結果

問題 No.2514 Twelvefold Way Returns
ユーザー akakimidoriakakimidori
提出日時 2023-11-19 17:10:36
言語 Rust
(1.77.0 + proconio)
結果
AC  
実行時間 90 ms / 3,000 ms
コード長 10,616 bytes
コンパイル時間 12,484 ms
コンパイル使用メモリ 379,548 KB
実行使用メモリ 5,376 KB
最終ジャッジ日時 2024-09-26 06:17:50
合計ジャッジ時間 15,763 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
5,248 KB
testcase_01 AC 2 ms
5,376 KB
testcase_02 AC 9 ms
5,376 KB
testcase_03 AC 2 ms
5,376 KB
testcase_04 AC 68 ms
5,376 KB
testcase_05 AC 55 ms
5,376 KB
testcase_06 AC 41 ms
5,376 KB
testcase_07 AC 1 ms
5,376 KB
testcase_08 AC 28 ms
5,376 KB
testcase_09 AC 27 ms
5,376 KB
testcase_10 AC 76 ms
5,376 KB
testcase_11 AC 2 ms
5,376 KB
testcase_12 AC 11 ms
5,376 KB
testcase_13 AC 1 ms
5,376 KB
testcase_14 AC 8 ms
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testcase_15 AC 22 ms
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testcase_16 AC 72 ms
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testcase_17 AC 37 ms
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testcase_18 AC 79 ms
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testcase_19 AC 84 ms
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testcase_20 AC 88 ms
5,376 KB
testcase_21 AC 86 ms
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testcase_22 AC 85 ms
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testcase_23 AC 25 ms
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testcase_24 AC 78 ms
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testcase_25 AC 31 ms
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testcase_26 AC 1 ms
5,376 KB
testcase_27 AC 86 ms
5,376 KB
testcase_28 AC 73 ms
5,376 KB
testcase_29 AC 50 ms
5,376 KB
testcase_30 AC 69 ms
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testcase_31 AC 78 ms
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testcase_32 AC 25 ms
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testcase_33 AC 1 ms
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testcase_34 AC 8 ms
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testcase_35 AC 70 ms
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testcase_36 AC 1 ms
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testcase_37 AC 1 ms
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testcase_38 AC 87 ms
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testcase_39 AC 90 ms
5,376 KB
testcase_40 AC 88 ms
5,376 KB
権限があれば一括ダウンロードができます
コンパイルメッセージ
warning: associated constants `PRIMITIVE_ROOT` and `ORDER` are never used
   --> src/main.rs:214:11
    |
198 | impl<const M: u32> ModInt<{ M }> {
    | -------------------------------- associated constants in this implementation
...
214 |     const PRIMITIVE_ROOT: u32 = primitive_root(M);
    |           ^^^^^^^^^^^^^^
215 |     const ORDER: usize = 1 << (M - 1).trailing_zeros();
    |           ^^^^^
    |
    = note: `#[warn(dead_code)]` on by default

ソースコード

diff # 

// exp のmod 3 で1の項のM乗のN項目が答え
// exp でmod3 で 1の項を取り出すには？
// 3乗根をw と置いて
//
// f(x) + f(wx) + f(w^2x) で0が取り出せる
// f(x) + w^2 f(wx) + wf(w^2x) でOKなはず
//
// N! [x^n] (e^x + w^2 e(wx) + w e^(w^2x))^m
// = N! [x^n] sum_{0 <= i, j, i + j <= m} M!/i!j!(M-i-j)! * w^(2j + M-i-j) * e^(ix + jwx + (M-i-j)w^2x)
// = sum_{i, j} C_{i, j} * w^(M-i+j) * (i+jw+(M-i-j)w^2)^n

type M = ModInt<998_244_353>;

fn main() {
    input!(n: usize, m: usize);
    let mut ans = M::zero();
    let pc = Precalc::new(m);
    let w = P(M::zero(), M::one());
    for i in 0..=m {
        for j in 0..=(m - i) {
            let k = m - i - j;
            let mut r = P(M::from(i), M::zero())
                + P(M::from(j), M::zero()) * w
                + P(M::from(k), M::zero()) * w * w;
            let mut n = n;
            let mut t = P(M::one(), M::zero());
            while n > 0 {
                if n & 1 == 1 {
                    t = t * r;
                }
                r = r * r;
                n >>= 1;
            }
            for _ in 0..(2 * j + k) {
                t = t * w;
            }
            let val = t.0 * pc.fact(m) * pc.ifact(i) * pc.ifact(j) * pc.ifact(k);
            ans += val;
        }
    }
    ans *= M::new(3).inv().pow(m as u64);
    println!("{}", ans);
}

