Naive Pattern Matching in C#

using System;
// Naive Pattern Matching in C#
//
// PURPOSE
// Naive pattern matching tries the pattern at every possible starting position. It is simple
// and useful for short patterns or as a correctness reference.
//
// METHOD
// At each alignment compare tokens until a mismatch or the whole pattern matches. Return the
// first complete match, or -1 after every alignment fails.
//
// COMPLEXITY
// O(nm) worst-case time and O(1) auxiliary space.
//
// CONTRACT
// Text and pattern are integer token arrays with lengths n and m. Empty pattern matches at
// zero. Text normalization/tokenization is outside the function.
// 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: 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 naive_match(ReadOnlySpan<int> text, ReadOnlySpan<int> pattern) {
        checked {
            int n = text.Length;
            int m = pattern.Length;
            alg_require(((n >= 0) && (n <= 1000000)));
            alg_require(((m >= 0) && (m <= 1000000)));
            alg_require((pattern.Length == m));
            alg_require((text.Length == n));
            int i = 0;
            int j = 0;
            while ((i <= (n - m))) {
                j = 0;
                while (((j < m) && (text[(i + j)] == pattern[j]))) {
                    j = (j + 1);
                }
                if ((j == m)) {
                    return i;
                }
                i = (i + 1);
            }
            return (-1);
        }
    }

    static void Main() {
        int[] text = new int[] {1, 2, 1, 2, 3};
        int[] pattern = new int[] {1, 2, 3};
        int result = naive_match(text, pattern);
        Console.WriteLine(result);
    }
}