queues
DESCRIPTION
Queues. Implementations. Outline. Queues Basic operations Examples of use Implementations Array-based and linked list-based. Building a Queue Class. In a queue, new values are always added at the front or head of the list - PowerPoint PPT PresentationTRANSCRIPT
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Queues
Implementations
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Outline
Queues Basic operations Examples of use
Implementations Array-based and linked list-based
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Building a Queue Class
In a queue, new values are always added at the front or head of the
list values are removed from the opposite end of the list,
the rear or tail
Examples of queues checkout at supermarket vehicles at toll booth ticket line at movies
Queue exhibits First-In-First-Out behavior
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QueueQueue: First In First Out (FIFO)
Toll Station Car comes, pays, leaves
Check-out in Big Y market Customer comes, checks out and leaves
ABCD OutputInput
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Queues in a Computer System
When a process (program) requires a certain resource
Printer
disk access on a network
characters in a keyboard buffer. When you enter data into the computer, the characters are kept in queue in a buffer until the operating system can deal with them.
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More Examples of Queue
In our daily life
Airport Security Check
Cinema Ticket Office
Bank, ATM
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Examples
Queue is a British word for line.
Expect O ( 1 ) time per queue operation because it is similar to a stack.
The word "queueing" and its derivatives are the only English words with five consecutive vowels.
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Applications
Queues are also useful for storing pending work:
Shortest paths problem (minimize the number of connecting flights between two arbitrary airports)
Operating Systems use queues to schedule tasks.
Queues are often used in simulations e.g. Simulating traffic at an intersection by creating a growing line of
automobiles waiting for the light to change.
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Abstract Data Types
Queue Operating on both ends Operations: EnQueue(in), DeQueue(out)
frontfrontrearrear
enqueueenqueuedequeuedequeue
ABC
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Printing Job Management
Many users send their printing jobs to ECS public printer
Printer will put them into a queue according to the arrival time and print the jobs one by one
These printing documents are A.doc, B.doc, C.doc and D.doc
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Printing Queue
ABC Now printing A.doc
BC A.doc is finished. Now printing B.doc
BC Now still printing B.docD.doc comes
D
A.doc B.doc C.doc arrive to printer.
CD
D
B.doc is finished. Now printing C.doc
C.doc is finished. Now printing D.doc
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First-in First-out (FIFO)
When we enqueue entries in the queue and then dequeue them one by one, we will get the items in the same order.
When we enqueue entries in the queue and then dequeue them one by one, we will get the items in the same order.
The first one enqueued is the first one dequeued. (FIFO)
The first one enqueued is the first one dequeued. (FIFO)
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Implementing a Queue Class
Implement as a LinkedListLinkedList insertions and deletions from either end are efficient,
occur in constant O(1) time good choice
Implement as an ArrayListArrayList Not as simple adding values at one end, removing at other end require
multiple shifts Need to use a circular array
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Implementing a Queue Class
Build a Queue from scratch build a linked structure to store the queue elements
Attributes required A handle for the head node - Head handle for tail node - Tail integer to store number of values in the queue - count use LinearNode
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Queue Structure
Head Size Tail
n
aQueue
. . .
. . .value0 value1 valuen-1
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Operations
enqueue add a new item at the rear
dequeue remove a item from the front
isEmpty check whether the queue is empty or not
size return the number of items in the queue
peek return the front item
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The QueueADT interface in UML
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Listing 7.1 Interface
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Abstract Data Type -
Same as Stack class, we use the T data type
Use an Arrayqueue, which stores all items that come in. T Queue[ ];
Other implementation with a Linked list we will address later.
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Queues: Simple Idea
Store items in an array with front item at index zero and back item at index rear. We will add items at one end of a queue and remove them from the other end.
Enqueue is easy: increment rear by one and store the new item in data[rear].
To get the next item, we retrieve data[front]. Dequeue is inefficient: all elements have to be shifted up one place.
Result: Dequeue will be O( N ).
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Two Solutions
Shifting all items to front in the array when dequeue operation. ( Too Costly… )
B A …… C1 0n-1 3 2
rear=3 front=0
C B ……1 0n-1 3 2
rear=2 front=0
A leaves
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Better Idea
Keep a Front index.
To Dequeue, increment front.
a b c d
Rear
a b c d
FrontFront
Front
Rear
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Array Implementation of Queue
B AD C
Max_Size rear front
After A leaves,
BD C
Max_Size rear front
1 0n-1 3 2
1 0n-1 3 2
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Circular Implementation
This implementation is O( 1 ) per operation. The problem is that there will be many empty places in the front of array and rear is always incremented.
So we will quickly reach the end of the array.
It is possible after Array.length enqueues, we are full, even if queue is logically nearly empty.
Solution: use wraparound to reuse the cells at the start of the array. To increment, add one, but if that goes past end, reset to zero using the mod operator.
