Dot Star Regular Expression Matching in Python

from bisect import bisect_left

# Dot Star Regular Expression Matching in Python
#
# PURPOSE
# This small matcher supports whole-sequence matching with a wildcard token and repetition
# of the preceding token.
#
# METHOD
# Use a table of prefix matches. A star can omit its preceding token or consume another
# matching text token. A non-star token extends the previous diagonal.
#
# COMPLEXITY
# O(nm) time and O(nm) space. Only dot and star semantics are supported; this is not a full
# regex engine.
#
# CONTRACT
# Tokens >=0 are literal; -1 is dot and -2 is star in the pattern. Star must follow a
# literal or dot, never another star. Returns 1 or 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
# 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: 1.
# 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 regex_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)
    for i, value in enumerate(pattern):
        alg_require(value >= -2 and (value != -2 or (i > 0 and pattern[i - 1] != -2)))
    dp: list[int] = [0] * alg_size((n + 1) * (m + 1))
    dp[0] = 1
    i: int = 0
    j: int = 2
    while j <= m:
        if pattern[j - 1] == -2:
            dp[j] = dp[j - 2]
        j += 1
    i = 1
    while i <= n:
        j = 1
        while j <= m:
            if pattern[j - 1] == -2:
                dp[i * (m + 1) + j] = dp[i * (m + 1) + j - 2]
                if pattern[j - 2] == -1 or pattern[j - 2] == text[i - 1]:
                    dp[i * (m + 1) + j] = max(dp[i * (m + 1) + j], dp[(i - 1) * (m + 1) + j])
            elif pattern[j - 1] == -1 or pattern[j - 1] == text[i - 1]:
                dp[i * (m + 1) + j] = dp[(i - 1) * (m + 1) + j - 1]
            j += 1
        i += 1
    return dp[n * (m + 1) + m]

text = [1, 1, 2]
pattern = [1, -2, 2]
result = regex_match(text, pattern)
print(result)