1. CHAPTER 7
Queues

2. Queues
A queue is a linear collection whose elements are added on one end and removed from another
Elements are removed in the same order they arrive
A queue is FIFO – first in, first out

3. A conceptual view of a queue

4. Basic operations Enqueue: Dequeue:
store a data item at the rear end of the queue
make rear to be the new end of the queue
Dequeue:
retrieve and remove a data item from the front of the queue
make front to be the element that was after the removed element

5. Example enqueue Item 1 enqueue Item 2 enqueue Item 3 dequeue

6. More operations on queues

7. ADT definition of Queue
Notation:
Q queue
e item of same type as the elements of Q
b boolean value

8. Operations InitQueue(Q) Procedure to initialize Q to an empty queue
Preconditions: none
Postconditions: Q empty

9. Operations Enqueue(Q,e) Dequeue(Q)  e size of Q decreased by 1
Procedure to place an item e into Q
Preconditions: Q not full
Postconditions: size of Q increased by 1
Dequeue(Q)  e
Procedure to remove and return the front item in Q if Q is not empty
Preconditions: Q not empty
Postconditions: front element removed,
size of Q decreased by 1

10. Operations
first(Q)  e
Procedure to return (without removing) the front item in Q if Q is not empty
Preconditions: Q not empty
Postconditions: Q not changed

11. Operations IsEmpty(Q)  b
Boolean function that returns TRUE if Q is empty
Preconditions: none
Postconditions: Q not changed

12. Queue AXIOMS q.InitQueue().IsEmpty() = true
q.MakeEmpty().IsEmpty() = true
Note: MakeEmpty is not listed in the textbook
q.Enqueue(g).IsEmpty() = false
q.First() = q

13. Queue applications Wait line simulations Radix sorting
Breadth-first search in a tree/graph

14. Linked implementation Array implementation
Queue implementation
The interface class
Linked implementation
Array implementation

15. The interface class public interface QueueADT<T> {
// Adds one element to the rear of this queue
public void enqueue (T element);
// Removes and returns the front element from this queue
public T dequeue();
// Returns without removing the front element of this queue
public T first();
// Returns true if this queue contains no elements
public boolean isEmpty();
// Returns the number of elements in this stack
public int size();
// Returns a string representation of this queue
public String toString(); }

16. Linked implementation
Internally, a queue is represented as a
linked list of nodes,
with a reference to the front of the queue,
a reference to the rear end of the queue,
and an integer count of the number of nodes in the queue
LinearNode class is reused to define the nodes

17. Linked implementation

18. Linked Implementation: Enqueue
Create a new node
If queue is empty
Make front equal to the new node
Make rear equal to the new node
Otherwise
Attach the new node to the rear end of the queue
Make rear to be the new node
Increment count

19. Linked Implementation: Enqueue
public void enqueue (T element) {
LinearNode<T> node = new LinearNode<T>(element);
if (isEmpty())
front = node;
else
rear.setNext (node);
rear = node;
count++; }

20. Linked Implementation: Dequeue
Get the contents of the front node
Make front to be the node after the first node, or null if this was the only node
Decrement count
If queue is empty
Make rear equal to null
Return the contents of the retrieved node

21. Linked Implementation: Dequeue
public T dequeue() throws EmptyCollectionException {
if (isEmpty())
throw new EmptyCollectionException ("queue");
T result = front.getElement();
front = front.getNext();
count--;
rear = null;
return result; }

22. Array implementation
A queue can be managed using an array in which index 0 represents one end
An integer value rear represents the next open slot in the array and the number of elements currently in the queue
The challenge with this approach is that a queue operates on both ends, so the elements in the array must be shifted to keep one end at index 0

23. Array implementation
Not efficient

24. Circular Array Implementation
If we don't fix one end of the queue at index 0, we won't have to shift the elements
A circular queue is an implementation of a queue using an array that conceptually loops around on itself

25. Circular arrays

26. A queue straddling the end of a circular array

27. Changes in a circular array implementation of a queue

28. Enqueue in circular array
When an element is enqueued, the value of rear is incremented
But it must take into account the need to loop back to 0:
rear = (rear+1) % queue.length;
Note that this array implementation can also reach capacity and may need enlarging

29. Dequeue in Circular Array
When an element is dequeued, the value of front is incremented
But it must take into account the need to loop back to 0:
front = (front+1) % queue.length;
The queue is empty when front becomes equal to rear

30. Complexity of the queue operations
The enqueue operation is O(1) for all implementations
The dequeue operation is O(1) for linked and circular array implementations, but O(n) for the noncircular array version

31. Examples 1a
Problem 1:
AppendQueue(Q,P): A procedure to append a queue P onto the end of a queue Q, leaving P empty.
Pre: queue P and queue Q, initialized (possibly empty)
Post: Q contains all elements originally in Q, followed by the elements that were in P in same
order. P is empty.

32. Examples 1b Algorithm: while not isEmpty(P) e  dequeue(P)
enqueue(Q,e)
Complexity of the algorithm: O(N), N - the number of elements in P.

33. Examples 2a
Problem 2:
ReverseQueue(Q): A procedure to reverse the elements in a queue Q, using a stack
Pre: queue Q, initialized (possibly empty)
Post: Q contains all elements re-written in reverse order

34. Examples 2b Algorithm: Create a new stack S while not isEmpty(Q)
push(S, dequeue(Q))
while not isEmpty(S)
enqueue(Q,pop(S))