Iterative Quick Sort in C#

using System;
// Iterative Quick Sort in C#
//
// PURPOSE
// Quick sort partitions around a pivot and sorts the two resulting regions. This iterative
// version stores pending intervals explicitly instead of using recursion.
//
// METHOD
// Choose a median-of-three pivot and partition into less-than, equal-to, and greater-than
// regions. Process the smaller region immediately and defer the larger one to keep the
// explicit stack bounded.
//
// COMPLEXITY
// O(n log n) average time, O(n squared) adversarial worst case. Equal-key input takes O(n).
// O(log n) pending intervals; 64 stack slots cover the supported bounded input lengths. Not
// stable.
//
// CONTRACT
// Sorts ascending in place and returns 0. Three-way partition handles repeated keys
// efficiently. Median-of-three reduces common fixed-endpoint pivot problems but does not
// provide introsort's worst-case guarantee.
// 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 quick_sort(Span<int> a) {
        checked {
            int n = a.Length;
            alg_require(((n >= 0) && (n <= 1000000)));
            alg_require((a.Length == n));
            int[] lefts = new int[alg_size(64)];
            int[] rights = new int[alg_size(64)];
            int top = 0;
            int low = 0;
            int high = (n - 1);
            int left = 0;
            int right = 0;
            int mid = 0;
            int pivot = 0;
            int temp = 0;
            while (((low < high) || (top > 0))) {
                if ((low >= high)) {
                    top = (top - 1);
                    low = lefts[top];
                    high = rights[top];
                }
                mid = (low + ((high - low) / 2));
                pivot = Math.Max(Math.Min(a[low], a[mid]), Math.Min(Math.Max(a[low], a[mid]), a[high]));
                left = low;
                mid = low;
                right = high;
                while ((mid <= right)) {
                    if ((a[mid] < pivot)) {
                        temp = a[left];
                        a[left] = a[mid];
                        a[mid] = temp;
                        left = (left + 1);
                        mid = (mid + 1);
                    } else {
                        if ((a[mid] > pivot)) {
                            temp = a[mid];
                            a[mid] = a[right];
                            a[right] = temp;
                            right = (right - 1);
                        } else {
                            mid = (mid + 1);
                        }
                    }
                }
                if (((left - low) < (high - right))) {
                    if (((right + 1) < high)) {
                        lefts[top] = (right + 1);
                        rights[top] = high;
                        top = (top + 1);
                    }
                    high = (left - 1);
                } else {
                    if ((low < (left - 1))) {
                        lefts[top] = low;
                        rights[top] = (left - 1);
                        top = (top + 1);
                    }
                    low = (right + 1);
                }
            }
            return 0;
        }
    }

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