#885210 (Rust) No.2390 Udon Coupon (Hard)

• 問題: No.2390 Udon Coupon (Hard)
• ユーザー: 👑 Mizar
• 提出日時: 2023-06-28 15:35:35
• 言語: Rust (1.77.0)
• 結果: AC
• 実行時間: 27 ms / 2,000 ms
• コード長: 2,728 bytes
• コンパイル時間: 712 ms
• コンパイル使用メモリ: 161,152 KB
• 実行使用メモリ: 5,376 KB
• 最終ジャッジ日時: 2024-04-15 20:44:19
• 合計ジャッジ時間: 2,568 ms
• ジャッジサーバーID （参考情報）: judge3 / judge1

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; 5,376 KB
testcase_02	AC	1 ms; 5,376 KB
testcase_03	AC	1 ms; 5,376 KB
testcase_04	AC	1 ms; 5,376 KB
testcase_05	AC	2 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	20 ms; 5,376 KB
testcase_10	AC	1 ms; 5,376 KB
testcase_11	AC	1 ms; 5,376 KB
testcase_12	AC	1 ms; 5,376 KB
testcase_13	AC	1 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	1 ms; 5,376 KB
testcase_23	AC	1 ms; 5,376 KB
testcase_24	AC	6 ms; 5,376 KB
testcase_25	AC	7 ms; 5,376 KB
testcase_26	AC	7 ms; 5,376 KB
testcase_27	AC	7 ms; 5,376 KB
testcase_28	AC	6 ms; 5,376 KB
testcase_29	AC	16 ms; 5,376 KB
testcase_30	AC	14 ms; 5,376 KB
testcase_31	AC	15 ms; 5,376 KB
testcase_32	AC	15 ms; 5,376 KB
testcase_33	AC	15 ms; 5,376 KB
testcase_34	AC	27 ms; 5,376 KB
testcase_35	AC	26 ms; 5,376 KB
testcase_36	AC	25 ms; 5,376 KB
testcase_37	AC	26 ms; 5,376 KB
testcase_38	AC	26 ms; 5,376 KB
testcase_39	AC	8 ms; 5,376 KB
testcase_40	AC	7 ms; 5,376 KB
testcase_41	AC	7 ms; 5,376 KB
testcase_42	AC	7 ms; 5,376 KB
testcase_43	AC	9 ms; 5,376 KB
testcase_44	AC	6 ms; 5,376 KB
testcase_45	AC	4 ms; 5,376 KB
testcase_46	AC	3 ms; 5,376 KB
testcase_47	AC	4 ms; 5,376 KB
testcase_48	AC	7 ms; 5,376 KB
testcase_49	AC	1 ms; 5,376 KB

ソースコード

// O((A_max)^2)解法
// 入力制約: 0 <= n <= 10^13, 0 < a_i <= 10^5, 0 < b_i, b_max * floor(n / a_min) <= 2^61
fn solve(n: u64, ab: [(u64, u64); 3]) -> u64 {
    let (a_min, a_max, b_min, b_max) = ab.iter().fold((!0u64, 0u64, !0u64, 0u64), |(a_min, a_max, b_min, b_max), &(a, b)| (a.min(a_min), a.max(a_max), b.min(b_min), b.max(b_max)));
    assert!(n <= 10_0000_0000_0000);
    assert!(a_min > 0 && a_max <= 100000 && b_min > 0 && b_max.saturating_mul(n / a_min) <= (1u64 << 61));
    let co_solve = |n: u64, ab: [(u64, u64); 3]| -> u64 {
        let [(ap, bp), (aq, bq), (ar, br)] = ab;
        // a_p_inv = ceil(2^63 / a_p) = floor((2^63 - 1) / a_p) + 1
        let apinv = ((1u64 << 63) - 1) / ap + 1;
        let (imax, jmax) = (ap * bq, ap * br);
        let (mut r, mut ibq, mut di) = (0, 0, n);
        while ibq < imax {
        	let (mut jbr, mut dj) = (0, di);
            while jbr < jmax {
                // 準定数を除数とする除算の定数倍高速化
                // 0 < a_p <= 10^5, 0 <= d_j <= n <= 10^13 < 2^63/10^5 <= 2^63 / a_p <= ceil(2^63 / a_p) = a_p_inv < ((2^63 / a_p) + 1)
                // quot = floor((n - (i * a_q + j * a_r)) / a_p) = floor(d / a_p) = floor((d * 2) * ceil(2^63 / a_p) / 2^64) - (0 または 1)
                let qsim = ((((dj * 2) as u128) * (apinv as u128)) >> 64) as u64;
                let quot = qsim - u64::from(qsim * ap > dj);
                debug_assert_eq!(dj / ap, quot);
                r.chmax(quot * bp + ibq + jbr);
				if let Some(d) = dj.checked_sub(ar) {
					dj = d;
					jbr += br;
				} else {
					break;
				}
            }
            if let Some(d) = di.checked_sub(aq) {
            	di = d;
	        	ibq += bq;
            } else {
            	break;
            }
        }
        r
    };
    co_solve(n, [ab[0], ab[1], ab[2]])
    .max(co_solve(n, [ab[1], ab[2], ab[0]]))
    .max(co_solve(n, [ab[2], ab[0], ab[1]]))
}

fn main() {
    let mut stdinlock = std::io::stdin().lock();
    let mut lines = std::io::BufRead::lines(&mut stdinlock).map_while(Result::ok);
	let n = lines.next().unwrap().parse::<u64>().unwrap();
	let ab = (0..3).map(|_| {
		let s = lines.next().unwrap();
		let mut t = s.split_whitespace();
		(
            t.next().unwrap().parse::<u64>().unwrap(),
            t.next().unwrap().parse::<u64>().unwrap(),
		)
	}).collect::<Vec<_>>();
    println!("{}", solve(n, [ab[0], ab[1], ab[2]]));
}

trait Change {
    fn chmax(&mut self, x: Self);
    fn chmin(&mut self, x: Self);
}
impl<T: PartialOrd> Change for T {
    fn chmax(&mut self, x: T) {
        if *self < x {
            *self = x;
        }
    }
    fn chmin(&mut self, x: T) {
        if *self > x {
            *self = x;
        }
    }
}