Data Structures Using Java 1
Chapter 7
Queues
Data Structures Using Java 2
Chapter Objectives
• Learn about queues• Examine various queue operations• Learn how to implement a queue as an array• Learn how to implement a queue as a linked list• Discover priority queues• Discover queue applications
Data Structures Using Java 3
Queues
• Definition: data structure in which the elements are added at one end, called the rear, and deleted from the other end, called the front or first
• First In First Out (LIFO) data structure
Data Structures Using Java 4
Basic Operations on a Queue
• initializeQueue: Initializes the queue to an empty state
• isEmptyQueue: Determines whether the queue is empty. If the queue is empty, it returns the value true; otherwise, it returns the value false
Data Structures Using Java 5
Basic Operations on a queue
• isFullQueue: Determines whether the queue is full. If the queue is full, it returns the value true; otherwise, it returns the value false
• front: Returns the front (first) element of the queue; the queue must exist
• back: Returns the front (first) element of the queue; the queue must exist
Data Structures Using Java 6
Basic Operations on a queue
• addQueue: Adds a new element to the rear of the queue; the queue must exist and must not be full
• deleteQueue: Removes the front element of the queue; the queue must exist and must not be empty
Data Structures Using Java 7
Queue Exception Class
• Adding an element to a full queue, and removing an element from an empty queue, generates errors and exceptions called queue overflow and queue underflow exception
• Exception classes designed to handle these exceptions
Data Structures Using Java 8
Implementation of Queues as Arrays
• Initially queue is empty; queueFront and queueRear point directly to first and last elements of queue
• To implement a queue as an array we need:– An array
– The variables queueFront and queueRear to keep track of the first and last elements of the queue
– The variable maxQueueSize to specify the maximum size of the queue
Data Structures Using Java 9
Implementation of Queues as Arrays
Data Structures Using Java 10
Implementation of Queues as Arrays
Data Structures Using Java 11
Circular Queue
• Possible problem: If a sequence of operations eventually sets index queueRear to point to last array position, it gives the impression that the queue is full.
• However, the queue has only two or three elements and front of the array is empty (see Figure 7-4).
Data Structures Using Java 12
Circular Queue
Data Structures Using Java 13
Circular Queue
Data Structures Using Java 14
Circular Queue
Data Structures Using Java 15
Implementation of Queues as Arrays
Case 1: Suppose that after certain operations, the array containing the queue is as shown below
Data Structures Using Java 16
Implementation of Queues as Arrays
deleteQueue operation results in an empty queue
Data Structures Using Java 17
Implementation of Queues as Arrays
Case 2: Let us now consider the queue shown below
Data Structures Using Java 18
Implementation of Queues as Arrays
Resulting array in Figure 7-11 represents a full queue
Data Structures Using Java 19
Full Queue vs. Empty Queue
• Problem: distinguishing between an empty and a full queue
• Arrays in Figures 7-9 and 7-11 have identical values for queueFront and queueRear
• Solutions:– Keep a count
– Let queueFront indicate index of array position preceding first element of queue, rather than index of actual first element itself (see Figure 7-12)
Data Structures Using Java 20
UML Diagram of theclass QueueClass
Data Structures Using Java 21
Initialize Queue
public void initializeQueue(){ for(int i = queueFront; i < queueRear;
i = (i + 1) % maxQueueSize)
list[i] = null; queueFront = 0; queueRear = maxQueueSize - 1; count = 0;}
Data Structures Using Java 22
Empty Queue and Full Queue
public boolean isEmptyQueue(){ return (count == 0);}
public boolean isFullQueue(){ return (count == maxQueueSize);}
Data Structures Using Java 23
front
public DataElement front() throws QueueUnderflowException
{
if(isEmptyQueue())
throw new QueueUnderflowException();
DataElement temp = list[queueFront].getCopy();
return temp;
}
Data Structures Using Java 24
back
public DataElement back() throws QueueUnderflowException
{ if(isEmptyQueue()) throw new QueueUnderflowException(); DataElement temp = list[queueRear].getCopy(); return temp; }
Data Structures Using Java 25
Add Queue
public void addQueue(DataElement queueElement) throws QueueOverflowException{ if(isFullQueue()) throw new QueueOverflowException(); queueRear = (queueRear + 1) % maxQueueSize; //use the
