Amortized analysis of stacks. Consider a stack with three operations: Push, Pop, and MultiPop(k). The MultiPop(k) operation is implemented as a series of k pops. Push and Pop each take 1 unit of time, and MultiPop(k) takes k units of time. Using amortized analysis, we determined that the average cost of an operation, over n operations, was 2 units of time.

Suppose that in addition to MultiPop(k), we want to implement a new operation MultiPush(k), which is a series of k pushes. Can we modify our amortized analysis to this case? Does amortized analysis help in this case? Why or why not? (Hint: think about what it means for amortized analysis to help. When would we want to use amortized analysis over standard analysis?)