サイクルソートを使用する

サイクルソート (cycle sort) は、各要素が整列後に置かれる位置を数え、その位置へ1要素ずつ書き込むサイクル(循環)を繰り返して配列を整える。

隣同士の交換を何度も行うバブルソートと異なり、書き込み回数を抑えたい場面(書き込みが読み取りより高コストなメディアなど)で理論的に注目される。

  1. サイクルの開始: 未処理の左端を start とする。そこにある値を item として保持する。
  2. 目標位置の計算: start より右側で item より小さい要素の個数を数え、start に足した位置を pos(書き込み先)とする。pos == start ならその要素はすでに正しい位置にあるので次へ進む。
  3. 1回目の書き込み: A[pos]item を入れ替える。item には追い出された値が入る。
  4. サイクルの継続: 追い出された item について手順2〜3を繰り返し、pos が再び start に戻るまで続ける。1サイクルで start の位置は確定する。
  5. 繰り返し: start を1つ進め、配列末尾の手前まで繰り返す。
procedure cycle_sort(A)
  n = length(A)
  for start from 0 to n - 2
    item = A[start]
    pos = start
    for i from start + 1 to n - 1
      if A[i] < item then
        pos = pos + 1
    if pos = start then
      continue
    while pos < n and A[pos] = item do
      pos = pos + 1
    swap(A[pos], item)
    while pos ≠ start
      pos = start
      for i from start + 1 to n - 1
        if A[i] < item then
          pos = pos + 1
      while pos < n and A[pos] = item do
        pos = pos + 1
      swap(A[pos], item)

等しい値が複数あるときは while A[pos] = item同値の衝突 を避け、同じ位置へ書き込まないようにする。 書き込み回数を抑えたい場面向けで、最悪計算量 O(n²) となり、インプレースだが一般に不安定である。

類似アルゴリズムとの相違点

バブルソートは隣接交換を繰り返す。サイクルソートは置換で各要素を最終位置へ直接送り、書き込み回数を抑えられる。

計算時間量および空間計算量を計測する

Size Average time Maximum time Average memory Maximum memory
256 0.000014 0.000206 1662 1668
512 0.000060 0.000514 1665 1672
1024 0.000227 0.000730 1674 1680
2048 0.000898 0.001239 1690 1696
4096 0.003498 0.006040 1721 1728
8192 0.014015 0.024486 1786 1792
16384 0.055415 0.317743 1918 1924
32768 0.226216 0.496424 2178 2184
計測に使用したコードを表示する

set -euo pipefail

WORKDIR="$(mktemp -d)"
trap 'rm -rf "$WORKDIR"' EXIT

cat > "$WORKDIR/Dockerfile" <<'EOF'
FROM rust:1.95.0

WORKDIR /app

RUN mkdir -p src

RUN cat > Cargo.toml <<'CARGO'
[package]
name = "rust-benchmark"
version = "0.1.0"
edition = "2021"

[profile.release]
lto = true
codegen-units = 1
panic = "abort"
CARGO

RUN cat > src/main.rs <<'RUST'
use std::{
    env,
    process::Command,
    time::{Duration, Instant},
};
const MIN_POWER: u32 = 8;
const MAX_POWER: u32 = 15;
const RUNS: usize = 8192;


fn cycle_sort(a: &mut [usize]) {
    let n = a.len();
    for cycle_start in 0..n.saturating_sub(1) {
        let mut item = a[cycle_start];
        let mut pos = cycle_start;
        for i in cycle_start + 1..n {
            if a[i] < item {
                pos += 1;
            }
        }
        if pos == cycle_start {
            continue;
        }
        while pos < n && a[pos] == item {
            pos += 1;
        }
        std::mem::swap(&mut a[pos], &mut item);
        while pos != cycle_start {
            pos = cycle_start;
            for i in cycle_start + 1..n {
                if a[i] < item {
                    pos += 1;
                }
            }
            while pos < n && a[pos] == item {
                pos += 1;
            }
            std::mem::swap(&mut a[pos], &mut item);
        }
    }
}


fn benchmark_sort(array: &mut [usize]) {

    cycle_sort(array);

