Heap Sort in C#

using System;
// Heap Sort in C#
//
// PURPOSE
// Heap sort uses a max heap so the largest remaining value can be moved to the end. It gives
// a worst-case time guarantee without a second array.
//
// METHOD
// Build a max heap from the bottom up. Swap its root with the last active element, shrink
// the heap, and sift the new root downward. The suffix is sorted after every extraction.
//
// COMPLEXITY
// O(n log n) time, O(1) auxiliary space; heap construction is O(n). Not 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 heap_sort(Span<int> a) {
        checked {
            int n = a.Length;
            alg_require(((n >= 0) && (n <= 1000000)));
            alg_require((a.Length == n));
            int start = ((n / 2) - 1);
            int end = (n - 1);
            int root = 0;
            int child = 0;
            int temp = 0;
            while ((start >= 0)) {
                root = start;
                while ((((2 * root) + 1) < n)) {
                    child = ((2 * root) + 1);
                    if ((((child + 1) < n) && (a[child] < a[(child + 1)]))) {
                        child = (child + 1);
                    }
                    if ((a[root] >= a[child])) {
                        break;
                    }
                    temp = a[root];
                    a[root] = a[child];
                    a[child] = temp;
                    root = child;
                }
                start = (start - 1);
            }
            while ((end > 0)) {
                temp = a[0];
                a[0] = a[end];
                a[end] = temp;
                root = 0;
                while ((((2 * root) + 1) < end)) {
                    child = ((2 * root) + 1);
                    if ((((child + 1) < end) && (a[child] < a[(child + 1)]))) {
                        child = (child + 1);
                    }
                    if ((a[root] >= a[child])) {
                        break;
                    }
                    temp = a[root];
                    a[root] = a[child];
                    a[child] = temp;
                    root = child;
                }
                end = (end - 1);
            }
            return 0;
        }
    }

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