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© 2004 Goodrich, Tamassia Queues1 5.2 Queues

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© 2004 Goodrich, Tamassia Queues2 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.

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© 2004 Goodrich, Tamassia Queues3 The Queue ADT (§5.2.1) 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).

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© 2004 Goodrich, Tamassia Queues4 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

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© 2004 Goodrich, Tamassia Queues5 Queue Example: The following table shows a series of queue operations and their effects on an initially empty queue Q of integer objects: OperationOutputFront Q Rear enqueue(5)-(5) enqueue(3)-(5,3) dequeue()5(3) enqueue(7)-(3,7) dequeue()3(7) front()7(7) dequeue()7() dequeue()“error”() isEmpty()true() enqueue(9)-(9) enqueue(8)-(9,8) Size()2(9,8) enqueue(3)-(9,8,3) enqueue(5)-(9,8,3,5 ) dequeue()9(8,7,3)

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© 2004 Goodrich, Tamassia Queues6 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

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© 2004 Goodrich, Tamassia Queues7 Queue Interface in Java Java interface corresponding to our Queue ADT Requires the definition of class EmptyQueueExceptio n No corresponding built-in Java class public interface Queue { public int size(); public boolean isEmpty(); public Object front() throws EmptyQueueException; public void enqueue(Object o); public Object dequeue() throws EmptyQueueException; }

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© 2004 Goodrich, Tamassia Queues8 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 Array-Based Queue Implementation

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© 2004 Goodrich, Tamassia Queues9 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 Q 012rf normal configuration f

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© 2004 Goodrich, Tamassia Queues10 Queue Operations Initially, we assign f = r =0, which indicates that the queue is empty. We use the modulo operator % (remainder of division) Algorithm size() return (N f + r) mod N Algorithm isEmpty() return (f r) Algorithm Front() if isEmpty() then throw EmptyQueueException else return Q[f] Q 012rf Q 012fr N-1

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© 2004 Goodrich, Tamassia Queues11 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 012rf Q 012fr N-1

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© 2004 Goodrich, Tamassia Queues12 Queue Operations (cont.) Operation dequeue throws an exception if the queue is empty This exception is specified in the queue ADT Algorithm dequeue() if isEmpty() then throw EmptyQueueException else {o Q[f] f (f + 1) mod N return o } Q 012rf Q 012fr N-1

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© 2004 Goodrich, Tamassia 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.

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© 2004 Goodrich, Tamassia Queues 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.

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© 2004 Goodrich, Tamassia Queues Implementing Queue with Linked Lists

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© 2004 Goodrich, Tamassia Queues 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.

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© 2004 Goodrich, Tamassia Linked Lists17 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 f r nodes elements

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© 2004 Goodrich, Tamassia Queues18 Application: Round Robin Schedulers We can implement a round robin scheduler using a queue, Q, by repeatedly performing the following steps: 1. e = Q.dequeue() 2. Service element e 3. Q.enqueue(e) The Queue Shared Service 1.Deque the next element 3.Enqueue the serviced element 2.Service the next element

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© 2004 Goodrich, Tamassia 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. Queues19

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© 2004 Goodrich, Tamassia Double-Ended Queues (cont.) Operation Output D addFirst(3) - (3) addFirst(5) - (5,3) removeFirst() 5 (3) addLast(7) - (3,7) removeFirst() 3 (7) removeLast() 7 () removeFirst() "error" () isEmpty() true () Queues20

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© 2004 Goodrich, Tamassia 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) Queues21

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© 2004 Goodrich, Tamassia Queues22

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© 2004 Goodrich, Tamassia Queues23

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© 2004 Goodrich, Tamassia Queues24

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