ビンゴソートで配列を並び替える
ビンゴソートを使用する
ビンゴソート (bingo sort) は、選択ソートの変形で、未整列範囲の最小値(ビンゴ)を一度見つけたら、その値と等しい要素をすべて確定位置へまとめて移し、次のビンゴを同じ走査の中で探す。
選択ソートが「要素ごと」に未整列範囲を走査するのに対し、ビンゴソートは「相異なる値ごと」に 1 回の走査で足りる。重複が多い入力では走査回数が減り、同値だらけのデータでは選択ソートより速くなりやすい。名前は、目的の値が現れたときに「ビンゴ!」と叫ぶイメージに由来する。
- 初回のビンゴ: 配列全体の最小値を
bingo、最大値をlargestとする。nextBingoをいったんlargestに置き、書き込み位置nextPosを0から始める。 - 同値の配置と次値の探索:
nextPosから末尾まで走査する。A[i] = bingoならA[i]とA[nextPos]を交換してnextPosを進める。それ以外でA[i] < nextBingoならnextBingoを更新する(次パスで使う次の最小値候補)。 - 次のビンゴへ: 1 パス終了後に
bingo = nextBingoとし、nextBingoを再びlargestに戻す。 - 終了条件:
bingo < nextBingoのあいだ手順 2〜3 を繰り返す。最後に残る最大値の塊は、より小さい値がすべて左側へ寄った時点で既に正しい位置にあるため、明示的な最終パスは不要である。
procedure bingo_sort(A)
n = length(A)
if n <= 1 then return
bingo = minimum(A)
largest = maximum(A)
nextBingo = largest
nextPos = 0
while bingo < nextBingo
startPos = nextPos
for i from startPos to n - 1
if A[i] = bingo then
swap(A[i], A[nextPos])
nextPos = nextPos + 1
else if A[i] < nextBingo then
nextBingo = A[i]
bingo = nextBingo
nextBingo = largest
最悪・平均は相異なる値の個数を m として Θ(n m)(すべて相異なれば選択ソートと同じ Θ(n²))、最良は Θ(n + m²) とされる。追加配列は不要(インプレース)で、一般に不安定である。
類似アルゴリズムとの相違点
選択ソートは最小を 1 要素ずつ確定するため、重複があってもほぼ毎回フル走査が要る。ビンゴソートは同値をまとめて確定し、走査回数を相異なる値の個数に近づける。カウンティングソートも重複に強いが、値域幅ぶんの計数配列を使う非比較ソートであり、ビンゴソートは比較ベースのインプレース変形である。
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 | 0.000031 | 0.002546 | 0 | 0 |
| 512 | 0.000110 | 0.000295 | 0 | 0 |
| 1024 | 0.000450 | 0.006707 | 0 | 0 |
| 2048 | 0.001870 | 0.013609 | 0 | 0 |
| 4096 | 0.007102 | 0.031042 | 0 | 0 |
| 8192 | 0.028429 | 0.078459 | 0 | 0 |
| 16384 | 0.115358 | 0.276796 | 0 | 0 |
| 32768 | 0.568974 | 1.921136 | 0 | 0 |
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::{
alloc::{GlobalAlloc, Layout, System},
env,
process::Command,
sync::atomic::{AtomicUsize, Ordering},
time::{Duration, Instant},
};
/// Counts live heap bytes and the high-water mark so auxiliary sort buffers
/// (swap Vecs, etc.) are measured as explicit heap growth during the sort.
struct TrackingAllocator;
static LIVE_BYTES: AtomicUsize = AtomicUsize::new(0);
static PEAK_BYTES: AtomicUsize = AtomicUsize::new(0);
fn record_alloc(size: usize) {
let live = LIVE_BYTES.fetch_add(size, Ordering::Relaxed) + size;
PEAK_BYTES.fetch_max(live, Ordering::Relaxed);
}
unsafe impl GlobalAlloc for TrackingAllocator {
unsafe fn alloc(&self, layout: Layout) -> *mut u8 {
let ptr = System.alloc(layout);
if !ptr.is_null() {
record_alloc(layout.size());
}
ptr
}
unsafe fn dealloc(&self, ptr: *mut u8, layout: Layout) {
LIVE_BYTES.fetch_sub(layout.size(), Ordering::Relaxed);
System.dealloc(ptr, layout);
}
unsafe fn alloc_zeroed(&self, layout: Layout) -> *mut u8 {
let ptr = System.alloc_zeroed(layout);
if !ptr.is_null() {
record_alloc(layout.size());
}
ptr
}
unsafe fn realloc(&self, ptr: *mut u8, layout: Layout, new_size: usize) -> *mut u8 {
let new_ptr = System.realloc(ptr, layout, new_size);
if !new_ptr.is_null() {
LIVE_BYTES.fetch_sub(layout.size(), Ordering::Relaxed);
record_alloc(new_size);
}
new_ptr
}
}
#[global_allocator]
static GLOBAL: TrackingAllocator = TrackingAllocator;
const MIN_POWER: u32 = 8;
const MAX_POWER: u32 = 15;
const RUNS: usize = 8192;
fn bingo_sort(a: &mut [usize]) {
let n = a.len();
if n <= 1 {
return;
}
let mut bingo = *a.iter().min().unwrap();
let largest = *a.iter().max().unwrap();
let mut next_bingo = largest;
let mut next_pos = 0;
while bingo < next_bingo {
let start_pos = next_pos;
for i in start_pos..n {
if a[i] == bingo {
a.swap(i, next_pos);
next_pos += 1;
} else if a[i] < next_bingo {
next_bingo = a[i];
}
}
bingo = next_bingo;
next_bingo = largest;
}
}
fn benchmark_sort(array: &mut [usize]) {
bingo_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],
);
// Seed 0 is a fixed point of the xorshift below, so it would degenerate into
// yet another all-equal case instead of a 4-value mix. Start at 1.
for seed in 1..=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 micros(d: Duration) -> u128 {
d.as_micros()
}
fn input_array(size: usize, seed: u64) -> Vec<usize> {
shuffled(size, seed)
}
/// Peak heap growth during `benchmark_sort`, in KiB (explicit buffers such as swap).
fn run_once(size: usize, seed: usize) -> (u128, usize) {
let mut array = input_array(size, seed as u64);
let base_bytes = LIVE_BYTES.load(Ordering::Relaxed);
PEAK_BYTES.store(base_bytes, Ordering::Relaxed);
let start = Instant::now();
benchmark_sort(&mut array);
let elapsed = start.elapsed();
let peak_bytes = PEAK_BYTES.load(Ordering::Relaxed);
let aux_kb = peak_bytes.saturating_sub(base_bytes) / 1024;
let expected: Vec<usize> = (1..=size).collect();
if array != expected {
panic!(
"sort failed with seed {} for size {}",
seed,
size
);
}
(micros(elapsed), aux_kb)
}
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 == "--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 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 aux_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;
}
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