Algorithms: Sorting

using System;
// LSD Radix Sort in C#
//
// PURPOSE
// LSD radix sort orders bounded nonnegative integers one byte at a time using stable
// counting passes.
//
// METHOD
// For each of four base-256 digits, count occurrences, compute cumulative positions, then
// distribute from right to left to preserve stability.
//
// COMPLEXITY
// O(4(n+256)) time and O(n+256) auxiliary space for 32-bit keys. Stable.
//
// CONTRACT
// Keys are nonnegative signed 32-bit integers. Sorts ascending in place, returns 0.
// Public APIs infer array lengths except in C, which accepts pointer/length pairs. Vertex
// counts and matrix dimensions remain explicit. Arrays must contain signed 32-bit integers.
// Sorted order, correct tree topology, and caller-owned data-structure invariants are
// preconditions; checking them on every query would change query complexity.
// Scalar and shape checks are included. Value-range checks are included where needed to
// prevent invalid indexing or nontermination. Allocation sizes are capped at 4,000,000
// workspace entries. Arithmetic outside Python raises an error on 32-bit overflow; Python
// uses arbitrary precision. Native allocation failures propagate. In-place outputs may be
// partly updated after arithmetic failure. These are single-threaded, in-memory
// implementations.
//
// LANGUAGE DETAILS
// C# / .NET 10: ReadOnlySpan<int> inputs, Span<int> outputs, primitive workspace arrays,
// Array.BinarySearch for LIS, and checked integer arithmetic. Invalid arguments and overflow
// throw exceptions.
//
// EXAMPLE
// Expected return: 0.
// Expected a after call: [0, 1, 255, 256, 65536].
// Run: Use Program.cs in a net10.0 console project; dotnet run.
// Tests for this exact source artifact run before publication. The accompanying source
// archive includes unit cases, runtime results, and source hashes.

class Program {
    static void alg_require(bool valid) { if (!valid) throw new ArgumentException("invalid algorithm input"); }
    static int alg_size(int n) { alg_require(n>=0 && n<=4000000); return n; }

    static int radix_sort(Span<int> a) {
        checked {
            int n = a.Length;
            alg_require(((n >= 0) && (n <= 1000000)));
            alg_require((a.Length == n));
            for (int alg_i = 0; alg_i < a.Length; alg_i++) {
                int alg_value = a[alg_i];
                alg_require((alg_value >= 0));
            }
            int[] output = new int[alg_size((n + 1))];
            int[] count = new int[alg_size(256)];
            int divisor = 1;
            int digit = 0;
            int pass_index = 0;
            int i = 0;
            while ((pass_index < 4)) {
                i = 0;
                while ((i < 256)) {
                    count[i] = 0;
                    i = (i + 1);
                }
                i = 0;
                while ((i < n)) {
                    digit = ((a[i] / divisor) % 256);
                    count[digit] = (count[digit] + 1);
                    i = (i + 1);
                }
                i = 1;
                while ((i < 256)) {
                    count[i] = (count[i] + count[(i - 1)]);
                    i = (i + 1);
                }
                i = (n - 1);
                while ((i >= 0)) {
                    digit = ((a[i] / divisor) % 256);
                    count[digit] = (count[digit] - 1);
                    output[count[digit]] = a[i];
                    i = (i - 1);
                }
                i = 0;
                while ((i < n)) {
                    a[i] = output[i];
                    i = (i + 1);
                }
                pass_index = (pass_index + 1);
                if ((pass_index < 4)) {
                    divisor = (divisor * 256);
                }
            }
            return 0;
        }
    }

    static void Main() {
        int[] a = new int[] {256, 1, 65536, 0, 255};
        int result = radix_sort(a);
        Console.WriteLine(result);
        // Expected a: [0, 1, 255, 256, 65536]
        Console.WriteLine("[" + string.Join(", ", a) + "]");
    }
}

