Counting Sort in Python

from bisect import bisect_left

# Counting Sort in Python
#
# PURPOSE
# Counting sort counts each possible key instead of comparing pairs. It is efficient when
# nonnegative integer keys occupy a small range.
#
# METHOD
# Count occurrences in a frequency array, then write each key the recorded number of times.
# The output prefix is sorted throughout reconstruction.
#
# COMPLEXITY
# O(n + k) time and O(k) auxiliary space, where k = maximum + 1. This key-only version does
# not demonstrate stable sorting of records.
#
# CONTRACT
# All n values must be between 0 and maximum inclusive. Sorts in place and returns 0. A huge
# maximum makes this approach unsuitable.
# 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 a after call: [1, 1, 3, 5].
# 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 counting_sort(a: list[int], maximum: int) -> int:
    alg_require(isinstance(a, list) and len(a) <= 1000000)
    alg_require(type(maximum) is int and -2147483648 <= maximum <= 2147483647)
    n: int = len(a)
    alg_require(n >= 0 and n <= 1000000)
    alg_require(len(a) == n)
    alg_require(maximum >= 0 and maximum <= 1000000)
    for value in a:
        alg_require(value >= 0 and value <= maximum)
    counts: list[int] = [0] * alg_size(maximum + 1)
    i: int = 0
    value: int = 0
    out: int = 0
    while i < n:
        counts[a[i]] += 1
        i += 1
    while value <= maximum:
        while counts[value] > 0:
            a[out] = value
            out += 1
            counts[value] -= 1
        value += 1
    return 0

a = [5, 1, 3, 1]
maximum = 5
result = counting_sort(a, maximum)
print(result)
print(a)
# Expected a: [1, 1, 3, 5]