Fixed Sliding Window Maximum Sum in Python

from bisect import bisect_left

# Fixed Sliding Window Maximum Sum in Python
#
# PURPOSE
# A fixed sliding window reuses the previous window sum rather than adding every window from
# scratch. This handles negative values as well as positive ones.
#
# METHOD
# Sum the first k entries. Advance one position by adding the entering value and subtracting
# the leaving value, keeping the largest total.
#
# COMPLEXITY
# O(n) time and O(1) auxiliary space.
#
# CONTRACT
# 1 <= k <= n. Returns the maximum sum over windows of exactly k elements. Totals must fit.
# 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: 9.
# 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 sliding_window_sum(a: list[int], k: int) -> int:
    alg_require(isinstance(a, (list, tuple)) and len(a) <= 1000000)
    alg_require(type(k) is int and -2147483648 <= k <= 2147483647)
    n: int = len(a)
    alg_require(n >= 0 and n <= 1000000)
    alg_require(len(a) == n)
    alg_require(k >= 1 and k <= n)
    total: int = 0
    i: int = 0
    while i < k:
        total += a[i]
        i += 1
    best: int = total
    while i < n:
        total += a[i] - a[i - k]
        best = max(best, total)
        i += 1
    return best

a = [2, 1, 5, 1, 3, 2]
k = 3
result = sliding_window_sum(a, k)
print(result)