        let mut fail = 0;
        while pass - fail > 1 {
            let mid = (pass + fail) / 2;
            if &self[mid - 1] >= val {
                pass = mid;
            } else {
                fail = mid;
            }
        }
        pass - 1
    }
    fn upper_bound(&self, val: &T) -> usize {
        let mut pass = self.len() + 1;
        let mut fail = 0;
        while pass - fail > 1 {
            let mid = (pass + fail) / 2;
            if &self[mid - 1] > val {
                pass = mid;
            } else {
                fail = mid;
            }
        }
        pass - 1
    }
}

// https://yukicoder.me/problems/no/1608 (3.5)
// 左に i 匹、右に n - i 匹落ちる場合: (左の i 匹目の落ちる時刻) >= (右の n - i 匹目の落ちる時刻) であればよい。
// \sum {j < k, A[k] >= L - A[j] } C(k - j - 1, i - j - 1) + [A[i] <= L - A[i + 1]]
// この形の和は (i, j を固定すれば) 累積和で加速できる。O(N^2)。
fn main() {
    let out = std::io::stdout();
    let mut out = BufWriter::new(out.lock());
    macro_rules! puts {($($format:tt)*) => (let _ = write!(out,$($format)*););}
    input! {
        n: usize, l: i64,
        a: [i64; n],
    }
    let (fac, invfac) = fact_init(n + 1);
    let mut acc = vec![vec![MInt::new(0); n + 1]; n];
    for i in 0..n {
        for k in i..n {
            acc[i][k + 1] = acc[i][k] + fac[k] * invfac[i] * invfac[k - i];
        }
    }
    let mut ans = vec![MInt::new(0); n];
    for i in 0..n {
        let mut left = MInt::new(0);
        let mut right = MInt::new(0);
        for j in 0..i {
            let kmin = max(j + 1, a.lower_bound(&(l - a[j])));
            left += acc[i - j - 1][n - j - 1] - acc[i - j - 1][kmin - j - 1];
            right += acc[i - j - 1][kmin - j - 1];
        }
        // <- <- ... <- -> ... -> ->
        if i > 0 && a[i - 1] >= l - a[i] {
            left += 1;
        } else {
            right += 1;
        }
        if i > 0 {
            ans[i - 1] += left;
        }
        ans[i] += right;
        eprintln!("{} => {} {}", i, left, right);
    }
    ans[n - 1] += 1; // all <-
    for i in 0..n {
        puts!("{}\n", ans[i]);
    }
}