<?php
declare(strict_types=1);
// LSD Radix Sort in PHP
//
// PURPOSE
// LSD radix sort orders bounded nonnegative integers one byte at a time using stable
// counting passes.
//
// METHOD
// For each of four base-256 digits, count occurrences, compute cumulative positions, then
// distribute from right to left to preserve stability.
//
// COMPLEXITY
// O(4(n+256)) time and O(n+256) auxiliary space for 32-bit keys. Stable.
//
// CONTRACT
// Keys are nonnegative signed 32-bit integers. Sorts ascending in place, returns 0.
// Public APIs infer array lengths except in C, which accepts pointer/length pairs. Vertex
// counts and matrix dimensions remain explicit. Arrays must contain signed 32-bit integers.
// Sorted order, correct tree topology, and caller-owned data-structure invariants are
// preconditions; checking them on every query would change query complexity.
// Scalar and shape checks are included. Value-range checks are included where needed to
// prevent invalid indexing or nontermination. Allocation sizes are capped at 4,000,000
// workspace entries. Arithmetic outside Python raises an error on 32-bit overflow; Python
// uses arbitrary precision. Native allocation failures propagate. In-place outputs may be
// partly updated after arithmetic failure. These are single-threaded, in-memory
// implementations.
//
// LANGUAGE DETAILS
// PHP 8.1+ on a 64-bit runtime: packed arrays, strict scalar types, read-only inputs by
// value using copy-on-write, references only for outputs, and checked 32-bit arithmetic.
// Invalid input and overflow throw exceptions. PHP arrays have higher overhead than native
// packed buffers in C/Java.
//
// EXAMPLE
// Expected return: 0.
// Expected a after call: [0, 1, 255, 256, 65536].
// Run: php example.php
// Tests for this exact source artifact run before publication. The accompanying source
// archive includes unit cases, runtime results, and source hashes.

function alg_require(bool $valid): void { if (!$valid) throw new InvalidArgumentException("invalid algorithm input"); }
function alg_checked(int|float $v): int { if ($v < -2147483648 || $v > 2147483647 || floor($v) != $v) throw new OverflowException("32-bit result overflow"); return (int)$v; }
function alg_add(int $a,int $b): int { return alg_checked($a+$b); }
function alg_sub(int $a,int $b): int { return alg_checked($a-$b); }
function alg_mul(int $a,int $b): int { return alg_checked($a*$b); }
function alg_size(int $n): int { alg_require($n>=0 && $n<=4000000); return $n; }

function radix_sort(array &$a): int {
    alg_require(array_is_list($a));
    $n = count($a);
    alg_require((($n >= 0) && ($n <= 1000000)));
    alg_require((count($a) == $n));
    for ($alg_i = 0; $alg_i < count($a); $alg_i++) {
        $alg_value = $a[$alg_i];
        alg_require(($alg_value >= 0));
    }
    $output = array_fill(0, alg_size(alg_add($n, 1)), 0);
    $count = array_fill(0, alg_size(256), 0);
    $divisor = 1;
    $digit = 0;
    $pass_index = 0;
    $i = 0;
    while (($pass_index < 4)) {
        $i = 0;
        while (($i < 256)) {
            $count[$i] = 0;
            $i = alg_add($i, 1);
        }
        $i = 0;
        while (($i < $n)) {
            $digit = (intdiv($a[$i], $divisor) % 256);
            $count[$digit] = alg_add($count[$digit], 1);
            $i = alg_add($i, 1);
        }
        $i = 1;
        while (($i < 256)) {
            $count[$i] = alg_add($count[$i], $count[alg_sub($i, 1)]);
            $i = alg_add($i, 1);
        }
        $i = alg_sub($n, 1);
        while (($i >= 0)) {
            $digit = (intdiv($a[$i], $divisor) % 256);
            $count[$digit] = alg_sub($count[$digit], 1);
            $output[$count[$digit]] = $a[$i];
            $i = alg_sub($i, 1);
        }
        $i = 0;
        while (($i < $n)) {
            $a[$i] = $output[$i];
            $i = alg_add($i, 1);
        }
        $pass_index = alg_add($pass_index, 1);
        if (($pass_index < 4)) {
            $divisor = alg_mul($divisor, 256);
        }
    }
    return 0;
}

$a = [256, 1, 65536, 0, 255];
$result = radix_sort($a);
echo $result, PHP_EOL;
// Expected a: [0, 1, 255, 256, 65536]
echo json_encode($a), PHP_EOL;

