#860122 (Rust) No.1191 数え上げを愛したい（数列編）

• 問題: No.1191 数え上げを愛したい（数列編）
• ユーザー: atcoder8
• 提出日時: 2023-04-16 10:48:32
• 言語: Rust (1.77.0 + proconio)
• 結果: AC
• 実行時間: 68 ms / 2,000 ms
• コード長: 17,998 bytes
• コンパイル時間: 17,560 ms
• コンパイル使用メモリ: 386,800 KB
• 実行使用メモリ: 5,248 KB
• 最終ジャッジ日時: 2024-10-11 21:24:53
• 合計ジャッジ時間: 16,830 ms
• ジャッジサーバーID （参考情報）: judge2 / judge4

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	15 ms; 5,248 KB
testcase_01	AC	33 ms; 5,248 KB
testcase_02	AC	35 ms; 5,248 KB
testcase_03	AC	52 ms; 5,248 KB
testcase_04	AC	43 ms; 5,248 KB
testcase_05	AC	5 ms; 5,248 KB
testcase_06	AC	68 ms; 5,248 KB
testcase_07	AC	47 ms; 5,248 KB
testcase_08	AC	48 ms; 5,248 KB
testcase_09	AC	47 ms; 5,248 KB
testcase_10	AC	2 ms; 5,248 KB
testcase_11	AC	2 ms; 5,248 KB
testcase_12	AC	67 ms; 5,248 KB
testcase_13	AC	63 ms; 5,248 KB
testcase_14	AC	54 ms; 5,248 KB
testcase_15	AC	1 ms; 5,248 KB
testcase_16	AC	1 ms; 5,248 KB
testcase_17	AC	1 ms; 5,248 KB
testcase_18	AC	1 ms; 5,248 KB
testcase_19	AC	1 ms; 5,248 KB
testcase_20	AC	1 ms; 5,248 KB
testcase_21	AC	1 ms; 5,248 KB
testcase_22	AC	15 ms; 5,248 KB
testcase_23	AC	1 ms; 5,248 KB
testcase_24	AC	1 ms; 5,248 KB
testcase_25	AC	1 ms; 5,248 KB

ソースコード

use atcoder8_library::modint::Modint998244353;

use crate::atcoder8_library::factorial::Factorial;

type Mint = Modint998244353;

fn main() {
    let (n, m, a, b) = {
        let mut line = String::new();
        std::io::stdin().read_line(&mut line).unwrap();
        let mut iter = line.split_whitespace();
        (
            iter.next().unwrap().parse::<usize>().unwrap(),
            iter.next().unwrap().parse::<usize>().unwrap(),
            iter.next().unwrap().parse::<usize>().unwrap(),
            iter.next().unwrap().parse::<usize>().unwrap(),
        )
    };

    if (n - 1) * a > b {
        println!("0");
        std::process::exit(0);
    }

    let mut fac: Factorial<Mint> = Factorial::new();

    let ans = (1..=(m - (n - 1) * a))
        .map(|s| fac.combinations_with_repetition(n, (s + b).min(m) - ((n - 1) * a + s)))
        .fold(Mint::new(0), |acc, x| acc + x)
        * fac.factorial(n);
    println!("{}", ans.val());
}

pub mod atcoder8_library {
    pub mod modint {
        use std::ops::{
            Add, AddAssign, Div, DivAssign, Mul, MulAssign, Neg, ShrAssign, Sub, SubAssign,
        };

        pub trait RemEuclidU32 {
            fn rem_euclid_u32(self, modulus: u32) -> u32;
        }

        /// Calculate the modular multiplicative inverse of `a` with `m` as modulus.
        pub fn modinv(a: u32, m: u32) -> u32 {
            assert!(m >= 2);

            let (mut a, mut b, mut s, mut t) = (a as i64, m as i64, 1, 0);
            while b != 0 {
                let q = a / b;
                a -= q * b;
                std::mem::swap(&mut a, &mut b);
                s -= q * t;
                std::mem::swap(&mut s, &mut t);
            }

            assert_eq!(
                a.abs(),
                1,
                "The inverse does not exist. gcd(a, m) = {}",
                a.abs()
            );

            s %= m as i64;
            if s < 0 {
                s += m as i64;
            }

            s as u32
        }

        /// This macro implements rem_euclid_u32 for signed integer types of 32 bits or less.
        macro_rules! impl_rem_euclid_u32_for_small_signed {
        ($($small_signed_type:tt),*) => {
            $(
                impl RemEuclidU32 for $small_signed_type {
                    fn rem_euclid_u32(self, modulus: u32) -> u32 {
                        let ret = (self as i32) % (modulus as i32);
                        if ret >= 0 {
                            ret as u32
                        } else {
                            (ret + modulus as i32) as u32
                        }
                    }
                }
            )*
        };
    }

