$2.$ We can implement a queue using two stacks:

Algorithm $1$ Enqueue$($x$)$

push$($stackB$,$ x$)$

Algorithm $2$ Dequeue$($x$)$

if stackA is empty then

while stackB is not empty do

x $=$ pop$($stackB$)$

push$($stackA$,$ x$)$

if stackA is not empty then

return pop$($stackA$)$

You can assume that stack operations push$()$ and pop$()$ take O$(1).$ Analyze the joint amortized

runtime for Enqueue$()$ and Dequeue$().$