// Gnome Sort in Java
//
// PURPOSE
// Gnome sort is a comparison-sort variant useful for understanding alternative ways to move
// misplaced values.
//
// METHOD
// Walk forward over ordered neighbors; on a mismatch swap them and step back until local
// order is restored.
//
// COMPLEXITY
// O(n squared) worst-case time and O(1) auxiliary space. Stable.
//
// CONTRACT
// Sorts ascending in place and returns 0. Intended for small collections; use a general-
// purpose O(n log n) sort for large workloads.
// Public APIs infer array lengths except in C, which accepts pointer/length pairs. Vertex
// counts and matrix dimensions remain explicit. Arrays must contain signed 32-bit integers.
// Sorted order, correct tree topology, and caller-owned data-structure invariants are
// preconditions; checking them on every query would change query complexity.
// Scalar and shape checks are included. Value-range checks are included where needed to
// prevent invalid indexing or nontermination. Allocation sizes are capped at 4,000,000
// workspace entries. Arithmetic outside Python raises an error on 32-bit overflow; Python
// uses arbitrary precision. Native allocation failures propagate. In-place outputs may be
// partly updated after arithmetic failure. These are single-threaded, in-memory
// implementations.
//
// LANGUAGE DETAILS
// Java 17+: primitive int arrays, Arrays.binarySearch for LIS, and Math exact arithmetic.
// Invalid input throws IllegalArgumentException; arithmetic overflow throws
// ArithmeticException.
//
// EXAMPLE
// Expected return: 0.
// Expected a after call: [1, 1, 3, 4].
// Run: javac AlgorithmExample.java && java AlgorithmExample
// Tests for this exact source artifact run before publication. The accompanying source
// archive includes unit cases, runtime results, and source hashes.

class AlgorithmExample {
    static void alg_require(boolean valid) { if (!valid) throw new IllegalArgumentException("invalid algorithm input"); }
    static int alg_size(int n) { alg_require(n>=0 && n<=4000000); return n; }

    static int gnome_sort(int[] a) {
        java.util.Objects.requireNonNull(a, "a");
        int n = a.length;
        alg_require(((n >= 0) && (n <= 1000000)));
        alg_require((a.length == n));
        int i = 0;
        int temp = 0;
        while ((i < n)) {
            if (((i == 0) || (a[Math.subtractExact(i, 1)] <= a[i]))) {
                i = Math.addExact(i, 1);
            } else {
                temp = a[i];
                a[i] = a[Math.subtractExact(i, 1)];
                a[Math.subtractExact(i, 1)] = temp;
                i = Math.subtractExact(i, 1);
            }
        }
        return 0;
    }

    public static void main(String[] args) {
        int[] a = new int[] {4, 1, 3, 1};
        int result = gnome_sort(a);
        System.out.println(result);
        // Expected a: [1, 1, 3, 4]
        System.out.println(java.util.Arrays.toString(a));
    }
}

"use strict";
// Gnome Sort in JavaScript
//
// PURPOSE
// Gnome sort is a comparison-sort variant useful for understanding alternative ways to move
// misplaced values.
//
// METHOD
// Walk forward over ordered neighbors; on a mismatch swap them and step back until local
// order is restored.
//
// COMPLEXITY
// O(n squared) worst-case time and O(1) auxiliary space. Stable.
//
// CONTRACT
// Sorts ascending in place and returns 0. Intended for small collections; use a general-
// purpose O(n log n) sort for large workloads.
// Public APIs infer array lengths except in C, which accepts pointer/length pairs. Vertex
// counts and matrix dimensions remain explicit. Arrays must contain signed 32-bit integers.
// Sorted order, correct tree topology, and caller-owned data-structure invariants are
// preconditions; checking them on every query would change query complexity.
// Scalar and shape checks are included. Value-range checks are included where needed to
// prevent invalid indexing or nontermination. Allocation sizes are capped at 4,000,000
// workspace entries. Arithmetic outside Python raises an error on 32-bit overflow; Python
// uses arbitrary precision. Native allocation failures propagate. In-place outputs may be
// partly updated after arithmetic failure. These are single-threaded, in-memory
// implementations.
//
// LANGUAGE DETAILS
// Node.js 18+: Int32Array inputs and workspaces provide compact integer storage. Automatic
// lengths and checked arithmetic reject values outside signed 32-bit. Invalid inputs or
// overflow throw RangeError.
//
// EXAMPLE
// Expected return: 0.
// Expected a after call: [1, 1, 3, 4].
// Run: node example.js
// Tests for this exact source artifact run before publication. The accompanying source
// archive includes unit cases, runtime results, and source hashes.

