#718289 (Rust) No.1753 Don't cheat.

• 問題: No.1753 Don't cheat.
• ユーザー: koba-e964
• 提出日時: 2021-11-20 00:34:14
• 言語: Rust (1.77.0 + proconio)
• 結果: AC
• 実行時間: 226 ms / 3,000 ms
• コード長: 5,507 bytes
• コンパイル時間: 13,343 ms
• コンパイル使用メモリ: 392,380 KB
• 実行使用メモリ: 6,944 KB
• 最終ジャッジ日時: 2024-06-10 12:25:57
• 合計ジャッジ時間: 21,984 ms
• ジャッジサーバーID （参考情報）: judge1 / judge2

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	220 ms; 6,812 KB
testcase_01	AC	221 ms; 6,940 KB
testcase_02	AC	221 ms; 6,940 KB
testcase_03	AC	220 ms; 6,940 KB
testcase_04	AC	221 ms; 6,940 KB
testcase_05	AC	220 ms; 6,940 KB
testcase_06	AC	219 ms; 6,944 KB
testcase_07	AC	223 ms; 6,940 KB
testcase_08	AC	223 ms; 6,944 KB
testcase_09	AC	222 ms; 6,940 KB
testcase_10	AC	223 ms; 6,944 KB
testcase_11	AC	222 ms; 6,944 KB
testcase_12	AC	224 ms; 6,940 KB
testcase_13	AC	223 ms; 6,944 KB
testcase_14	AC	222 ms; 6,944 KB
testcase_15	AC	223 ms; 6,944 KB
testcase_16	AC	224 ms; 6,940 KB
testcase_17	AC	223 ms; 6,940 KB
testcase_18	AC	225 ms; 6,944 KB
testcase_19	AC	222 ms; 6,940 KB
testcase_20	AC	224 ms; 6,940 KB
testcase_21	AC	222 ms; 6,940 KB
testcase_22	AC	223 ms; 6,940 KB
testcase_23	AC	221 ms; 6,940 KB
testcase_24	AC	226 ms; 6,944 KB
testcase_25	AC	224 ms; 6,940 KB
testcase_26	AC	224 ms; 6,944 KB
testcase_27	AC	224 ms; 6,940 KB
testcase_28	AC	224 ms; 6,940 KB
testcase_29	AC	226 ms; 6,944 KB
testcase_30	AC	224 ms; 6,944 KB
testcase_31	AC	225 ms; 6,944 KB

ソースコード

// https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8
macro_rules! input {
    ($($r:tt)*) => {
        let stdin = std::io::stdin();
        let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock()));
        let mut next = move || -> String{
            bytes.by_ref().map(|r|r.unwrap() as char)
                .skip_while(|c|c.is_whitespace())
                .take_while(|c|!c.is_whitespace())
                .collect()
        };
        input_inner!{next, $($r)*}
    };
}

macro_rules! input_inner {
    ($next:expr) => {};
    ($next:expr,) => {};
    ($next:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };
}

macro_rules! read_value {
    ($next:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
    };
    ($next:expr, $t:ty) => ($next().parse::<$t>().expect("Parse error"));
}

/// 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> Default for ModInt<M> {
        fn default() -> Self { Self::new_internal(0) }
    }
    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> From<i64> for ModInt<M> {
        fn from(x: i64) -> Self { Self::new(x) }
    }
} // 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>;

// https://yukicoder.me/problems/no/1753 (4)
// xorsum = i であり i を含まないような列になる確率を求めたい。
// xor 畳み込みを conv と表現すると、求める確率分布は a[0] * (id + A + A conv A + ...) / asum
// である。これは a[0] / H(1 - A) のアダマール変換 (を 2^? で割ったもの) である。
fn main() {
    input! {
        n: usize,
        a: [i64; n + 1],
    }
    let s: i64 = a.iter().sum();
    let sinv = MInt::new(s).inv();
    const B: usize = 10;
    let mut tot = MInt::new(0);
    for i in 1..1 << B {
        let mut dp = vec![MInt::new(0); 1 << B];
        for j in 1..n + 1 {
            if i != j {
                dp[j] = sinv * a[j];
            }
        }
        for j in 0..B {
            for k in 0..1 << B {
                if (k & 1 << j) == 0 {
                    let x = dp[k];
                    let y = dp[k | 1 << j];
                    dp[k] = x + y;
                    dp[k | 1 << j] = x - y;
                }
            }
        }
        for j in 0..1 << B {
            dp[j] = (-dp[j] + 1).inv();
        }
        let inv2 = MInt::new(2).inv();
        for j in 0..B {
            for k in 0..1 << B {
                if (k & 1 << j) == 0 {
                    let x = dp[k];
                    let y = dp[k | 1 << j];
                    dp[k] = (x + y) * inv2;
                    dp[k | 1 << j] = (x - y) * inv2;
                }
            }
        }
        tot += dp[i] * a[0] * sinv;
    }
    println!("{}", tot);
}