#704324 (Rust) No.1696 Nonnil

• 問題: No.1696 Nonnil
• ユーザー: koba-e964
• 提出日時: 2021-10-02 17:58:19
• 言語: Rust (1.77.0 + proconio)
• 結果: AC
• 実行時間: 74 ms / 3,500 ms
• コード長: 7,723 bytes
• コンパイル時間: 14,129 ms
• コンパイル使用メモリ: 377,184 KB
• 実行使用メモリ: 54,804 KB
• 最終ジャッジ日時: 2024-07-20 12:55:11
• 合計ジャッジ時間: 17,637 ms
• ジャッジサーバーID （参考情報）: judge5 / judge1

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	2 ms; 5,376 KB
testcase_09	AC	7 ms; 5,376 KB
testcase_10	AC	10 ms; 5,376 KB
testcase_11	AC	8 ms; 5,376 KB
testcase_12	AC	8 ms; 5,376 KB
testcase_13	AC	7 ms; 5,376 KB
testcase_14	AC	38 ms; 19,728 KB
testcase_15	AC	19 ms; 7,304 KB
testcase_16	AC	44 ms; 22,540 KB
testcase_17	AC	26 ms; 15,892 KB
testcase_18	AC	27 ms; 12,556 KB
testcase_19	AC	1 ms; 5,376 KB
testcase_20	AC	1 ms; 5,376 KB
testcase_21	AC	19 ms; 12,176 KB
testcase_22	AC	30 ms; 15,116 KB
testcase_23	AC	28 ms; 13,968 KB
testcase_24	AC	27 ms; 14,088 KB
testcase_25	AC	40 ms; 20,372 KB
testcase_26	AC	29 ms; 16,652 KB
testcase_27	AC	35 ms; 19,728 KB
testcase_28	AC	37 ms; 16,520 KB
testcase_29	AC	24 ms; 14,352 KB
testcase_30	AC	20 ms; 11,920 KB
testcase_31	AC	24 ms; 15,788 KB
testcase_32	AC	27 ms; 17,164 KB
testcase_33	AC	39 ms; 17,808 KB
testcase_34	AC	20 ms; 13,196 KB
testcase_35	AC	27 ms; 15,888 KB
testcase_36	AC	74 ms; 54,804 KB
testcase_37	AC	69 ms; 48,396 KB
testcase_38	AC	68 ms; 47,632 KB
testcase_39	AC	51 ms; 28,304 KB
testcase_40	AC	58 ms; 34,640 KB
testcase_41	AC	32 ms; 11,276 KB
testcase_42	AC	1 ms; 5,376 KB

ソースコード

#[allow(unused_imports)]
use std::cmp::*;
// 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),* )) => { ($(read_value!($next, $t)),*) };
    ($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>;

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
    }
}

trait Change { fn chmax(&mut self, x: Self); fn chmin(&mut self, x: Self); }
impl<T: PartialOrd> Change for T {
    fn chmax(&mut self, x: T) { if *self < x { *self = x; } }
    fn chmin(&mut self, x: T) { if *self > x { *self = x; } }
}

// Tags: many-intervals, dp
fn main() {
    input! {
        n: i64, k: usize,
        m: usize,
        lr: [(usize1, usize); m],
    }
    let mut lr = lr;
    const INF: usize = 1 << 30; 
    {
        let mut buc = vec![INF; k];
        for &(l, r) in &lr {
            buc[l] = min(buc[l], r);
        }
        lr = vec![];
        let mut mi = k + 2;
        for i in (0..k).rev() {
            if buc[i] < mi {
                lr.push((i, buc[i]));
                mi = min(mi, buc[i]);
            }
        }
        lr.reverse();
    }
    let m = lr.len();
    let mut ls = vec![0; m + 1];
    for i in 0..m {
        ls[i] = lr[i].0;
    }
    ls[m] = k;
    let mut dp = vec![vec![MInt::new(0); k + 1]; m];
    let mut acc = vec![vec![MInt::new(0); k + 1]; m + 1];
    let mut acc_diag = vec![vec![MInt::new(0); k + 1]; m + 1];
    acc[m][k] = 1.into();
    acc_diag[m][0] = 1.into();
    for i in (0..m).rev() {
        let (l, r) = lr[i];
        let mut me = vec![MInt::new(0); k + 1];
        let idx = lr.lower_bound(&(r, 0));
        for j in r..k + 1 {
            me[j - (r - l)] -= acc[idx][j];
        }
        if i + 1 < idx {
            let (lnxt, rnxt) = lr[i + 1];
            assert!(r < rnxt);
            assert!(lnxt < r);
            for j in 0..k - l + 1 {
                me[j + l] += acc_diag[idx][j];
                me[j + l] -= acc_diag[i + 1][j];
            }
        }
        for j in l..k + 1 {
            acc[i][j] = acc[i + 1][j] + me[j];
            acc_diag[i][j - l] = acc_diag[i + 1][j - l] + me[j];
            dp[i][j] = me[j];
        }
    }
    let mut tot = MInt::new(0);
    for i in 0..k + 1 {
        tot += acc[0][i] * MInt::new(i as i64).pow(n);
    }
    println!("{}", tot);
}