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Circular Example - Array
Both Front and Rear wraparound as needed.
b c d
b c d
FrontRear
e f
e fg
Front Rear
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Circular Array
Wrapped around array
B A …… C1 0n-1 3 2
rear=3 front=0
A
BC
0
23
n-1
1
rear=3
front=0
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EnQueue & DeQueue In Circular Array
EnQueue rear = (rear + 1) MOD n
A
BC
0
23
n-1
1
rear=3
• DeQueue– front = (front + 1) MOD n
BC
0
23
n-1
1
front=1
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Empty/Full In Circular Array
When rear equals front, Queue is empty
When (rear + 1) MOD n equals front, Queue is full
Circular array with capacity n at most can hold n-1 items.
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Java Implementation- Array
Mostly straightforward; maintain:
Front Rear Current number of items in queue
Only tricky part is array doubling because contiguity of wraparound must be maintained.
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EnsureCapacity
Invariant of the Queue ADT (Array version):
The number of items is stored in the instance variable size .
For a non-empty queue the items are stored in a circular array beginning at data[front] and continuing to data[rear].
For an empty queue, size is zero and data is a reference to an array, but no reference is kept to front and rear
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Implemention of EnsureCapacity
If size is non-zero, and front is less than rear, then a new array is allocated and the data from data[front] to data[rear] is copied using System.arraycopy.
If size is non-zero and front is greater rear, a new array is allocated .
The items from data[front] to the end are copied followed by the items from data[0] to data[rear]. Two separate calls to System.arraycopy are activated.
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ARRAY IMPLEMENTATION
C D ?
frontrear
B C D
front rear
A B
? ?A
data
Bigger Array
? ? ? ? ?
The EnsureCapacity method requires several steps before a new array is created and the elements copies.
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Linked List Implementation
The class LinkedQueue has the following invariant:
Size -The number of items in the queue
The items are stored in linked list with front at the head node and rear at the final node.
The instance variable front is the head reference and rear is the tail reference.
For the empty queue, both front and rear are null.
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Code for Enqueue
In the case of the empty list, both rear and front must be null:
LinearNode<T> node = new LinearNode<T>(item, null);
if( isEmpty())
{ // insert first item
front = node;
rear = front;
}
else { // insert item that is not first, add to end
rear.next=node;
rear = rear.next;// or rear = node
}
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Code for Dequeue
In the case of the empty list, both rear and front must point to the first node:
if( isEmpty())
{ // throw an exception
}
//* Remove the first object from the queue - same as removeFirst public T dequeue() throws EmptyQueueException { // store element in Front node in a variable of type T // advance front to the next node // decrement count if (count == 0) //set tail to null; // the queue is now empty // return variable of type T; }
}
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The queue after adding element E
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Customer Service In Fleet Bank
Suppose there is only one customer service available in Fleet Bank in Saturday morning
In every 3 minutes, a new customer arrives at the end of waiting line
Each customer will need 5 minutes for the service
Print out the information after the first 30 minutes
What variables do we need?
The time of arriving and leaving for each customers How many customers are in the line? Who is the current serving customer?
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public class BankServiceQueue { public void run() { //Create a new queue
QueuePT<T> que = new ArrayQueuePT<T>(100); int time = 0; int incustomer = 0; int servicetime = 0;
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Customer In Service// what's going on in 30 minutes while ( time <= 30 ) { // if queue is not empty, one customer service is working
// customer leaves when finished service, service time is 5 minutes if( servicetime == 5 ) { dequeue start another job } }
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New Customer Comes // in every 3 minutes, there is a new customer coming.
if( time%3==0 )
{
// enqueue a customer
// print it out and start all over again
}
time = time + 1;
}
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Priority Queues
In an operating system which queues up tasks to be performed by the CPU, some jobs are more important than others. E. G. answering a system call over printing a file.
Priorities are assigned to the jobs. A Priority Queue stores not only the item but its priority.
Jobs are dequeued according to their priority and jobs with the same priority are dequeued according to which entered first.
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Priority Queue ADT
In some operating systems, there are multiple queues with different priorities.
An array of queues might be used if the number of priorities is sufficiently small.
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Priority Queue --- Air Travel
Only one check-in service in United Airline at airport
Two waiting lines for passengers one is First class service the other is Economy class service
Passengers in the first-class waiting line have higher priority to check in than those in the economy-class waiting line.
