結果

問題 No.1547 [Cherry 2nd Tune *] 偶然の勝利の確率
ユーザー akakimidoriakakimidori
提出日時 2021-06-11 22:20:26
言語 Rust
(1.77.0 + proconio)
結果
AC  
実行時間 89 ms / 2,000 ms
コード長 12,661 bytes
コンパイル時間 16,963 ms
コンパイル使用メモリ 388,600 KB
実行使用メモリ 6,820 KB
最終ジャッジ日時 2024-12-15 00:52:03
合計ジャッジ時間 19,348 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge5
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
6,820 KB
testcase_01 AC 1 ms
6,820 KB
testcase_02 AC 4 ms
6,816 KB
testcase_03 AC 1 ms
6,816 KB
testcase_04 AC 1 ms
6,820 KB
testcase_05 AC 1 ms
6,816 KB
testcase_06 AC 1 ms
6,820 KB
testcase_07 AC 1 ms
6,816 KB
testcase_08 AC 1 ms
6,816 KB
testcase_09 AC 1 ms
6,820 KB
testcase_10 AC 1 ms
6,820 KB
testcase_11 AC 1 ms
6,816 KB
testcase_12 AC 1 ms
6,816 KB
testcase_13 AC 16 ms
6,816 KB
testcase_14 AC 11 ms
6,820 KB
testcase_15 AC 6 ms
6,820 KB
testcase_16 AC 8 ms
6,816 KB
testcase_17 AC 7 ms
6,820 KB
testcase_18 AC 8 ms
6,816 KB
testcase_19 AC 3 ms
6,820 KB
testcase_20 AC 50 ms
6,820 KB
testcase_21 AC 5 ms
6,816 KB
testcase_22 AC 1 ms
6,816 KB
testcase_23 AC 87 ms
6,816 KB
testcase_24 AC 88 ms
6,820 KB
testcase_25 AC 88 ms
6,816 KB
testcase_26 AC 87 ms
6,820 KB
testcase_27 AC 88 ms
6,816 KB
testcase_28 AC 88 ms
6,816 KB
testcase_29 AC 88 ms
6,820 KB
testcase_30 AC 89 ms
6,816 KB
testcase_31 AC 88 ms
6,816 KB
testcase_32 AC 88 ms
6,820 KB
testcase_33 AC 88 ms
6,816 KB
testcase_34 AC 10 ms
6,816 KB
testcase_35 AC 9 ms
6,820 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

diff # 

// ---------- begin ModInt ----------
mod modint {

    #[allow(dead_code)]
    pub struct Mod;
    impl ConstantModulo for Mod {
        const MOD: u32 = 998_244_353;
    }

    #[allow(dead_code)]
    pub struct StaticMod;
    static mut STATIC_MOD: u32 = 0;
    impl Modulo for StaticMod {
        fn modulo() -> u32 {
            unsafe { STATIC_MOD }
        }
    }

    #[allow(dead_code)]
    impl StaticMod {
        pub fn set_modulo(p: u32) {
            unsafe {
                STATIC_MOD = p;
            }
        }
    }

    use std::marker::*;
    use std::ops::*;

    pub trait Modulo {
        fn modulo() -> u32;
    }

    pub trait ConstantModulo {
        const MOD: u32;
    }

    impl<T> Modulo for T
    where
        T: ConstantModulo,
    {
        fn modulo() -> u32 {
            T::MOD
        }
    }

    pub struct ModInt<T>(pub u32, PhantomData<T>);

    impl<T> Clone for ModInt<T> {
        fn clone(&self) -> Self {
            ModInt::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 d = self.0 + rhs.0;
            if d >= T::modulo() {
                d -= T::modulo();
            }
            ModInt::new_unchecked(d)
        }
    }

    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 d = T::modulo() + self.0 - rhs.0;
            if d >= T::modulo() {
                d -= T::modulo();
            }
            ModInt::new_unchecked(d)
        }
    }

    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;
            ModInt::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.0 == 0 {
                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: 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 m = T::modulo() as i64;
            ModInt::new((val % m + m) as u32)
        }
    }

    #[allow(dead_code)]
    impl<T> ModInt<T> {
        pub fn new_unchecked(d: u32) -> Self {
            ModInt(d, 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
        }
    }

    #[allow(dead_code)]
    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.0 != 0);
            self.pow(T::modulo() as u64 - 2)
        }
    }
}
// ---------- end ModInt ----------
// ---------- begin Precalc ----------
mod precalc {
    use super::modint::*;
    #[allow(dead_code)]
    pub struct Precalc<T> {
        inv: Vec<ModInt<T>>,
        fact: Vec<ModInt<T>>,
        ifact: Vec<ModInt<T>>,
    }
    #[allow(dead_code)]
    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 + 1) {
                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 {
                inv: inv,
                fact: fact,
                ifact: ifact,
            }
        }
        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 comb(&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 ----------

use modint::*;
type M = ModInt<Mod>;

