シャトルソートで配列を並び替える
シャトルソートを使用する
シャトルソート (shuttle sort) は、各走査で新しい位置の要素を左方向へ隣接交換で運びながら、先頭側の整列済み区間をひとつずつ広げていく。
値が左へ「往復するシャトル」のように見えることから名付けられた。
- 整列済み領域: 最初は先頭要素だけを整列済みとみなす。
i回目の走査: インデックスiの要素をキーと見て、A[i-1] > A[i]なら隣接交換しiを左へ進める。順序が正しくなるまで繰り返す。- 走査完了:
i回目の走査の終わりで[0, i]が昇順に整列済みとなる。 - 終了:
i = n - 1まで走査を繰り返す。
procedure shuttle_sort(A)
n = length(A)
for i from 1 to n - 1
j = i
while j > 0 and A[j - 1] > A[j] then
swap(A[j - 1], A[j])
j = j - 1
整列済みに近い入力では O(n) に近づき、安定ソートである。
類似アルゴリズムとの相違点
ノームソートは単一位置を前後へ動かす。シェーカーソートは両端から未整列区間を狭める。シャトルは走査ごとに先頭側の整列済み区間を 1 つずつ広げる。
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 | 0.000008 | 0.000039 | 1678 | 1684 |
| 512 | 0.000026 | 0.000070 | 1682 | 1688 |
| 1024 | 0.000088 | 0.000167 | 1690 | 1696 |
| 2048 | 0.000342 | 0.000419 | 1706 | 1712 |
| 4096 | 0.001334 | 0.002223 | 1738 | 1744 |
| 8192 | 0.005492 | 0.020039 | 1801 | 1808 |
| 16384 | 0.021904 | 0.074351 | 1934 | 1940 |
| 32768 | 0.071984 | 0.137185 | 2194 | 2200 |
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 insertion_sort(a: &mut [usize]) {
for i in 1..a.len() {
let mut j = i;
while j > 0 && a[j - 1] > a[j] {
a.swap(j - 1, j);
j -= 1;
}
}
}
fn shuttle_sort(a: &mut [usize]) {
insertion_sort(a);
}
fn benchmark_sort(array: &mut [usize]) {
shuttle_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