How do i answer this Show how to implement First in First ou

How do i answer this?

Show how to implement First in First out with a priority Queue. Show also how to implement a stack in a priority Queue.

First-in-first-out Queue can be implemented by using a min-priority Queue.

Running time theta(1), since, the newly added element has the maximum priority and thus stay at the last position.

Worst case running time theta(log (k-1))

Since one min-heapify required.

Reduce the priority for each element in the Queue from x to x-1

Running time theta(k-1)

K leftarrow k-1

1leftarrow 0

Last –in-first-out Queue can implemented by using a max-priority Queue.

Notice that (k-1) is the maximum priority in the Queue.

K leftarrow k+1

Worst case running time theta(log k),

Since, the newly added element has the maximum priority and thus to be pop up the root.

Running time theta (log(k-1)),

Since one max - heapify required.