結果

問題 No.1431 東大文系数学2020第2問改
ユーザー koba-e964koba-e964
提出日時 2021-11-01 22:37:04
言語 Rust
(1.77.0 + proconio)
結果
AC  
実行時間 1,342 ms / 5,000 ms
コード長 5,897 bytes
コンパイル時間 15,789 ms
コンパイル使用メモリ 379,460 KB
実行使用メモリ 142,592 KB
最終ジャッジ日時 2024-10-10 15:50:23
合計ジャッジ時間 24,291 ms
ジャッジサーバーID
（参考情報） 		judge1 / 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 1 ms
5,248 KB
testcase_02 AC 1 ms
5,248 KB
testcase_03 AC 644 ms
142,464 KB
testcase_04 AC 1 ms
5,248 KB
testcase_05 AC 681 ms
142,380 KB
testcase_06 AC 138 ms
142,464 KB
testcase_07 AC 137 ms
142,464 KB
testcase_08 AC 218 ms
142,464 KB
testcase_09 AC 1,342 ms
142,440 KB
testcase_10 AC 490 ms
142,464 KB
testcase_11 AC 141 ms
142,464 KB
testcase_12 AC 640 ms
142,592 KB
testcase_13 AC 289 ms
142,464 KB
testcase_14 AC 327 ms
142,592 KB
testcase_15 AC 277 ms
142,464 KB
testcase_16 AC 183 ms
142,464 KB
testcase_17 AC 144 ms
142,464 KB
testcase_18 AC 144 ms
142,464 KB
testcase_19 AC 1,324 ms
142,464 KB
testcase_20 AC 147 ms
142,464 KB
testcase_21 AC 816 ms
142,484 KB
testcase_22 AC 268 ms
65,612 KB
testcase_23 AC 1,325 ms
142,564 KB
testcase_24 AC 1,338 ms
142,336 KB
testcase_25 AC 1 ms
5,248 KB
testcase_26 AC 3 ms
5,248 KB
testcase_27 AC 1 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

diff # 

#[allow(unused_imports)]
use std::cmp::*;
#[allow(unused_imports)]
use std::collections::*;
use std::io::Read;

#[allow(dead_code)]
fn getline() -> String {
    let mut ret = String::new();
    std::io::stdin().read_line(&mut ret).ok().unwrap();
    ret
}

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;
        }
    }
}

#[allow(dead_code)]
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, 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> ::std::fmt::Debug for ModInt<M> {
        fn fmt(&self, f: &mut ::std::fmt::Formatter) -> ::std::fmt::Result {
            let (mut a, mut b, _) = red(self.x, M::m());
            if b < 0 {
                a = -a;
                b = -b;
            }
            write!(f, "{}/{}", a, b)
        }
    }
    impl<M: Mod> From<i64> for ModInt<M> {
        fn from(x: i64) -> Self { Self::new(x) }
    }
    // Finds the simplest fraction x/y congruent to r mod p.
    // The return value (x, y, z) satisfies x = y * r + z * p.
    fn red(r: i64, p: i64) -> (i64, i64, i64) {
        if r.abs() <= 10000 {
            return (r, 1, 0);
        }
        let mut nxt_r = p % r;
        let mut q = p / r;
        if 2 * nxt_r >= r {
            nxt_r -= r;
            q += 1;
        }
        if 2 * nxt_r <= -r {
            nxt_r += r;
            q -= 1;
        }
        let (x, z, y) = red(nxt_r, r);
        (x, y - q * z, z)
    }
} // mod mod_int

macro_rules! define_mod {
    ($struct_name: ident, $modulo: expr) => {
        #[derive(Copy, Clone, PartialEq, Eq, PartialOrd, Ord, Hash)]
        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>;

// Depends on MInt.rs
fn fact_init(w: usize) -> (Vec<MInt>, Vec<MInt>) {
    let mut fac = vec![MInt::new(1); w];
    let mut invfac = vec![0.into(); w];
    for i in 1..w {
        fac[i] = fac[i - 1] * i as i64;
    }
    invfac[w - 1] = fac[w - 1].inv();
    for i in (0..w - 1).rev() {
        invfac[i] = invfac[i + 1] * (i as i64 + 1);
    }
    (fac, invfac)
}

fn main() {
    let n: usize = get();
    let m: usize = get();
    let k: usize = get();
    let k = 2 * n - k;
    let (fac, invfac) = fact_init(n * max(2, n) + 2);
    // \sum_{i + j = k} C(n, i) C(n, j) C(i, x) C(j, y) = C(2n-x-y, k-x-y)C(n,x)C(n,y)
    let mut tot = MInt::new(0);
    for x in 0..min(n, k) + 1 {
        for y in 0..min(n, k - x) + 1 {
            if x * y >= m {
                let tmp = fac[x * y] * invfac[m] * invfac[x * y - m]
                    * fac[2 * n - x - y] * invfac[k - x - y] * invfac[2 * n - k]
                    * fac[n] * invfac[n - x] * invfac[x]
                    * fac[n] * invfac[n - y] * invfac[y];
                if (x + y + k) % 2 == 0 {
                    tot += tmp;
                } else {
                    tot -= tmp;
                }
            }
        }
    }
    println!("{}", tot);
}
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