}

fn is_non_decreasing(a: &[usize]) -> bool {
    a.windows(2).all(|w| w[0] <= w[1])
}

fn same_multiset(a: &[usize], b: &[usize]) -> bool {
    if a.len() != b.len() {
        return false;
    }

    let mut left = a.to_vec();
    let mut right = b.to_vec();
    left.sort_unstable();
    right.sort_unstable();
    left == right
}

fn check_correctness_case(label: &str, mut input: Vec<usize>) {
    let original = input.clone();

    benchmark_sort(&mut input);

    if !is_non_decreasing(&input) {
        panic!("correctness case {}: output is not sorted", label);
    }

    if !same_multiset(&input, &original) {
        panic!("correctness case {}: elements were lost or added", label);
    }
}

fn few_unique_values(size: usize, unique: usize, seed: u64) -> Vec<usize> {
    let mut state = seed;

    (0..size)
        .map(|_| {
            state ^= state << 13;
            state ^= state >> 7;
            state ^= state << 17;
            (state as usize % unique) + 1
        })
        .collect()
}

fn run_correctness_checks() {
    check_correctness_case("empty", vec![]);
    check_correctness_case("single", vec![42]);
    check_correctness_case("duplicates", vec![3, 1, 3, 2, 1, 2]);
    check_correctness_case("sorted", vec![1, 2, 3, 4, 5]);
    check_correctness_case("reverse", vec![5, 4, 3, 2, 1]);
    check_correctness_case("all_equal", vec![7, 7, 7, 7]);
    check_correctness_case("skewed_range", vec![1_000_000, 2, 1_000_001, 1, 999_999]);
    // Static-buffer Grail skips the in-buffer build when key collection is sparse
    // (ideal_buffer = false). Exercising that path catches regressions in buffer gating.
    check_correctness_case(
        "few_keys_len16",
        vec![2, 2, 2, 2, 2, 2, 2, 2, 4, 3, 1, 2, 3, 4, 1, 4],
    );
    for seed in 0..32 {
        check_correctness_case(
            &format!("few_keys_len32_seed_{seed}"),
            few_unique_values(32, 4, seed),
        );
    }
}


fn shuffled(size: usize, seed: u64) -> Vec<usize> {
    let mut v: Vec<usize> = (1..=size).collect();

    let mut state = seed;

    for i in (1..size).rev() {
        state ^= state << 13;
        state ^= state >> 7;
        state ^= state << 17;

        let j = (state as usize) % (i + 1);

        v.swap(i, j);
    }

    v
}

fn memory_usage_kb() -> usize {
    // VmHWM (peak RSS, KiB). Reported memory subtracts a per-size baseline that only
    // holds the input array, so the table reflects auxiliary space during sorting.
    let contents = std::fs::read_to_string("/proc/self/status")
        .unwrap_or_default();

    for line in contents.lines() {
        if let Some(rest) = line.strip_prefix("VmHWM:") {
            let kb = rest
                .split_whitespace()
                .next()
                .unwrap_or("0")
                .parse::<usize>()
                .unwrap_or(0);

            return kb;
        }
    }

    0
}

fn micros(d: Duration) -> u128 {
    d.as_micros()
}

fn input_array(size: usize, seed: u64) -> Vec<usize> {
    shuffled(size, seed)
}

fn run_baseline(size: usize) -> usize {
    let _hold = input_array(size, 1);
    memory_usage_kb()
}

fn run_once(size: usize, seed: usize) -> (u128, usize) {
    let mut array = input_array(size, seed as u64);

    let start = Instant::now();

    benchmark_sort(&mut array);

    let elapsed = start.elapsed();
    let mem = memory_usage_kb();

    let expected: Vec<usize> = (1..=size).collect();
    if array != expected {
        panic!(
            "sort failed with seed {} for size {}",
            seed,
            size
        );
    }

