Algorithms: Sorting

#include <stdio.h>
#include <stdlib.h>
#include <stdint.h>
#include <limits.h>
#include <errno.h>
// 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
// 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 shell_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 gap = (n / 2);
    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    int i = 0;
    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 = (gap > 0);
        if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
        if (!alg_condition) break;
        i = gap;
        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 = i;
            if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
            while (1) {
                int alg_condition = ((j >= gap) && (a[alg_sub(j, gap, &alg_error)] > key));
                if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
                if (!alg_condition) break;
                a[j] = a[alg_sub(j, gap, &alg_error)];
                if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
                j = alg_sub(j, gap, &alg_error);
                if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
            }
            a[j] = 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; }
        }
        gap = (gap / 2);
        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 = shell_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

# Shell Sort in Python
#
# 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
# 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 shell_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)
    gap: int = n // 2
    i: int = 0
    j: int = 0
    key: int = 0
    while gap > 0:
        i = gap
        while i < n:
            key = a[i]
            j = i
            while j >= gap and a[j - gap] > key:
                a[j] = a[j - gap]
                j -= gap
            a[j] = key
            i += 1
        gap = gap // 2
    return 0

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

"use strict";
// Shell Sort in JavaScript
//
// 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
// 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 shell_sort(a) {
    alg_require(a instanceof Int32Array);
    let n = a.length;
    alg_require(((n >= 0) && (n <= 1000000)));
    alg_require((a.length == n));
    let gap = Math.floor(n / 2);
    let i = 0;
    let j = 0;
    let 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 = Math.floor(gap / 2);
    }
    return 0;
}

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

// Shell Sort in Java
//
// 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
// 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 shell_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 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[Math.subtractExact(j, gap)] > key))) {
                    a[j] = a[Math.subtractExact(j, gap)];
                    j = Math.subtractExact(j, gap);
                }
                a[j] = key;
                i = Math.addExact(i, 1);
            }
            gap = (gap / 2);
        }
        return 0;
    }

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