Too many array comparisons - In-place quicksort

Question

I implemented in-place quickSort that use the middle of the array as pivot. I have some test cases I need to fulfill, however my code seems to run to many comparisons. For the array-list:

[10, 4, 33, 44, 17, 20, 3, 2, 9, 82, 38, 67, 55, 11, 32, 23, 19, 7, 6, 14, 29, 10, 10]

I should get 142 comparisons, however I get 196.

This is my code:

comparisons = 0

def addComparison() -> bool:
    global comparisons
    comparisons += 1
    return True

def quicksort(arr_list: list, lower_bound: int, upper_bound: int) -> list:
    if upper_bound > lower_bound:
        index = split_arr(arr_list, lower_bound, upper_bound)
        quicksort(arr_list, lower_bound, index)
        quicksort(arr_list, index+1, upper_bound)
    addComparison()

def split_arr(arr_list: list, lower_bound: int, upper_bound: int) -> int:
    global comparisons
    pivot_index = (lower_bound + upper_bound) // 2
    pivot_elem  = arr_list[pivot_index]

    while lower_bound <= upper_bound:

        left = lower_bound
        while addComparison() and arr_list[left] < pivot_elem:
            left += 1
        
        right = upper_bound
        while addComparison() and arr_list[right] > pivot_elem:
            right -= 1
        
        if left < right:
            arr_list[left], arr_list[right] = arr_list[right], arr_list[left]
            lower_bound = left  + 1
            upper_bound = right - 1
        else:
            return right
    return upper_bound

unsorted_list = [10, 4, 33, 44, 17, 20, 3, 2, 9, 82, 38, 67, 55, 11, 32, 23, 19, 7, 6, 14, 29, 10, 10]

quicksort(unsorted_list, 0, len(unsorted_list) - 1)

assert comparisons == 142

Answer 1

You have implemented a different partition scheme than your instructor, which will change the actual number of comparisons on a specific data set.

Your instructor seems to have implemented the basic "pivot on the last item" partition scheme -- slightly modified by swapping the middle item to the last item, with no comparison. I get 142 on that data set with that algorithm.

Using the terminology at https://en.wikipedia.org/wiki/Quicksort you implemented Hoare partition scheme, but you were expected to use Lomuto (which was probably covered in class).

I don't want to post too much, but if I am correct, then
your code used 195 comparisons and 29 swaps, and
the instructor's code used 142 comparisons and 87 swaps.