Monotonic Deque Sliding Maximum in Python

from bisect import bisect_left

# Monotonic Deque Sliding Maximum in Python
#
# PURPOSE
# A monotonic deque returns every fixed-window maximum in linear time.
#
# METHOD
# Keep candidate indices in decreasing value order. Discard expired indices from the front
# and dominated candidates from the back; the front is the current maximum.
#
# COMPLEXITY
# O(n) time; O(n) allocated index-buffer space in this linear-buffer implementation, with at
# most k live candidates.
#
# CONTRACT
# 1 <= k <= n. output has n-k+1 entries. Writes maximum values and returns output length.
# 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.
# Expected output after call: [3, 3, 5, 5, 6, 7].
# 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_maximum(a: list[int], k: int, output: list[int]) -> int:
    alg_require(isinstance(a, (list, tuple)) and len(a) <= 1000000)
    alg_require(type(k) is int and -2147483648 <= k <= 2147483647)
    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 - k + 1)
    alg_require(k >= 1 and k <= n)
    queue: list[int] = [0] * alg_size(n)
    head: int = 0
    tail: int = 0
    i: int = 0
    while i < n:
        while head < tail and queue[head] <= i - k:
            head += 1
        while head < tail and a[queue[tail - 1]] <= a[i]:
            tail -= 1
        queue[tail] = i
        tail += 1
        if i >= k - 1:
            output[i - k + 1] = a[queue[head]]
        i += 1
    return n - k + 1

a = [1, 3, -1, -3, 5, 3, 6, 7]
k = 3
output = [0, 0, 0, 0, 0, 0]
result = sliding_maximum(a, k, output)
print(result)
# Expected output: [3, 3, 5, 5, 6, 7]
print(output)