        /// This macro implements rem_euclid_u32 for 64-bit signed integer types (including isize).
        macro_rules! impl_rem_euclid_u32_for_large_signed {
        ($($large_signed_type:tt),*) => {
            $(
                impl RemEuclidU32 for $large_signed_type {
                    fn rem_euclid_u32(self, modulus: u32) -> u32 {
                        let ret = (self as i64) % (modulus as i64);
                        if ret >= 0 {
                            ret as u32
                        } else {
                            (ret + modulus as i64) as u32
                        }
                    }
                }
            )*
        };
    }

        /// This macro implements rem_euclid_u32 for unsigned integer types greater than 32 bits.
        macro_rules! impl_rem_euclid_u32_for_small_unsigned {
        ($($small_unsigned_type:tt),*) => {
            $(
                impl RemEuclidU32 for $small_unsigned_type {
                    fn rem_euclid_u32(self, modulus: u32) -> u32 {
                        self as u32 % modulus
                    }
                }
            )*
        };
    }

        /// This macro implements rem_euclid_u32 for 64-bit and larger unsigned integer types (including usize).
        macro_rules! impl_rem_euclid_u32_for_large_unsigned {
        ($($large_unsigned_type:tt),*) => {
            $(
                impl RemEuclidU32 for $large_unsigned_type {
                    fn rem_euclid_u32(self, modulus: u32) -> u32 {
                        (self % modulus as $large_unsigned_type) as u32
                    }
                }
            )*
        };
    }

        // Implement rem_euclid_u32 for signed integer types of 32 bits or less.
        impl_rem_euclid_u32_for_small_signed!(i8, i16, i32);

        // Implement rem_euclid_u32 for 64-bit signed integer types (including isize).
        impl_rem_euclid_u32_for_large_signed!(i64, isize);

        // Implement rem_euclid_u32 for unsigned integer types of 32 bits or more.
        impl_rem_euclid_u32_for_small_unsigned!(u8, u16, u32);

        // Implement rem_euclid_u32 for unsigned integer types (including usize) of 64 bits or more.
        impl_rem_euclid_u32_for_large_unsigned!(u64, u128, usize);

        // Implement rem_euclid_u32 for i128.
        impl RemEuclidU32 for i128 {
            fn rem_euclid_u32(self, modulus: u32) -> u32 {
                let ret = self % (modulus as i128);
                if ret >= 0 {
                    ret as u32
                } else {
                    (ret + modulus as i128) as u32
                }
            }
        }

        pub trait Pow<T: Copy + ShrAssign> {
            fn pow(self, n: T) -> Self;
        }

        /// Macro to overload binary operation with `$modint_type` for each integer type
        macro_rules! impl_ops {
        ($modint_type:tt, $($other_type:tt),*) => {
            $(
                impl Add<$other_type> for $modint_type {
                    type Output = Self;

                    fn add(self, rhs: $other_type) -> Self::Output {
                        self + Self::new(rhs)
                    }
                }

                impl Add<$modint_type> for $other_type {
                    type Output = $modint_type;

                    fn add(self, rhs: $modint_type) -> Self::Output {
                        $modint_type::new(self) + rhs
                    }
                }

                impl Sub<$other_type> for $modint_type {
                    type Output = Self;

                    fn sub(self, rhs: $other_type) -> Self::Output {
                        self - Self::new(rhs)
                    }
                }

                impl Sub<$modint_type> for $other_type {
                    type Output = $modint_type;

                    fn sub(self, rhs: $modint_type) -> Self::Output {
                        $modint_type::new(self) - rhs
                    }
                }

                impl Mul<$other_type> for $modint_type {
                    type Output = Self;

                    fn mul(self, rhs: $other_type) -> Self::Output {
                        self * Self::new(rhs)
                    }
                }

                impl Mul<$modint_type> for $other_type {
                    type Output = $modint_type;

