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)