#896697 (Rust) No.2074 Product is Square ?

• 問題: No.2074 Product is Square ?
• ユーザー: koba-e964
• 提出日時: 2023-07-30 02:25:03
• 言語: Rust (1.77.0 + proconio)
• 結果: AC
• 実行時間: 204 ms / 2,000 ms
• コード長: 6,132 bytes
• コンパイル時間: 21,080 ms
• コンパイル使用メモリ: 389,108 KB
• 実行使用メモリ: 5,248 KB
• 最終ジャッジ日時: 2024-10-08 15:18:22
• 合計ジャッジ時間: 24,274 ms
• ジャッジサーバーID （参考情報）: judge4 / judge2

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	2 ms; 5,248 KB
testcase_02	AC	2 ms; 5,248 KB
testcase_03	AC	2 ms; 5,248 KB
testcase_04	AC	3 ms; 5,248 KB
testcase_05	AC	2 ms; 5,248 KB
testcase_06	AC	2 ms; 5,248 KB
testcase_07	AC	2 ms; 5,248 KB
testcase_08	AC	2 ms; 5,248 KB
testcase_09	AC	3 ms; 5,248 KB
testcase_10	AC	2 ms; 5,248 KB
testcase_11	AC	63 ms; 5,248 KB
testcase_12	AC	63 ms; 5,248 KB
testcase_13	AC	200 ms; 5,248 KB
testcase_14	AC	68 ms; 5,248 KB
testcase_15	AC	63 ms; 5,248 KB
testcase_16	AC	64 ms; 5,248 KB
testcase_17	AC	203 ms; 5,248 KB
testcase_18	AC	68 ms; 5,248 KB
testcase_19	AC	63 ms; 5,248 KB
testcase_20	AC	63 ms; 5,248 KB
testcase_21	AC	202 ms; 5,248 KB
testcase_22	AC	72 ms; 5,248 KB
testcase_23	AC	67 ms; 5,248 KB
testcase_24	AC	62 ms; 5,248 KB
testcase_25	AC	202 ms; 5,248 KB
testcase_26	AC	70 ms; 5,248 KB
testcase_27	AC	64 ms; 5,248 KB
testcase_28	AC	63 ms; 5,248 KB
testcase_29	AC	204 ms; 5,248 KB
testcase_30	AC	71 ms; 5,248 KB
testcase_31	AC	1 ms; 5,248 KB
testcase_32	AC	1 ms; 5,248 KB
testcase_33	AC	1 ms; 5,248 KB

コンパイルメッセージ

warning: unused import: `std::collections::*`
 --> src/main.rs:1:5
  |
1 | use std::collections::*;
  |     ^^^^^^^^^^^^^^^^^^^
  |
  = note: `#[warn(unused_imports)]` on by default

warning: function `add_mod` is never used
  --> src/main.rs:55:8
   |
55 |     fn add_mod(x: i64, y: i64, n: i64) -> i64 {
   |        ^^^^^^^
   |
   = note: `#[warn(dead_code)]` on by default

warning: function `mul_mod` is never used
  --> src/main.rs:60:8
   |
60 |     fn mul_mod(x: i64, mut y: i64, n: i64) -> i64 {
   |        ^^^^^^^

warning: function `mod_pow` is never used
  --> src/main.rs:73:8
   |
73 |     fn mod_pow(x: i64, mut e: i64, n: i64) -> i64 {
   |        ^^^^^^^

warning: function `is_prime` is never used
  --> src/main.rs:84:12
   |
84 |     pub fn is_prime(n: i64) -> bool {
   |            ^^^^^^^^

warning: function `pollard_rho` is never used
   --> src/main.rs:109:8
    |
109 |     fn pollard_rho(n: i64, c: &mut i64) -> i64 {
    |        ^^^^^^^^^^^

warning: function `factorize` is never used
   --> src/main.rs:141:12
    |
141 |     pub fn factorize(x: i64) -> Vec<(i64, usize)> {
    |            ^^^^^^^^^

ソースコード

use std::collections::*;
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, [ $t:tt ]) => {{
        let len = read_value!($next, usize);
        read_value!($next, [$t; len])
    }};
    ($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 nth(a: i64, n: i64) -> i64 {
    let mut pass = 0;
    let mut fail = std::cmp::min(a, 1 << ((60 + n - 1) / n)) + 1;
    while fail - pass > 1 {
        let mid = (fail + pass) / 2;
        let mut tmp = 1i64;
        for _ in 0..n {
            tmp = tmp.saturating_mul(mid);
        }
        if tmp <= a {
            pass = mid;
        } else {
            fail = mid;
        }
    }
    pass
}

fn is_sq(a: i64) -> bool {
    let s = nth(a, 2);
    s * s == a
}

fn main() {
    let out = std::io::stdout();
    let mut out = BufWriter::new(out.lock());
    macro_rules! puts {($($format:tt)*) => (let _ = write!(out,$($format)*););}
    input! {
        n: usize,
        a: [[i64]; n],
    }
    for mut a in a {
        let n = a.len();
        loop {
            let mut changed = false;
            for i in 0..n {
                for j in 0..i {
                    let g = pollard_rho::gcd(a[i], a[j]);
                    if g != 1 {
                        a[i] /= g;
                        a[j] /= g;
                        changed = true;
                    }
                }
            }
            if !changed {
                break;
            }
        }
        puts!("{}\n", if a.into_iter().all(is_sq) {
            "Yes"
        } else {
            "No"
        });
    }
}