#853250 (Rust) No.2237 Xor Sum Hoge

• 問題: No.2237 Xor Sum Hoge
• ユーザー: koba-e964
• 提出日時: 2023-03-26 17:44:37
• 言語: Rust (1.77.0)
• 結果: AC
• 実行時間: 1,631 ms / 10,000 ms
• コード長: 9,228 bytes
• コンパイル時間: 718 ms
• コンパイル使用メモリ: 177,952 KB
• 実行使用メモリ: 10,856 KB
• 最終ジャッジ日時: 2023-10-19 13:48:09
• 合計ジャッジ時間: 60,348 ms
• ジャッジサーバーID （参考情報）: judge15 / judge13

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	1,620 ms; 10,856 KB
testcase_01	AC	1,605 ms; 10,064 KB
testcase_02	AC	1,600 ms; 10,064 KB
testcase_03	AC	1,598 ms; 10,064 KB
testcase_04	AC	1,602 ms; 10,064 KB
testcase_05	AC	1,602 ms; 10,064 KB
testcase_06	AC	1,601 ms; 10,064 KB
testcase_07	AC	1,602 ms; 10,064 KB
testcase_08	AC	1,600 ms; 10,064 KB
testcase_09	AC	1,602 ms; 10,064 KB
testcase_10	AC	1,600 ms; 10,064 KB
testcase_11	AC	1,603 ms; 10,328 KB
testcase_12	AC	1,606 ms; 10,592 KB
testcase_13	AC	1,619 ms; 10,856 KB
testcase_14	AC	1,612 ms; 10,592 KB
testcase_15	AC	1,607 ms; 10,328 KB
testcase_16	AC	1,621 ms; 10,592 KB
testcase_17	AC	1,613 ms; 10,592 KB
testcase_18	AC	1,607 ms; 10,328 KB
testcase_19	AC	1,607 ms; 10,328 KB
testcase_20	AC	1,620 ms; 10,592 KB
testcase_21	AC	1,620 ms; 10,856 KB
testcase_22	AC	1,621 ms; 10,856 KB
testcase_23	AC	1,619 ms; 10,856 KB
testcase_24	AC	1,617 ms; 10,856 KB
testcase_25	AC	1,618 ms; 10,856 KB
testcase_26	AC	1,620 ms; 10,856 KB
testcase_27	AC	1,620 ms; 10,856 KB
testcase_28	AC	1,621 ms; 10,856 KB
testcase_29	AC	1,618 ms; 10,856 KB
testcase_30	AC	1,631 ms; 10,856 KB
testcase_31	AC	1,607 ms; 10,064 KB
testcase_32	AC	1,603 ms; 10,064 KB
testcase_33	AC	1,604 ms; 10,064 KB
testcase_34	AC	1,601 ms; 10,064 KB

ソースコード

use std::io::Read;

fn get_word() -> String {
    let stdin = std::io::stdin();
    let mut stdin=stdin.lock();
    let mut u8b: [u8; 1] = [0];
    loop {
        let mut buf: Vec<u8> = Vec::with_capacity(16);
        loop {
            let res = stdin.read(&mut u8b);
            if res.unwrap_or(0) == 0 || u8b[0] <= b' ' {
                break;
            } else {
                buf.push(u8b[0]);
            }
        }
        if buf.len() >= 1 {
            let ret = String::from_utf8(buf).unwrap();
            return ret;
        }
    }
}

fn get<T: std::str::FromStr>() -> T { get_word().parse().ok().unwrap() }

/// 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> From<i64> for ModInt<M> {
        fn from(x: i64) -> Self { Self::new(x) }
    }
} // 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)
}

