結果

問題 No.1873 Bracket Swapping
ユーザー akakimidoriakakimidori
提出日時 2023-05-07 21:19:49
言語 Rust
(1.77.0 + proconio)
結果
AC  
実行時間 105 ms / 2,000 ms
コード長 9,206 bytes
コンパイル時間 13,164 ms
コンパイル使用メモリ 382,560 KB
実行使用メモリ 5,248 KB
最終ジャッジ日時 2024-11-24 20:14:47
合計ジャッジ時間 15,363 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge2
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 1 ms
5,248 KB
testcase_01 AC 1 ms
5,248 KB
testcase_02 AC 1 ms
5,248 KB
testcase_03 AC 10 ms
5,248 KB
testcase_04 AC 5 ms
5,248 KB
testcase_05 AC 5 ms
5,248 KB
testcase_06 AC 43 ms
5,248 KB
testcase_07 AC 1 ms
5,248 KB
testcase_08 AC 78 ms
5,248 KB
testcase_09 AC 77 ms
5,248 KB
testcase_10 AC 60 ms
5,248 KB
testcase_11 AC 1 ms
5,248 KB
testcase_12 AC 33 ms
5,248 KB
testcase_13 AC 26 ms
5,248 KB
testcase_14 AC 77 ms
5,248 KB
testcase_15 AC 17 ms
5,248 KB
testcase_16 AC 1 ms
5,248 KB
testcase_17 AC 41 ms
5,248 KB
testcase_18 AC 1 ms
5,248 KB
testcase_19 AC 4 ms
5,248 KB
testcase_20 AC 65 ms
5,248 KB
testcase_21 AC 1 ms
5,248 KB
testcase_22 AC 6 ms
5,248 KB
testcase_23 AC 105 ms
5,248 KB
testcase_24 AC 73 ms
5,248 KB
testcase_25 AC 82 ms
5,248 KB
testcase_26 AC 41 ms
5,248 KB
testcase_27 AC 59 ms
5,248 KB
testcase_28 AC 5 ms
5,248 KB
testcase_29 AC 1 ms
5,248 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 # 

fn main() {
    input! {
        s: bytes,
        k: usize,
    }
    let mut dp = vec![vec![M::one()]];
    for &c in s.iter() {
        let mut next = vec![vec![M::zero(); dp[0].len() + 1]; dp.len() + 1];
        for (d, dp) in dp.iter().enumerate() {
            for (h, &w) in dp.iter().enumerate().filter(|p| !p.1.is_zero()) {
                if c == b'(' {
                    next[d][h + 1] += w;
                } else {
                    next[d + 1][h + 1] += w;
                }
                if h > 0 {
                    next[d][h - 1] += w;
                }
            }
        }
        dp = next;
    }
    let mut dp = dp.iter().map(|dp| dp[0]).collect::<Vec<_>>();
    dp.truncate(s.len() / 2 + 1);
    type Mat = Vec<Vec<M>>;
    let n = dp.len();
    let mul = |a: &Mat, b: &Mat| -> Mat {
        let mut c = vec![vec![M::zero(); n]; n];
        for (c, a) in c.iter_mut().zip(a.iter()) {
            for (a, b) in a.iter().zip(b.iter()) {
                for (c, b) in c.iter_mut().zip(b.iter()) {
                    *c += *a * *b;
                }
            }
        }
        c
    };
    let m = s.len() / 2;
    let mut r = vec![vec![M::zero(); n]; n];
    for i in 0..n {
        if i + 1 <= m {
            r[i + 1][i] += M::from((m - i).pow(2));
        }
        if i > 0 {
            r[i - 1][i] += M::from(i.pow(2));
        }
        r[i][i] += M::from(s.len() * (s.len() - 1) / 2 - i.pow(2) - (m - i).pow(2));
    }
    let mut t = vec![vec![M::zero(); n]; n];
    for i in 0..n {
        t[i][i] = M::one();
    }
    let mut k = k;
    while k > 0 {
        if k & 1 == 1 {
            t = mul(&t, &r);
        }
        r = mul(&r, &r);
        k >>= 1;
    }
    let ans = t[0].iter().zip(dp.iter()).fold(M::zero(), |s, p| s + *p.0 * *p.1);
    println!("{}", ans);
}

