Heap Sort in Python

from bisect import bisect_left

# Heap Sort in Python
#
# PURPOSE
# Heap sort uses a max heap so the largest remaining value can be moved to the end. It gives
# a worst-case time guarantee without a second array.
#
# METHOD
# Build a max heap from the bottom up. Swap its root with the last active element, shrink
# the heap, and sift the new root downward. The suffix is sorted after every extraction.
#
# COMPLEXITY
# O(n log n) time, O(1) auxiliary space; heap construction is O(n). Not stable.
#
# CONTRACT
# Sorts n elements 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: [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 heap_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)
    start: int = n // 2 - 1
    end: int = n - 1
    root: int = 0
    child: int = 0
    temp: int = 0
    while start >= 0:
        root = start
        while 2 * root + 1 < n:
            child = 2 * root + 1
            if child + 1 < n and a[child] < a[child + 1]:
                child += 1
            if a[root] >= a[child]:
                break
            temp = a[root]
            a[root] = a[child]
            a[child] = temp
            root = child
        start -= 1
    while end > 0:
        temp = a[0]
        a[0] = a[end]
        a[end] = temp
        root = 0
        while 2 * root + 1 < end:
            child = 2 * root + 1
            if child + 1 < end and a[child] < a[child + 1]:
                child += 1
            if a[root] >= a[child]:
                break
            temp = a[root]
            a[root] = a[child]
            a[child] = temp
            root = child
        end -= 1
    return 0

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