#690529 (Rust) No.1648 Sum of Powers

• 問題: No.1648 Sum of Powers
• ユーザー: koba-e964
• 提出日時: 2021-08-17 16:43:00
• 言語: Rust (1.77.0 + proconio)
• 結果: AC
• 実行時間: 17 ms / 2,000 ms
• コード長: 6,392 bytes
• コンパイル時間: 14,250 ms
• コンパイル使用メモリ: 383,172 KB
• 実行使用メモリ: 7,000 KB
• 最終ジャッジ日時: 2024-10-10 15:08:41
• 合計ジャッジ時間: 16,441 ms
• ジャッジサーバーID （参考情報）: judge2 / judge5

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	15 ms; 6,884 KB
testcase_01	AC	5 ms; 6,816 KB
testcase_02	AC	13 ms; 6,824 KB
testcase_03	AC	14 ms; 7,000 KB
testcase_04	AC	15 ms; 6,880 KB
testcase_05	AC	15 ms; 6,820 KB
testcase_06	AC	14 ms; 6,872 KB
testcase_07	AC	15 ms; 6,864 KB
testcase_08	AC	15 ms; 6,816 KB
testcase_09	AC	15 ms; 6,820 KB
testcase_10	AC	14 ms; 6,880 KB
testcase_11	AC	15 ms; 6,872 KB
testcase_12	AC	15 ms; 6,880 KB
testcase_13	AC	17 ms; 6,880 KB
testcase_14	AC	15 ms; 6,816 KB
testcase_15	AC	14 ms; 6,996 KB
testcase_16	AC	14 ms; 6,880 KB
testcase_17	AC	15 ms; 6,872 KB
testcase_18	AC	14 ms; 6,880 KB
testcase_19	AC	14 ms; 6,876 KB
testcase_20	AC	14 ms; 6,876 KB
testcase_21	AC	14 ms; 7,000 KB
testcase_22	AC	14 ms; 6,820 KB
testcase_23	AC	14 ms; 6,880 KB
testcase_24	AC	14 ms; 6,868 KB
testcase_25	AC	15 ms; 6,992 KB
testcase_26	AC	14 ms; 6,876 KB
testcase_27	AC	15 ms; 6,876 KB
testcase_28	AC	15 ms; 6,820 KB
testcase_29	AC	15 ms; 6,872 KB
testcase_30	AC	15 ms; 6,816 KB
testcase_31	AC	15 ms; 6,876 KB
testcase_32	AC	14 ms; 6,872 KB
testcase_33	AC	14 ms; 6,884 KB
testcase_34	AC	14 ms; 6,816 KB
testcase_35	AC	15 ms; 6,880 KB
testcase_36	AC	15 ms; 6,996 KB
testcase_37	AC	15 ms; 6,876 KB
testcase_38	AC	14 ms; 6,820 KB
testcase_39	AC	16 ms; 6,900 KB
testcase_40	AC	14 ms; 6,876 KB
testcase_41	AC	16 ms; 6,816 KB
testcase_42	AC	14 ms; 6,880 KB
testcase_43	AC	14 ms; 6,880 KB
testcase_44	AC	14 ms; 6,880 KB
testcase_45	AC	15 ms; 6,996 KB
testcase_46	AC	15 ms; 6,816 KB
testcase_47	AC	14 ms; 6,820 KB
testcase_48	AC	6 ms; 6,816 KB
testcase_49	AC	15 ms; 6,820 KB
testcase_50	AC	16 ms; 6,996 KB
testcase_51	AC	6 ms; 6,820 KB
testcase_52	AC	14 ms; 6,820 KB
testcase_53	AC	14 ms; 6,876 KB
testcase_54	AC	14 ms; 6,872 KB
testcase_55	AC	14 ms; 7,000 KB
testcase_56	AC	14 ms; 6,884 KB
testcase_57	AC	1 ms; 6,816 KB

ソースコード

use std::collections::*;
// 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, $t:ty) => ($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, 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>;

fn mul((a, b): (MInt, MInt), (x, y): (MInt, MInt), d: MInt) -> (MInt, MInt) {
    (a * x + b * y * d, a * y + b * x)
}

fn baby_step_giant_step((a, mut b): (MInt, MInt), (x, mut y): (MInt, MInt), d: MInt) -> i64 {
    if d.x == 0 {
        b = 0.into();
        y = 0.into();
    }
    const BUC: usize = 110_000;
    let inv = {
        let nrm = a * a - d * b * b;
        let ni = nrm.inv();
        (a * ni, -b * ni)
    };
    eprintln!("a = {:?}, b = {:?}, d = {:?}, inv = {:?}", a, b, d, inv);
    let mut memo = HashMap::new();
    let mut cur = (MInt::new(1), MInt::new(0));
    for i in 0..BUC {
        memo.insert(cur, i as i64);
        cur = mul(cur, inv, d);
    }
    let mut now = mul(cur, (x, y), d);
    for i in 0..BUC {
        if let Some(&idx) = memo.get(&now) {
            return (i + 1) as i64 * BUC as i64 - idx;
        }
        now = mul(now, cur, d);
    }
    panic!();
}

// Tags: baby-step-giant-step, number-theory
fn main() {
    // In order to avoid potential stack overflow, spawn a new thread.
    let stack_size = 104_857_600; // 100 MB
    let thd = std::thread::Builder::new().stack_size(stack_size);
    thd.spawn(|| solve()).unwrap().join().unwrap();
}

fn solve() {
    input!(a: i64, b: i64, p: i64, q: i64);
    assert!(a * a >= 4 * b);
    if b == 0 {
        if a == 0 {
            println!("2");
            return;
        }
        let x = baby_step_giant_step((a.into(), 0.into()), (q.into(), 0.into()), 1.into());
        println!("{}", x + 1);
        return;
    }
    let inv2 = MInt::new(2).inv();
    let d = MInt::new(a * a - 4 * b);
    let u = (MInt::new(p) * 2 - MInt::new(a * q)) * inv2 * d.inv();
    let x = baby_step_giant_step((inv2 * a, inv2), (inv2 * q, u), d);
    println!("{}", x + 1);
}