// FFT (in-place, verified as NTT only)
// R: Ring + Copy
// Verified by: https://judge.yosupo.jp/submission/53831
// Adopts the technique used in https://judge.yosupo.jp/submission/3153.
mod fft {
    use std::ops::*;
    // n should be a power of 2. zeta is a primitive n-th root of unity.
    // one is unity
    // Note that the result is bit-reversed.
    pub fn fft<R>(f: &mut [R], zeta: R, one: R)
        where R: Copy +
        Add<Output = R> +
        Sub<Output = R> +
        Mul<Output = R> {
        let n = f.len();
        assert!(n.is_power_of_two());
        let mut m = n;
        let mut base = zeta;
        unsafe {
            while m > 2 {
                m >>= 1;
                let mut r = 0;
                while r < n {
                    let mut w = one;
                    for s in r..r + m {
                        let &u = f.get_unchecked(s);
                        let d = *f.get_unchecked(s + m);
                        *f.get_unchecked_mut(s) = u + d;
                        *f.get_unchecked_mut(s + m) = w * (u - d);
                        w = w * base;
                    }
                    r += 2 * m;
                }
                base = base * base;
            }
            if m > 1 {
                // m = 1
                let mut r = 0;
                while r < n {
                    let &u = f.get_unchecked(r);
                    let d = *f.get_unchecked(r + 1);
                    *f.get_unchecked_mut(r) = u + d;
                    *f.get_unchecked_mut(r + 1) = u - d;
                    r += 2;
                }
            }
        }
    }
    pub fn inv_fft<R>(f: &mut [R], zeta_inv: R, one: R)
        where R: Copy +
        Add<Output = R> +
        Sub<Output = R> +
        Mul<Output = R> {
        let n = f.len();
        assert!(n.is_power_of_two());
        let zeta = zeta_inv; // inverse FFT
        let mut zetapow = Vec::with_capacity(20);
        {
            let mut m = 1;
            let mut cur = zeta;
            while m < n {
                zetapow.push(cur);
                cur = cur * cur;
                m *= 2;
            }
        }
        let mut m = 1;
        unsafe {
            if m < n {
                zetapow.pop();
                let mut r = 0;
                while r < n {
                    let &u = f.get_unchecked(r);
                    let d = *f.get_unchecked(r + 1);
                    *f.get_unchecked_mut(r) = u + d;
                    *f.get_unchecked_mut(r + 1) = u - d;
                    r += 2;
                }
                m = 2;
            }
            while m < n {
                let base = zetapow.pop().unwrap();
                let mut r = 0;
                while r < n {
                    let mut w = one;
                    for s in r..r + m {
                        let &u = f.get_unchecked(s);
                        let d = *f.get_unchecked(s + m) * w;
                        *f.get_unchecked_mut(s) = u + d;
                        *f.get_unchecked_mut(s + m) = u - d;
                        w = w * base;
                    }
                    r += 2 * m;
                }
                m *= 2;
            }
        }
    }
}

// f(N, B, C) を問題の解として、再帰で解くことにすると f の呼び出し方は N * 60 通り程度。
// このままだと各呼び出しに O(N) 時間かかるので間に合わない。
// f の呼び出し方は f(N, (B >> i) - j, C >> i) に限られるので、これを dp[i][j] と呼ぶことにすれば
// 遷移は dp[i][j] += dp[i + 1][(j + k) >> 1] * C(N, k) なので、NTT で加速できる。
// 計算量は O(N log N log B)-time である。
// https://yukicoder.me/problems/no/2237 (4)
// Tags: ntt, fft, dp
fn main() {
    let n: usize = get();
    let b: i64 = get();
    let c: i64 = get();
    let (fac, invfac) = fact_init(n + 1);
    let mut comb_even = vec![MInt::new(0); W];
    let mut comb_odd = vec![MInt::new(0); W];
    const W: usize = 1 << 18;
    for i in 0..n + 1 {
        if i % 2 == 0 {
            comb_even[(W - i) % W] = fac[n] * invfac[i] * invfac[n - i];
        } else {
            comb_odd[(W - i) % W] = fac[n] * invfac[i] * invfac[n - i];
        }
    }
    let zeta = MInt::new(3).pow((MOD - 1) / W as i64);
    fft::fft(&mut comb_even, zeta, 1.into());
    fft::fft(&mut comb_odd, zeta, 1.into());
    let mut dp = vec![MInt::new(0); W];
    let mut ep = vec![MInt::new(0); W];
    dp[0] += 1;
    for pos in 0..60 {
        for i in 0..W {
            ep[i] = 0.into();
        }
        let b = (b >> (59 - pos)) & 1;
        let c = (c >> (59 - pos)) & 1;
        for i in 0..2 * n + 1 {
            ep[2 * i + b as usize] = dp[i];
        }
        fft::fft(&mut ep, zeta, 1.into());
        if c == 0 {
            for i in 0..W {
                ep[i] *= comb_even[i];
            }
        } else {
            for i in 0..W {
                ep[i] *= comb_odd[i];
            }
        }
        fft::inv_fft(&mut ep, zeta.inv(), 1.into());
        for i in 0..2 * n + 1 {
            dp[i] = ep[i];
        }
    }
    let factor = MInt::new(W as i64).pow(MOD - 1 - 60);
    println!("{}", dp[0] * factor);
}