# Exercise 10.1.7

Show how to implement a stack using two queues. Analyze the running time of the stack operations.

We have two queues and mark one of them as active. `PUSH`

queues an element on
the active queue. `POP`

should dequeue all but one element of the active queue
and queue them on the inactive. The roles of the queues are then reversed, and
the final element left in the (now) inactive queue is returned.

The `PUSH`

operation is $\Theta(1)$, but the `POP`

operation is $\Theta(n)$
where $n$ is the number of elements in the stack.