Knuth Morris Pratt Pattern Matching in Python

from bisect import bisect_left

# Knuth Morris Pratt Pattern Matching in Python
#
# PURPOSE
# KMP avoids rechecking text tokens by remembering which matched pattern suffix is also a
# prefix. The prefix table tells where to resume after a mismatch.
#
# METHOD
# Build the longest proper prefix/suffix table for the pattern. During matching, fall back
# through that table without moving the text position backward. A full matched prefix gives
# the first occurrence.
#
# COMPLEXITY
# O(n+m) time and O(m) auxiliary space.
#
# CONTRACT
# Inputs are integer token sequences. Empty pattern matches at 0. Returns first matching
# index or -1. KMP does not define Unicode tokenization.
# 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 kmp_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)
    if m == 0:
        return 0
    prefix: list[int] = [0] * alg_size(m + 1)
    i: int = 1
    j: int = 0
    while i < m:
        while j > 0 and pattern[i] != pattern[j]:
            j = prefix[j - 1]
        if pattern[i] == pattern[j]:
            j += 1
        prefix[i] = j
        i += 1
    i = 0
    j = 0
    while i < n:
        while j > 0 and text[i] != pattern[j]:
            j = prefix[j - 1]
        if text[i] == pattern[j]:
            j += 1
        if j == m:
            return i - m + 1
        i += 1
    return -1

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