                    fn mul(self, rhs: $modint_type) -> Self::Output {
                        $modint_type::new(self) * rhs
                    }
                }

                impl Div<$other_type> for $modint_type {
                    type Output = Self;

                    fn div(self, rhs: $other_type) -> Self::Output {
                        self / Self::new(rhs)
                    }
                }

                impl Div<$modint_type> for $other_type {
                    type Output = $modint_type;

                    fn div(self, rhs: $modint_type) -> Self::Output {
                        $modint_type::new(self) / rhs
                    }
                }

                impl AddAssign<$other_type> for $modint_type {
                    fn add_assign(&mut self, other: $other_type) {
                        *self = *self + Self::new(other);
                    }
                }

                impl SubAssign<$other_type> for $modint_type {
                    fn sub_assign(&mut self, other: $other_type) {
                        *self = *self - Self::new(other);
                    }
                }

                impl MulAssign<$other_type> for $modint_type {
                    fn mul_assign(&mut self, other: $other_type) {
                        *self = *self * Self::new(other);
                    }
                }

                impl DivAssign<$other_type> for $modint_type {
                    fn div_assign(&mut self, other: $other_type) {
                        *self = *self / Self::new(other);
                    }
                }
            )*
        };
    }

        /// This macro defines powers of Modint for unsigned integer types.
        macro_rules! impl_power_for_unsigned {
        ($modint_type:tt, $($unsigned_type:tt),*) => {
            $(
                impl Pow<$unsigned_type> for $modint_type {
                    fn pow(self, mut n: $unsigned_type) -> Self {
                        let mut ret = Self::new(1);
                        let mut mul = self;
                        while n != 0 {
                            if n & 1 == 1 {
                                ret *= mul;
                            }
                            mul *= mul;
                            n >>= 1;
                        }
                        ret
                    }
                }
            )*
        };
    }

        /// This macro defines powers of Modint for signed integer types of 32 bits or less.
        macro_rules! impl_power_for_small_signed {
        ($modint_type:tt, $($small_signed_type:tt),*) => {
            $(
                impl Pow<$small_signed_type> for $modint_type {
                    fn pow(self, n: $small_signed_type) -> Self {
                        if n >= 0 {
                            self.pow(n as u32)
                        } else {
                            self.pow(-n as u32).inv()
                        }
                    }
                }
            )*
        };
    }

        /// This macro defines the power of Modint for 64-bit signed integer types (including isize).
        macro_rules! impl_power_for_large_signed {
        ($modint_type:tt, $($large_signed_type:tt),*) => {
            $(
                impl Pow<$large_signed_type> for $modint_type {
                    fn pow(self, n: $large_signed_type) -> Self {
                        if n >= 0 {
                            self.pow(n as u64)
                        } else {
                            self.pow(-n as u64).inv()
                        }
                    }
                }
            )*
        };
    }

        /// This macro generates Modint by specifying the type name and modulus.
        macro_rules! generate_modint {
            ($modint_type:tt, $modulus:literal) => {
                #[derive(Debug, Default, Hash, Clone, Copy, PartialEq, Eq)]
                pub struct $modint_type {
                    val: u32,
                }

                impl $modint_type {
                    const MOD: u32 = $modulus;
                }

                impl $modint_type {
                    pub fn new<T: RemEuclidU32>(val: T) -> Self {
                        Self {
                            val: val.rem_euclid_u32($modulus),
                        }
                    }

                    pub fn frac<T: RemEuclidU32>(numer: T, denom: T) -> Self {
                        Self::new(numer) / Self::new(denom)
                    }

                    pub fn raw(val: u32) -> Self {
                        Self { val }
                    }

                    pub fn val(&self) -> u32 {
                        self.val
                    }

                    pub fn inv(&self) -> Self {
                        Self::new(modinv(self.val, $modulus))
                    }
                }

                impl<T: RemEuclidU32> From<T> for $modint_type {
                    fn from(val: T) -> Self {
                        Self::new(val)
                    }
                }

                impl Add for $modint_type {
                    type Output = Self;

                    fn add(self, rhs: Self) -> Self::Output {
                        Self::new(self.val + rhs.val)
                    }
                }

                impl Sub for $modint_type {
                    type Output = Self;

                    fn sub(self, rhs: Self) -> Self::Output {
                        Self::new(self.val + $modulus - rhs.val)
                    }
                }

                impl Mul for $modint_type {
                    type Output = Self;

                    fn mul(self, rhs: Self) -> Self::Output {
                        Self::new(self.val as u64 * rhs.val as u64)
                    }
                }

                impl Div for $modint_type {
                    type Output = Self;

