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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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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(i) Suppose an initially empty stack S has executed a total of 30 push operations,20 top operations, and 18 pop operations, 8 of which raised Empty errors that were caught and ignored. What is the maximum and current size of S? Clearly write how you calculated the current size of S based on the stack operations. How many overflow errors would have occurred during the push operations?

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?

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