1. ADT Queue (Array Implementation)

2. ADT Queue (Array Implementation)
Array implementation of the queue…a fixed size array is used to store the data elements.
As data elements are enqueued & served the queue crawls through the array from low to high index values.
As the queue crawls forward, it also expands and contracts.

3. ADT Queue (Array Implementation)
Head
Tail
After one
En-queue and
one Serve
Head
Tail

4. ADT Queue (Array Implementation)
Head
Tail
Where to
En-queue this?

5. ADT Queue (Array Implementation)
MaxSize-1
Tail
Head
Wrap Round

6. ADT Queue (Array Implementation)
Tail
Head
MaxSize - 1

7. Adapted from Pearson Education, Inc.
An empty Queue
[0]
[1]
[2]
[3]
[4]
Front
Back 4
Enqueue at back 
incr back then store item
The queue is EMPTY
( Back + 1 ) % size =
( ) % = 0
== Front = 0
Adapted from Pearson Education, Inc.

8. Adapted from Pearson Education, Inc.
enQueue A
[0] A
[1]
[2]
[3]
[4]
Front
Back
The queue is not EMPTY
( Back + 1 ) % size =
( ) % = 1
=/= Front = 0
Adapted from Pearson Education, Inc.

9. Adapted from Pearson Education, Inc.
enQueue X
[0] A
[1] X
[2]
[3]
[4]
Front
Back 1
The queue is not EMPTY
( Back + 1 ) % size =
( ) % = 2
=/= Front = 0
Adapted from Pearson Education, Inc.

10. enQueue G, B, and Z – it’s full now
Same As
When
Queue
Was
empty
[0] A
[1] X
[2] G
[3] B
[4] Z
Front
Back 4
Dequeue from Front
Serve front then incr front
The queue is FULL
BUT
( Back + 1 ) % size =
( ) % = 0
== Front = 0
Adapted from Pearson Education, Inc.

11. Adapted from Pearson Education, Inc.
deQueue
[0]
[1] X
[2] G
[3] B
[4] Z
Front 1
Back 4
The queue is not Empty
And not full
( Back + 1 ) % size =
( ) % = 0
=/= Front = 1
Adapted from Pearson Education, Inc.

12. Adapted from Pearson Education, Inc.
deQueue
[0]
[1]
[2] G
[3] B
[4] Z
Front 2
Back 4
Let’s enqueue 2 more:
W and K
The queue is not Empty
( Back + 1 ) % size =
( ) % = 0
=/= Front = 2
Adapted from Pearson Education, Inc.

13. Adapted from Pearson Education, Inc.
enQueue W
[0] W
[1]
[2] G
[3] B
[4] Z
Front 2
Back
The queue is not Empty
( Back + 1 ) % size =
( ) % = 1
=/= Front = 2
Adapted from Pearson Education, Inc.

14. enQueue K – it’s full again
[0] W
[1] K
[2] G
[3] B
[4] Z
Front 2
Back 1
How can we avoid the condition for empty and full being the same?
The queue is FULL
BUT
( Back + 1 ) % size =
( ) % = 2
== Front = 2
Adapted from Pearson Education, Inc.

15. Start with an empty Queue again
[0]
[1]
[2]
[3]
[4]
Front
Back 4
One Location remains unused
The queue is EMPTY
( Back + 1 ) % size =
( ) % = 0
== Front = 0
Adapted from Pearson Education, Inc.

16. enQueue A [0] A [1] [2] [3] [4] Front Back One Location remains unused
Back
One Location remains unused
The queue is not EMPTY
( Back + 1 ) % size =
( ) % = 1
=/= Front = 0
Adapted from Pearson Education, Inc.

17. enQueue X [0] A [1] X [2] [3] [4] 1 Front Back
Back 1
One Location remains unused
The queue is not EMPTY
( Back + 1 ) % size =
( ) % = 2
=/= Front = 1
Adapted from Pearson Education, Inc.

18. enQueue G, and B – it’s full now
Different
From
When
Queue
Was
empty
[0] A
[1] X
[2] G
[3] B
[4]
Front
Back 3
One Location remains unused
The queue is FULL
( Back + 2 ) % size =
( ) % = 0
== Front = 0
Adapted from Pearson Education, Inc.

19. deQueue [0] [1] X [2] G [3] B [4] 1 3 Front Back
One Location remains unused
The queue is not Empty
And not full
( Back + 2 ) % size =
( ) % = 0
=/= Front = 1
Adapted from Pearson Education, Inc.

20. deQueue [0] [1] [2] G [3] B [4] 2 3 Let’s enqueue 2 more: W and K
Front 2
Back 3
One Location remains unused
Let’s enqueue 2 more:
W and K
The queue is not Empty
( Back + 1 ) % size =
( ) % = 4
=/= Front = 2
Adapted from Pearson Education, Inc.

21. enQueue W [0] [1] [2] G [3] B [4] W 2 4 Front Back
One Location remains unused
The queue is not Empty
( Back + 1 ) % size =
( ) % = 0
=/= Front = 2
Adapted from Pearson Education, Inc.

22. enQueue K [0] K [1] [2] G [3] B [4] W 2 Let’s enqueue 1 more: Z Front
Back
One Location remains unused
Let’s enqueue 1 more: Z
The queue is not Empty
( Back + 1 ) % size =
( ) % = 1
=/= Front = 2
Adapted from Pearson Education, Inc.

23. enQueue Z – can’t do it… already full
[0] K
[1]
[2] G
[3] B
[4] W
Front 2
Back
One Location remains unused
The queue is FULL
( Back + 2 ) % size =
( ) % = 2
== Front = 2
Adapted from Pearson Education, Inc.

24. ADT Queue (Array Implementaion)
public class ArrayQueue <T> {
private int maxsize;
private int size;
private int head, tail;
private T[] nodes;
/** Creates a new instance of ArrayQueue */
public ArrayQueue(int n) {
maxsize = n;
size = 0;
head = tail = 0;
nodes = (T[]) new Object[n]; }

25. ADT Queue (Array Implementation)
public boolean full () {
return size == maxsize ? true : false; }
public int length () {
return size;
public void enqueue(T e) {
nodes[tail] = e;
tail = (tail + 1) % maxsize;
size++;

26. ADT Queue -Array Implementation
public T serve () {
T e = nodes[head];
head = (head + 1) % maxsize;
size--;
return e; }