Algorithms: Sorting

"use strict";
// Insertion Sort in JavaScript
//
// PURPOSE
// Insertion sort grows a sorted prefix by inserting the next value into its proper position.
// It works well for small or nearly sorted arrays.
//
// METHOD
// Save the next key, shift larger prefix values to the right, then place the key in the gap.
// Using a strict comparison preserves the relative order of equal values.
//
// COMPLEXITY
// O(n squared) worst-case time, O(n) best-case time, O(1) auxiliary space. Stable.
//
// CONTRACT
// Sorts n elements 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
// 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, 5].
// 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 insertion_sort(a) {
    alg_require(a instanceof Int32Array);
    let n = a.length;
    alg_require(((n >= 0) && (n <= 1000000)));
    alg_require((a.length == n));
    let i = 1;
    let j = 0;
    let key = 0;
    while ((i < n)) {
        key = a[i];
        j = alg_sub(i, 1);
        while (((j >= 0) && (a[j] > key))) {
            a[alg_add(j, 1)] = a[j];
            j = alg_sub(j, 1);
        }
        a[alg_add(j, 1)] = key;
        i = alg_add(i, 1);
    }
    return 0;
}

let a = new Int32Array([5, 1, 3, 1]);
let result = insertion_sort(a);
console.log(result);
console.log(a);
// Expected a: [1, 1, 3, 5]

// Insertion Sort in Java
//
// PURPOSE
// Insertion sort grows a sorted prefix by inserting the next value into its proper position.
// It works well for small or nearly sorted arrays.
//
// METHOD
// Save the next key, shift larger prefix values to the right, then place the key in the gap.
// Using a strict comparison preserves the relative order of equal values.
//
// COMPLEXITY
// O(n squared) worst-case time, O(n) best-case time, O(1) auxiliary space. Stable.
//
// CONTRACT
// Sorts n elements 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
// 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, 5].
// 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 insertion_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 = 1;
        int j = 0;
        int key = 0;
        while ((i < n)) {
            key = a[i];
            j = Math.subtractExact(i, 1);
            while (((j >= 0) && (a[j] > key))) {
                a[Math.addExact(j, 1)] = a[j];
                j = Math.subtractExact(j, 1);
            }
            a[Math.addExact(j, 1)] = key;
            i = Math.addExact(i, 1);
        }
        return 0;
    }

    public static void main(String[] args) {
        int[] a = new int[] {5, 1, 3, 1};
        int result = insertion_sort(a);
        System.out.println(result);
        System.out.println(java.util.Arrays.toString(a));
        // Expected a: [1, 1, 3, 5]
    }
}

<?php
declare(strict_types=1);
// Shell Sort in PHP
//
// PURPOSE
// Shell sort applies insertion sort to elements separated by a gap. Early passes move values
// over long distances before a final gap-one pass.
//
// METHOD
// Start at n/2 and halve the gap. For each gap, insert each value into its gap-separated
// sorted subsequence. Gap one finishes the full ordering.
//
// COMPLEXITY
// O(n squared) worst-case time for this halving gap sequence; O(1) auxiliary space. Not
// stable.
//
// CONTRACT
// Sorts n elements ascending in place; returns 0. Complexity depends on the chosen gap
// sequence.
// 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: [1, 1, 3, 5].
// 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 shell_sort(array &$a): int {
    alg_require(array_is_list($a));
    $n = count($a);
    alg_require((($n >= 0) && ($n <= 1000000)));
    alg_require((count($a) == $n));
    $gap = intdiv($n, 2);
    $i = 0;
    $j = 0;
    $key = 0;
    while (($gap > 0)) {
        $i = $gap;
        while (($i < $n)) {
            $key = $a[$i];
            $j = $i;
            while ((($j >= $gap) && ($a[alg_sub($j, $gap)] > $key))) {
                $a[$j] = $a[alg_sub($j, $gap)];
                $j = alg_sub($j, $gap);
            }
            $a[$j] = $key;
            $i = alg_add($i, 1);
        }
        $gap = intdiv($gap, 2);
    }
    return 0;
}

