結果

問題 No.1611 Minimum Multiple with Double Divisors
ユーザー koba-e964koba-e964
提出日時 2021-12-02 14:37:48
言語 Rust
(1.77.0)
結果
AC  
実行時間 967 ms / 2,000 ms
コード長 6,536 bytes
コンパイル時間 3,385 ms
コンパイル使用メモリ 163,292 KB
実行使用メモリ 4,500 KB
最終ジャッジ日時 2023-09-18 10:17:27
合計ジャッジ時間 10,654 ms
ジャッジサーバーID
（参考情報） 		judge11 / judge14
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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 967 ms
4,380 KB
testcase_01 AC 194 ms
4,380 KB
testcase_02 AC 196 ms
4,380 KB
testcase_03 AC 196 ms
4,380 KB
testcase_04 AC 195 ms
4,384 KB
testcase_05 AC 196 ms
4,380 KB
testcase_06 AC 197 ms
4,376 KB
testcase_07 AC 199 ms
4,380 KB
testcase_08 AC 197 ms
4,376 KB
testcase_09 AC 197 ms
4,384 KB
testcase_10 AC 40 ms
4,380 KB
testcase_11 AC 59 ms
4,376 KB
testcase_12 AC 60 ms
4,384 KB
testcase_13 AC 60 ms
4,380 KB
testcase_14 AC 59 ms
4,384 KB
testcase_15 AC 60 ms
4,380 KB
testcase_16 AC 59 ms
4,376 KB
testcase_17 AC 59 ms
4,380 KB
testcase_18 AC 60 ms
4,376 KB
testcase_19 AC 1 ms
4,376 KB
testcase_20 AC 2 ms
4,380 KB
testcase_21 AC 1 ms
4,500 KB
testcase_22 AC 2 ms
4,380 KB
testcase_23 AC 2 ms
4,380 KB
testcase_24 AC 1 ms
4,380 KB
testcase_25 AC 1 ms
4,376 KB
testcase_26 AC 2 ms
4,384 KB
testcase_27 AC 1 ms
4,376 KB
testcase_28 AC 1 ms
4,380 KB
testcase_29 AC 1 ms
4,380 KB
testcase_30 AC 1 ms
4,380 KB
testcase_31 AC 1 ms
4,380 KB
testcase_32 AC 1 ms
4,376 KB
testcase_33 AC 1 ms
4,376 KB
testcase_34 AC 1 ms
4,376 KB
testcase_35 AC 1 ms
4,376 KB
testcase_36 AC 1 ms
4,380 KB
testcase_37 AC 1 ms
4,380 KB
testcase_38 AC 1 ms
4,376 KB
権限があれば一括ダウンロードができます
コンパイルメッセージ
warning: unused import: `std::cmp::*`
 --> Main.rs:1:5
  |
1 | use std::cmp::*;
  |     ^^^^^^^^^^^
  |
  = note: `#[warn(unused_imports)]` on by default

warning: 1 warning emitted

ソースコード

diff # 

use std::cmp::*;
use std::io::{Write, BufWriter};
// 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"));
}

// https://judge.yosupo.jp/submission/5155
mod pollard_rho {
    /// binary gcd
    pub fn gcd(mut x: i64, mut y: i64) -> i64 {
        if y == 0 { return x; }
        if x == 0 { return y; }
        let k = (x | y).trailing_zeros();
        y >>= k;
        x >>= x.trailing_zeros();
        while y != 0 {
            y >>= y.trailing_zeros();
            if x > y { let t = x; x = y; y = t; }
            y -= x;
        }
        x << k
    }

    fn add_mod(x: i64, y: i64, n: i64) -> i64 {
        let z = x + y;
        if z >= n { z - n } else { z }
    }

    fn mul_mod(x: i64, mut y: i64, n: i64) -> i64 {
        assert!(x >= 0);
        assert!(x < n);
        let mut sum = 0;
        let mut cur = x;
        while y > 0 {
            if (y & 1) == 1 { sum = add_mod(sum, cur, n); }
            cur = add_mod(cur, cur, n);
            y >>= 1;
        }
        sum
    }

    fn mod_pow(x: i64, mut e: i64, n: i64) -> i64 {
        let mut prod = if n == 1 { 0 } else { 1 };
        let mut cur = x % n;
        while e > 0 {
            if (e & 1) == 1 { prod = mul_mod(prod, cur, n); }
            e >>= 1;
            if e > 0 { cur = mul_mod(cur, cur, n); }
        }
        prod
    }

