#906612 (Rust) No.2437 Fragile Multiples of 11

• 問題: No.2437 Fragile Multiples of 11
• ユーザー: koba-e964
• 提出日時: 2023-08-21 09:20:51
• 言語: Rust (1.77.0)
• 結果: AC
• 実行時間: 1 ms / 2,000 ms
• コード長: 5,922 bytes
• コンパイル時間: 1,376 ms
• コンパイル使用メモリ: 159,192 KB
• 実行使用メモリ: 4,384 KB
• 最終ジャッジ日時: 2023-08-21 09:20:57
• 合計ジャッジ時間: 3,108 ms
• ジャッジサーバーID （参考情報）: judge13 / judge14

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	1 ms; 4,380 KB
testcase_01	AC	1 ms; 4,380 KB
testcase_02	AC	1 ms; 4,380 KB
testcase_03	AC	1 ms; 4,380 KB
testcase_04	AC	1 ms; 4,376 KB
testcase_05	AC	1 ms; 4,380 KB
testcase_06	AC	1 ms; 4,380 KB
testcase_07	AC	1 ms; 4,384 KB
testcase_08	AC	1 ms; 4,376 KB
testcase_09	AC	1 ms; 4,376 KB
testcase_10	AC	1 ms; 4,380 KB
testcase_11	AC	1 ms; 4,380 KB
testcase_12	AC	1 ms; 4,376 KB
testcase_13	AC	1 ms; 4,380 KB
testcase_14	AC	1 ms; 4,376 KB
testcase_15	AC	1 ms; 4,380 KB
testcase_16	AC	1 ms; 4,380 KB
testcase_17	AC	1 ms; 4,384 KB
testcase_18	AC	1 ms; 4,380 KB
testcase_19	AC	1 ms; 4,376 KB
testcase_20	AC	1 ms; 4,376 KB
testcase_21	AC	1 ms; 4,384 KB
testcase_22	AC	1 ms; 4,376 KB
testcase_23	AC	1 ms; 4,380 KB
testcase_24	AC	1 ms; 4,380 KB
testcase_25	AC	1 ms; 4,380 KB
testcase_26	AC	1 ms; 4,380 KB
testcase_27	AC	1 ms; 4,384 KB
testcase_28	AC	1 ms; 4,380 KB
testcase_29	AC	1 ms; 4,376 KB
testcase_30	AC	1 ms; 4,380 KB
testcase_31	AC	1 ms; 4,380 KB
testcase_32	AC	1 ms; 4,380 KB
testcase_33	AC	1 ms; 4,380 KB

コンパイルメッセージ

warning: unused import: `std::io::Read`
 --> Main.rs:5:5
  |
5 | use std::io::Read;
  |     ^^^^^^^^^^^^^
  |
  = note: `#[warn(unused_imports)]` on by default

warning: 1 warning emitted

ソースコード

#[allow(unused_imports)]
use std::cmp::*;
#[allow(unused_imports)]
use std::collections::*;
use std::io::Read;

fn getline() -> String {
    let mut ret = String::new();
    std::io::stdin().read_line(&mut ret).ok().unwrap();
    ret
}

/// 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> Default for ModInt<M> {
        fn default() -> Self { Self::new_internal(0) }
    }
    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)]
        pub 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>;

// https://yukicoder.me/problems/no/2437 (3.5)
// 壊れやすくない 11 の倍数について、以下が成り立つ:
// 取り除く桁を b とすると 10^k(10a + b) + c と 10^k a + c がともに 11 の倍数であるため、10a + b = a (mod 11) である。
// つまり b = 2a (mod 11) である。
// そのため、桁 DP で以下の情報を持てば良い:
// dp[X と等しい?][mod 11][壊れやすい?]
fn main() {
    // In order to avoid potential stack overflow, spawn a new thread.
    let stack_size = 104_857_600; // 100 MB
    let thd = std::thread::Builder::new().stack_size(stack_size);
    thd.spawn(|| solve()).unwrap().join().unwrap();
}

fn solve() {
    getline();
    let x: Vec<_> = getline().trim().bytes().collect();
    let n = x.len();
    let mut dp = vec![[[[MInt::new(0); 2]; 11]; 2]; n + 1];
    dp[0][1][0][1] += 1;
    for i in 0..n {
        for eq in 0..2 {
            for m in 0..11 {
                for fr in 0..2 {
                    let old = dp[i][eq][m][fr];
                    for j in 0..[10, (x[i] - b'0') as usize + 1][eq] {
                        let neq = eq & if (x[i] - b'0') as usize == j {
                            1
                        } else {
                            0
                        };
                        let nfr = fr & if (9 * m + j) % 11 == 0 {
                            0
                        } else {
                            1
                        };
                        dp[i + 1][neq][(10 * m + j) % 11][nfr] += old;
                    }
                }
            }
        }
        if i > 0 {
            for j in 1..10 {
                dp[i + 1][0][j][1] += 1;
            }
        }
    }
    let ans = dp[n][0][0][1] + dp[n][1][0][1];
    println!("{}", ans);
}