$a = [5, 1, 3, 1];
$result = shell_sort($a);
echo $result, PHP_EOL;
echo json_encode($a), PHP_EOL;
// Expected a: [1, 1, 3, 5]

using System;
// Shell Sort in C#
//
// PURPOSE
// Shell sort applies insertion sort to elements separated by a gap. Early passes move values
// over long distances before a final gap-one pass.
//
// METHOD
// Start at n/2 and halve the gap. For each gap, insert each value into its gap-separated
// sorted subsequence. Gap one finishes the full ordering.
//
// COMPLEXITY
// O(n squared) worst-case time for this halving gap sequence; O(1) auxiliary space. Not
// stable.
//
// CONTRACT
// Sorts n elements ascending in place; returns 0. Complexity depends on the chosen gap
// sequence.
// 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: [1, 1, 3, 5].
// 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 shell_sort(Span<int> a) {
        checked {
            int n = a.Length;
            alg_require(((n >= 0) && (n <= 1000000)));
            alg_require((a.Length == n));
            int gap = (n / 2);
            int i = 0;
            int j = 0;
            int key = 0;
            while ((gap > 0)) {
                i = gap;
                while ((i < n)) {
                    key = a[i];
                    j = i;
                    while (((j >= gap) && (a[(j - gap)] > key))) {
                        a[j] = a[(j - gap)];
                        j = (j - gap);
                    }
                    a[j] = key;
                    i = (i + 1);
                }
                gap = (gap / 2);
            }
            return 0;
        }
    }

    static void Main() {
        int[] a = new int[] {5, 1, 3, 1};
        int result = shell_sort(a);
        Console.WriteLine(result);
        Console.WriteLine("[" + string.Join(", ", a) + "]");
        // Expected a: [1, 1, 3, 5]
    }
}

#include <stdio.h>
#include <vector>
#include <algorithm>
#include <stdexcept>
#include <cstdint>
#include <limits>
// Shell Sort in C++
//
// PURPOSE
// Shell sort applies insertion sort to elements separated by a gap. Early passes move values
// over long distances before a final gap-one pass.
//
// METHOD
// Start at n/2 and halve the gap. For each gap, insert each value into its gap-separated
// sorted subsequence. Gap one finishes the full ordering.
//
// COMPLEXITY
// O(n squared) worst-case time for this halving gap sequence; O(1) auxiliary space. Not
// stable.
//
// CONTRACT
// Sorts n elements ascending in place; returns 0. Complexity depends on the chosen gap
// sequence.
// 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++17: const vector references for inputs, mutable references for outputs, RAII workspace,
// standard lower_bound for LIS. Invalid inputs throw invalid_argument; overflow throws
// overflow_error; allocation failure propagates bad_alloc.
//
// EXAMPLE
// Expected return: 0.
// Expected a after call: [1, 1, 3, 5].
// Run: g++ -std=c++17 -O2 example.cpp -o example && ./example
// Tests for this exact source artifact run before publication. The accompanying source
// archive includes unit cases, runtime results, and source hashes.

static int alg_min(int a, int b) { return a < b ? a : b; }
static int alg_max(int a, int b) { return a > b ? a : b; }
static void alg_require(bool valid) { if (!valid) throw std::invalid_argument("invalid algorithm input"); }
static int alg_checked(int64_t v) { if (v < INT32_MIN || v > INT32_MAX) throw std::overflow_error("32-bit result overflow"); return (int)v; }
static int alg_add(int a,int b) { return alg_checked((int64_t)a+b); }
static int alg_sub(int a,int b) { return alg_checked((int64_t)a-b); }
static int alg_mul(int a,int b) { return alg_checked((int64_t)a*b); }
static size_t alg_size(int n) { alg_require(n>=0 && n<=4000000); return (size_t)n; }

int shell_sort(std::vector<int>& a) {
    alg_require(a.size() <= 1000000);
    int n = (int)a.size();
    alg_require(((n >= 0) && (n <= 1000000)));
    alg_require(((int)a.size() == n));
    int gap = (n / 2);
    int i = 0;
    int j = 0;
    int key = 0;
    while ((gap > 0)) {
        i = gap;
        while ((i < n)) {
            key = a[i];
            j = i;
            while (((j >= gap) && (a[alg_sub(j, gap)] > key))) {
                a[j] = a[alg_sub(j, gap)];
                j = alg_sub(j, gap);
            }
            a[j] = key;
            i = alg_add(i, 1);
        }
        gap = (gap / 2);
    }
    return 0;
}

int main(void) {
    std::vector<int> a = {5, 1, 3, 1};
    int result = shell_sort(a);
    printf("%d\n", result);
    for (int z = 0; z < 4; z++) printf("%d ", a[z]);
    printf("\n");
    // Expected a: [1, 1, 3, 5]
    return 0;
}