## Python, math, find_min_recursion.py

``````from __future__ import annotations

# Divide and Conquer algorithm
def find_min(nums: list[int | float], left: int, right: int) -> int | float:
"""
find min value in list
:param nums: contains elements
:param left: index of first element
:param right: index of last element
:return: min in nums

>>> for nums in ([3, 2, 1], [-3, -2, -1], [3, -3, 0], [3.0, 3.1, 2.9]):
...     find_min(nums, 0, len(nums) - 1) == min(nums)
True
True
True
True
>>> nums = [1, 3, 5, 7, 9, 2, 4, 6, 8, 10]
>>> find_min(nums, 0, len(nums) - 1) == min(nums)
True
>>> find_min([], 0, 0)
Traceback (most recent call last):
...
ValueError: find_min() arg is an empty sequence
>>> find_min(nums, 0, len(nums)) == min(nums)
Traceback (most recent call last):
...
IndexError: list index out of range
>>> find_min(nums, -len(nums), -1) == min(nums)
True
>>> find_min(nums, -len(nums) - 1, -1) == min(nums)
Traceback (most recent call last):
...
IndexError: list index out of range
"""
if len(nums) == 0:
raise ValueError("find_min() 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_min = find_min(nums, left, mid)  # find min in range[left, mid]
right_min = find_min(nums, mid + 1, right)  # find min in range[mid + 1, right]

return left_min if left_min <= right_min else right_min

if __name__ == "__main__":
import doctest

doctest.testmod(verbose=True)
``````