// ---------- begin input macro ----------
// reference: https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8
#[macro_export]
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
    ($($r:tt)*) => {
        let s = {
            use std::io::Read;
            let mut s = String::new();
            std::io::stdin().read_to_string(&mut s).unwrap();
            s
        };
        let mut iter = s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
}

#[macro_export]
macro_rules! input_inner {
    ($iter:expr) => {};
    ($iter:expr, ) => {};
    ($iter:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($iter, $t);
        input_inner!{$iter $($r)*}
    };
}

#[macro_export]
macro_rules! read_value {
    ($iter:expr, ( $($t:tt),* )) => {
        ( $(read_value!($iter, $t)),* )
    };
    ($iter:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($iter, $t)).collect::<Vec<_>>()
    };
    ($iter:expr, chars) => {
        read_value!($iter, String).chars().collect::<Vec<char>>()
    };
    ($iter:expr, bytes) => {
        read_value!($iter, String).bytes().collect::<Vec<u8>>()
    };
    ($iter:expr, usize1) => {
        read_value!($iter, usize) - 1
    };
    ($iter:expr, $t:ty) => {
        $iter.next().unwrap().parse::<$t>().expect("Parse error")
    };
}
// ---------- end input macro ----------
// ---------- begin modint ----------
use std::marker::*;
use std::ops::*;

pub trait Modulo {
    fn modulo() -> u32;
}

pub struct ConstantModulo<const M: u32>;

impl<const M: u32> Modulo for ConstantModulo<{ M }> {
    fn modulo() -> u32 {
        M
    }
}

pub struct ModInt<T>(u32, PhantomData<T>);

impl<T> Clone for ModInt<T> {
    fn clone(&self) -> Self {
        Self::new_unchecked(self.0)
    }
}

impl<T> Copy for ModInt<T> {}

impl<T: Modulo> Add for ModInt<T> {
    type Output = ModInt<T>;
    fn add(self, rhs: Self) -> Self::Output {
        let mut v = self.0 + rhs.0;
        if v >= T::modulo() {
            v -= T::modulo();
        }
        Self::new_unchecked(v)
    }
}

impl<T: Modulo> AddAssign for ModInt<T> {
    fn add_assign(&mut self, rhs: Self) {
        *self = *self + rhs;
    }
}

impl<T: Modulo> Sub for ModInt<T> {
    type Output = ModInt<T>;
    fn sub(self, rhs: Self) -> Self::Output {
        let mut v = self.0 - rhs.0;
        if self.0 < rhs.0 {
            v += T::modulo();
        }
        Self::new_unchecked(v)
    }
}

impl<T: Modulo> SubAssign for ModInt<T> {
    fn sub_assign(&mut self, rhs: Self) {
        *self = *self - rhs;
    }
}

impl<T: Modulo> Mul for ModInt<T> {
    type Output = ModInt<T>;
    fn mul(self, rhs: Self) -> Self::Output {
        let v = self.0 as u64 * rhs.0 as u64 % T::modulo() as u64;
        Self::new_unchecked(v as u32)
    }
}

impl<T: Modulo> MulAssign for ModInt<T> {
    fn mul_assign(&mut self, rhs: Self) {
        *self = *self * rhs;
    }
}

impl<T: Modulo> Neg for ModInt<T> {
    type Output = ModInt<T>;
    fn neg(self) -> Self::Output {
        if self.is_zero() {
            Self::zero()
        } else {
            Self::new_unchecked(T::modulo() - self.0)
        }
    }
}

impl<T> std::fmt::Display for ModInt<T> {
    fn fmt<'a>(&self, f: &mut std::fmt::Formatter<'a>) -> std::fmt::Result {
        write!(f, "{}", self.0)
    }
}

impl<T> std::fmt::Debug for ModInt<T> {
    fn fmt<'a>(&self, f: &mut std::fmt::Formatter<'a>) -> std::fmt::Result {
        write!(f, "{}", self.0)
    }
}

impl<T> Default for ModInt<T> {
    fn default() -> Self {
        Self::zero()
    }
}

impl<T: Modulo> std::str::FromStr for ModInt<T> {
    type Err = std::num::ParseIntError;
    fn from_str(s: &str) -> Result<Self, Self::Err> {
        let val = s.parse::<u32>()?;
        Ok(ModInt::new(val))
    }
}

