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 17.1, Problem 1E
Program Plan Intro

To decide whether it is possible to push k items onto the stack would require O(1) time on the amortized cost of the stack operations by using the MULTIPUSH operation.

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Question 3 a. "Queues and stacks are used in many real-life situations". In your own words, clearly distinguish between queues and stacks; and give one example of real-life situations in which each of them is used. b. In an array-based implementation of a stack, which end of the contents of the array represent the bottom of the stack and why? c. If the size of circular queue K is 4 with indices number from 0 to 3 what would be the state of the queue after the following set of 8 operations below. Show in a diagram the state of queue K after each of the 8 operations. K. enqueue (“F"), K. enqueue (“R"), K. dequeue(), K. enqueue (“P"), dequeue(), K.front(), K. enqueue (“Z"), K. enqueue (“G") d. Why are insertions and deletions at the logical end of the array more efficient than insertions and deletions in the interior of the array?
Problem Statement: We can store k stacks in a single array if we use the data structure suggested in Figure 1 shown below, for the case k = 3. We push and pop from each stack as suggested in connection with Figure 2 below. However, if pushing onto stack i causes TOP(i) to equal BOTTOM(i – 1), we first move all the stacks so that there is an appropriate size gap between each adjacent pair of stacks. For example, we might make the gaps above all stacks equal, or we might make the gap above stack i proportional to the current size of stack i (on the theory that larger stacks are likely to grow sooner, and we want to postpone as long as possible the next reorganization). 1 stack 1 3 stack 2 bottom stack 3 3 top stackspace Figure 1 top first element second element maxlength last element elements
The pseudocode of Figure 6.16 illustrates the basic push() and pop() operations of an array-based stack. Assuming that this algorithm could be used in a concurrent environment, answer the following questions:a. What data have a race condition?b. How could the race condition be fixed?
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