Sure, here's the updated code with comments and tests:

def quick_sort(arr):
    """
    This function implements the quick sort algorithm to sort an input array in ascending order.

    Parameters:
        arr (list): The input list to be sorted

    Returns:
        list: The sorted list

    """
    # Base case: If the input list is empty or contains only one element, return it as is
    if len(arr) <= 1:
        return arr
    else:
        # Choose the first element of the list as the pivot
        pivot = arr[0]

        # Partition the input list into two sub-lists based on the pivot
        left = []
        right = []
        for i in range(1, len(arr)):
            if arr[i] < pivot:
                left.append(arr[i])
            else:
                right.append(arr[i])

        # Recursively apply quick sort to the two sub-lists and concatenate the results
        return quick_sort(left) + [pivot] + quick_sort(right)


# Tests
arr1 = [3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5]
sorted_arr1 = quick_sort(arr1)
print(sorted_arr1)  # Output: [1, 1, 2, 3, 3, 4, 5, 5, 5, 6, 9]

arr2 = [5, 4, 3, 2, 1]
sorted_arr2 = quick_sort(arr2)
print(sorted_arr2)  # Output: [1, 2, 3, 4, 5]

arr3 = []
sorted_arr3 = quick_sort(arr3)
print(sorted_arr3)  # Output: []

arr4 = [1]
sorted_arr4 = quick_sort(arr4)
print(sorted_arr4)  # Output: [1]

arr5 = [1, 1, 1, 1, 1]
sorted_arr5 = quick_sort(arr5)
print(sorted_arr5)  # Output: [1, 1, 1, 1, 1]

arr6 = [2, 1]
sorted_arr6 = quick_sort(arr6)
print(sorted_arr6)  # Output: [1, 2]


In the tests, we have included several input lists of varying length and content to check that the function can handle edge cases and return the expected output for each input.
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