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**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:

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**Implementation of Queues as Arrays (continued)**

Case 2: C++ Programming: Program Design Including Data Structures, Fourth Edition

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**Implementation of Queues as Arrays (continued)**

Problem: Figures and 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)**

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Exercise Consider the following queue where circular QUEUE is allocated 6 memory cells: FRONT = 2, REAR = 5 QUEUE: _______, London, Berlin, Rome, Paris, _______ Describe the queue, including FRONT and REAR, as the following operations take place: Athens is added Two cities are deleted Madrid is added Moscow is added Three cities are deleted 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

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