Algorithm 4 Stack Implemented using Two Queues

Require: $Q_1$ and $Q_2$ are two queues.

Ensure: Implementation of stack operations with $Q_1$ and $Q_2$ .

1: // Calculate the number of elements in a queue

2:procedure QueueSize( $Q$ )

3:if $Q.head \le Q.tail$ then

4:return $Q.tail - Q.head$

5:end if

6:return $Q.length + Q.tail - Q.head$

7:end procedure

8:

9: $Q_a = Q_1$ // the active queue

10: $Q_i = Q_2$ // the inactive queue

11: // Swap the active and inactive queue

12:procedure Toggle()

13: $tmp = Q_a$

14: $Q_a = Q_i$

15: $Q_i = tmp$

16:end procedure

17:

18:procedure Push( $x$ )

19:Enqueue( $Q_a, x$ )

20:end procedure

21:

22:procedure Pop()

23:while QueueSize( $Q_a$ ) $>1$ do

24: $x =$ Dequeue( $Q_a$ )

25:Enqueue( $Q_i, x$ )

26:end while

27:Toggle()

28:return Dequeue( $Q_i$ )

29:end procedure