Suppose you are implementing a list of stacks. Let's say you decide to implement both the general list (the list of stacks) and each individual stack using a double linked list. Assume that there are currently N stacks in the list, and each stack has a maximum of K items, where N and K are both large. You are going to iterate through the general list and apply a single operation to each stack as you encounter it. Now answer the following four questions, using big-Theta notation: What is the average-case time complexity of pushing one additional item into each stack? What is the worst-case time complexity of pushing one additional item into each stack? What is the average-case time complexity of popping one item from each stack? What is the worst-case time complexity of popping one additional item from each stack?

C++ Programming: From Problem Analysis to Program Design
8th Edition
ISBN:9781337102087
Author:D. S. Malik
Publisher:D. S. Malik
Chapter17: Linked Lists
Section: Chapter Questions
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(2) Answer the following questions concerning lists, stacks, and queues

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(d) Suppose you are implementing a list of stacks. Let's say you decide to implement both the general list (the list of stacks) and each individual stack using a double linked list. Assume that there are currently N stacks in the list, and each stack has a maximum of K items, where N and K are both large. You are going to iterate through the general list and apply a single operation to each stack as you encounter it. Now answer the following four questions, using big-Theta notation: What is the average-case time complexity of pushing one additional item into each stack? What is the worst-case time complexity of pushing one additional item into each stack? What is the average-case time complexity of popping one item from each stack? What is the worst-case time complexity of popping one additional item from each stack? (For pops, if the stack is empty, you can assume that the pop itself is a constant-time operation and does something reasonable.)

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