To show that the amortized cost of ENQUEUE and DEQUEUE operation is O ( 1 ) to implement a queue by using two stacks.

Question

Want to see the full answer?

Answer 1

Question

Chapter 17.3, Problem 6E

Program Plan Intro

To show that the amortized cost of ENQUEUE and DEQUEUE operation is O(1) to implement a queue by using two stacks.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Students have asked these similar questions

Please assume that you have been given an implementation of a stack that supports both push and pop in O(1) time. With this information, you would like to implement a queue with these stacks. (a) In what way can you efficiently implement a queue using two of these stacks? “Efficiently” in this case means in a way which will allow you to do part B. (b) Please prove that the amortized cost of each dequeue and enqueue operation is O(1) for your stack-based queue by using the aggregate amortized analysis technique.

Consider the following implementation of a queue using 2 stacks. Let S1 andS2 be the two stacks and initially are both empty. enqueue(x): Push x into S1.dequeue(x): If S2 is not empty, then pop an item from S2 and return it. If S2 isempty, pop all items from S1 and push them into S2, then pop an item S2 and returnit. Show that the amortized cost for each queue operation is O(1).

Implement a queue Q using two stacks S1 and S2 so that the operations ENQUEUE(Q, X) and DEQUEUE(Q, Y), where Q is presumably a queue and X is the element to be added to Q and Y is the element deleted from Q, are handled by the stacks that function as a queue. Assume that only stacks are accessible to the ADT functions of PUSH, POP, and EMPTYSTACK. Show how your technique operates on the lists "a," "b," and "c," which the stacks S1 and S2 will use as a queue.