                    #[allow(clippy::suspicious_arithmetic_impl)]
                    fn div(self, rhs: Self) -> Self::Output {
                        self * rhs.inv()
                    }
                }

                impl AddAssign for $modint_type {
                    fn add_assign(&mut self, other: Self) {
                        *self = *self + other;
                    }
                }

                impl SubAssign for $modint_type {
                    fn sub_assign(&mut self, other: Self) {
                        *self = *self - other;
                    }
                }

                impl MulAssign for $modint_type {
                    fn mul_assign(&mut self, other: Self) {
                        *self = *self * other;
                    }
                }

                impl DivAssign for $modint_type {
                    fn div_assign(&mut self, other: Self) {
                        *self = *self / other;
                    }
                }

                impl Neg for $modint_type {
                    type Output = Self;

                    fn neg(self) -> Self::Output {
                        Self::new(Self::MOD - self.val)
                    }
                }

                // Define a binary operation between each integer type and $modint_type.
                impl_ops!(
                    $modint_type,
                    i8,
                    i16,
                    i32,
                    i64,
                    i128,
                    isize,
                    u8,
                    u16,
                    u32,
                    u64,
                    u128,
                    usize
                );

                // Define powers of Modint for unsigned integer types.
                impl_power_for_unsigned!($modint_type, u8, u16, u32, u64, u128, usize);

                // Define powers of Modint for signed integer types of 32 bits or less.
                impl_power_for_small_signed!($modint_type, i8, i16, i32);

                // Define Modint powers for 64-bit signed integer types (including isize).
                impl_power_for_large_signed!($modint_type, i64, isize);

                // Define the power of Modint for 128-bit signed integer types.
                impl Pow<i128> for $modint_type {
                    fn pow(self, n: i128) -> Self {
                        if n >= 0 {
                            self.pow(n as u128)
                        } else {
                            self.pow(-n as u128).inv()
                        }
                    }
                }
            };
        }

        // Define Modint with 998244353 as modulus
        generate_modint!(Modint998244353, 998244353);

        // Define Modint with 1000000007 as modulus
        generate_modint!(Modint1000000007, 1000000007);
    }

    pub mod factorial {
        use std::ops::{Div, Mul};

        pub struct Factorial<T> {
            fac: Vec<T>,
        }

        impl<T> Default for Factorial<T>
        where
            T: Clone + From<usize> + Mul<Output = T> + Div<Output = T>,
        {
            fn default() -> Self {
                Self::new()
            }
        }

        impl<T> Factorial<T>
        where
            T: Clone + From<usize> + Mul<Output = T> + Div<Output = T>,
        {
            /// Constructs a new, empty `Factorial<T>`.
            pub fn new() -> Self {
                Self {
                    fac: vec![T::from(1)],
                }
            }

            /// Returns the factorial of `n`.
            pub fn factorial(&mut self, n: usize) -> T {
                if self.fac.len() < n + 1 {
                    for i in (self.fac.len() - 1)..n {
                        self.fac.push(self.fac[i].clone() * (i + 1).into());
                    }
                }
                self.fac[n].clone()
            }

            /// Returns the number of choices when selecting `k` from `n` and arranging them in a row.
            pub fn permutations(&mut self, n: usize, k: usize) -> T {
                if n < k {
                    T::from(0)
                } else {
                    self.factorial(n) / self.factorial(n - k)
                }
            }

            /// Returns the number of choices to select `k` from `n`.
            pub fn combinations(&mut self, n: usize, k: usize) -> T {
                if n < k {
                    T::from(0)
                } else {
                    self.factorial(n) / (self.factorial(k) * self.factorial(n - k))
                }
            }

            /// Calculate the number of cases when sample of `k` elements from a set of `n` elements, allowing for duplicates.
            pub fn combinations_with_repetition(&mut self, n: usize, k: usize) -> T {
                if n == 0 {
                    if k == 0 {
                        T::from(1)
                    } else {
                        T::from(0)
                    }
                } else {
                    self.combinations(n + k - 1, k)
                }
            }
        }
    }
}