#977433 (Rust) No.2613 Sum of Combination

提出ソース

結果

問題	No.2613 Sum of Combination
ユーザー	koba-e964
提出日時	2024-04-26 02:16:28
言語	Rust (1.77.0 + proconio)
結果	AC
実行時間	375 ms / 4,500 ms
コード長	10,170 bytes
コンパイル時間	950 ms
コンパイル使用メモリ	171,668 KB
実行使用メモリ	17,920 KB
最終ジャッジ日時	2024-04-26 02:16:45
合計ジャッジ時間	11,411 ms
ジャッジサーバーID （参考情報）	judge5 / judge4

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 6,812 KB
testcase_01	AC	1 ms 6,944 KB
testcase_02	AC	8 ms 6,940 KB
testcase_03	AC	1 ms 6,944 KB
testcase_04	AC	1 ms 6,940 KB
testcase_05	AC	1 ms 6,944 KB
testcase_06	AC	1 ms 6,940 KB
testcase_07	AC	1 ms 6,940 KB
testcase_08	AC	1 ms 6,944 KB
testcase_09	AC	1 ms 6,940 KB
testcase_10	AC	1 ms 6,940 KB
testcase_11	AC	1 ms 6,944 KB
testcase_12	AC	2 ms 6,940 KB
testcase_13	AC	11 ms 6,940 KB
testcase_14	AC	11 ms 6,944 KB
testcase_15	AC	6 ms 6,940 KB
testcase_16	AC	11 ms 6,940 KB
testcase_17	AC	11 ms 6,940 KB
testcase_18	AC	10 ms 6,944 KB
testcase_19	AC	11 ms 6,944 KB
testcase_20	AC	1 ms 6,940 KB
testcase_21	AC	1 ms 6,940 KB
testcase_22	AC	23 ms 6,944 KB
testcase_23	AC	368 ms 16,596 KB
testcase_24	AC	369 ms 16,640 KB
testcase_25	AC	363 ms 15,360 KB
testcase_26	AC	375 ms 17,752 KB
testcase_27	AC	181 ms 10,240 KB
testcase_28	AC	371 ms 17,680 KB
testcase_29	AC	371 ms 17,156 KB
testcase_30	AC	373 ms 17,784 KB
testcase_31	AC	372 ms 16,984 KB
testcase_32	AC	369 ms 16,724 KB
testcase_33	AC	374 ms 17,860 KB
testcase_34	AC	370 ms 17,800 KB
testcase_35	AC	369 ms 17,868 KB
testcase_36	AC	372 ms 17,880 KB
testcase_37	AC	370 ms 17,824 KB
testcase_38	AC	369 ms 17,580 KB
testcase_39	AC	373 ms 17,692 KB
testcase_40	AC	373 ms 17,640 KB
testcase_41	AC	373 ms 17,664 KB
testcase_42	AC	373 ms 17,756 KB
testcase_43	AC	371 ms 17,876 KB
testcase_44	AC	371 ms 17,920 KB
testcase_45	AC	1 ms 6,940 KB
testcase_46	AC	1 ms 6,940 KB
testcase_47	AC	1 ms 6,940 KB
testcase_48	AC	1 ms 6,940 KB
testcase_49	AC	1 ms 6,944 KB
testcase_50	AC	367 ms 17,808 KB
testcase_51	AC	370 ms 17,880 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

raw source code

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)]
        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>;

// 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;
            }
        }
    }
}

// Depends on: fft.rs, MInt.rs
// Verified by: ABC269-Ex (https://atcoder.jp/contests/abc269/submissions/39116328)
pub struct FPSOps<M: mod_int::Mod> {
    gen: mod_int::ModInt<M>,
}

impl<M: mod_int::Mod> FPSOps<M> {
    pub fn new(gen: mod_int::ModInt<M>) -> Self {
        FPSOps { gen: gen }
    }
}

impl<M: mod_int::Mod> FPSOps<M> {
    pub fn add(&self, mut a: Vec<mod_int::ModInt<M>>, mut b: Vec<mod_int::ModInt<M>>) -> Vec<mod_int::ModInt<M>> {
        if a.len() < b.len() {
            std::mem::swap(&mut a, &mut b);
        }
        for i in 0..b.len() {
            a[i] += b[i];
        }
        a
    }
    pub fn mul(&self, a: Vec<mod_int::ModInt<M>>, b: Vec<mod_int::ModInt<M>>) -> Vec<mod_int::ModInt<M>> {
        type MInt<M> = mod_int::ModInt<M>;
        if a.is_empty() || b.is_empty() {
            return vec![];
        }
        let n = a.len() - 1;
        let m = b.len() - 1;
        let mut p = 1;
        while p <= n + m { p *= 2; }
        let mut f = vec![MInt::new(0); p];
        let mut g = vec![MInt::new(0); p];
        for i in 0..n + 1 { f[i] = a[i]; }
        for i in 0..m + 1 { g[i] = b[i]; }
        let fac = MInt::new(p as i64).inv();
        let zeta = self.gen.pow((M::m() - 1) / p as i64);
        fft::fft(&mut f, zeta, 1.into());
        fft::fft(&mut g, zeta, 1.into());
        for i in 0..p { f[i] *= g[i] * fac; }
        fft::inv_fft(&mut f, zeta.inv(), 1.into());
        f.truncate(n + m + 1);
        f
    }
}

// O(40p)
fn find_generator(p: usize) -> usize {
    fn is_gen(g: usize, p: usize) -> bool {
        let mut cur = g;
        for _ in 1..p - 1 {
            if cur == 1 {
                return false;
            }
            cur = cur * g % p;
        }
        true
    }
    if p == 2 {
        return 1;
    }
    let mut g = 2;
    loop {
        if is_gen(g, p) {
            return g;
        }
        g += 1;
    }
}

// https://yukicoder.me/problems/no/2613 (3.5)
// Ref: https://techtipshoge.blogspot.com/2012/04/facebook-hacker-cup-2011-round2-scott.html
// Tags: discrete-logarithm, lucas-theorem, generator-of-finite-fields
fn main() {
    let mut n: i64 = get();
    let p: usize = get();
    let pp = p as i64;
    let mut dig = vec![];
    while n > 0 {
        dig.push((n % pp) as usize);
        n /= pp;
    }
    let g = find_generator(p);
    let mut log = vec![0; p];
    let mut exp = vec![0; p - 1];
    let mut cur = 1;
    for i in 0..p - 1 {
        log[cur] = i;
        exp[i] = cur;
        cur = cur * g % p;
    }
    let mut logfac = vec![0; p];
    for i in 1..p {
        logfac[i] = (logfac[i - 1] + log[i]) % (p - 1);
    }
    let mut cur = vec![MInt::new(0); p - 1];
    cur[0] += 1;
    let ops = FPSOps::new(MInt::new(3));
    for d in dig {
        let mut me = vec![MInt::new(0); p - 1];
        for i in 0..d + 1 {
            let idx = (2 * p - 2 + logfac[d] - logfac[i] - logfac[d - i]) % (p - 1);
            me[idx] += 1;
        }
        let tmp = ops.mul(cur, me);
        cur = vec![MInt::new(0); p - 1];
        cur.copy_from_slice(&tmp[..p - 1]);
        for i in p - 1..2 * p - 3 {
            cur[i - (p - 1)] += tmp[i];
        }
    }
    let mut tot = MInt::new(0);
    for i in 0..p - 1 {
        tot += cur[i] * exp[i] as i64;
    }
    println!("{}", tot);
}