#[derive(Clone, Copy, Debug)]
struct P(M, M);

impl Add for P {
    type Output = Self;
    fn add(self, rhs: Self) -> Self {
        Self(self.0 + rhs.0, self.1 + rhs.1)
    }
}

impl Mul for P {
    type Output = Self;
    fn mul(self, rhs: Self) -> Self {
        let p = self.1 * rhs.1;
        Self(self.0 * rhs.0 - p, self.0 * rhs.1 + self.1 * rhs.0 - p)
    }
}

// ---------- 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 ----------

use std::ops::*;

// ---------- begin trait ----------
pub trait Zero: Sized + Add<Self, Output = Self> {
    fn zero() -> Self;
    fn is_zero(&self) -> bool;
}

pub trait One: Sized + Mul<Self, Output = Self> {
    fn one() -> Self;
    fn is_one(&self) -> bool;
}

pub trait Ring: Zero + One + Sub<Output = Self> {}

pub trait Field: Ring + Div<Output = Self> {}
// ---------- end trait ----------
// ---------- begin modint ----------
pub const fn pow_mod(mut r: u32, mut n: u32, m: u32) -> u32 {
    let mut t = 1;
    while n > 0 {
        if n & 1 == 1 {
            t = (t as u64 * r as u64 % m as u64) as u32;
        }
        r = (r as u64 * r as u64 % m as u64) as u32;
        n >>= 1;
    }
    t
}

pub const fn primitive_root(p: u32) -> u32 {
    let mut m = p - 1;
    let mut f = [1; 30];
    let mut k = 0;
    let mut d = 2;
    while d * d <= m {
        if m % d == 0 {
            f[k] = d;
            k += 1;
        }
        while m % d == 0 {
            m /= d;
        }
        d += 1;
    }
    if m > 1 {
        f[k] = m;
        k += 1;
    }
    let mut g = 1;
    while g < p {
        let mut ok = true;
        let mut i = 0;
        while i < k {
            ok &= pow_mod(g, (p - 1) / f[i], p) > 1;
            i += 1;
        }
        if ok {
            break;
        }
        g += 1;
    }
    g
}

pub const fn is_prime(n: u32) -> bool {
    if n <= 1 {
        return false;
    }
    let mut d = 2;
    while d * d <= n {
        if n % d == 0 {
            return false;
        }
        d += 1;
    }
    true
}

#[derive(Clone, Copy, PartialEq, Eq)]
pub struct ModInt<const M: u32>(u32);

impl<const M: u32> ModInt<{ M }> {
    const REM: u32 = {
        let mut t = 1u32;
        let mut s = !M + 1;
        let mut n = !0u32 >> 2;
        while n > 0 {
            if n & 1 == 1 {
                t = t.wrapping_mul(s);
            }
            s = s.wrapping_mul(s);
            n >>= 1;
        }
        t
    };
    const INI: u64 = ((1u128 << 64) % M as u128) as u64;
    const IS_PRIME: () = assert!(is_prime(M));
    const PRIMITIVE_ROOT: u32 = primitive_root(M);
    const ORDER: usize = 1 << (M - 1).trailing_zeros();
    const fn reduce(x: u64) -> u32 {
        let _ = Self::IS_PRIME;
        let b = (x as u32 * Self::REM) as u64;
        let t = x + b * M as u64;
        let mut c = (t >> 32) as u32;
        if c >= M {
            c -= M;
        }
        c as u32
    }
    const fn multiply(a: u32, b: u32) -> u32 {
        Self::reduce(a as u64 * b as u64)
    }
    pub const fn new(v: u32) -> Self {
        assert!(v < M);
        Self(Self::reduce(v as u64 * Self::INI))
    }
    pub const fn const_mul(&self, rhs: Self) -> Self {
        Self(Self::multiply(self.0, rhs.0))
    }
    pub const fn pow(&self, mut n: u64) -> Self {
        let mut t = Self::new(1);
        let mut r = *self;
        while n > 0 {
            if n & 1 == 1 {
                t = t.const_mul(r);
            }
            r = r.const_mul(r);
            n >>= 1;
        }
        t
    }
    pub const fn inv(&self) -> Self {
        assert!(self.0 != 0);
        self.pow(M as u64 - 2)
    }
    pub const fn get(&self) -> u32 {
        Self::reduce(self.0 as u64)
    }
    pub const fn zero() -> Self {
        Self::new(0)
    }
    pub const fn one() -> Self {
        Self::new(1)
    }
}

