Data StructuresData Structures

Chapter 12

Chapter ContentsChapter Contents

Chapter Objectives12.1 Introductory Example: Counting Internet

Addresses12.2 The ArrayList and LinkedList Classes12.3 Example: A Stack Application and Class12.4 Example: A Queue Class12.5 An Introduction to TreesPart of the Picture: Data Structures12.6 Graphical/Internet Java: A PolygonSketcher

Class

Chapter ObjectivesChapter Objectives

Study the Java collection classes, ArrayList and LinkedList

Show how to build collection classes Study the stack and queue structures Learn about linked structures

linked lists and binary trees Implement and use linked structures Discover how collection classes are

used in graphical programming

Review ArraysReview Arrays

An array stores a sequence of valuestype [] anArray = new type [ capacity ];

Drawback:– capacity of array fixed– must know max number of values at

compile time– either the program runs out of space or

wastes spaceSolution: collection classes

– capacity can grow and shrink as program runs

12.1 Introductory Example: 12.1 Introductory Example: Counting Internet AddressesCounting Internet Addresses

Internet TCP/IP addresses provide for two names for each computer– A host name, meaningful to humans– an IP address, meaningful to computers

Problem: – network administrator needs to review file of IP

addresses using a network gateway Solution:

– read file of addresses– keep track of addresses and how many times

each address shows up in the file

Class Class AddressCounterAddressCounter Note source code, Figure 12.1 Attributes

– maximum message length– address– count

Methods– constructor– comparison method, equals()– count incrementer– accessors for address, count– to-string converter for output

Class Class GatewayUsageCounterGatewayUsageCounter

Note source code, Figure 12.2Purpose

– counts IP addresses using an array listReceives name of text file from args[0]

Action:– reads IP address from file– prints listing of IP addresses and access

count for eachNote use of ArrayList class

– can grow or shrink as needed

12.2 The 12.2 The ArrayList ArrayList and and LinkedList LinkedList ClassesClasses

Collection classes provide capability to grow and shrink as needed

Categories of collection classes– Lists: store collection of items, some of

which may be the same– Sets: store collection of items with no

duplicates– Maps: store collections of pairs, each

associates a key with an objectNote List methods, table 12.1

ArrayList ArrayList ClassClassImplements the List using an array

– by using an Object array, can store any reference type

– cannot directly store primitive types– can indirectly store such values by using

instances of their wrapper typesConsider the declaration:ArrayList addressSequence = newArrayList();

AddressSeqeunce size array

0

Adding to Adding to addressSequenceaddressSequence

The commandaddressSequence.add(anAddressCounter);

– appends anAddressCounter object to the sequence

The system will then …

AddressSeqeunce size array

0

[0] [1] [2] . . . [m-1]

128.159.4.201

Allocate the arrayMake first element

point to the AddressCounter

1

Update size attribute of the ArrayList

Updating Updating addressSequenceaddressSequence

Consider the command((AddressCounter) addressSequence.get(index)).incrementCount();// assume index == 1

AddressSeqeunce size array

2

[0] [1] [2] . . . [m-1]

128.159.4.2011, 1 123.111.222.333, 1

Gets this objectCast it as an AddressCounter

object

123.111.222.333, 2

Increment the count attribute

123.111.345.444, 1

Enlarging the Enlarging the AddressSequence AddressSequence ArrayArray

When allocated array is full, adding another element forces replacing array with larger one– new array of n > m allocated– values from old array copied into new

array– old array replaced by new oneAddressSeqeunce size array

2

[0] [1] [2] . . . [n-1]

128.159.4.2011, 1 123.111.222.333, 1

ArrayList ArrayList DrawbackDrawback

Problems arise from using an array– values can be added only at back of ArrayList

– to insert a value and "shift" others after it requires extensive copying of values

– similarly, deleting a value requires shiftingWe need a slightly different structure

to allow simple insertions and deletions– the LinkedList class will accomplish this

The The LinkedList LinkedList ClassClass

GivenLinkedList alist = new LinkedList();. . .aList.add(new(integer(88));aList.add(new(integer(77));aList.add(new(integer(66));

Resulting object shown

at left

Resulting object shown

at left

aList

head size tail

3

6688 77

Linked List ContainersLinked List Containers

aList

head size tail

3

6688 77

Nodes:

•Contain 3 handles

•link to next node

•link to previous node

•link to stored object

•Links to next and previous make it a doubly linked list

Nodes:

•Contain 3 handles

•link to next node

•link to previous node

•link to stored object

•Links to next and previous make it a doubly linked list

Attributes:

•link to first item in the list

•size of the list

•link to last item in the list

Attributes:

•link to first item in the list

•size of the list

•link to last item in the list

Variations on Linked ListsVariations on Linked Lists

Lists can be linked doubly as shownLists can also be linked in one

direction only– attribute would not need link to tail– node needs forward link and pointer to

data only– last item in list has link set to null

Lists can be circularly linked– last node has link to first node

Using a Using a LinkedListLinkedList

Solve the IP address counter to use LinkedList

Note source code, Figure 12.3– receives text file via args[0]– reads IP addresses from file– prints listing of distinct IP addresses and

number of times found in file

Using a Using a LinkedListLinkedList

Given the commandLinkedList addressSequence = new LinkedList();

Uses the LinkedList constructor to build an empty list

head size tail

0

addressSequence

Adding to the Linked ListAdding to the Linked List

Results of command for first addaddressSequence.add(anAddressCounter);

head size tail

0

addressSequence

123.111.345.444, 1

•Successive adds

• create more nodes and data values

•adjust links

Accessing Values in a Linked Accessing Values in a Linked ListList

Must use the .get method((AddressCounter) addresssSequence.get(index)).incrementCount();

A LinkedList has no array with an index to access an element

get method must …– begin at head node– iterate through index nodes to find match– return reference of object in that node

Command then does cast and incrementCount()

Accessing Values in a Linked Accessing Values in a Linked ListList

To print successive values for the output

for (int i = 0; i < addressSequence.size(); i++)

System.out.println(addressSequence.get(i));

size method determines limit of

loop counter

get(i) starts at first node, iterates i times to reach

desired node

•Note that each get(i) must pass over the same first i-1 nodes previously accessed

•This is inefficient

Accessing Values in a Linked Accessing Values in a Linked ListList

An alternative, more efficient access algorithmListIterator it = addressSequence.listIterator();while (it.hasNext()) System.out.println( it.next());

A ListIterator is an object that iterates across the values in a list

The next() method does the following:1. save handle to current node's object2. advances iterator to next node using successor

attribute3. returns handle saved in step 1, so object pointed to

can be output

Inserting Nodes Anywhere in Inserting Nodes Anywhere in a Linked Lista Linked List

Recall problem with ArrayList – can add only at end of the list– linked list has capability to insert nodes

anywhere We can say

addressSequence.add(n, new anAddressCounter);

Which will …– build a new node– update head and tail links if required– update node handle links to place new node to

be nth item in the list– allocates memory for the data item

Choosing the Proper ListChoosing the Proper ListAlgorithm EfficiencyAlgorithm Efficiency

"Time-efficiency" is not a real-time issue– rather an issue of how many steps an

algorithm requiresLinear time

– time proportional to n– referred to as O(n), "order n"

Constant time– expressed as O(1)

Demonstration of EfficiencyDemonstration of Efficiency

Note sample program ListTimer, Figure 12.4, demonstrates performance

Observations– appending to either ArrayList or LinkedList structures takes negligible time

– far more time-consuming to access middle value in a LinkedList than an ArrayList

– far more time consuming to insert values into an ArrayList than a LinkedList

Conclusions on EfficiencyConclusions on Efficiency

If problem involves many accesses to interior of a sequence– sequence should be stored in an ArrayList

If problems involves many insertions, deletions not at end– sequence should be stored in LinkedList

If neither of these is the case– it doesn't matter which is used

12.3 Example: a 12.3 Example: a Stack Stack Application and ClassApplication and Class

Consider an algorithm which converts from a base 10 number system to another number system.

