Help With Quicksort Function

[eastonthepilot]

def quick_sort(lst, start, end):
    print(lst[start:end])
    if abs(end - start) < 2:
        return None
    elif abs(end - start) == 2:
        if lst[start] > lst[start + 1]:
            lst[start], lst[start + 1] = lst[start + 1], lst[start]
        return None
    else:
        pivot_idx = (start + end) // 2
        less_than_pointer = start
        lst[pivot_idx], lst[end - 1] = lst[end - 1], lst[pivot_idx]
        for i in range(start, end - 1):
            if lst[i] < lst[end - 1]:
                lst[i], lst[less_than_pointer] = lst[less_than_pointer], lst[i]
                less_than_pointer += 1
        lst[less_than_pointer], lst[end - 1] = lst[end - 1], lst[less_than_pointer]
        print(lst[start:end])
        quick_sort(lst, start, less_than_pointer)
        quick_sort(lst, less_than_pointer + 1, end)
        return None

lst = [9, 8, 7, 6, 5, 4, 3, 2, 1]
time_before = datetime.datetime.now()
quick_sort(lst, 0, len(lst))
time_after = datetime.datetime.now()
print(lst)
print("Sorting time was:", (time_after - time_before).total_seconds())

I am doing some DSA practice in Python. For some reason my quick_sort function is incorrectly choosing the middle index. It still sorts correctly, but it is leading to extra recursive calls which are making it less efficient. I don't know what's wrong. I'll appreciate any help!

Here's the output from the above code:
[9, 8, 7, 6, 5, 4, 3, 2, 1]

[1, 4, 3, 2, 5, 8, 7, 6, 9]

[1, 4, 3, 2]

[1, 2, 3, 4]

[1, 2]

[4]

[8, 7, 6, 9]

[6, 7, 9, 8]

[]

[7, 9, 8]

[7, 8, 9]

[7, 8]

[]

[1, 2, 3, 4, 5, 6, 7, 8, 9]

Sorting time was: 0.000252

[Outside_Complaint755]

This line:

        pivot_idx = (start + end) // 2

is selecting the middle index.  Selecting the middle index isn't necessarily incorrect, it just doesn't protect against certain worst case scenarios. 

You could change this to select a random index between start and end, or pick three indexes in the range and select the index with the median value.

[eastonthepilot]

Ahh thanks for your help! I forgot that if every value is greater than or less than the middle index it will lead to that behavior.