ノームソートを使用する

ノームソート (gnome sort / stupid sort) は、現在位置から隣との大小関係を見ながら前後へ動き、昇順になるまで繰り返す。

庭のノームが植木鉢を整える様子になぞらえて名付けられたとされている。

処理の状態は現在位置 pos(しばしば「ノームの足元」などと呼ぶ)だけでよいことから、状態機械として読みやすく、コードも短く書けるという利点がある。

  1. pos = 0 から始める。配列の左端から眺めていく。
  2. pos == 0 または A[pos] >= A[pos - 1] のとき:いま見ている並びがローカルに問題ないので1ステップ進み、pos += 1 とする。
  3. それ以外:隣との順序が逆なので隣どうしを交換し、pos -= 1 してひとつ戻って再チェックする(より左側とも整合させる)。
  4. pos == n になるまで繰り返す。
procedure gnome_sort(A)
  pos = 0
  while pos < length(A)
    if pos = 0 or A[pos] >= A[pos - 1] then
      pos = pos + 1
    else
      swap(A[pos], A[pos - 1])
      pos = pos - 1

整列済みなら O(n)、逆順に近いと O(n²) になり、安定ソートである。

類似アルゴリズムとの相違点

シャトルソートは走査ごとに整列済み接頭辞を広げる。ノームソートは単一の位置を前後に動かすだけで、不整合が見つかるたびにその場で直す。

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 0.000027 0.000066 62 68
512 0.000099 0.000151 62 68
1024 0.000375 0.000482 58 64
2048 0.001320 0.001751 66 72
4096 0.004183 0.006520 62 68
8192 0.013232 0.024517 62 68
16384 0.049299 0.085966 61 68
32768 0.181072 0.266576 62 68
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 gnome_sort(a: &mut [usize]) {
    let mut i = 1;
    while i < a.len() {
        if i == 0 || a[i - 1] <= a[i] {
            i += 1;
        } else {
            a.swap(i - 1, i);
            i -= 1;
        }
    }
}


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

    gnome_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