(e) 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 vector. 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: 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.) Note that this question is the same as part (d) except that the general list and the stacks have been implemented with vectors instead of linked lists.

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