chapter objectives

Chapter Objectives Learn how to represent a waiting line (queue) Become proficient using the methods in the Queue Understand how to implement the Queue interface using

a single-linked list, a circular array double-linked list

Analyze the pros and cons for different Queue implementations

Become familiar with the Deque interface its methods Simulate the operation of a physical system that has one

or more waiting lines

CS340 1

Queue• The queue, like the stack, is a widely used data structure• A queue differs from a stack in one important way

• A stack is LIFO list – Last-In, First-Out• while a queue is FIFO list, First-In, First-Out

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Queue Abstract Data Type

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Queue Abstract Data Type Line of customers waiting for serviceSimilar to a stack

We do not access the “middle” objects Pointer in the head as in stack Additional pointer on tail

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More Queues Operating systems use queues to

keep track of tasks ensure that the tasks are carried out in the order they were

generated Print queue

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Specification for a Queue Interface

The Queue interface implements the Collection interface

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Class LinkedList Implements the Queue Interface

LinkedList class implements the Queue interfaceQueue<String> names = new LinkedList<String>();

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Implementing the Queue Interface

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Using a Double-Linked List to Implement the Queue Interface

Insertion and removal from either end of a double-linked list is ???

Problem: Other LinkedList methods in addition to the ones required and permitted by the Queue interface

Solution: Create a new class with a LinkedList component

CS340 9

Using a Single-Linked List to Implement a Queue

• Insertions are at the rear of a queue and removals are from the front

• We need a reference to the last list node so that insertions can be performed at O(1)

• The number of elements in the queue is changed by methods insert and remove

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Implementing a Queue Using an Array Single- or double-linked list is time efficient BUT Space inefficiencies

Storage space increased due to references stored in the nodes Array Implementation

Insertion at rear of array is ?? Removal from the front is ?? Removal from rear of array is ?? Insertion at the front is ??

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[ 0 ]

An array of integers to implement a queue of integers

4 8 6

We don't care what's inthis part of the array.

[ 1 ] [ 2 ] [ 3 ] [ 4 ] size3

first0

last2

Implementing a Queue Using an Array

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dequeue()

[ 0 ] . . .

8 6

[ 1 ] [ 2 ] [ 3 ] [ 4 ]size3

first0

last2

4

[ 0 ]

8 6

[ 1 ] [ 2 ] [ 3 ] [ 4 ] size2

first0

last1


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dequeue()

[ 0 ]

8 6

[ 1 ] [ 2 ] [ 3 ] [ 4 ]size3

first0

last2

4

[ 0 ]

6

[ 1 ] [ 2 ] [ 3 ] [ 4 ] size2

first0

last1

8


CS340 14

dequeue() takes O(n)!

dequeue()

size3

first0

last2

[ 0 ]

4[ 1 ]

8

[ 2 ]

6

[ 3 ]

[ 4 ]

Solution: Cyclic ArrayCS340 15

size2

first1

last2

[ 0 ]

[ 1 ]

8

[ 2 ]

6

[ 3 ]

[ 4 ]

enqueue(2) dequeue() dequeue() enqueue(12) enqueue(5)

Cyclic Array (cont.)CS340 16

size3

first3

last0

[ 0 ]

[ 1 ]

[ 2 ] [ 3 ]

[ 4 ]

2

12

5

Cyclic Array (cont.)

CS340 17

Implementing a Queue Using a Circular Array (cont.)

18


CS340 19


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size = 0front = 0

rear = 4

public ArrayQueue(int initCapacity) { capacity = initCapacity; theData = (E[])new Object[capacity]; front = 0; rear = capacity – 1; size = 0;}

ArrayQueue q = new ArrayQueue(5);

capacity = 5


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size = 0front = 0

rear = 4

public boolean offer(E item) { if (size == capacity) { reallocate(); } size++; rear = (rear + 1) % capacity; theData[rear] = item; return true;}

q.offer('*');

capacity = 5

1rear = 0

*


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size = 1front = 0

rear = 1


q.offer('+');

capacity = 5

2rear = 0

*

+


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size = 2front = 0

rear = 1


q.offer('/');

capacity = 5

3*

+

rear = 2 /


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size = 3front = 0

rear = 3public boolean offer(E item) { if (size == capacity) { reallocate(); } size++; rear = (rear + 1) % capacity; theData[rear] = item; return true;}

q.offer('-');

capacity = 5

4*

+

rear = 2 /

-


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size = 4front = 0

rear = 4


q.offer('A');

capacity = 5

5*

+

rear = 3

/

A

-

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size = 5front = 0

public E poll() { if (size == 0) { return null } E result = theData[front]; front = (front + 1) % capacity; size--; return result;}

next = q.poll();

capacity = 5

4*

+

/

-

result = '*'

front = 1

Arear = 4


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size = 4

front = 1

public E poll() { if (size == 0) { return null } E result = theData[front]; front = (front + 1) % capacity; size--; return result;}

next = q.poll();

capacity = 5

3*

+

/

-

result = '+'

front = 2

Arear = 4


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size = 3


q.offer('B');

capacity = 5

4*

+

/

-

front = 2

Arear = 4

rear = 0 B


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size = 4


q.offer('C');

capacity = 5

5B

+

/

-

front = 2

A

rear = 0

rear = 1 C


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size = 5


q.offer('D');

