Kadane Maximum Subarray in Python

from bisect import bisect_left

# Kadane Maximum Subarray in Python
#
# PURPOSE
# Kadane algorithm finds the largest sum of a contiguous nonempty subarray. At each
# position, a best ending subarray either extends the previous one or starts here.
#
# METHOD
# Track the best sum ending at the current position and the best seen anywhere. If extending
# is worse than restarting, start at the current value.
#
# COMPLEXITY
# O(n) time and O(1) auxiliary space.
#
# CONTRACT
# n >= 1. Returns the maximum sum, including the largest element when all values are
# negative. Sums must fit the integer type.
# 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: 6.
# 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 maximum_subarray(a: list[int]) -> int:
    alg_require(isinstance(a, (list, tuple)) and len(a) <= 1000000)
    n: int = len(a)
    alg_require(n >= 0 and n <= 1000000)
    alg_require(len(a) == n)
    alg_require(n >= 1)
    ending: int = a[0]
    best: int = a[0]
    i: int = 1
    while i < n:
        ending = max(a[i], ending + a[i])
        best = max(best, ending)
        i += 1
    return best

a = [-2, 1, -3, 4, -1, 2, 1, -5, 4]
result = maximum_subarray(a)
print(result)