// ---------- begin Matrix ----------
mod matrix {
    use std::ops::*;
    pub trait SemiRing: Add<Output = Self> + Mul<Output = Self> + Copy {
        fn zero() -> Self;
        fn one() -> Self;
    }
    pub trait Inverse: SemiRing {
        fn is_zero() -> bool;
        fn inv(self) -> Self;
    }
    #[derive(Clone)]
    pub struct SquareMatrix<R> {
        size: usize,
        buf: Box<[R]>,
    }
    #[allow(dead_code)]
    impl<R: SemiRing> SquareMatrix<R> {
        pub fn zero(size: usize) -> Self {
            SquareMatrix {
                size: size,
                buf: vec![R::zero(); size * size].into_boxed_slice(),
            }
        }
        pub fn identity(size: usize) -> Self {
            let mut e = Self::zero(size);
            for i in 0..size {
                e.buf[i * size + i] = R::one();
            }
            e
        }
        pub fn set_at(&mut self, x: usize, y: usize, val: R) {
            assert!(x < self.size && y < self.size);
            self.buf[x * self.size + y] = val;
        }
        pub fn get_at(&self, x: usize, y: usize) -> R {
            assert!(x < self.size && y < self.size);
            self.buf[x * self.size + y]
        }
        pub fn get_mut(&mut self, x: usize, y: usize) -> &mut R {
            assert!(x < self.size && y < self.size);
            &mut self.buf[x * self.size + y]
        }
        pub fn matadd(&self, rhs: &Self) -> Self {
            assert!(self.size == rhs.size);
            let buf: Vec<R> = self
                .buf
                .iter()
                .zip(rhs.buf.iter())
                .map(|p| *p.0 + *p.1)
                .collect();
            SquareMatrix {
                size: self.size,
                buf: buf.into_boxed_slice(),
            }
        }
        pub fn matmul(&self, rhs: &Self) -> Self {
            let size = self.size;
            assert!(size == rhs.size);
            let mut res = Self::zero(size);
            for (x, a) in res.buf.chunks_mut(size).zip(self.buf.chunks(size)) {
                for (a, b) in a.iter().zip(rhs.buf.chunks(size)) {
                    for (x, b) in x.iter_mut().zip(b.iter()) {
                        *x = *x + *a * *b;
                    }
                }
            }
            res
        }
        pub fn mat_pow(&self, mut n: usize) -> Self {
            let size = self.size;
            let mut t = Self::identity(size);
            let mut s = self.clone();
            while n > 0 {
                if n & 1 == 1 {
                    t = t.matmul(&s);
                }
                s = s.matmul(&s);
                n >>= 1;
            }
            t
        }
    }
    #[allow(dead_code)]
    impl<R: SemiRing + Sub<Output = R>> SquareMatrix<R> {
        pub fn matsub(&self, rhs: &Self) -> Self {
            assert!(self.size == rhs.size);
            let buf: Vec<R> = self
                .buf
                .iter()
                .zip(rhs.buf.iter())
                .map(|p| *p.0 - *p.1)
                .collect();
            SquareMatrix {
                size: self.size,
                buf: buf.into_boxed_slice(),
            }
        }
    }
    /*
    #[allow(dead_code)]
    impl<R: Inverse + Sub<Output = R>> SquareMatrix<R> {
        pub fn inverse(&self) -> Self {
        }
    }
    */
}
// ---------- end Matrix ----------
// ---------- begin input macro ----------
// reference: https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8
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_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_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 matrix::*;

impl SemiRing for M {
    fn zero() -> Self {
        M::zero()
    }
    fn one() -> Self {
        M::one()
    }
}

type Mat = SquareMatrix<M>;

fn run() {
    input! {
        a: (M, M, usize),
        b: (M, M, usize),
        k: usize,
    }
    let p = a.0 * a.1.inv();
    let q = b.0 * b.1.inv();
    let size = a.2 + b.2 + 1;
    let mut trans = Mat::identity(size);
    let mut mat = Mat::zero(size);
    mat.set_at(size - 1, size - 1, M::one());
    mat.set_at(0, 0, M::one());
    for src in 1..(size - 1) {
        let mut prob = M::one();
        for dst in src..size {
            mat.set_at(src, dst, prob * (M::one() - p));
            prob *= p;
        }
        *mat.get_mut(src, size - 1) += prob;
    }
    trans = trans.matmul(&mat);
    let mut mat = Mat::zero(size);
    mat.set_at(size - 1, size - 1, M::one());
    mat.set_at(0, 0, M::one());
    for src in 1..(size - 1) {
        let mut prob = M::one();
        for dst in (0..=src).rev() {
            mat.set_at(src, dst, prob * (M::one() - q));
            prob *= q;
        }
        *mat.get_mut(src, 0) += prob;
    }
    trans = trans.matmul(&mat);
    let pow = trans.mat_pow(k);
    println!("{}\n{}", pow.get_at(b.2, size - 1), pow.get_at(b.2, 0));
}

fn main() {
    run();
}
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