Question

Suppose I want to implement the public member functions of a Stack (push, pop, top, size, isEmpty). However, instead of the private member data we had in class, I have only a single Queue.

You may assume that the Queue has unbounded capacity, but is otherwise as per the one shown in class. Explain at a high level (you do not need to provide C++ code, but someone should be able to understand how you would code it from what you wrote) how you would implement each of those functions using just that Queue. Note that you must use the Queue’s public interface (enqueue, dequeue, etc) and cannot access the underlying private member data. For each function, give the running time in O notation in terms of n, the number of elements currently in the stack.

Answer 1

solution:-

given the data

Implementing a Stack using Queue structure can be done it two ways – either by making push operation costly or by making pop operation costly. If we are implementing with first type, then whenever we need to push a value to the stack, we add it to the queue, loop for size-1 times, dequeue value from front and enqueue it to the back, so that the element added will be at the front of the queue and can be accessed by simply calling dequeue() method of the queue. The time complexity would be linear for push and constant for pop, assuming the complexity of enqueue/dequeue operations for the Queue to be used is constant. In the second type (pop operation costly), we need constant time for push operation and linear time for pop, since we need to remove and restore size-1 number of elements to get the top value of the stack.

Please find the below pseudocode/high level description of each methods. Let q be the underlying Queue structure, and it has methods enqueue(), dequeue(), front(), size() and isEmpty()

push(element): (linear time)

q.enqueue(elem)

for i in 1 to q.size()-1:

                frontElem=q.front()

                q.dequeue()

q.enqueue(frontElem)

end for

pop(): (constant time)

elem=q.front()

q.dequeue()

return elem

top(): (constant time)

return q.front()

size(): (constant time)

return q.size()

isEmpty():(constant time)

return q.isEmpty()

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