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from sys import maxsize

def array_equalization(vector: list[int], step_size: int) -> int:

"""

This algorithm equalizes all elements of the input vector

to a common value, by making the minimal number of

"updates" under the constraint of a step size (step_size).

>>> array_equalization([1, 1, 6, 2, 4, 6, 5, 1, 7, 2, 2, 1, 7, 2, 2], 4)

>>> array_equalization([22, 81, 88, 71, 22, 81, 632, 81, 81, 22, 92], 2)

>>> array_equalization([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 5)

>>> array_equalization([22, 22, 22, 33, 33, 33], 2)

>>> array_equalization([1, 2, 3], 0)

Traceback (most recent call last):

ValueError: Step size must be positive and non-zero.

>>> array_equalization([1, 2, 3], -1)

Traceback (most recent call last):

ValueError: Step size must be positive and non-zero.

>>> array_equalization([1, 2, 3], 0.5)

Traceback (most recent call last):

ValueError: Step size must be an integer.

>>> array_equalization([1, 2, 3], maxsize)

"""

if step_size <= 0:

raise ValueError("Step size must be positive and non-zero.")

if not isinstance(step_size, int):

raise ValueError("Step size must be an integer.")

unique_elements = set(vector)

min_updates = maxsize

for element in unique_elements:

elem_index = 0

updates = 0

while elem_index < len(vector):

if vector[elem_index] != element:

updates += 1

elem_index += step_size

else:

elem_index += 1

min_updates = min(min_updates, updates)

return min_updates

if __name__ == "__main__":

from doctest import testmod

testmod()

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