To convert from 95ten to base eight:Use repeateddivision byeight, takingremaindersin reverseorder

0

8 1 remainder 1

8 11 remainder 3

8 95 remainder 7

1 3 7eight

Need for a StackNeed for a Stack

The remainders are generated in the opposite order that they must be output

If we were able to …– generate them– hold on to them as generated– access (display) them in the

reverse order

THEN we have used a stack 7

3

1

1 3 7

Stack ContainerStack Container

A stack is maintained Last-In-First-Out(not unlike a stack of plates in a cafeteria)

Standard operations– isEmpty(): returns true or false– top(): returns copy of value at top of

stack (without removing it)– push(v): adds a value v at the top of the

stack– pop(): removes and returns value at top

Number Base Conversion Number Base Conversion AlgorithmAlgorithm

1. Create an empty stack to hold numbers2. Repeat following while number != 0

a) Calculate remainder = number % baseb) Push remainder onto stack of remaindersc) Replace number = number / base

3. Declare result as an empty String4. While stack not empty do the following:

a) Remove remainder from top of stackb) Convert remainder to base equivalentc) Concatenate base equivalent to result

5. Return result

Implementing a Implementing a Stack Stack ClassClass

Note use of Stack class in source code, Figure 12.6, implementation in Figure 12.7

Implemented with LinkedList attribute variable to store values– this is a "has-a" relationship, the Stack

has a LinkedList– contrast the "is-a" relationship

Java's Java's Stack Stack ClassClass

Java has a Stack class which extends the Vector class

Author notes implementation as a subclass of Vector provides inheritance of methods inappropriate for a Stack– suggests this violates rule of thumb for

use of the extends– Vector contains messages not

appropriate that should not be used in Stack

12.4 Example: Building a 12.4 Example: Building a Queue Queue ClassClass

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 tailExamples of queues

– checkout at supermarket– vehicles at toll booth– ticket line at movies

Queue exhibits First-In-First-Out behavior

Queues in a Computer Queues in a Computer SystemSystem

When a process (program) requires a certain resource– printer– disk access on a network– characters in a keyboard buffer

Queue Manipulation Operations– isEmpty(): returns true or false– first(): returns copy of value at front– add(v): adds a new value at rear of queue– remove(): removes, returns value at front

Implementing a Implementing a Queue Queue ClassClass

Implement as a LinkedListLinkedList attribute value– insertions and deletions from either end

are efficient, occur in constant O(1) time– good choice

Implement as an ArrayListArrayList attribute– poor choice– adding values at one end, removing at

other end require multiple shifts

Implementing a Implementing a Queue Queue ClassClass

Build a Queue from scratch– build a linked structure to store the queue

elementsAttributes required

– handle for the head node– handle for tail node– integer to store number of values in the

queue– use SinglyLinkedNode class, source

code, Figure 12.8

Queue Queue StructureStructure

myHead mySize myTail

n

aQueue

. . .

. . .value0 value1 valuen-1

Queue Queue Class MethodsClass Methods

Constructor– set myHead, myTail to null– set mySize to zero

isEmpty()– return results of comparison mySize == 0

front()– return myHead.getValue() // unless empty

Queue Queue Class MethodsClass Methods

add()– create new node, update attribute

variables– if queue is empty, must also update myHead

remove()– must check if class not empty

otherwise …– save handle to first object– adjust head to refer to node– update mySize

Note source code for whole class, Figure 12.9

Note source code for whole class, Figure 12.9

12.5 An Introduction to Trees12.5 An Introduction to Trees

We seek a way to organized a linked structure so that …– elements can be searched more quickly

than in a linearly linked structure– also provide for easy insertion/deletion– permit access in less than O(n) time

Recall binary search strategy– look in middle of list– keep looking in middle of subset above or

below current location in list– until target value found

Visualize Binary SearchVisualize Binary Search

13 28 35 49 62 66 80

Drawn as a binary tree

49

28

13 35

66

62 80

Tree TerminologyTree Terminology

A tree consists of:– finite collection of nodes– non empty tree has a root node– root node has no incoming links– every other node in the tree can be reached

from the root by unique sequence of links

49

28

13 35

66

62 80

Leaf nodes

Sibling nodes

Parent

and

child nodes

Applications of TreesApplications of Trees

Genealogical tree– pictures a person's descendants and

ancestorsGame trees

– shows configurations possible in a game such as the Towers of Hanoi problem

Parse trees– used by compiler to check syntax and

meaning of expressions such as 2 * ( 3 + 4 )

Examples of Binary TreesExamples of Binary Trees

Each node has at most two childrenUseful in modeling processes where a

test has only two possible outcomes– true or false– coin toss, heads or tails

Each unique path can be described by the sequence of outcomes

Can be applied to decision trees in expert systems of artificial intelligence

Implementing Binary TreesImplementing Binary Trees

Binary tree represented by multiply linked structure– each node has two links and a handle to

the data– one link to left child, other to the right

Value

myValue

myRightChildmyLeftChild

Implementing Binary TreesImplementing Binary Trees

Declaration of BinaryTreeNode class

public class BinaryTreeNode{// … methods go here// Attributesprivate BinaryTreeNode myLeftChild, myRightChild;private Object myValue; }

