LSD Radix Sort in Python

from bisect import bisect_left

# LSD Radix Sort in Python
#
# PURPOSE
# LSD radix sort orders bounded nonnegative integers one byte at a time using stable
# counting passes.
#
# METHOD
# For each of four base-256 digits, count occurrences, compute cumulative positions, then
# distribute from right to left to preserve stability.
#
# COMPLEXITY
# O(4(n+256)) time and O(n+256) auxiliary space for 32-bit keys. Stable.
#
# CONTRACT
# Keys are nonnegative signed 32-bit integers. Sorts ascending in place, 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 a after call: [0, 1, 255, 256, 65536].
# 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 radix_sort(a: list[int]) -> int:
    alg_require(isinstance(a, list) and len(a) <= 1000000)
    n: int = len(a)
    alg_require(n >= 0 and n <= 1000000)
    alg_require(len(a) == n)
    for value in a:
        alg_require(value >= 0)
    output: list[int] = [0] * alg_size(n + 1)
    count: list[int] = [0] * alg_size(256)
    divisor: int = 1
    digit: int = 0
    pass_index: int = 0
    i: int = 0
    while pass_index < 4:
        i = 0
        while i < 256:
            count[i] = 0
            i += 1
        i = 0
        while i < n:
            digit = a[i] // divisor % 256
            count[digit] += 1
            i += 1
        i = 1
        while i < 256:
            count[i] += count[i - 1]
            i += 1
        i = n - 1
        while i >= 0:
            digit = a[i] // divisor % 256
            count[digit] -= 1
            output[count[digit]] = a[i]
            i -= 1
        i = 0
        while i < n:
            a[i] = output[i]
            i += 1
        pass_index += 1
        if pass_index < 4:
            divisor *= 256
    return 0

a = [256, 1, 65536, 0, 255]
result = radix_sort(a)
print(result)
# Expected a: [0, 1, 255, 256, 65536]
print(a)