サイクルソートで配列を並び替える
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。
- 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。 - 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。 - 1回目の書き込み:
A[pos]とitemを入れ替える。itemには追い出された値が入る。 - 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。 - 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 で 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