CHAPTER 7

1. CHAPTER 7 Queues

2. Queues • A queueis 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: • 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 frontto be the element that was after the removed element

5. Example • enqueue Item 1 • enqueue Item 2 • enqueue Item 3 • dequeue • enqueue Item 4 Item 4 Item 3 Item 2 Item 3 Item 2 Item 1 Item 3 Item 2 Item 2 Item 1 Item 1

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) 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. 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--; if (isEmpty()) 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))