In the following five problems, you modify the Array class

defined in this chapter to make it behave more like

Python$$s list class. For each solution, include code that tests your

modifications to the Array class. I have given starter file for each

problem as a hint.

$1.$ Add an instance variable logicalSize to the Array class. This

variable is initially $0$ and will track the number of items currently

available to users of the array.

Then add the method size$()$ to the Array class. This method

should return the array$$s logical size. The method $\_\_$len$\_\_$ should

still return the array$$s capacity or physical size.

$2.$ Add the methods grow and shrink to the Array class. These

methods should use the strategies discussed in this chapter to

increase or decrease the length of the list contained in the array.

Make sure that the physical size of the array does not shrink

below the user$-$specified capacity and that the array$$s cells use the

fill value when the array$$s size is increased.

$3.$ Add the methods insert and pop to the Array class. These

methods should use the strategies discussed in this chapter,

including adjusting the length of the array, if necessary.

The insert method expects a position and an item as arguments

and inserts the item at the given position. If the position is greater

than or equal to the array$$s logical size, the method inserts the

item after the last item currently available in the array.

The pop method expects a position as an argument and removes

and returns the item at that position. The pop method$$s

precondition is index $$ size$().$ The remove method should

also reset the vacated array cell to the fill value.

$4.$ Add the method $\_\_$eq$\_\_$ to the Array class. Python runs this

method when an Array object appears as the left operand of