capacity = 5B

+

/

-

front = 2

A

rear = 1 C


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size = 5

private void reallocate() { int newCapacity = 2 * capacity; E[] newData = (E[])new Object[newCapacity]; int j = front; for (int i = 0; i < size; i++) { newData[i] = theData[j]; j = (j + 1) % capacity; } front = 0; rear = size – 1; capacity = newCapacity; theData = newData;}

q.offer('D');

capacity = 5B

+

/

-

front = 2

A

rear = 1 C

B

+/

-

front = 2

A

rear = 1 C

newCapacity = 10

theData


CS340 32


size = 5


q.offer('D');

capacity = 5

B

+/

-

front = 2

A

rear = 1 C

newCapacity = 10

j = 2

i = 0

newData

theData

CS340 33


size = 5


q.offer('D');

capacity = 5

B

+/

-

front = 2

A

rear = 1 C

newCapacity = 10

j = 2

i = 0

/

/

j = 3

i = 1

newData

theData

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size = 5


q.offer('D');

capacity = 5

B

+/

-

front = 2

A

rear = 1 C

newCapacity = 10

j = 3

i = 1

-

-

j = 4

i = 2

/

newData

theData

CS340 35


size = 5


q.offer('D');

capacity = 5

B

+/

-

front = 2

A

rear = 1 C

newCapacity = 10

j = 0

i = 2

A

A

j = 4i = 3

/

-

newData

theData

CS340 36


size = 5


q.offer('D');

capacity = 5

B

+/

-

front = 2

A

rear = 1 C

newCapacity = 10

j = 1

i = 3

B

B

j = 0

i = 4

/

-

A

newData

theData

CS340 37


size = 5


q.offer('D');

capacity = 5

B

+/

-

front = 2

A

rear = 1 C

newCapacity = 10

j = 2

i = 4

C

C

j = 1

i = 5

/

-

A

B

newData

theData

newData

CS340 38


size = 5


q.offer('D');

capacity = 5front = 2

rear = 1

newCapacity = 10

C

i = 5

/

-

A

B

B

+/

-

A

C

j = 2

C

theData

front = 0

rear = 4

10

CS340 39


size = 5

q.offer('D');

capacity = 5

C

/

-

A

B

newData

front = 0

rear = 4

10


6

rear = 5 D

Implementing Class ArrayQueue<E>.Iter (cont.)

private class Iter implements Iterator<E> { private int index; private int count = 0;

public Iter() { index = front; }

@Override public boolean hasNext() { return count < size; } ....

CS340 40

• Just as for class ListQueue<E>, we must implement the missing:

• Queue methods • class Iter





CS340 41

• Just as for class ListQueue<E>, we must implement the missing Queue methods and an inner class Iter to fully implement the Queue interface

index stores the subscript of the next element to be accessed





CS340 42


The constructor initializes index to front when a new Iter object is created





CS340 43


count keeps track of the number of items accessed so far





CS340 44


hasNext() returns true if count is less than size


@Override public E next() { if (!hasNext()) { throw new NoSuchElementException(); } E returnValue = theData[index]; index = (index + 1) % capacity; count+; return returnValue; }

@Override public void remove { throw new UnsupportedOperationException(); } }

CS340 45


next() returns the element at position index and increments Iter's fields index and count


@Override public E next() { if (!hasNext()) { throw new NoSuchElementException(); } E returnValue = theData[index]; index = (index + 1) % capacity; count+; return returnValue; }

@Override public void remove { throw new UnsupportedOperationException(); } }

CS340 46


remove() throws an exception because removing an item other than the first item violates the queue's contract

Comparing the Three Implementations• Computation time

• Comparable in terms of computation time• All operations are O(1)• Although reallocating an array is O(n), its is amortized over n items,

so the cost per item is O(1)

CS340 47

Comparing the Three Implementations (cont.)

Storage Linked-list implementations require more storage due to the extra

space required for the links A double-linked list requires 1.5 times the storage of a single-

linked list A circular array requires half the storage of a single-linked list to

store the same number of elements But a recently reallocated circular array is half empty

CS340 48

The Deque Interface

Section 4.4

CS340 49

Deque Interface• Deque: double-ended queue• Allows insertions and removals from both ends • The Java Collections Framework provides two

implementations of the Deque interface• ArrayDeque • LinkedList

CS340 50

Deque Example

CS340 51

Deque Interface (cont.)• The Deque interface can be used as a

• Queue• Stack

52

Simulating Waiting Lines Using Queues

CS340 53

Simulating Waiting Lines Using Queues Simulation is used to study the performance of a physical

system by using a physical, mathematical, or computer model of the system

CS340 54

Simulating Waiting Lines Using Queues (cont.)

• A branch of mathematics called queuing theory studies such problems

CS340 55

Simulating Google webserver

• You are working for google and need to estimate how many servers you need for the new data center

• The servers receive requests with an exponential arrival process with average 1,000 requests/sec

• The servers serve with average rate 1,800 requests /sec

• You need to provision for peak and low times. • During peak the rate increases to 1,700 req/seq for

duration1 hr• Overnight the server falls to 500 rer/sec for duration 6 hrs

• Simulate 1000 requests on the server.

CS340 56

Simulating Google webserver

• Find:The average waiting time of a requestTo decrease the waiting to half time, would it be better

to use two servers or double the rate of the e-commerce server to 2x?

How many servers do you need to have 0 sec delay?

CS340 57

chapter objectives

Documents

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