#733470 (Rust) No.1815 K色問題

提出ソース

結果

問題	No.1815 K色問題
ユーザー	akakimidori
提出日時	2022-01-22 16:00:07
言語	Rust (1.77.0 + proconio)
結果	AC
実行時間	218 ms / 2,000 ms
コード長	8,348 bytes
コンパイル時間	13,377 ms
コンパイル使用メモリ	398,548 KB
実行使用メモリ	5,248 KB
最終ジャッジ日時	2024-09-29 22:39:24
合計ジャッジ時間	14,940 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	1 ms 5,248 KB
testcase_04	AC	1 ms 5,248 KB
testcase_05	AC	1 ms 5,248 KB
testcase_06	AC	54 ms 5,248 KB
testcase_07	AC	14 ms 5,248 KB
testcase_08	AC	136 ms 5,248 KB
testcase_09	AC	10 ms 5,248 KB
testcase_10	AC	15 ms 5,248 KB
testcase_11	AC	40 ms 5,248 KB
testcase_12	AC	1 ms 5,248 KB
testcase_13	AC	1 ms 5,248 KB
testcase_14	AC	191 ms 5,248 KB
testcase_15	AC	218 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

raw source code

// ---------- 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<1_000_000_007>>;

fn read() -> (u64, u64, u64) {
    let mut s = String::new();
    use std::io::Read;
    std::io::stdin().read_to_string(&mut s).unwrap();
    let a = s
        .trim()
        .split_whitespace()
        .flat_map(|s| s.parse())
        .collect::<Vec<_>>();
    (a[0], a[1], a[2])
}

fn main() {
    let (n, m, k) = read();
    let k = k as usize;
    let pc = Precalc::new(k);
    let mut ans = M::zero();
    let mut sign = M::one();
    for i in (1..=k).rev() {
        let way = if n == 1 {
            let k = M::from(i);
            k * (k - M::one()).pow(m - 1)
        } else if n == 2 {
            let k = M::from(i);
            k * (k - M::one()) * (k * k - M::new(3) * k + M::new(3)).pow(m - 1)
        } else {
            type Mat = [[M; 2]; 2];
            let mul = |a: &Mat, b: &Mat| -> Mat {
                let mut c = Mat::default();
                for (c, a) in c.iter_mut().zip(a) {
                    for (a, b) in a.iter().zip(b) {
                        for (c, b) in c.iter_mut().zip(b) {
                            *c += *a * *b;
                        }
                    }
                }
                c
            };
            let k = M::from(i);
            let mut r = Mat::default();
            r[0][0] = [1i64, -6, 14, -13]
                .iter()
                .fold(M::zero(), |s, a| s * k + M::from(*a));
            r[0][1] = [1i64, -6, 13, -10]
                .iter()
                .fold(M::zero(), |s, a| s * k + M::from(*a));
            r[1][0] = [1i64, -4, 5]
                .iter()
                .fold(M::zero(), |s, a| s * k + M::from(*a));
            r[1][1] = [1i64, -3, 3]
                .iter()
                .fold(M::zero(), |s, a| s * k + M::from(*a));
            let mut t = [[M::one(), M::zero()], [M::zero(), M::one()]];
            let mut m = m - 1;
            while m > 0 {
                if m & 1 == 1 {
                    t = mul(&t, &r);
                }
                r = mul(&r, &r);
                m >>= 1;
            }
            let a = [
                k * k * k - M::new(3) * k * k + M::new(2) * k,
                k * (k - M::one()),
            ];
            t.iter()
                .map(|t| t.iter().zip(a.iter()))
                .flatten()
                .fold(M::zero(), |s, p| s + *p.0 * *p.1)
        };
        ans += sign * pc.binom(k, i) * way;
        sign = -sign;
    }
    println!("{}", ans);
}

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結果

テストケース

ソースコード