    (micros(elapsed), mem)
}

fn run_baseline_child(args: &[String]) {
    let size = args[2].parse::<usize>().expect("invalid size");
    let mem = run_baseline(size);
    println!("{}", mem);
}

fn run_child(args: &[String]) {
    let size = args[2].parse::<usize>().expect("invalid size");
    let seed = args[3].parse::<usize>().expect("invalid seed");
    let (elapsed_us, mem) = run_once(size, seed);
    println!("{} {}", elapsed_us, mem);
}

fn main() {
    let args: Vec<String> = env::args().collect();
    if args.get(1).is_some_and(|arg| arg == "--baseline-once") {
        run_baseline_child(&args);
        return;
    }
    if args.get(1).is_some_and(|arg| arg == "--run-once") {
        run_child(&args);
        return;
    }

    run_correctness_checks();

    println!(
        "| {:>10} | {:>15} | {:>15} | {:>15} | {:>15} |",
        "Size",
        "Average time",
        "Maximum time",
        "Average memory",
        "Maximum memory"
    );

    println!(
        "|{:-<11}:|{:-<16}:|{:-<16}:|{:-<16}:|{:-<16}:|",
        "",
        "",
        "",
        "",
        ""
    );

    for power in MIN_POWER..=MAX_POWER {
        let size = 1usize << power;

        let baseline_output = Command::new(env::current_exe().expect("failed to find current executable"))
            .arg("--baseline-once")
            .arg(size.to_string())
            .output()
            .expect("failed to run benchmark baseline process");

        if !baseline_output.status.success() {
            panic!(
                "benchmark baseline process failed: {}",
                String::from_utf8_lossy(&baseline_output.stderr)
            );
        }

        let baseline_stdout = String::from_utf8(baseline_output.stdout)
            .expect("baseline process returned non-UTF-8 output");
        let baseline_mem = baseline_stdout
            .split_whitespace()
            .next()
            .expect("missing baseline memory usage")
            .parse::<usize>()
            .expect("invalid baseline memory usage");

        let mut total_time: u128 = 0;
        let mut max_time: u128 = 0;

        let mut total_mem: usize = 0;
        let mut max_mem: usize = 0;

        for seed in 1..=RUNS {
            let output = Command::new(env::current_exe().expect("failed to find current executable"))
                .arg("--run-once")
                .arg(size.to_string())
                .arg(seed.to_string())
                .output()
                .expect("failed to run benchmark child process");

            if !output.status.success() {
                panic!(
                    "benchmark child process failed: {}",
                    String::from_utf8_lossy(&output.stderr)
                );
            }

            let stdout = String::from_utf8(output.stdout)
                .expect("child process returned non-UTF-8 output");
            let mut fields = stdout.split_whitespace();
            let elapsed_us = fields
                .next()
                .expect("missing elapsed time")
                .parse::<u128>()
                .expect("invalid elapsed time");
            let mem = fields
                .next()
                .expect("missing memory usage")
                .parse::<usize>()
                .expect("invalid memory usage");

            total_time += elapsed_us;

            if elapsed_us > max_time {
                max_time = elapsed_us;
            }

            let aux_mem = mem.saturating_sub(baseline_mem);

            total_mem += aux_mem;

            if aux_mem > max_mem {
                max_mem = aux_mem;
            }
        }

        let avg_time = total_time / RUNS as u128;
        let avg_mem = total_mem / RUNS;

        println!(
            "| {:>10} | {:>15} | {:>15} | {:>15} | {:>15} |",
            size,
            format!("{}.{:06}", avg_time / 1_000_000, avg_time % 1_000_000),
            format!("{}.{:06}", max_time / 1_000_000, max_time % 1_000_000),
            avg_mem,
            max_mem
        );
    }
}
RUST

RUN cargo build --release

CMD ["./target/release/rust-benchmark"]
EOF

docker build -t rust-benchmark "$WORKDIR"
docker run --rm --init rust-benchmark