#363123 (Rust) No.854 公平なりんご分配

• 問題: No.854 公平なりんご分配
• ユーザー: koba-e964
• 提出日時: 2019-07-27 01:33:06
• 言語: Rust (1.77.0 + proconio)
• 結果: AC
• 実行時間: 1,883 ms / 3,153 ms
• コード長: 6,909 bytes
• コンパイル時間: 18,053 ms
• コンパイル使用メモリ: 378,888 KB
• 実行使用メモリ: 123,972 KB
• 最終ジャッジ日時: 2024-07-02 10:24:29
• 合計ジャッジ時間: 31,232 ms
• ジャッジサーバーID （参考情報）: judge2 / judge4

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	1 ms; 5,376 KB
testcase_04	AC	1 ms; 5,376 KB
testcase_05	AC	1 ms; 5,376 KB
testcase_06	AC	1 ms; 5,376 KB
testcase_07	AC	1 ms; 5,376 KB
testcase_08	AC	1 ms; 5,376 KB
testcase_09	AC	1 ms; 5,376 KB
testcase_10	AC	1 ms; 5,376 KB
testcase_11	AC	1 ms; 5,376 KB
testcase_12	AC	2 ms; 5,376 KB
testcase_13	AC	2 ms; 5,376 KB
testcase_14	AC	1 ms; 5,376 KB
testcase_15	AC	1 ms; 5,376 KB
testcase_16	AC	1 ms; 5,376 KB
testcase_17	AC	1 ms; 5,376 KB
testcase_18	AC	1 ms; 5,376 KB
testcase_19	AC	1 ms; 5,376 KB
testcase_20	AC	1 ms; 5,376 KB
testcase_21	AC	1 ms; 5,376 KB
testcase_22	AC	4 ms; 5,376 KB
testcase_23	AC	3 ms; 5,376 KB
testcase_24	AC	5 ms; 5,376 KB
testcase_25	AC	3 ms; 5,376 KB
testcase_26	AC	6 ms; 5,376 KB
testcase_27	AC	5 ms; 5,376 KB
testcase_28	AC	4 ms; 5,376 KB
testcase_29	AC	2 ms; 5,376 KB
testcase_30	AC	3 ms; 5,376 KB
testcase_31	AC	6 ms; 5,376 KB
testcase_32	AC	55 ms; 27,392 KB
testcase_33	AC	62 ms; 15,744 KB
testcase_34	AC	113 ms; 37,120 KB
testcase_35	AC	78 ms; 29,696 KB
testcase_36	AC	58 ms; 5,376 KB
testcase_37	AC	50 ms; 25,984 KB
testcase_38	AC	39 ms; 21,504 KB
testcase_39	AC	170 ms; 39,552 KB
testcase_40	AC	72 ms; 13,824 KB
testcase_41	AC	82 ms; 24,156 KB
testcase_42	AC	97 ms; 36,436 KB
testcase_43	AC	121 ms; 25,344 KB
testcase_44	AC	124 ms; 34,048 KB
testcase_45	AC	129 ms; 8,960 KB
testcase_46	AC	160 ms; 33,792 KB
testcase_47	AC	60 ms; 19,584 KB
testcase_48	AC	89 ms; 35,900 KB
testcase_49	AC	92 ms; 36,736 KB
testcase_50	AC	52 ms; 25,600 KB
testcase_51	AC	160 ms; 35,456 KB
testcase_52	AC	135 ms; 16,896 KB
testcase_53	AC	75 ms; 16,256 KB
testcase_54	AC	133 ms; 19,584 KB
testcase_55	AC	48 ms; 16,256 KB
testcase_56	AC	37 ms; 17,024 KB
testcase_57	AC	67 ms; 14,208 KB
testcase_58	AC	124 ms; 7,552 KB
testcase_59	AC	35 ms; 12,544 KB
testcase_60	AC	91 ms; 14,336 KB
testcase_61	AC	48 ms; 5,376 KB
testcase_62	AC	102 ms; 12,544 KB
testcase_63	AC	92 ms; 13,184 KB
testcase_64	AC	30 ms; 6,400 KB
testcase_65	AC	71 ms; 32,128 KB
testcase_66	AC	61 ms; 9,856 KB
testcase_67	AC	112 ms; 21,632 KB
testcase_68	AC	117 ms; 10,752 KB
testcase_69	AC	66 ms; 39,168 KB
testcase_70	AC	41 ms; 13,824 KB
testcase_71	AC	49 ms; 14,976 KB
testcase_72	AC	82 ms; 5,376 KB
testcase_73	AC	66 ms; 26,240 KB
testcase_74	AC	135 ms; 31,872 KB
testcase_75	AC	71 ms; 15,232 KB
testcase_76	AC	125 ms; 25,344 KB
testcase_77	AC	116 ms; 35,840 KB
testcase_78	AC	132 ms; 11,776 KB
testcase_79	AC	133 ms; 22,400 KB
testcase_80	AC	122 ms; 23,424 KB
testcase_81	AC	95 ms; 24,192 KB
testcase_82	AC	1,781 ms; 123,776 KB
testcase_83	AC	618 ms; 123,904 KB
testcase_84	AC	1,883 ms; 123,776 KB
testcase_85	AC	462 ms; 123,776 KB
testcase_86	AC	320 ms; 123,852 KB
testcase_87	AC	665 ms; 123,904 KB
testcase_88	AC	657 ms; 123,972 KB
testcase_89	AC	662 ms; 123,904 KB
testcase_90	AC	666 ms; 123,904 KB
testcase_91	AC	662 ms; 123,904 KB
testcase_92	AC	679 ms; 123,904 KB
testcase_93	AC	674 ms; 123,904 KB

