Counting Sort in C#

using System;
// Counting Sort in C#
//
// PURPOSE
// Counting sort counts each possible key instead of comparing pairs. It is efficient when
// nonnegative integer keys occupy a small range.
//
// METHOD
// Count occurrences in a frequency array, then write each key the recorded number of times.
// The output prefix is sorted throughout reconstruction.
//
// COMPLEXITY
// O(n + k) time and O(k) auxiliary space, where k = maximum + 1. This key-only version does
// not demonstrate stable sorting of records.
//
// CONTRACT
// All n values must be between 0 and maximum inclusive. Sorts in place and returns 0. A huge
// maximum makes this approach unsuitable.
// 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 counting_sort(Span<int> a, int maximum) {
        checked {
            int n = a.Length;
            alg_require(((n >= 0) && (n <= 1000000)));
            alg_require((a.Length == n));
            alg_require(((maximum >= 0) && (maximum <= 1000000)));
            for (int alg_i = 0; alg_i < a.Length; alg_i++) {
                int alg_value = a[alg_i];
                alg_require(((alg_value >= 0) && (alg_value <= maximum)));
            }
            int[] counts = new int[alg_size((maximum + 1))];
            int i = 0;
            int value = 0;
            int out_value = 0;
            while ((i < n)) {
                counts[a[i]] = (counts[a[i]] + 1);
                i = (i + 1);
            }
            while ((value <= maximum)) {
                while ((counts[value] > 0)) {
                    a[out_value] = value;
                    out_value = (out_value + 1);
                    counts[value] = (counts[value] - 1);
                }
                value = (value + 1);
            }
            return 0;
        }
    }

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