Algorithm 2 Double Ended Queue

Require: $Q$ is an array of length $Q.length$ indexed from $1$ with two attributes $Q.head$ and $Q.tail$ initialized to be $1$

Ensure: Implementation of deque operations that handle overflow and underflow

1: // Inserts elements to the front of deque.

2:procedure HeadEnqueue( $Q, x$ )

3:if QueueFull( $Q$ ) then

4:error "overflow"

5:else

6:if $Q.head == 1$ then

7: $Q.head = Q.length$

8:else

9: $Q.head = Q.head - 1$

10: $Q[Q.head] = x$

11:end if

12:end if

13:end procedure

14:

15: // Inserts elements to the back of deque.

16:procedure TailEnqueue( $Q, x$ )

17:if QueueFull( $Q$ ) then

18:error "overflow"

19:else

20: $Q[Q.tail] = x$

21:if $Q.tail == Q.length$ then

22: $Q.tail = 1$

23:else

24: $Q.tail = Q.tail + 1$

25:end if

26:end if

27:end procedure

28:

29: // Deletes elements from the front of deque.

30:procedure HeadDequeue( $Q$ )

31:if QueueEmpty( $Q$ ) then

32:error "underflow"

33:else

34: $x = Q[Q.head]$

35:if $Q.head == Q.length$ then

36: $Q.head = 1$

37:else

38: $Q.head = Q.head + 1$

39:end if

40:return $x$

41:end if

42:end procedure

43:

44: // Deletes elements from the back of deque.

45:procedure TailDequeue( $Q$ )

46:if QueueEmpty( $Q$ ) then

47:error "underflow"

48:else

49:if $Q.tail == 1$ then

50: $Q.tail = Q.length$

51:else

52: $Q.tail = Q.tail - 1$

53:end if

54:return $Q[Q.tail]$

55:end if

56:end procedure