impl<const M: u32> Add for ModInt<{ M }> {
    type Output = Self;
    fn add(self, rhs: Self) -> Self::Output {
        let mut v = self.0 + rhs.0;
        if v >= M {
            v -= M;
        }
        Self(v)
    }
}

impl<const M: u32> Sub for ModInt<{ M }> {
    type Output = Self;
    fn sub(self, rhs: Self) -> Self::Output {
        let mut v = self.0 - rhs.0;
        if self.0 < rhs.0 {
            v += M;
        }
        Self(v)
    }
}

impl<const M: u32> Mul for ModInt<{ M }> {
    type Output = Self;
    fn mul(self, rhs: Self) -> Self::Output {
        self.const_mul(rhs)
    }
}

impl<const M: u32> Div for ModInt<{ M }> {
    type Output = Self;
    fn div(self, rhs: Self) -> Self::Output {
        self * rhs.inv()
    }
}

impl<const M: u32> AddAssign for ModInt<{ M }> {
    fn add_assign(&mut self, rhs: Self) {
        *self = *self + rhs;
    }
}

impl<const M: u32> SubAssign for ModInt<{ M }> {
    fn sub_assign(&mut self, rhs: Self) {
        *self = *self - rhs;
    }
}

impl<const M: u32> MulAssign for ModInt<{ M }> {
    fn mul_assign(&mut self, rhs: Self) {
        *self = *self * rhs;
    }
}

impl<const M: u32> DivAssign for ModInt<{ M }> {
    fn div_assign(&mut self, rhs: Self) {
        *self = *self / rhs;
    }
}

impl<const M: u32> Neg for ModInt<{ M }> {
    type Output = Self;
    fn neg(self) -> Self::Output {
        if self.0 == 0 {
            self
        } else {
            Self(M - self.0)
        }
    }
}

impl<const M: u32> std::fmt::Display for ModInt<{ M }> {
    fn fmt<'a>(&self, f: &mut std::fmt::Formatter<'a>) -> std::fmt::Result {
        write!(f, "{}", self.get())
    }
}

impl<const M: u32> std::fmt::Debug for ModInt<{ M }> {
    fn fmt<'a>(&self, f: &mut std::fmt::Formatter<'a>) -> std::fmt::Result {
        write!(f, "{}", self.get())
    }
}

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

impl<const M: u32> From<usize> for ModInt<{ M }> {
    fn from(val: usize) -> ModInt<{ M }> {
        ModInt::new((val % M as usize) as u32)
    }
}
// ---------- end modint ----------
// ---------- begin precalc ----------
pub struct Precalc<const MOD: u32> {
    fact: Vec<ModInt<MOD>>,
    ifact: Vec<ModInt<MOD>>,
    inv: Vec<ModInt<MOD>>,
}

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

impl<const M: u32> Zero for ModInt<{ M }> {
    fn zero() -> Self {
        Self::zero()
    }
    fn is_zero(&self) -> bool {
        self.0 == 0
    }
}

impl<const M: u32> One for ModInt<{ M }> {
    fn one() -> Self {
        Self::one()
    }
    fn is_one(&self) -> bool {
        self.get() == 1
    }
}

impl<const M: u32> Ring for ModInt<{ M }> {}
impl<const M: u32> Field for ModInt<{ M }> {}

// ---------- begin array op ----------
0