ソースコード

#[allow(unused_imports)]
use std::cmp::*;
#[allow(unused_imports)]
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),* )) => {
        ( $(read_value!($next, $t)),* )
    };

    ($next:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
    };

    ($next:expr, chars) => {
        read_value!($next, String).chars().collect::<Vec<char>>()
    };

    ($next:expr, usize1) => {
        read_value!($next, usize) - 1
    };

    ($next:expr, [ $t:tt ]) => {{
        let len = read_value!($next, usize);
        (0..len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
    }};

    ($next:expr, $t:ty) => {
        $next().parse::<$t>().expect("Parse error")
    };
}

mod pollard_rho {
    use std::collections::HashMap;
    /// binary gcd
    pub fn gcd(mut x: i64, mut y: i64) -> i64 {
        if y == 0 { return x; }
        if x == 0 { return y; }
        let mut sh = 0;
        while ((x | y) & 1) == 0 {
            x >>= 1; y >>= 1; sh += 1;
        }
        while (x & 1) == 0 { x >>= 1; }
        while y != 0 {
            while (y & 1) == 0 { y >>= 1; }
            if x > y { let t = x; x = y; y = t; }
            y -= x;
        }
        x << sh
    }

    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);
            }
            cur = mul_mod(cur, cur, n);
            e >>= 1;
        }
        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 mut e = 0;
        while (d & 1) == 0 {
            d >>= 1;
            e += 1;
        }
        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 {
        if n % 2 == 0 { return 2; }
        loop {
            let mut x: i64 = 2;
            let mut y = 2;
            let mut d = 1;
            let cc = *c;
            let f = |i| add_mod(mul_mod(i, i, n), cc, n);
            while d == 1 {
                x = f(x);
                y = f(f(y));
                d = gcd((x - y).abs(), n);
            }
            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::new();
        }
        let mut hm = 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 solve() {
    let out = std::io::stdout();
    let mut out = BufWriter::new(out.lock());
    macro_rules! puts {
        ($($format:tt)*) => (write!(out,$($format)*).unwrap());
    }
    input! {
        n: usize,
        a: [i32; n],
        plr: [(i64, usize1, usize)],
    }
    const W: usize = 2001;
    let mut fac = vec![0; W];
    for i in 2..W {
        fac[i] = i;
    }
    for i in 2..W {
        if fac[i] != i { continue; }
        for j in 2..(W - 1) / i + 1 {
            fac[i * j] = i;
        }
    }
    let primes: Vec<_> = (2..W).filter(|&i| fac[i] == i).collect();
    let m = primes.len();
    let mut inv = vec![0; W];
    for i in 0..m {
        inv[primes[i]] = i;
    }
    let mut acc = vec![vec![0i32; n + 1]; m];
    let mut zero = vec![0i32; n + 1];
    for i in 0..n {
        for j in 0..m {
            acc[j][i + 1] = acc[j][i];
        }
        zero[i + 1] = zero[i];
        if a[i] == 0 {
            zero[i + 1] += 1;
            continue;
        }
        let mut v = a[i];
        while v > 1 {
            let p = fac[v as usize];
            v /= p as i32;
            let idx = inv[p];
            acc[idx][i + 1] += 1;
        }
    }
    for &(p, l, r) in &plr {
        let res = pollard_rho::factorize(p);
        // eprintln!("p = {}, res = {:?}", p, res);
        let mut ans = true;
        if zero[r] == zero[l] {
            for &(p, e) in &res {
                if p >= W as i64 {
                    ans = false;
                    break;
                }
                let idx = inv[p as usize];
                let diff = acc[idx][r] - acc[idx][l];
                if diff < e as i32 {
                    ans = false;
                    break;
                }
            }
        }
        puts!("{}\n", if ans { "Yes" } else { "NO" });
    }
}

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();
}