結果

問題 No.2440 Accuracy of Integer Division Approximate Functions
ユーザー 👑 MizarMizar
提出日時 2023-08-24 18:15:52
言語 Rust
(1.77.0)
結果
AC  
実行時間 8 ms / 2,000 ms
コード長 4,382 bytes
コンパイル時間 5,360 ms
コンパイル使用メモリ 147,136 KB
実行使用メモリ 4,384 KB
最終ジャッジ日時 2023-08-24 20:31:09
合計ジャッジ時間 5,795 ms
ジャッジサーバーID
（参考情報） 		judge14 / judge13
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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 1 ms
4,376 KB
testcase_01 AC 8 ms
4,376 KB
testcase_02 AC 8 ms
4,380 KB
testcase_03 AC 8 ms
4,380 KB
testcase_04 AC 8 ms
4,380 KB
testcase_05 AC 8 ms
4,376 KB
testcase_06 AC 8 ms
4,376 KB
testcase_07 AC 7 ms
4,376 KB
testcase_08 AC 7 ms
4,380 KB
testcase_09 AC 7 ms
4,380 KB
testcase_10 AC 7 ms
4,384 KB
testcase_11 AC 8 ms
4,376 KB
testcase_12 AC 8 ms
4,376 KB
testcase_13 AC 8 ms
4,380 KB
testcase_14 AC 8 ms
4,376 KB
testcase_15 AC 8 ms
4,380 KB
testcase_16 AC 5 ms
4,380 KB
testcase_17 AC 5 ms
4,376 KB
testcase_18 AC 5 ms
4,376 KB
testcase_19 AC 6 ms
4,376 KB
testcase_20 AC 5 ms
4,380 KB
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ソースコード

diff # 

// calc sum_{i=0}^{n-1} floor((ai + b) / m) (mod 2^64)
pub fn floor_sum_unsigned_mod64(n: u64, mut m: u128, a: u64, b: u64) -> u64 {
    let (mut ans, mut n, mut a, mut b) = (0u64, n as u128, a as u128, b as u128);
    // 2^64 <= max(n, m, a, b) < 2^128, a * n + b < 2^128, a < 2^64
    while (n | m | a | b) >> 64 != 0 {
        if a >= m {
            ans = ans.wrapping_add(((n * (n - 1) >> 1).wrapping_mul(a / m)) as u64);
            a %= m;
        }
        if b >= m {
            ans = ans.wrapping_add((n.wrapping_mul(b / m)) as u64);
            b %= m;
        }
        let y_max = a * n + b;
        if y_max < m {
            return ans;
        }
        (n, b, m, a) = (y_max / m, y_max % m, a, m);
    }
    let (mut n, mut m, mut a, mut b) = (n as u64, m as u64, a as u64, b as u64);
    // 2^32 <= max(n, m, a, b) < 2^64
    while (n | m | a | b) >> 32 != 0 {
        if a >= m {
            ans = ans.wrapping_add(
                ((n >> 1).wrapping_mul(if (n & 1) == 0 { n - 1 } else { n })).wrapping_mul(a / m),
            );
            a %= m;
        }
        if b >= m {
            ans = ans.wrapping_add(n.wrapping_mul(b / m));
            b %= m;
        }
        let y_max = (a as u128) * (n as u128) + (b as u128);
        if (y_max >> 64) == 0 {
            let y_max = y_max as u64;
            if y_max < m {
                return ans;
            }
            (n, b) = (y_max / m, y_max % m);
        } else {
            (n, b) = ((y_max / (m as u128)) as u64, (y_max % (m as u128)) as u64);
        }
        (m, a) = (a, m);
    }
    // max(n, m, a, b) < 2^32
    loop {
        if a >= m {
            ans = ans.wrapping_add(
                ((n >> 1).wrapping_mul(if (n & 1) == 0 { n - 1 } else { n })).wrapping_mul(a / m),
            );
            a %= m;
        }
        if b >= m {
            ans = ans.wrapping_add(n.wrapping_mul(b / m));
            b %= m;
        }
        let y_max = a * n + b;
        if y_max < m {
            return ans;
        }
        (n, b, m, a) = (y_max / m, y_max % m, a, m);
    }
}

// calc min(floor(a * 2^s / b), 2^64 - 1)
pub fn solve_div_helper(a: u64, b: u128, mut s: u32) -> u64 {
    assert!(b < (1u128 << 127));
    if b == 0 {
        return !0u64;
    }
    let (mut ans, mut a) = (0u64, a as u128);
    loop {
        let t = s.min(a.leading_zeros());
        a <<= t;
        if ans > 0 {
            if ans.leading_zeros() < t {
                return !0u64;
            }
            ans <<= t;
        }
        s -= t;
        ans = match u64::try_from(a / b).ok().and_then(|q| ans.checked_add(q)) {
            Some(ans) => ans,
            None => return !0u64,
        };
        a %= b;
        if s == 0 {
            return ans;
        }
    }
}

pub fn solve(mut n: u64, d: u64, m: u64, s: u32) -> u64 {
    use std::cmp::Ordering::*;
    assert!(n < (1u64 << 60));
    assert!(d < (1u64 << 60) && d > 0);
    assert!(m < (1u64 << 60));
    assert!(s < 121);
    let (pow2s, dm) = (1u128 << s, (d as u128) * (m as u128));
    n = n.min(solve_div_helper(d, dm.abs_diff(pow2s), s));
    match pow2s.cmp(&dm) {
        Equal => n,
        Less => n
            .wrapping_sub(floor_sum_unsigned_mod64(n + 1, pow2s, m, 0))
            .wrapping_add(floor_sum_unsigned_mod64(n + 1, d as u128, 1, 0)),
        Greater => n
            .wrapping_add(floor_sum_unsigned_mod64(n + 1, pow2s, m, 0))
            .wrapping_sub(floor_sum_unsigned_mod64(n + 1, d as u128, 1, 0)),
    }
}

fn main() {
    use std::io::prelude::*;
    let tins = std::time::Instant::now();
    let stdin = std::io::stdin();
    let stdout = std::io::stdout();
    let stdinlock = stdin.lock();
    let stdoutlock = stdout.lock();
    let mut bufwriter = std::io::BufWriter::new(stdoutlock);
    let mut lines = stdinlock.lines();
    let q = lines.next().unwrap().unwrap().parse::<usize>().unwrap();
    for _ in 0..q {
        let l = lines.next().unwrap().unwrap();
        let mut token = l.split_ascii_whitespace();
        let n = token.next().unwrap().parse::<u64>().unwrap();
        let d = token.next().unwrap().parse::<u64>().unwrap();
        let m = token.next().unwrap().parse::<u64>().unwrap();
        let s = token.next().unwrap().parse::<u32>().unwrap();
        writeln!(&mut bufwriter, "{}", solve(n, d, m, s)).unwrap();
    }
    eprintln!("{}us", tins.elapsed().as_micros());
}
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