Dutch National Flag Partition in C#

using System;
// Dutch National Flag Partition in C#
//
// PURPOSE
// Three-way partition groups zeros, ones, and twos in one pass. The same idea is useful for
// grouping values around a pivot.
//
// METHOD
// Keep a zero prefix, a one middle, an unknown interval, and a two suffix. Swap a zero left,
// advance past a one, or swap a two right and re-examine the incoming unknown value.
//
// COMPLEXITY
// O(n) time and O(1) auxiliary space. Not stable.
//
// CONTRACT
// Every value must be 0, 1, or 2. Mutates the array into sorted order and 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: [0, 0, 1, 2, 2].
// 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 dutch_flag(Span<int> a) {
        checked {
            int n = a.Length;
            alg_require(((n >= 0) && (n <= 1000000)));
            alg_require((a.Length == n));
            for (int alg_i = 0; alg_i < a.Length; alg_i++) {
                int alg_value = a[alg_i];
                alg_require(((alg_value >= 0) && (alg_value <= 2)));
            }
            int low = 0;
            int mid = 0;
            int high = (n - 1);
            int temp = 0;
            while ((mid <= high)) {
                if ((a[mid] == 0)) {
                    temp = a[low];
                    a[low] = a[mid];
                    a[mid] = temp;
                    low = (low + 1);
                    mid = (mid + 1);
                } else {
                    if ((a[mid] == 1)) {
                        mid = (mid + 1);
                    } else {
                        temp = a[mid];
                        a[mid] = a[high];
                        a[high] = temp;
                        high = (high - 1);
                    }
                }
            }
            return 0;
        }
    }

    static void Main() {
        int[] a = new int[] {2, 0, 1, 2, 0};
        int result = dutch_flag(a);
        Console.WriteLine(result);
        Console.WriteLine("[" + string.Join(", ", a) + "]");
        // Expected a: [0, 0, 1, 2, 2]
    }
}