Naive Pattern Matching in Python

from bisect import bisect_left

# Naive Pattern Matching in Python
#
# 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
# 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 naive_match(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)
    i: int = 0
    j: int = 0
    while i <= n - m:
        j = 0
        while j < m and text[i + j] == pattern[j]:
            j += 1
        if j == m:
            return i
        i += 1
    return -1

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