1. Circular Queues: Implemented using Arrays
Damian Gordon

2. Circular Queues
We can also have a circular queue:

3. Circular Queues We can also have a circular queue:
A queue where the start and end of the queue are joined together.

4. Circular Queues Head Tail We can also have a circular queue: 7 43 6 143 6 1 12 35 5 2 22 99 4
Tail 3

5. Circular Queues Head Tail We can also have a circular queue: 7 6 1 126 1 12 35 5 2 22 99 4
Tail 3

6. Circular Queues Head Tail We can also have a circular queue: 7 6 1 126 1 12 68 35 5 2
Tail 22 99 4 3

7. Circular Queues Head Tail We can also have a circular queue: 7 6 1 126 1
Tail 12 54 68 35 5 2 22 99 4 3

8. Circular Queues Tail Head We can also have a circular queue: 7 6 1 546 1
Tail 54
Head 68 35 5 2 22 99 4 3

9. Circular Queues Tail Head We can also have a circular queue: 7 17 6 117 6 1 54
Head 68 35 5 2 22 99 4 3

10. Circular Queues Tail Head We can also have a circular queue: 7 17 81 617 81 6 1 54
Head 68 35 5 2 22 99 4 3

11. Circular Queues Tail Head We can also have a circular queue: 7 17 81 617 81 6 1 54 43
Head 68 35 5 2 22 99 4 3

12. Simple Simulation

13. Queues Queue Head Tail MaxSize
We will implement a queue as an array called Queue.
Head
Tail 1 2 3 4 5 6
Queue
MaxSize

14. Queues Queue Head Tail MaxSize
We will implement a queue as an array called Queue.
Head
Tail 1 2 3 4 5 6
Queue
MaxSize

15. Queues Queue Head Tail MaxSize
We will implement a queue as an array called Queue.
Head
Tail 1 2 3 4 5 6
Queue
MaxSize

16. Queues Queue Head Tail MaxSize
We will implement a queue as an array called Queue.
Head
Tail 1 2 3 4 5 6
Queue
MaxSize

17. Queues Queue Head Tail MaxSize
We will implement a queue as an array called Queue.
Head
Tail 1 2 3 4 5 6
Queue
MaxSize

18. Queues Queue Head Tail MaxSize
We will implement a queue as an array called Queue.
Head
Tail 1 2 3 4 5 6
Queue
MaxSize

19. Queues Queue Head Tail MaxSize
We will implement a queue as an array called Queue.
Tail
Head 1 2 3 4 5 6
Queue
MaxSize

20. End of Simulation

21. Circular Queues Queue Head Tail MaxSize
How does that work, let’s DeleteFromQ()
Head
Tail 31 1 41 2 59 3 26 53 4 5 6
Queue
MaxSize

22. Circular Queues Queue Head Tail MaxSize Now AddtoQ(55) 41 1 2 59 26 341 1 2 59 26 3 53 4 5 6
Queue
MaxSize

23. Circular Queues Queue Head Tail MaxSize Now let’s DeleteFromQ() 1 41 21 41 2 59 3 26 4 53 5 55 6
Queue
MaxSize

24. Circular Queues Queue Head Tail MaxSize Now AddtoQ(34) 1 2 59 26 3 531 2 59 26 3 53 4 5 55 6
Queue
MaxSize

25. Circular Queues Queue Head Tail MaxSize Now AddtoQ(12) 1 2 59 3 26 41 2 59 3 26 4 53 5 55 6 34
Queue
MaxSize

26. Circular Queues
Tail
Head 12 1 2 59 3 26 4 53 5 55 6 34
Queue
MaxSize

27. Circular Queues
So Tail starts at 4, goes to 5, goes to 6, goes to 0, goes to 1, etc.
So it’s Tail = Tail + 1,
But…

28. Circular Queues
So Tail starts at 4, goes to 5, goes to 6, goes to 0, goes to 1, etc.
So it’s Tail = Tail + 1,
But…
To be circular it goes as follows:
4->5->6->0->1->2->3->4->5->6->0->1->2->3->4->5->6->0->1->etc.