    pub fn is_prime(n: i64) -> bool {
        if n <= 1 { return false; }
        let small = [2, 3, 5, 7, 11, 13];
        if small.iter().any(|&u| u == n) { return true; }
        if small.iter().any(|&u| n % u == 0) { return false; }
        let mut d = n - 1;
        let e = d.trailing_zeros();
        d >>= e;
        // https://miller-rabin.appspot.com/
        let a = [2, 325, 9375, 28178, 450775, 9780504, 1795265022];
        a.iter().all(|&a| {
            if a % n == 0 { return true; }
            let mut x = mod_pow(a, d, n);
            if x == 1 { return true; }
            for _ in 0..e {
                if x == n - 1 {
                    return true;
                }
                x = mul_mod(x, x, n);
                if x == 1 { return false; }
            }
            x == 1
        })
    }

    fn pollard_rho(n: i64, c: &mut i64) -> i64 {
        // An improvement with Brent's cycle detection algorithm is performed.
        // https://maths-people.anu.edu.au/~brent/pub/pub051.html
        if n % 2 == 0 { return 2; }
        loop {
            let mut x: i64; // tortoise
            let mut y = 2; // hare
            let mut d = 1;
            let cc = *c;
            let f = |i| add_mod(mul_mod(i, i, n), cc, n);
            let mut r = 1;
            // We don't perform the gcd-once-in-a-while optimization
            // because the plain gcd-every-time algorithm appears to
            // outperform, at least on judge.yosupo.jp :)
            while d == 1 {
                x = y;
                for _ in 0..r {
                    y = f(y);
                    d = gcd((x - y).abs(), n);
                    if d != 1 { break; }
                }
                r *= 2;
            }
            if d == n {
                *c += 1;
                continue;
            }
            return d;
        }
    }

    /// Outputs (p, e) in p's ascending order.
    pub fn factorize(x: i64) -> Vec<(i64, usize)> {
        if x <= 1 { return vec![]; }
        let mut hm = std::collections::HashMap::new();
        let mut pool = vec![x];
        let mut c = 1;
        while let Some(u) = pool.pop() {
            if is_prime(u) {
                *hm.entry(u).or_insert(0) += 1;
                continue;
            }
            let p = pollard_rho(u, &mut c);
            pool.push(p);
            pool.push(u / p);
        }
        let mut v: Vec<_> = hm.into_iter().collect();
        v.sort();
        v
    }
} // mod pollard_rho

fn gcd(mut x: i64, mut y: i64) -> i64 {
    while y != 0 {
        let r = x % y;
        x = y;
        y = r;
    }
    x
}

// Returns a table pr that satisfies pr[i] <=> i is prime (0 <= i < n).
// Complexity: O(n log log n)
fn is_primes_tbl(n: usize) -> Vec<bool> {
    if n <= 2 {
        return vec![false; n];
    }
    let mut pr = vec![true; n];
    pr[0] = false;
    pr[1] = false;
    for i in 2..n {
        if !pr[i] { continue; }
        for j in 2..(n - 1) / i {
            pr[i * j] = false;
        }
    }
    pr
}

// https://yukicoder.me/problems/no/1611 (2.5)
fn main() {
    let out = std::io::stdout();
    let mut out = BufWriter::new(out.lock());
    macro_rules! puts {($($format:tt)*) => (let _ = write!(out,$($format)*););}
    input! {
        t: usize,
        x: [i64; t],
    }
    const W: usize = 1000;
    let pr = is_primes_tbl(W);
    for x in x {
        let mut mi = 0;
        for i in 2..W {
            if !pr[i] { continue; }
            if x % i as i64 == 0 { continue; }
            mi = i as i64;
            break;
        }
        for i in 2..mi {
            let mut orig = 1;
            let mut added = 1;
            let g = gcd(i, x);
            let pe = pollard_rho::factorize(g);
            let mut y = x;
            let mut j = i;
            for &(p, _) in &pe {
                let mut fx = 0;
                let mut fi = 0;
                while y % p == 0 {
                    fx += 1;
                    y /= p;
                }
                while j % p == 0 {
                    fi += 1;
                    j /= p;
                }
                orig *= fx + 1;
                added *= fx + fi + 1;
            }
            if j == 1 && added == 2 * orig {
                mi = i;
                break;
            }
        }
        puts!("{}\n", x * mi);
    }
}
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