mod //operator to advance
queueRear //because the array is
circular count++; list[queueRear] = queueElement.getCopy();}
Data Structures Using Java 26
Delete Queue
public void deleteQueue() throws QueueUnderflowException{ if(isEmptyQueue()) throw new QueueUnderflowException(); count--; list[queueFront] = null; queueFront = (queueFront + 1) % maxQueueSize; //use the mod //operator to advance queueFront //because the array is circular }
Data Structures Using Java 27
Constructor
• Constructor – creates an array of the size specified by the user– Default value is 100– Initializes queueFront queueRear to indicate
that the queue is empty
Data Structures Using Java 28
Linked Queue as an ADT
Data Structures Using Java 29
Empty and Full Queue
• Queue is empty if queueFront is NULL
• Queue is full only if we run out of memory
Data Structures Using Java 30
addQueue
• Adds a new element to the end of the queue
• Access the reference variable queueRear to implement addQueue
Data Structures Using Java 31
Front, Back, and Delete Queue
• If queue is nonempty:– operation front returns the first element of the queue
– operation back returns the last element of the queue
– operation deleteQueue removes the first element of the queue
• If queue is empty:– method front terminates the program
– method back terminates the program
Data Structures Using Java 32
Priority Queue
• FIFO rules of a queue are relaxed
• Customers or jobs with higher priority are pushed to front of queue
• To implement:– use an ordinary linked list, which keeps the
items in order from the highest to lowest priority
– use a treelike structure
Data Structures Using Java 33
Application of Queues
• Simulation: technique in which one system models the behavior of another system; used when it is too expensive or dangerous to experiment with real systems
• Simulation examples:– wind tunnels used to experiment with design of car
bodies– flight simulators used to train airline pilots
• Computer simulations: objects being usually represented as data
Data Structures Using Java 34
Theater Problem• The manager of a local movie theater is hearing
complaints from customers about the time they have to wait in line to buy tickets. The theater currently has only one cashier.
• Another theater is preparing to open in the neighborhood and the manager is afraid of losing customers. The manager wants to hire enough cashiers so that a customer does not have to wait too long to buy a ticket, but does not want to hire extra cashiers on a trial basis and potentially waste time and money.
• One thing that the manager would like to know is the average time a customer has to wait for service.
• The manager wants someone to write a program to simulate the behavior of the theater.
Data Structures Using Java 35
Queuing System
• Server: object that provides the service• Customer: object receiving the service• transaction time: service time; time it takes
to serve a customer • time-driven simulation: clock is
implemented as a counter and the passage of time (e.g. 1 minute) can be implemented by incrementing the counter (by 1)
Data Structures Using Java 36
Application of Queues
Data Structures Using Java 37
Application of Queues
Data Structures Using Java 38
Application of Queues
Data Structures Using Java 39
waitingCustomerQueueclass WaitingCustomerQueue extends QueueClass{ //default constructor public WaitingCustomerQueue() { super(); } //constructor with a parameter public WaitingCustomerQueue(int size) { super(size); } //copy constructor public WaitingCustomerQueue(WaitingCustomerQueue otherQ) { super(otherQ); } //Method to increment the waiting time of each //customer in the queue by one time unit. //Postcondition: The waiting time of each customer in // the queue is incremented by one time unit. public void updateWaitingQueue() { //Definition as given below. }}
Data Structures Using Java 40
Poisson Distribution
Need to know the number of customers arriving at a given time unit and how long it takes to serve each customer.
Use Poisson distribution from statistics, which says probability of y events occurring at a given time is given by:
where is the expected value that y events occur at that time.
Data Structures Using Java 41
Chapter Summary
• Queue Data Structure– Restricted Version of arrays and linked
list
– Basic operations
• First In First Out (FIFO)
• Queues Implemented as Arrays
Data Structures Using Java 42
Chapter Summary
• Queues Implemented as Linked Lists
• Priority Queues
• Application of Queues