29. Circular Queues
So Tail starts at 4, goes to 5, goes to 6, goes to 0, goes to 1, etc.
So it’s Tail = Tail + 1,
But…
Tail = (Tail + 1) % 7

30. Circular Queues
So Tail starts at 4, goes to 5, goes to 6, goes to 0, goes to 1, etc.
So it’s Tail = Tail + 1,
But…
Tail = (Tail + 1) % 7
So Tail % 7 works as follows:
4 % 7 = 4
5 % 7 = 5
6 % 7 = 6
7 % 7 = 0
8 % 7 = 1

31. Circular Queues
So Tail starts at 4, goes to 5, goes to 6, goes to 0, goes to 1, etc.
So it’s Tail = Tail + 1,
But…
Tail = (Tail + 1) % 7
So Tail % MaxSize works as follows:
4 % MaxSize = 4
5 % MaxSize = 5
6 % MaxSize = 6
7 % MaxSize = 0
8 % MaxSize = 1

32. Circular Queues We will look at implementing the following modules:
IsFull()
Check if the queue is full
IsEmpty()
AddToQ(N)
Add a new item (N) to the back of the queue
DeleteFromQ()
Remove the front value from the queue
ClearQ()
Empty the queue

33. Circular Queues Tail Head IsFull() 1 41 2 59 26 3 4 7
if Head = (Tail % MaxSize) + 1
If they have caught up to each other, then it’s full.
Tail 7 17 81 6 1 54 43 1 41 2 59 26 3 4
Head 68 35 5 2 22 99 4 3

34. Circular Queues Tail MaxSize Head IsFull() 81 1 35 2 99 22 3 4 68 54 5
if Head = (Tail % MaxSize) + 1
If they have caught up to each other, then it’s full.
Tail
Head 81 1 35 2 99 22 3 4 68 54 5 6 17
MaxSize

35. Circular Queues
MODULE IsFull(): Boolean Full; IF Head = (Tail + 1) % MaxSize THEN Full <- True; ELSE Full <- False; ENDIF; RETURN Full; END.

36. Circular Queues Or MODULE IsFull():
RETURN Head = (Tail + 1) % MaxSize;
END.

37. Circular Queues Tail Head IsEmpty() 1 41 59 2 26 3 4 if Tail = Head 76 1 1 41 59 2 26 3 4 5 2 4 3

38. Circular Queues Queue MaxSize Head Tail IsEmpty() 1 2 3 4 5 6
if Tail = Head
Head
Tail 1 2 3 4 5 6
Queue
MaxSize

39. Circular Queues
MODULE IsEmpty(): Boolean Empty; IF Head = Tail THEN Empty <- True; ELSE Empty <- False; ENDIF; RETURN Empty; END.

40. Circular Queues Or
MODULE IsEmpty():
RETURN Head = Tail;
END.

41. Circular Queues
AddToQ(17) 7 6 1
Tail 54
Head 68 35 5 2 22 99 4 3

42. Circular Queues
AddToQ(81)
Tail 7 17 6 1 54
Head 68 35 5 2 22 99 4 3

43. Circular Queues Tail Head AddToQ(43) 7 17 81 6 1 54 68 35 5 2 22 99 417 81 6 1 54
Head 68 35 5 2 22 99 4 3

44. Circular Queues Tail Head Queue is Full! 7 17 81 6 1 43 54 68 35 5 217 81 6 1 54 43
Head 68 35 5 2 22 99 4 3

45. Circular Queues Queue Head Tail MaxSize AddToQ(N) 31 1 41 2 59 3 26 53
Increment the Tail pointer % MaxSize, and add to the Tail.
Head
Tail 31 1 41 2 59 3 26 53 4 5 6
Queue
MaxSize

46. Circular Queues
MODULE AddToQ(N): IF IsFull() = True THEN Print “Queue is Full”; ELSE Tail <- (Tail + 1) % MaxSize; Queue[Tail] <- N; ENDIF; END.

47. Circular Queues Head Tail DeleteFromQ() 7 43 6 1 12 54 68 35 5 2 22 9943 6 1
Tail 12 54 68 35 5 2 22 99 4 3

48. Circular Queues Head Tail DeleteFromQ() 7 6 1 12 54 68 35 5 2 22 99 46 1
Tail 12 54 68 35 5 2 22 99 4 3

49. Circular Queues
DeleteFromQ() 7 6 1
Tail 54
Head 68 35 5 2 22 99 4 3

50. Circular Queues Queue Head Tail MaxSize DeleteFromQ() 31 1 41 2 59 3
Write Head value into N, and add one to Head
Head
Tail 31 1 41 2 59 3 26 53 4 5 6
Queue
MaxSize

51. Circular Queues
MODULE DeleteFromQ(): N <- 0; IF IsEmpty() = True THEN Print “Queue is Empty”; ELSE N <- Queue[Head]; Head <- (Head + 1) % MaxSize; ENDIF; RETURN N; END.

52. Circular Queues Tail Head ClearQ() 1 41 59 2 26 3 4
Set Tail = Head = 0
Tail
Head 7 6 1 1 41 59 2 26 3 4 5 2 4 3

53. Circular Queues Queue MaxSize Head Tail ClearQ() 1 2 3 4 5 6
Set Tail = Head = -1
Head
Tail 1 2 3 4 5 6
Queue
MaxSize

54. Circular Queues
MODULE ClearQ(): Tail <- -1; Head <- Tail; END.

55. etc.