Question 8\ Let

\\\\alpha inZ_()>=2

be an arbitrary integer of value greater than or equal to 2 . Suppose we are performing\ operations on a data structure

D

where the cost of the

k^(th)

operation

o_(k)

is defined by\ if

k

is a power of

\\\\alpha

, and 1 otherwise\ Use the potential method to show that the amortized cost of an operation

o_(k)

is

O(1)

. Justify all\ statements briefly and show all steps.\ Note that you will need to carefully define a potential function and show that it is valid for full\ points.\ Upload

Let Z2 be an arbitrary integer of value greater than or equal to 2 . Suppose we are performing operations on a data structure D where the cost of the kth operation ok is defined by cost(ok)={k if k is a power of , and 1 otherwise Use the potential method to show that the amortized cost of an operation ok is O(1). Justify all statements briefly and show all steps. Note that you will need to carefully define a potential function and show that it is valid for full points. Upl