Z Algorithm in Python

from bisect import bisect_left

# Z Algorithm in Python
#
# PURPOSE
# The Z array records how many tokens match the prefix at every position.
#
# METHOD
# Maintain the rightmost matching interval. Reuse a previously computed Z value when inside
# it, then extend only beyond its boundary.
#
# COMPLEXITY
# O(n) time and O(1) auxiliary space beyond caller-owned output.
#
# CONTRACT
# Integer token input; output has n entries. Defines Z[0]=0; returns 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: 0.
# Expected output after call: [0, 2, 1, 0, 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 z_array(a: list[int], output: list[int]) -> int:
    alg_require(isinstance(a, (list, tuple)) and len(a) <= 1000000)
    alg_require(isinstance(output, list) and len(output) <= 1000000)
    n: int = len(a)
    alg_require(n >= 0 and n <= 1000000)
    alg_require(len(a) == n)
    alg_require(len(output) == n)
    left: int = 0
    right: int = 0
    i: int = 0
    while i < n:
        output[i] = 0
        i += 1
    i = 1
    while i < n:
        if i <= right:
            output[i] = min(right - i + 1, output[i - left])
        while i + output[i] < n and a[output[i]] == a[i + output[i]]:
            output[i] += 1
        if i + output[i] - 1 > right:
            left = i
            right = i + output[i] - 1
        i += 1
    return 0

a = [1, 1, 1, 2, 1]
output = [0, 0, 0, 0, 0]
result = z_array(a, output)
print(result)
# Expected output: [0, 2, 1, 0, 1]
print(output)