Introduction to Algorithms
Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
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Chapter 10.1, Problem 1E
Program Plan Intro

To model the given stack operations on an initially empty stack S stored in array S[1..6] as per figure 10.1 of the textbook.

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multiple choice: consider an array based implementation of a stack and its push operation. Beginning with an array of length 1 = (2^0), consider where the array’s length will be doubled whenever an insertion(via the push operation) is attempted when the array is full. What is the amortized complexity of performing a sequence of n push operations. a) Θ(log n) b) Θ(n) c) Θ(n^2) d) Θ(1)
Consider an empty stack STK of size 5 (array-based implementation). What will be the output after applying the following stack operations? Draw a diagram in support of your answer. How many elements are there in the stack at the end of the processing?                       [15+5] POP(), PUSH(25), PUSH(20), POP(), POP(), PUSH(45), PUSH(15), POP(), PUSH(30), PUSH(17), PUSH(33), PUSH(24), PUSH(54), POP(), PUSH(99)
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.
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