DATA STRUCTURE & ALGORITHMS

CHAPTER 4: QUEUE

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Queues

• Queue: list of homogeneous elements• Elements are:

– Added at one end (the back or rear)– Deleted from the other end (the front)

• First In First Out (FIFO) data structure– Middle elements are inaccessible

• Example:– Waiting line in a bank

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Queue Operations

• Some of the queue operations are:– initializeQueue– isEmptyQueue– isFullQueue– front– back– addQueue– deleteQueue

• Abstract class queueADT defines these operations

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Implementation of Queues as Arrays• You need at least four (member)

variables:– An array to store the queue elements– queueFront and queueRear

• To keep track of first and last elements

– maxQueueSize• To specify the maximum size of the queue

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Implementation of Queues as Arrays (continued)

• To add an element to the queue:– Advance queueRear to next array position – Add element to position pointed by queueRear

• Example: array size is 100; originally empty

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Implementation of Queues as Arrays (continued)• To delete an element from the queue:

– Retrieve element pointed to by queueFront– Advance queueFront to next queue element

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Implementation of Queues as Arrays (continued)• Will this queue design work?

– Suppose A stands for adding an element to the queue

– And D stands for deleting an element from the queue

– Consider the following sequence of operations:• AAADADADADADADADA...

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Implementation of Queues as Arrays (continued)• The sequence AAADADADADADADADA... would eventually set queueRear to point to the last array position– Giving the impression that the queue is full

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Implementation of Queues as Arrays (continued)• Solution 1:

– When the queue overflows to the rear (i.e., queueRear points to the last array position):• Check value of queueFront• If value of queueFront indicates that there is room in

the front of the array, slide all of the queue elements toward the first array position

• Problem: too slow for large queues• Solution 2: assume that the array is circular

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Implementation of Queues as Arrays (continued)• To advance the index in a (logically)

circular array:

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Implementation of Queues as Arrays (continued)

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Implementation of Queues as Arrays (continued)• Case 1:

C++ Programming: Program Design Including Data Structures, Fourth Edition

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Implementation of Queues as Arrays (continued)• Case 2:

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Implementation of Queues as Arrays (continued)

• Problem:– Figures 18-47 and 18-49 have identical

values for queueFront and queueRear– However, the former represents an empty

queue, whereas the latter shows a full queue

• Solution?

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Implementation of Queues as Arrays (continued)• Solution 1: keep a count

– Incremented when a new element is added to the queue

– Decremented when an element is removed– Initially, set to 0– Very useful if user (of queue) frequently

needs to know the number of elements in the queue

• We will implement this solution

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Implementation of Queues as Arrays (continued)• Solution 2: let queueFront indicate index of

the array position preceding the first element– queueRear still indicates index of last one– Queue empty if:

• queueFront == queueRear

– Slot indicated by queueFront is reserved• Queue can hold 99 (not 100) elements

– Queue full if the next available space is the reserved slot indicated by queueFront

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Implementation of Queues as Arrays (continued)

Exercise

Consider the following queue where circular QUEUE is allocated 6 memory cells:FRONT = 2, REAR = 5QUEUE: _______, London, Berlin, Rome, Paris, _______Describe the queue, including FRONT and REAR, as the following operations take place:1. Athens is added2. Two cities are deleted3. Madrid is added4. Moscow is added5. Three cities are deleted6. Oslo is added

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Empty Queue and Full Queue

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Initialize Queue

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Front

• Returns the first element of the queue

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Back

• Returns the last element of the queue

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addQueue

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deleteQueue

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Constructors and Destructors

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Constructors and Destructors (continued)• The array to store the queue elements

is created dynamically– When the queue object goes out of scope,

the destructor simply deallocates the memory occupied by the array

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Linked Implementation of Queues• Array size is fixed: only a finite number of

queue elements can be stored in it• The array implementation of the queue

requires array to be treated in a special way– Together with queueFront and queueRear

• The linked implementation of a queue simplifies many of the special cases of the array implementation– In addition, the queue is never full

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Linked Implementation of Queues (continued)• Elements are added at one end and

removed from the other– We need to know the front of the queue

and the rear of the queue• Two pointers: queueFront and queueRear

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Empty and Full Queue

• The queue is empty if queueFront is NULL

• The queue is never full

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Initialize Queue

• Initializes queue to an empty state– Must remove all the elements, if any

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addQueue

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front and back Operations

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deleteQueue

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Default Constructor

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Queue Derived from the class unorderedLinkedListType

• The linked implementation of a queue is similar to the implementation of a linked list created in a forward manner– addQueue is similar to insertFirst– initializeQueue is like initializeList– isEmptyQueue is similar to isEmptyList– deleteQueue can be implemented as before– queueFront is the same as first– queueRear is the same as last

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Application of Queues: Simulation• Simulation: a technique in which one

system models the behavior of another system

• Computer simulations using queues as the data structure are called queuing systems

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Summary (continued)

• Queue: items are added at one end and removed from the other end– First In First Out (FIFO) data structure– Operations: add, remove, initialize, destroy,

check if queue is empty/full– Can be implemented as array or linked list– Middle elements should not be accessed– Restricted versions of arrays and linked

lists