結果

問題 No.1304 あなたは基本が何か知っていますか？私は知っています．
ユーザー akakimidori
提出日時 2023-04-29 09:20:59
言語 Rust
(1.83.0 + proconio)
結果
AC  
実行時間 1 ms / 2,000 ms
コード長 9,828 bytes
コンパイル時間 17,933 ms
コンパイル使用メモリ 404,896 KB
実行使用メモリ 6,944 KB
最終ジャッジ日時 2024-06-12 18:16:35
合計ジャッジ時間 15,128 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge5
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 1
other AC * 74
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ソースコード

diff #
プレゼンテーションモードにする

fn main() {
    input! {
        n: usize,
        k: usize,
        x: usize,
        y: usize,
        a: [usize; k],
    }
    if n == 1 {
        let ans = a.iter().filter(|&a| x <= *a && *a <= y).count();
        println!("{}", ans);
        return;
    }
    let m = std::cmp::max(*a.iter().max().unwrap(), y).next_power_of_two();
    let mut h = vec![M::zero(); m];
    for a in a.iter() {
        h[*a] += M::one();
    }
    fwht(&mut h);
    let mut g = h.iter().map(|h| *h * *h).collect::<Vec<_>>();
    ifwht(&mut g);
    g[0] = M::zero();
    fwht(&mut g);
    for (g, h) in g.iter_mut().zip(h.iter()) {
        let mut dp = [*g, *h];
        let mut r = [[*h, -M::from(k - 1)], [M::one(), M::zero()]];
        let mut n = n - 2;
        while n > 0 {
            if n & 1 == 1 {
                let mut next = [M::zero(); 2];
                for (next, r) in next.iter_mut().zip(r.iter()) {
                    for (r, dp) in r.iter().zip(dp.iter()) {
                        *next += *dp * *r;
                    }
                }
                dp = next;
            }
            let mut next = [[M::zero(); 2]; 2];
            for (next, a) in next.iter_mut().zip(r.iter()) {
                for (a, b) in a.iter().zip(r.iter()) {
                    for (next, b) in next.iter_mut().zip(b.iter()) {
                        *next += *a * *b;
                    }
                }
            }
            r = next;
            n >>= 1;
        }
        *g = dp[0];
    }
    ifwht(&mut g);
    let ans = g[x..=y].iter().fold(M::zero(), |s, a| s + *a);
    println!("{}", ans);
}
fn fwht(a: &mut [M]) {
    bitwise_transform(a, |a, b| {
        let x = *a + *b;
        let y = *a - *b;
        *a = x;
        *b = y;
    });
}
fn ifwht(a: &mut [M]) {
    let inv = M::new(2).inv();
    bitwise_transform(a, |a, b| {
        let x = (*a + *b) * inv;
        let y = (*a - *b) * inv;
        *a = x;
        *b = y;
    });
}
// ---------- 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>>;
// ---------- begin bitwise transform ----------
pub fn bitwise_transform<T, F>(a: &mut [T], mut f: F)
where
    F: FnMut(&mut T, &mut T),
{
    let n = a.len().trailing_zeros() as usize;
    assert!(a.len() == 1 << n);
    for i in 0..n {
        for a in a.chunks_exact_mut(2 << i) {
            let (x, y) = a.split_at_mut(1 << i);
            for (x, y) in x.iter_mut().zip(y) {
                f(x, y);
            }
        }
    }
}
// ---------- end bitwise transform ----------
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