Rabin Karp Pattern Matching in Python

from bisect import bisect_left

# Rabin Karp Pattern Matching in Python
#
# 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
# Python 3.9+: automatic lengths, native lists, arbitrary-precision arithmetic, and
# bisect_left for LIS. Invalid scalar/shape inputs raise ValueError. Integer element types
# and sorted/tree invariants remain caller preconditions.
#
# EXAMPLE
# Expected return: 2.
# Run: python example.py
# Tests for this exact source artifact run before publication. The accompanying source
# archive includes unit cases, runtime results, and source hashes.

def alg_require(condition):
    if not condition:
        raise ValueError("invalid algorithm input; see contract")
def alg_size(n):
    alg_require(0 <= n <= 4000000)
    return n

def rabin_karp(text: list[int], pattern: list[int]) -> int:
    alg_require(isinstance(text, (list, tuple)) and len(text) <= 1000000)
    alg_require(isinstance(pattern, (list, tuple)) and len(pattern) <= 1000000)
    n: int = len(text)
    m: int = len(pattern)
    alg_require(n >= 0 and n <= 1000000)
    alg_require(m >= 0 and m <= 1000000)
    alg_require(len(pattern) == m)
    alg_require(len(text) == n)
    for value in text:
        alg_require(value >= 0 and value <= 255)
    for value in pattern:
        alg_require(value >= 0 and value <= 255)
    if m == 0:
        return 0
    if m > n:
        return -1
    power: int = 1
    target_hash: int = 0
    window_hash: int = 0
    i: int = 0
    j: int = 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 += 1
    i = 0
    while i <= n - m:
        if target_hash == window_hash:
            j = 0
            while j < m and text[i + j] == pattern[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 += 1
    return -1

text = [1, 2, 1, 2, 3]
pattern = [1, 2, 3]
result = rabin_karp(text, pattern)
print(result)