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from __future__ import annotations

# Divide and Conquer algorithm

def find_max(nums: list[int | float], left: int, right: int) -> int | float:

"""

find max value in list

:param nums: contains elements

:param left: index of first element

:param right: index of last element

:return: max in nums

>>> for nums in ([3, 2, 1], [-3, -2, -1], [3, -3, 0], [3.0, 3.1, 2.9]):

... find_max(nums, 0, len(nums) - 1) == max(nums)

True

True

True

True

>>> nums = [1, 3, 5, 7, 9, 2, 4, 6, 8, 10]

>>> find_max(nums, 0, len(nums) - 1) == max(nums)

True

>>> find_max([], 0, 0)

Traceback (most recent call last):

...

ValueError: find_max() arg is an empty sequence

>>> find_max(nums, 0, len(nums)) == max(nums)

Traceback (most recent call last):

...

IndexError: list index out of range

>>> find_max(nums, -len(nums), -1) == max(nums)

True

>>> find_max(nums, -len(nums) - 1, -1) == max(nums)

Traceback (most recent call last):

...

IndexError: list index out of range

"""

if len(nums) == 0:

raise ValueError("find_max() arg is an empty sequence")

if (

left >= len(nums)

or left < -len(nums)

or right >= len(nums)

or right < -len(nums)

):

raise IndexError("list index out of range")

if left == right:

return nums[left]

mid = (left + right) >> 1 # the middle

left_max = find_max(nums, left, mid) # find max in range[left, mid]

right_max = find_max(nums, mid + 1, right) # find max in range[mid + 1, right]

return left_max if left_max >= right_max else right_max

if __name__ == "__main__":

import doctest

doctest.testmod(verbose=True)