カウンティングソートで配列を並び替える
カウンティングソートを使用する
カウンティングソート (counting sort) は、各値が何回現れるかを数え、その出現回数からソート後の並びを復元する(要素同士を直接比較しない)。
キーの取りうる値の範囲 k が入力長 n と同程度かそれより小さいとき、比較ソートの Ω(n log n) より有利になりうる。
- 出現回数の集計: 入力配列を走査し、値
vごとの出現回数count[v]を増やす。 - 累積和(安定版): 安定ソートにする場合は
countを累積和に変換し、各値の書き込み開始位置を決める。 - 出力への配置:
countに従い、出力配列(または元配列の上書き)へ値を順に書き込む。安定版では入力を後ろから走査して同値の相対順序を保つ。
procedure counting_sort(A)
if length(A) = 0 then return
minVal = minimum(A)
maxVal = maximum(A)
range = maxVal - minVal + 1
count[0..range-1] = 0
for each x in A
count[x - minVal] = count[x - minVal] + 1
idx = 0
for v from 0 to range - 1
repeat count[v] times
A[idx] = minVal + v
idx = idx + 1
値域幅 k が小さいとき O(n + k) となり、比較ソートの Ω(n log n) 下界を超えられる。安定ソートである。
整数のように値域が狭いデータや、バケットのインデックスに直結できるキーに向く。一方で k が極端に大きいと補助配列だけでメモリを大量に消費するため、汎用の比較ソートに置き換える判断が必要になる。
類似アルゴリズムとの相違点
基数ソート・バケットソートと同様に値域に依存する。自己インデックスソートと実装が一致することが多いが、キーをソート空間のアドレスとみなす枠組みが異なる。
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 | 0.000001 | 0.000039 | 57 | 64 |
| 512 | 0.000003 | 0.000053 | 69 | 76 |
| 1024 | 0.000006 | 0.000078 | 70 | 76 |
| 2048 | 0.000012 | 0.000593 | 78 | 84 |
| 4096 | 0.000024 | 0.000145 | 94 | 100 |
| 8192 | 0.000049 | 0.000359 | 126 | 132 |
| 16384 | 0.000132 | 0.000427 | 58 | 64 |
| 32768 | 0.000248 | 0.000948 | 112 | 144 |
| 65536 | 0.000495 | 0.005273 | 372 | 404 |
| 131072 | 0.001069 | 0.004554 | 890 | 932 |
| 262144 | 0.001868 | 0.004632 | 1919 | 2060 |
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 = 18;
const RUNS: usize = 8192;
fn counting_sort(a: &mut [usize]) {
if a.is_empty() {
return;
}
let min = *a.iter().min().unwrap();
let max = *a.iter().max().unwrap();
let span = max - min + 1;
let mut count = vec![0usize; span];
for &x in a.iter() {
count[x - min] += 1;
}
let mut idx = 0;
for (offset, &cnt) in count.iter().enumerate() {
let value = min + offset;
for _ in 0..cnt {
a[idx] = value;
idx += 1;
}
}
}
fn benchmark_sort(array: &mut [usize]) {
counting_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