Pointers to succeeding nodes

Handle to stored value

Implementing Binary TreesImplementing Binary Trees

BinaryTreeNode is only one of the attributes of a BinaryTree class

Also need an attribute that keeps track of the number of nodes in the tree

public class BinaryTree extends Object{// … methodsprivate BinaryTreeNode myRoot;private int mySize;}

Visualizing a BinaryTreeVisualizing a BinaryTree

46

6317

3

myRoot mySize

aBTree

Binary Search TreesBinary Search Trees

Search Algorithm1. Initialize a handle currentNode to

the node containing the root2. Repeatedly do the following:

If target_item < currentNode.myValue set currentNode = currentNode.leftChild

If target_item > currentNode.myValueset currentNode = currentNode.rightChild

Elseterminate repetition because target_item has been found

Tree TraversalsTree Traversals

A traversal is moving through the binary tree, visiting each node exactly once

– for now order not important Traverse Algorithm

1. Visit the root and process its contents2. Traverse the left subtree

1. visit its root, process2. traverse left sub-sub tree3. traverse right sub-sub tree

3. Traverse the right subtree1. …

Tree Traversal is RecursiveTree Traversal is Recursive

If the binary tree is empty thendo nothing

Else L: Traverse the left subtreeN: Visit the rootR: Traverse the right subtree

The "anchor"

The inductive step

Traversal OrderTraversal Order

Three possibilities for inductive step …Left subtree, Node, Right subtree

the inorder traversal

Node, Left subtree, Right subtreethe preorder traversal

Left subtree, Right subtree, Nodethe postorder traversal

Constructing Binary Search Constructing Binary Search TreesTrees

Repeatedly insert elements into a BST that is initially empty

Descend tree, looking for place to insert the item– Set parentNode = currentNode– change currentNode to its left or right child– if value being inserted is not in the tree, currentNode will eventually become null and …

– parentNode will indicate the parent of a new node to contain the value

12.6 Graphical/Internet Java:12.6 Graphical/Internet Java:A A PolygonSketcherPolygonSketcher

This will illustrate usage of container class to store graphical data

The program will use the mouse to draw a closed geometric figure called a polygon

The program should distinguish between– mouse clicks: connect current (x,y) to

previous (x,y) with a line segment– dragging the mouse: "rubber banding" the

line segment

BehaviorBehavior

PolygonSketcher

UndoUndo ClearClear CompleteComplete QuitQuit

DesignDesign

To support the "repeated undo" feature– need a LIFO structure, suggests a stack

To the support the "complete" command button– need capability to access first point where

user clicked mouse– this suggests not a stack

We create our own PointList class– gives push() and pop() capabilities– also allows access to value at other end

CodingCoding

To represent mouse-click points– int array for x-coordinates– int array for matching y-coordinates– total number of points

Note PointList class declaration, Figure 12.11

Methods– pushPoint() // two versions– popPoint() // returns a point– accessor methods

The The SketchPanel SketchPanel ClassClass

Class needs listener methods– MouseListener interface listens for button

events, handles the events– MouseMotionListener interface listens for

mouse movements, handles them Our sketcher will override methods …

– mousePressed() – mouseDragged()

Other methods we need:– eraseLastLine() for the Undo button– eraseAllLines() for the Clear button– completePolygon() for the Complete button

Note source code in Figure 12.12

Note source code in Figure 12.12

PolygonSketcher PolygonSketcher ClassClass

Builds the GUI– including a central SketchPanel

Listens for mouse button clicksWhen button click events happen

– actionPerformed() method sends appropriate messages to the SketchPanel

Note source code, Figure 12.13

Part of the Picture:Part of the Picture:Data StructuresData Structures

Java provides standard classes– ArrayList– LinkedList

Standard classes used to solve variety of problems

Wise use of these data structures simply solutions to many problems

Attention should be given to efficiency of structure for particular task at hand

Other Data StructuresOther Data Structures

Set interface implemented by HashSet and TreeSet classes

Map interface implemented by TreeMap and HashTable classes

Collections class– variety of utility methods for

manipulating collections