impl<T: Modulo> From<usize> for ModInt<T> {
    fn from(val: usize) -> ModInt<T> {
        ModInt::new_unchecked((val % T::modulo() as usize) as u32)
    }
}

impl<T: Modulo> From<u64> for ModInt<T> {
    fn from(val: u64) -> ModInt<T> {
        ModInt::new_unchecked((val % T::modulo() as u64) as u32)
    }
}

impl<T: Modulo> From<i64> for ModInt<T> {
    fn from(val: i64) -> ModInt<T> {
        let mut v = ((val % T::modulo() as i64) + T::modulo() as i64) as u32;
        if v >= T::modulo() {
            v -= T::modulo();
        }
        ModInt::new_unchecked(v)
    }
}

impl<T> ModInt<T> {
    pub fn new_unchecked(n: u32) -> Self {
        ModInt(n, PhantomData)
    }
    pub fn zero() -> Self {
        ModInt::new_unchecked(0)
    }
    pub fn one() -> Self {
        ModInt::new_unchecked(1)
    }
    pub fn is_zero(&self) -> bool {
        self.0 == 0
    }
}

impl<T: Modulo> ModInt<T> {
    pub fn new(d: u32) -> Self {
        ModInt::new_unchecked(d % T::modulo())
    }
    pub fn pow(&self, mut n: u64) -> Self {
        let mut t = Self::one();
        let mut s = *self;
        while n > 0 {
            if n & 1 == 1 {
                t *= s;
            }
            s *= s;
            n >>= 1;
        }
        t
    }
    pub fn inv(&self) -> Self {
        assert!(!self.is_zero());
        self.pow(T::modulo() as u64 - 2)
    }
    pub fn fact(n: usize) -> Self {
        (1..=n).fold(Self::one(), |s, a| s * Self::from(a))
    }
    pub fn perm(n: usize, k: usize) -> Self {
        if k > n {
            return Self::zero();
        }
        ((n - k + 1)..=n).fold(Self::one(), |s, a| s * Self::from(a))
    }
    pub fn binom(n: usize, k: usize) -> Self {
        if k > n {
            return Self::zero();
        }
        let k = k.min(n - k);
        let mut nu = Self::one();
        let mut de = Self::one();
        for i in 0..k {
            nu *= Self::from(n - i);
            de *= Self::from(i + 1);
        }
        nu * de.inv()
    }
}
// ---------- end modint ----------
// ---------- begin precalc ----------
pub struct Precalc<T> {
    fact: Vec<ModInt<T>>,
    ifact: Vec<ModInt<T>>,
    inv: Vec<ModInt<T>>,
}

impl<T: Modulo> Precalc<T> {
    pub fn new(n: usize) -> Precalc<T> {
        let mut inv = vec![ModInt::one(); n + 1];
        let mut fact = vec![ModInt::one(); n + 1];
        let mut ifact = vec![ModInt::one(); n + 1];
        for i in 2..=n {
            fact[i] = fact[i - 1] * ModInt::new_unchecked(i as u32);
        }
        ifact[n] = fact[n].inv();
        if n > 0 {
            inv[n] = ifact[n] * fact[n - 1];
        }
        for i in (1..n).rev() {
            ifact[i] = ifact[i + 1] * ModInt::new_unchecked((i + 1) as u32);
            inv[i] = ifact[i] * fact[i - 1];
        }
        Precalc { fact, ifact, inv }
    }
    pub fn inv(&self, n: usize) -> ModInt<T> {
        assert!(n > 0);
        self.inv[n]
    }
    pub fn fact(&self, n: usize) -> ModInt<T> {
        self.fact[n]
    }
    pub fn ifact(&self, n: usize) -> ModInt<T> {
        self.ifact[n]
    }
    pub fn perm(&self, n: usize, k: usize) -> ModInt<T> {
        if k > n {
            return ModInt::zero();
        }
        self.fact[n] * self.ifact[n - k]
    }
    pub fn binom(&self, n: usize, k: usize) -> ModInt<T> {
        if k > n {
            return ModInt::zero();
        }
        self.fact[n] * self.ifact[k] * self.ifact[n - k]
    }
}
// ---------- end precalc ----------

type M = ModInt<ConstantModulo<998_244_353>>;
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