Rabin Karp Pattern Matching in C#

using System;
// Rabin Karp Pattern Matching in C#
//
// PURPOSE
// Rabin-Karp uses a rolling hash to filter candidate matches, then compares tokens to
// guarantee correctness despite hash collisions.
//
// METHOD
// Hash the pattern and first window modulo a small prime. At each position verify matching
// hashes, then remove the old token and append the new one.
//
// COMPLEXITY
// Expected O(n+m) time on suitable data; O(nm) worst case due to verification. O(1)
// auxiliary space.
//
// CONTRACT
// Tokens are integers in [0,255]. Empty pattern matches at zero. Returns first index or -1;
// not a cryptographic hash.
// 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 rabin_karp(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));
            for (int alg_i = 0; alg_i < text.Length; alg_i++) {
                int alg_value = text[alg_i];
                alg_require(((alg_value >= 0) && (alg_value <= 255)));
            }
            for (int alg_i = 0; alg_i < pattern.Length; alg_i++) {
                int alg_value = pattern[alg_i];
                alg_require(((alg_value >= 0) && (alg_value <= 255)));
            }
            if ((m == 0)) {
                return 0;
            }
            if ((m > n)) {
                return (-1);
            }
            int power = 1;
            int target_hash = 0;
            int window_hash = 0;
            int i = 0;
            int j = 0;
            while ((i < m)) {
                target_hash = (((target_hash * 256) + pattern[i]) % 10007);
                window_hash = (((window_hash * 256) + text[i]) % 10007);
                if ((i < (m - 1))) {
                    power = ((power * 256) % 10007);
                }
                i = (i + 1);
            }
            i = 0;
            while ((i <= (n - m))) {
                if ((target_hash == window_hash)) {
                    j = 0;
                    while (((j < m) && (text[(i + j)] == pattern[j]))) {
                        j = (j + 1);
                    }
                    if ((j == m)) {
                        return i;
                    }
                }
                if ((i < (n - m))) {
                    window_hash = (((window_hash - ((text[i] * power) % 10007)) + 10007) % 10007);
                    window_hash = (((window_hash * 256) + text[(i + m)]) % 10007);
                }
                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 = rabin_karp(text, pattern);
        Console.WriteLine(result);
    }
}