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Priority Queue
Two queues one is high priority queue
the other is low priority queue
Service rules: First serve the people in high priority queue
If no passengers are in high priority queue, serve the passengers in low priority queue
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Two Queues
High Priority Queue, will come in hpQue
Low Priority Queue, will come in lpQue
D CHCheck In
G F E B A
High Priority Queue
Low Priority Queue
Customers coming in
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Pseudocode For Arrival
Passengers Arrival: if( new Passenger comes )
{
if( is First Class)
hpQue.enqueue( new Passenger );
else
lpQue.enqueue( new Passenger );
}
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Pseudocode For Service
Check-In Service: if( hpQue is not empty )
{
serve the passenger from high priority queue,
hpQue.dequeue();
}
else {
serve the passenger from low priority queue,
lpQue.dequeue();
}
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Implementation for Queue
public class ArrayQueuePT
{
private final static int DEFAULT_CAPACITY = 100;
// suppose the default capacity for this queue is 100.
private T queue[ ];
// The array that holds the items
private int rear, front;
// index of rear, front item in the queue; }
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ArrayQueuePT Constructor// Creates a queue with the default capacitypublic ArrayQueuePT<T> () {
this(DEFAULT_CAPACITY); // creates this queue with the default capacity}// Creates a queue with a user-specified capacitypublic ArrayQueuePT (int capacity) {
if (capacity < 2)throw new IllegalArgumentException ("Capacity must be > 1");
queue =<T> new Object[capacity];rear = front = 0;
}
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ArrayQueuePT --- Size()
How many items currently in the queue?
public int size()
{
return count;
}
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ArrayQueuePT --- isEmpty/isFull
// check whether the queue is empty
public boolean isEmpty()
{
return size() == 0;
}
// check whether the queue is full
public boolean isFull()
{
return size() == queue.length-1;
}
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ArrayQueuePT --- enqueue()
public void enqueue(T item)
{
if (item == null)
throw new IllegalArgumentException ("Item is null");
if (isFull())
ensureCapacity();
queue[rear] = item;
rear = (rear + 1)%queue.length;
}
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ArrayQueuePT --- dequeue()
public T dequeue( ) {
if (isEmpty())throw new IllegalStateException (“Queue is empty");
T frontItem = queue[front]; queue[front] = null; front = (front + 1)%queue.length;
return frontItem;}
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ArrayQueuePT peek() Method
public T peek()
{
if (isEmpty())
throw new IllegalStateException (“Queue is empty");
return queue[front];
}
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Interface
Users don’t need to know how Queue is implemented.
Users only need to know how they can operate the Queue.
There are many ways to implement Queue, but all of them have the same interfaces
insert, dequeue(), peek, isFull, isEmpty
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Interface for Queue
public interface QueuePT<T>
{
public boolean isEmpty();
public boolean isFull();
public T peek();
public T dequeue();
public void enqueue(T item);
public int size();
}
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Implementation of ArrayQueuePT Class
public class ArrayQueuePT<T> implements QueuePT<T>
{
private final static int DEFAULT_CAPACITY = 100;
private T queue[]; // The array holds the queue
private int rear, front;
// index of rear, front items in queue
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Create an object of ArrayQueuePT
// create a queue with default capacity
QueuePT<T> myqueue = new ArrayQueuePT<T>();
// create a queue with 1024 elements
QueuePT<T> queue = new ArrayQueuePT<T>(1024);
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The operations on a queue
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The QueueADT interface in UML
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Coded Messages
Let's use a queue to help us encode and decode messages
A Caesar cipher encodes a message by shifting each letter in a message by a constant amount k
If k is 5, A becomes F, B becomes G, etc.
However, this is fairly easy to break
An improvement can be made by changing how much a letter is shifted depending on where the letter is in the message
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Coded Messages
A repeating key is a series of integers that determine how much each character is shifted
For example, consider the repeating key
3 1 7 4 2 5
The first character in the message is shifted 3, the next 1, the next 7, and so on
When the key is exhausted, we just start over at the beginning of the key
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An encoded message using a repeating key
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Coded Messages
We'll use a queue to store the values of the key
We'll dequeue a value when needed
After using a key value, we then enqueue it back onto the end of the queue
That way the queue represents the constantly cycling values in the key
See Codes.java (page 183)
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Listing 7.2
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Listing 7.2 (cont.)
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UML description of Codes program
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Printing Job Management
4 documents are ready to print
Print the printer status
When a new document comes
which document is finished
Using ArrayQueuePT
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New Printing Jobs come
public void printstatus() { QueuePT que = new ArrayQueuePT( ); //Create a newqueue System.out.println("Printing job: Null "); //print the printer status // new printing jobs come, a.doc, b.doc, c.doc, d.doc System.out.println("New printing job: a.doc"); que.enqueue( "a.doc" ); System.out.println("New printing job: b.doc"); que.enqueue( "b.doc" ); System.out.println("New printing job: c.doc"); que.enqueue( "c.doc" ); System.out.println("New printing job: d.doc"); que.enqueue( "d.doc" );
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Finishing Printing Jobs // print the printer status
System.out.println("\nPrinting job: there are "
+ que.size() + " jobs in the queue");
System.out.println(" " + que.dequeue() + " is Finished");
System.out.println(" " + que.dequeue() + " is Finished");
System.out.println(" " + que.dequeue() + " is Finished");
System.out.println(" " + que.dequeue() + " is Finished");
}