Z Algorithm in C#

using System;
// Z Algorithm in C#
//
// PURPOSE
// The Z array records how many tokens match the prefix at every position.
//
// METHOD
// Maintain the rightmost matching interval. Reuse a previously computed Z value when inside
// it, then extend only beyond its boundary.
//
// COMPLEXITY
// O(n) time and O(1) auxiliary space beyond caller-owned output.
//
// CONTRACT
// Integer token input; output has n entries. Defines Z[0]=0; 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 output after call: [0, 2, 1, 0, 1].
// 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 z_array(ReadOnlySpan<int> a, Span<int> output) {
        checked {
            int n = a.Length;
            alg_require(((n >= 0) && (n <= 1000000)));
            alg_require((a.Length == n));
            alg_require((output.Length == n));
            int left = 0;
            int right = 0;
            int i = 0;
            while ((i < n)) {
                output[i] = 0;
                i = (i + 1);
            }
            i = 1;
            while ((i < n)) {
                if ((i <= right)) {
                    output[i] = Math.Min(((right - i) + 1), output[(i - left)]);
                }
                while ((((i + output[i]) < n) && (a[output[i]] == a[(i + output[i])]))) {
                    output[i] = (output[i] + 1);
                }
                if ((((i + output[i]) - 1) > right)) {
                    left = i;
                    right = ((i + output[i]) - 1);
                }
                i = (i + 1);
            }
            return 0;
        }
    }

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