Quickselect in C#

using System;
// Quickselect in C#
//
// PURPOSE
// Quickselect finds a zero-based order statistic without fully sorting the input.
//
// METHOD
// Partition around the middle-position pivot using a three-way partition. Retain only the
// side containing rank k, or return the pivot when k lies in the equal region.
//
// COMPLEXITY
// O(n) expected time for random input; O(n squared) worst case for this deterministic pivot.
// O(1) auxiliary space.
//
// CONTRACT
// 0 <= k < n. Mutates input. Returns the kth smallest value, counting duplicates.
// 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: 5.
// Expected a after call: [2, 2, 5, 7, 9].
// 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 quickselect(Span<int> a, int k) {
        checked {
            int n = a.Length;
            alg_require(((n >= 0) && (n <= 1000000)));
            alg_require((a.Length == n));
            alg_require(((k >= 0) && (k < n)));
            int low = 0;
            int high = (n - 1);
            int left = 0;
            int mid = 0;
            int right = 0;
            int pivot = 0;
            int temp = 0;
            while ((low <= high)) {
                pivot = a[(low + ((high - low) / 2))];
                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 ((k < left)) {
                    high = (left - 1);
                } else {
                    if ((k > right)) {
                        low = (right + 1);
                    } else {
                        return pivot;
                    }
                }
            }
            return (-1);
        }
    }

    static void Main() {
        int[] a = new int[] {7, 2, 9, 2, 5};
        int k = 2;
        int result = quickselect(a, k);
        Console.WriteLine(result);
        // Expected a: [2, 2, 5, 7, 9]
        Console.WriteLine("[" + string.Join(", ", a) + "]");
    }
}