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(a) Describe how to simulate a queue using two stacks, L and R: Each of the two primary queue operations, enqueue and dequeue, should be implemented by performing certain stack operations (push and pop) on L and/or R.
Explain exactly what stack operations you will use for this simulation. The cost of one stack operation is 1. Your strategy must have O(1) amortized time complexity for both queue operations, assuming that there will be a mix of n such operations. This is to be analyzed in the following three ways:
(b) Provide a quick argument to analyze the time complexity per element in your strategy. In other words, what could possibly happen to one element of data in this simulated queue, and what would be its contribution to the total time complexity?
(c) Use the accounting method to amortize.
(d) Use the potential method to amortize.
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