function alg_require(valid) { if (!valid) throw new RangeError("invalid algorithm input"); }
function alg_checked(v) { if (!Number.isInteger(v) || v < -2147483648 || v > 2147483647) throw new RangeError("32-bit result overflow"); return v; }
function alg_add(a,b) { return alg_checked(a+b); }
function alg_sub(a,b) { return alg_checked(a-b); }
function alg_mul(a,b) { return alg_checked(a*b); }
function alg_size(n) { alg_require(Number.isInteger(n) && n>=0 && n<=4000000); return n; }

function gnome_sort(a) {
    alg_require(a instanceof Int32Array);
    let n = a.length;
    alg_require(((n >= 0) && (n <= 1000000)));
    alg_require((a.length == n));
    let i = 0;
    let temp = 0;
    while ((i < n)) {
        if (((i == 0) || (a[alg_sub(i, 1)] <= a[i]))) {
            i = alg_add(i, 1);
        } else {
            temp = a[i];
            a[i] = a[alg_sub(i, 1)];
            a[alg_sub(i, 1)] = temp;
            i = alg_sub(i, 1);
        }
    }
    return 0;
}

let a = new Int32Array([4, 1, 3, 1]);
let result = gnome_sort(a);
console.log(result);
// Expected a: [1, 1, 3, 4]
console.log(Array.from(a));

from bisect import bisect_left

# Gnome Sort in Python
#
# PURPOSE
# Gnome sort is a comparison-sort variant useful for understanding alternative ways to move
# misplaced values.
#
# METHOD
# Walk forward over ordered neighbors; on a mismatch swap them and step back until local
# order is restored.
#
# COMPLEXITY
# O(n squared) worst-case time and O(1) auxiliary space. Stable.
#
# CONTRACT
# Sorts ascending in place and returns 0. Intended for small collections; use a general-
# purpose O(n log n) sort for large workloads.
# Public APIs infer array lengths except in C, which accepts pointer/length pairs. Vertex
# counts and matrix dimensions remain explicit. Arrays must contain signed 32-bit integers.
# Sorted order, correct tree topology, and caller-owned data-structure invariants are
# preconditions; checking them on every query would change query complexity.
# Scalar and shape checks are included. Value-range checks are included where needed to
# prevent invalid indexing or nontermination. Allocation sizes are capped at 4,000,000
# workspace entries. Arithmetic outside Python raises an error on 32-bit overflow; Python
# uses arbitrary precision. Native allocation failures propagate. In-place outputs may be
# partly updated after arithmetic failure. These are single-threaded, in-memory
# implementations.
#
# LANGUAGE DETAILS
# Python 3.9+: automatic lengths, native lists, arbitrary-precision arithmetic, and
# bisect_left for LIS. Invalid scalar/shape inputs raise ValueError. Integer element types
# and sorted/tree invariants remain caller preconditions.
#
# EXAMPLE
# Expected return: 0.
# Expected a after call: [1, 1, 3, 4].
# Run: python example.py
# Tests for this exact source artifact run before publication. The accompanying source
# archive includes unit cases, runtime results, and source hashes.

def alg_require(condition):
    if not condition:
        raise ValueError("invalid algorithm input; see contract")
def alg_size(n):
    alg_require(0 <= n <= 4000000)
    return n

def gnome_sort(a: list[int]) -> int:
    alg_require(isinstance(a, list) and len(a) <= 1000000)
    n: int = len(a)
    alg_require(n >= 0 and n <= 1000000)
    alg_require(len(a) == n)
    i: int = 0
    temp: int = 0
    while i < n:
        if i == 0 or a[i - 1] <= a[i]:
            i += 1
        else:
            temp = a[i]
            a[i] = a[i - 1]
            a[i - 1] = temp
            i -= 1
    return 0

a = [4, 1, 3, 1]
result = gnome_sort(a)
print(result)
# Expected a: [1, 1, 3, 4]
print(a)