#### Peak

```"""
Finding the peak of a unimodal list using divide and conquer.
A unimodal array is defined as follows: array is increasing up to index p,
then decreasing afterwards. (for p >= 1)
An obvious solution can be performed in O(n),
to find the maximum of the array.
(From Kleinberg and Tardos. Algorithm Design.
Addison Wesley 2006: Chapter 5 Solved Exercise 1)
"""
from __future__ import annotations

def peak(lst: list[int]) -> int:
"""
Return the peak value of `lst`.
>>> peak([1, 2, 3, 4, 5, 4, 3, 2, 1])
5
>>> peak([1, 10, 9, 8, 7, 6, 5, 4])
10
>>> peak([1, 9, 8, 7])
9
>>> peak([1, 2, 3, 4, 5, 6, 7, 0])
7
>>> peak([1, 2, 3, 4, 3, 2, 1, 0, -1, -2])
4
"""
# middle index
m = len(lst) // 2

# choose the middle 3 elements
three = lst[m - 1 : m + 2]

# if middle element is peak
if three > three and three > three:
return three

# if increasing, recurse on right
elif three < three:
if len(lst[:m]) == 2:
m -= 1
return peak(lst[m:])

# decreasing
else:
if len(lst[:m]) == 2:
m += 1
return peak(lst[:m])

if __name__ == "__main__":
import doctest

doctest.testmod()
```  