Queues

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Queues

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Title: Queues

1
Queues

Implementations

2
Outline

Queues
Basic operations
Examples of use
Implementations
Array-based and linked list-based

3
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

4
Queue

Queue First In First Out (FIFO)
Toll Station
Car comes, pays, leaves
Check-out in Big Y market
Customer comes, checks out and leaves

Output
Input
5
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.

6
More Examples of Queue

In our daily life
Airport Security Check
Cinema Ticket Office
Bank, ATM

7
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.

8
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.

9
Abstract Data Types

Queue
Operating on both ends
Operations EnQueue(in), DeQueue(out)

enqueue
dequeue
A
B
C
front
rear
10
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

11
Printing Queue

A.doc B.doc C.doc arrive to printer.

Now printing A.doc
A
B
C
B
C
A.doc is finished. Now printing B.doc
D.doc comes
B
C
Now still printing B.doc
D
C
D
B.doc is finished. Now printing C.doc
D
C.doc is finished. Now printing D.doc
12
First-in First-out (FIFO)
The first one enqueued is the first one dequeued.
(FIFO)
When we enqueue entries in the queue and then
dequeue them one by one, we will get the items in
the same order.
13
Implementing a Queue Class

Implement as a LinkedList
insertions and deletions from either end are
efficient, occur in constant O(1) time
good choice
Implement as an ArrayList
Not as simple
adding values at one end, removing at other end
require multiple shifts
Need to use a circular array

14
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

15
Queue Structure
Head Size Tail
aQueue
n
. . .
. . .
value0
value1
valuen-1
16
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

17
The QueueADT interface in UML
18
Listing 7.1 Interface
19
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.

20
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 datarear.
To get the next item, we retrieve datafront.
Dequeue is inefficient all elements have to be
shifted up one place.
Result Dequeue will be O( N ).

21
Two Solutions

Shifting all items to front in the array when
dequeue operation. ( Too Costly )

A leaves
1
0
n-1
3
2
1
0
n-1
3
2
B
A

C
C
B

rear3
front0
rear2
front0
22
Better Idea

Keep a Front index.
To Dequeue, increment front.

Front
Front
Rear
Front
23
Array Implementation of Queue

1
0
n-1
3
2
B
A
D
C
rear
front
Max_Size
After A leaves,
1
0
n-1
3
2
B
D
C
rear
front
Max_Size
24
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.

25
Circular Example - Array

Both Front and Rear wraparound as needed.

Rear
Front
b
c
d
e
f
Front
Rear
b
c
d
e
f
g
26
Circular Array

Wrapped around array

rear3
3
2
C
1
front0
1
0
n-1
3
2
B
B
A

C
A
0
n-1
rear3
front0
27
EnQueue DeQueue In Circular Array

DeQueue
front (front 1) MOD n

EnQueue
rear (rear 1) MOD n

rear3
front1
3
3
2
2
C
C
1
1
B
B
A
0
0
n-1
n-1
28
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.

29
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.

30
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 datafront and
continuing to datarear.
For an empty queue, size is zero and data is a
reference to an array, but no reference is kept
to front and rear

31
Implemention of EnsureCapacity

If size is non-zero, and front is less than rear,
then a new array is allocated and the data from
datafront to datarear is copied using
System.arraycopy.
If size is non-zero and front is greater rear, a
new array is allocated .
The items from datafront to the end are copied
followed by the items from data0 to datarear.
Two separate calls to System.arraycopy are
activated.

32
ARRAY IMPLEMENTATION
front
rear
The EnsureCapacity method requires several steps
before a new array is created and the elements
copies.
C
D
?
A
B
data
B
C
D
?
?
A
?
?
?
?
?
front
rear
Bigger Array
33
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.

34
Code for Enqueue

In the case of the empty list, both rear and
front must be null
LinearNodeltTgt node new LinearNodeltTgt(item,
null)
if( isEmpty())
// insert first item
front node
rear front
else // insert item that is not first,
add to end
rear.nextnode
rear rear.next// or rear node

35
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

9/11/2015
35
36
The queue after adding element E
37
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?

public class BankServiceQueue
public void run()
//Create a new queue
QueuePTltTgt que new ArrayQueuePTltTgt(100)
int time 0
int incustomer 0
int servicetime 0

39
Customer In Service

// what's going on in 30 minutes
while ( time lt 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

40
New Customer Comes

// in every 3 minutes, there is a new customer
coming.
if( time30 )
// enqueue a customer
// print it out and start all over again
time time 1

41
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.

42
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.

43
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.

44
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

45
Two Queues

High Priority Queue, will come in hpQue
Low Priority Queue, will come in lpQue

High Priority Queue
Check In
Customers coming in
D
C
H
G
F
E
B
A
Low Priority Queue
46
Pseudocode For Arrival

Passengers Arrival
if( new Passenger comes )
if( is First Class)
hpQue.enqueue( new Passenger )
else
lpQue.enqueue( new Passenger )

47
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()

48
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

49
ArrayQueuePT Constructor

// Creates a queue with the default capacity
public ArrayQueuePTltTgt ()
this(DEFAULT_CAPACITY) // creates this queue
with the default capacity
// Creates a queue with a user-specified capacity
public ArrayQueuePT (int capacity)
if (capacity lt 2)
throw new IllegalArgumentException ("Capacity
must be gt 1")
queue ltTgt new Objectcapacity
rear front 0

50
ArrayQueuePT --- Size()

How many items currently in the queue?
public int size()
return count

51
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

52
ArrayQueuePT --- enqueue()

public void enqueue(T item)
if (item null)
throw new IllegalArgumentException ("Item is
null")
if (isFull())
ensureCapacity()
queuerear item
rear (rear 1)queue.length

53
ArrayQueuePT --- dequeue()

public T dequeue( )
if (isEmpty())
throw new IllegalStateException (Queue is
empty")
T frontItem queuefront
queuefront null
front (front 1)queue.length
return frontItem

54
ArrayQueuePT peek() Method

public T peek()
if (isEmpty())
throw new IllegalStateException (Queue is
empty")
return queuefront

55
Interface

Users dont 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

56
Interface for Queue

public interface QueuePTltTgt
public boolean isEmpty()
public boolean isFull()
public T peek()
public T dequeue()
public void enqueue(T item)
public int size()

57
Implementation of ArrayQueuePT Class

public class ArrayQueuePTltTgt implements
QueuePTltTgt
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

58
Create an object of ArrayQueuePT

// create a queue with default capacity
QueuePTltTgt myqueue new ArrayQueuePTltTgt()
// create a queue with 1024 elements
QueuePTltTgt queue new ArrayQueuePTltTgt(1024)

59
The operations on a queue
60
The QueueADT interface in UML
61
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

62
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

63
An encoded message using a repeating key
64
Coded Messages