Dutch National Flag Partition in Python

from bisect import bisect_left

# Dutch National Flag Partition in Python
#
# PURPOSE
# Three-way partition groups zeros, ones, and twos in one pass. The same idea is useful for
# grouping values around a pivot.
#
# METHOD
# Keep a zero prefix, a one middle, an unknown interval, and a two suffix. Swap a zero left,
# advance past a one, or swap a two right and re-examine the incoming unknown value.
#
# COMPLEXITY
# O(n) time and O(1) auxiliary space. Not stable.
#
# CONTRACT
# Every value must be 0, 1, or 2. Mutates the array into sorted order and 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, 0, 1, 2, 2].
# 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 dutch_flag(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 and value <= 2)
    low: int = 0
    mid: int = 0
    high: int = n - 1
    temp: int = 0
    while mid <= high:
        if a[mid] == 0:
            temp = a[low]
            a[low] = a[mid]
            a[mid] = temp
            low += 1
            mid += 1
        elif a[mid] == 1:
            mid += 1
        else:
            temp = a[mid]
            a[mid] = a[high]
            a[high] = temp
            high -= 1
    return 0

a = [2, 0, 1, 2, 0]
result = dutch_flag(a)
print(result)
print(a)
# Expected a: [0, 0, 1, 2, 2]