1. Queues
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5.2 Queues
Queues
Dr Zeinab Eid

2. Definition:
a Queue is a collection of objects that are inserted and removed according to the first-in-first-out (FIFI – LILO) principle.
That is, elements can be inserted at any time, but only the element that has been in the queue the longest (first inserted) can be removed at any time.
Usually, elements enter a queue at the Rear, and are accessed or removed from the Front.
Queues

3. Queues
The Queue ADT (§5.2.1)
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The Queue ADT stores a sequence of arbitrary objects.
Insertions and deletions follow the first-in first-out scheme.
Insertions are restricted to the end of the sequence (Rear).
Accesses and removals are restricted to the first element of the sequence (Front).
Queues
Dr Zeinab Eid

4. Main queue operations:
The queue abstract data type (ADT) supports the following methods (operations):
Main queue operations:
enqueue(e): inserts an element e at the end of the queue
dequeue(): removes and returns the element at the front of the queue
Auxiliary queue operations:
front(): returns the element at the front without removing it
size(): returns an integer value that indicates the number of elements stored in the queue
isEmpty(): returns a Boolean value that indicates whether the queue is empty
Exceptions:
Attempting the execution of dequeue or front on an empty queue throws an EmptyQueueException
Queues

5. Queue Example: The following table shows a series of queue operations and their effects on an initially empty queue Q of integer objects:
Operation
Output
Front Q Rear
enqueue(5) -
(5)
enqueue(3)
(5,3)
dequeue() 5
(3)
enqueue(7)
(3,7) 3
(7)
front() 7 ()
“error”
isEmpty()
true
enqueue(9)
(9)
enqueue(8)
(9,8)
Size() 2
(9,8,3)
(9,8,3,5 ) 9
(8,7,3)
Queues

6. Applications of Queues
Direct applications
Waiting lists, theaters, reservation centers,… etc
Access to shared resources (e.g., printer)
Multiprogramming
Indirect applications
Auxiliary data structure for algorithms
Component of other data structures
Queues

7. Queue Interface in Java
public interface Queue {
public int size();
public boolean isEmpty();
public Object front() throws EmptyQueueException;
public void enqueue(Object o);
public Object dequeue() throws EmptyQueueException; }
Java interface corresponding to our Queue ADT
Requires the definition of class EmptyQueueException
No corresponding built-in Java class
Queues

8. 5.2.2 Array-Based Queue Implementation
a- Simple Array Implementation
Using an array Q, of fixed size N, to store queue elements.
If we let Front is Q[0], and let queue grow from left to right, as in case of Stack, it’s not efficient solution.
It requires moving all queue-elements forward one-array cell, each time we perform dequeue operation.
Such an implementation requires O(n) time to perform dequeue-method, where n is the current elements in queue.
Queues

9. b- Using an Array in a Circular Way
To avoid moving objects once they are placed in Q, and to execute queue methods in a constant time O(1)
Use an array of fixed size N in a circular fashion
Define two integer variables to keep track of the front and rear array cells
f index of the front element in Q, first nonempty cell of array
r index to the next available empty array cell in Q, rear element
Array location r is kept empty
normal configuration f<r Q 1 2 r f
N-1
wrapped-around configuration f>r Q 1 2 f r
N-1
Queues

10. Queue Operations Q 1 2 r f Q 1 2 f r Algorithm size()
return (N - f + r) mod N
Algorithm isEmpty()
return (f = r)
Algorithm Front()
if isEmpty() then
throw EmptyQueueException
else return Q[f]
Initially, we assign
f = r =0, which indicates that the queue is empty.
We use the modulo operator % (remainder of division) Q 1 2 r f
N-1 Q 1 2 f r
N-1
Queues

11. Queue Operations (cont.)
Algorithm enqueue(o)
if size() = N  1 then
throw FullQueueException
else
{ Q[r]  o
r  (r + 1) mod N }
Operation enqueue throws an exception if the array is full
This exception is implementation-dependent Q 1 2 r f
N-1 Q 1 2 f r
N-1
Queues

12. Queue Operations (cont.)
Algorithm dequeue()
if isEmpty() then
throw EmptyQueueException
else
{o  Q[f]
f  (f + 1) mod N
return o }
Operation dequeue throws an exception if the queue is empty
This exception is specified in the queue ADT Q 1 2 r f
N-1 Q 1 2 f r
N-1
Queues

13. Queue Operations (cont.)
Method and Time
Size O(1)
isEmpty O(1)
Front O(1)
Enqueue O(1)
Dequeue O(1)
Disadvantage of the array-based queue implementation:
fixed capacity value.

14. 5.2.3 Implementing Queue with Linked Lists
we choose the front of the queue to be at the head of the list
the rear of the queue to be at the tail of the list.
we remove from the head and insert at the tail.
Queues

15. 5.2.3 Implementing Queue with Linked Lists
Queues

16. 5.2.3 Implementing Queue with Linked Lists
Each method of the singly linked list implementation of the queue ADT runs in O(1) time.
We avoid the need to specify a maximum size for the queue but this benefit comes at the expense of increasing the amount of space used per element.
We must take care with special cases
where the queue is empty before an enqueue
where the queue becomes empty after a dequeue.
Queues

17. Queue with a Singly Linked List
We can implement a queue with a singly linked list
The front element is stored at the first node
The rear element is stored at the last node
The space used is O(n) and each operation of the Queue ADT takes O(1) time r
nodes f 
elements
Linked Lists

18. Application: Round Robin Schedulers
We can implement a round robin scheduler using a queue, Q, by repeatedly performing the following steps:
e = Q.dequeue()
Service element e
Q.enqueue(e)
The Queue
Shared
Service 1 .
Deque the
next element 3
Enqueue the
serviced element 2
Service the
Queues

19. Double-Ended Queues (deque)( "D.Q.")
Supports insertion and deletion at both the front and the rear of the queue.
The Deque Abstract Data Type
 addFirst(e): Insert a new element e at the beginning of the deque.
 addLast(e): Insert a new element e at the end of the deque.
 removeFirst(): Remove and return the first element of the deque; an error occurs if the deque is empty.
removeLast(): Remove and return the last element of the deque; an error occurs if the deque is empty.
getFirst(): Return the first element of the deque; an error occurs if the deque is empty.
getLast(): Return the last element of the deque; an error occurs if the deque is empty.
size(): Return the number of elements of the deque.
isEmpty(): Determine if the deque is empty.
Queues

20. Double-Ended Queues (cont.)
Operation Output D
addFirst(3) (3)
addFirst(5) (5,3)
removeFirst() (3)
addLast(7) (3,7)
removeFirst() (7)
removeLast() ()
removeFirst() "error" ()
isEmpty() true ()
Queues

21. Implementing a Deque Doubly linked list:
Since the deque requires insertion and removal at both ends of a list, using a singly linked list to implement a deque would be inefficient.
Method Time
size, isEmpty O(1)
getFirst, getLast O(1)
add First, addLast O(1)
removeFirst, removeLast O(1)
Queues

22. Queues

23. Queues

24. Queues