Algorithms: Sorting

<?php
declare(strict_types=1);
// Insertion Sort in PHP
//
// 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
// 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 insertion_sort(array &$a): int {
    alg_require(array_is_list($a));
    $n = count($a);
    alg_require((($n >= 0) && ($n <= 1000000)));
    alg_require((count($a) == $n));
    $i = 1;
    $j = 0;
    $key = 0;
    while (($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;
}

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

using System;
// Insertion Sort in C#
//
// 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
// 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 insertion_sort(Span<int> a) {
        checked {
            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 = (i - 1);
                while (((j >= 0) && (a[j] > key))) {
                    a[(j + 1)] = a[j];
                    j = (j - 1);
                }
                a[(j + 1)] = key;
                i = (i + 1);
            }
            return 0;
        }
    }

    static void Main() {
        int[] a = new int[] {5, 1, 3, 1};
        int result = insertion_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>
// Insertion Sort in C++
//
// 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
// 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 insertion_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 i = 1;
    int j = 0;
    int 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;
}

int main(void) {
    std::vector<int> a = {5, 1, 3, 1};
    int result = insertion_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;
}

#include <stdio.h>
#include <stdlib.h>
#include <stdint.h>
#include <limits.h>
#include <errno.h>
// Insertion Sort in C
//
// 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
// C99: checked calloc/free workspace, const input pointers, explicit size_t lengths. Errors
// return INT_MIN with errno=EINVAL, ERANGE, or ENOMEM. Check errno before using a result.
// Input/output arrays must not alias. No variable-length stack arrays.
//
// EXAMPLE
// Expected return: 0.
// Expected a after call: [1, 1, 3, 5].
// Run: gcc -std=c99 -O2 example.c -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 int alg_checked(int64_t v, int *error) {
    if (v < INT_MIN || v > INT_MAX) { *error = 1; return 0; }
    return (int)v;
}
static int alg_add(int a, int b, int *e) { return alg_checked((int64_t)a+b,e); }
static int alg_sub(int a, int b, int *e) { return alg_checked((int64_t)a-b,e); }
static int alg_mul(int a, int b, int *e) { return alg_checked((int64_t)a*b,e); }

int insertion_sort(int *a, size_t a_length) {
    int alg_error = 0;
    int alg_result = INT_MIN;
    errno = 0;
    if (a_length > 1000000 || (a_length && !a)) { errno = EINVAL; alg_result = INT_MIN; goto alg_cleanup; }
    int n = (int)a_length;
    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    if (!(((n >= 0) && (n <= 1000000)))) { errno = EINVAL; alg_result = INT_MIN; goto alg_cleanup; }
    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    if (!(((int)a_length == n))) { errno = EINVAL; alg_result = INT_MIN; goto alg_cleanup; }
    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    int i = 1;
    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    int j = 0;
    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    int key = 0;
    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    while (1) {
        int alg_condition = (i < n);
        if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
        if (!alg_condition) break;
        key = a[i];
        if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
        j = alg_sub(i, 1, &alg_error);
        if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
        while (1) {
            int alg_condition = ((j >= 0) && (a[j] > key));
            if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
            if (!alg_condition) break;
            a[alg_add(j, 1, &alg_error)] = a[j];
            if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
            j = alg_sub(j, 1, &alg_error);
            if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
        }
        a[alg_add(j, 1, &alg_error)] = key;
        if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
        i = alg_add(i, 1, &alg_error);
        if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    }
    alg_result = 0;
    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    goto alg_cleanup;
alg_cleanup:
    return alg_result;
}

int main(void) {
    int a[] = {5, 1, 3, 1};
    int result = insertion_sort(a, 4);
    printf("%d\n", result);
    for (int z = 0; z < 4; z++) printf("%d ", a[z]);
    printf("\n");
    // Expected a: [1, 1, 3, 5]
    if (errno) { perror("algorithm"); return 1; }
    return 0;
}

from bisect import bisect_left

# Insertion Sort in Python
#
# 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
# 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, 5].
# 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 insertion_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 = 1
    j: int = 0
    key: int = 0
    while i < n:
        key = a[i]
        j = i - 1
        while j >= 0 and a[j] > key:
            a[j + 1] = a[j]
            j -= 1
        a[j + 1] = key
        i += 1
    return 0

a = [5, 1, 3, 1]
result = insertion_sort(a)
print(result)
print(a)
# Expected a: [1, 1, 3, 5]