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Data Structures Chapter 12 Chapter Contents Chapter Objectives 12.1 Introductory Example: Counting Internet Addresses 12.2 The ArrayList and LinkedList Classes 12.3 Example: A Stack Application and Class 12.4 Example: A Queue Class 12.5 An Introduction to Trees

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data structures

Data Structures

Chapter 12

chapter contents
Chapter Contents

Chapter Objectives

12.1 Introductory Example: Counting Internet Addresses

12.2 The ArrayListand LinkedList Classes

12.3 Example: A Stack Application and Class

12.4 Example: A Queue Class

12.5 An Introduction to Trees

Part of the Picture: Data Structures

12.6 Graphical/Internet Java: A PolygonSketcher Class

chapter objectives
Chapter 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 arrays
Review 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 space
  • Solution: collection classes
    • capacity can grow and shrink as program runs
12 1 introductory example counting internet addresses
12.1 Introductory Example: Counting 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 addresscounter
Class AddressCounter
  • 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 gatewayusagecounter
Class GatewayUsageCounter
  • Note source code, Figure 12.2
  • Purpose
    • counts IP addresses using an array list
  • Receives name of text file from args[0]
  • Action:
    • reads IP address from file
    • prints listing of IP addresses and access count for each
  • Note use of ArrayList class
    • can grow or shrink as needed
12 2 the arraylist and linkedlist classes
12.2 The ArrayList and LinkedList Classes
  • 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 object
  • Note List methods, table 12.1
arraylist class
ArrayList Class
  • Implements 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 types
  • Consider the declaration:ArrayList addressSequence = newArrayList();

AddressSeqeunce

sizearray

0

adding to addresssequence

Update size attribute of the ArrayList

Allocate the array

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

128.159.4.201

Adding to addressSequence
  • The commandaddressSequence.add(anAddressCounter);
    • appends anAddressCounter object to the sequence
  • The system will then …

Make first element point to the AddressCounter

AddressSeqeunce

sizearray

1

0

updating addresssequence

Cast it as an AddressCounter object

Gets this object

Increment the count attribute

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

128.159.4.2011, 1

123.111.222.333, 2

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

AddressSeqeunce

sizearray

2

123.111.222.333, 1

enlarging the addresssequence array

128.159.4.2011, 1

Enlarging the AddressSequence Array
  • 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 one

AddressSeqeunce

sizearray

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

2

123.111.345.444, 1

123.111.222.333, 1

arraylist drawback
ArrayList Drawback
  • 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 shifting
  • We need a slightly different structure to allow simple insertions and deletions
    • the LinkedList class will accomplish this
the linkedlist class
The LinkedList Class
  • GivenLinkedList alist = new LinkedList();. . .aList.add(new(integer(88));aList.add(new(integer(77));aList.add(new(integer(66));

aList

headsizetail

3

Resulting object shown at left

88

77

66

linked list containers

Attributes:

  • link to first item in the list
  • size of the list
  • link to last item in the 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
Linked List Containers

aList

headsizetail

3

88

77

66

variations on linked lists
Variations on Linked Lists
  • Lists can be linked doubly as shown
  • Lists 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 linkedlist
Using a LinkedList
  • 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 linkedlist18

addressSequence

headsizetail

0

Using a LinkedList
  • Given the commandLinkedList addressSequence = new LinkedList();
  • Uses the LinkedList constructor to build an empty list
adding to the linked list

addressSequence

headsizetail

0

Adding to the Linked List
  • Results of command for first addaddressSequence.add(anAddressCounter);
  • Successive adds
    • create more nodes and data values
    • adjust links

123.111.345.444, 1

accessing values in a linked list
Accessing Values in a Linked List
  • 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 list21

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

sizemethod determines limit of loop counter

Accessing Values in a Linked List
  • To print successive values for the output

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

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

  • Note that each get(i) must pass over the same first i-1 nodes previously accessed
  • This is inefficient
accessing values in a linked list22
Accessing Values in a Linked List
  • 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:
    • save handle to current node's object
    • advances iterator to next node using successor attribute
    • returns handle saved in step 1, so object pointed to can be output
inserting nodes anywhere in a linked list
Inserting Nodes Anywhere in a Linked List
  • Recall problem with ArrayList
    • can add only at end of the list
    • linked list has capability to insert nodes anywhere
  • We can sayaddressSequence.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 list algorithm efficiency
Choosing the Proper ListAlgorithm Efficiency
  • "Time-efficiency" is not a real-time issue
    • rather an issue of how many steps an algorithm requires
  • Linear time
    • time proportional to n
    • referred to as O(n), "order n"
  • Constant time
    • expressed as O(1)
demonstration of efficiency
Demonstration 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 efficiency
Conclusions 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 stack application and class

1 3 7eight

12.3 Example: a Stack Application 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
need for a stack
Need 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

1

3

1 3 7

7

stack container
Stack 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 algorithm
Number Base Conversion Algorithm
  • Create an empty stack to hold numbers
  • Repeat following while number != 0
    • Calculate remainder = number % base
    • Push remainder onto stack of remainders
    • Replace number = number / base
  • Declare result as an empty String
  • While stack not empty do the following:
    • Remove remainder from top of stack
    • Convert remainder to base equivalent
    • Concatenate base equivalent to result
  • Return result
implementing a stack class
Implementing a Stack Class
  • 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 aLinkedList
    • contrast the "is-a" relationship
java s stack class
Java's Stack Class
  • 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 queue class
12.4 Example: 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
queues in a computer system
Queues in a Computer System
  • 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 queue class
Implementing a Queue Class
  • Implement as a LinkedList attribute value
    • insertions and deletions from either end are efficient, occur in constant O(1) time
    • good choice
  • Implement as an ArrayList attribute
    • poor choice
    • adding values at one end, removing at other end require multiple shifts
implementing a queue class36
Implementing a Queue Class
  • Build a Queue from scratch
    • build a linked structure to store the queue elements
  • Attributes 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 structure
Queue Structure

aQueue

myHeadmySizemyTail

n

. . .

value0

value1

. . .

valuen-1

queue class methods
Queue Class 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 class methods39
Queue Class Methods
  • add()
    • create new node, update attribute variables
    • if queue is empty, must also update myHead
  • remove()
    • must check if class not emptyotherwise …
    • save handle to first object
    • adjust head to refer to node
    • update mySize

Note source code for whole class, Figure 12.9

12 5 an introduction to trees
12.5 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 search

Drawn as a binary tree

49

28

66

80

62

13

35

Visualize Binary Search

13 28 35 49 62 66 80

tree terminology

Sibling nodes

Parent

and

child nodes

Leaf nodes

Tree 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

66

80

62

13

35

applications of trees
Applications of Trees
  • Genealogical tree
    • pictures a person's descendants and ancestors
  • Game 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 trees
Examples of Binary Trees
  • Each node has at most two children
  • Useful 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 trees
Implementing 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

myValue

Value

myLeftChild

myRightChild

implementing binary trees46

Pointers to succeeding nodes

Handle to stored value

Implementing Binary Trees
  • Declaration of BinaryTreeNode classpublic class BinaryTreeNode{// … methods go here// Attributesprivate BinaryTreeNode myLeftChild, myRightChild;private Object myValue; }
implementing binary trees47
Implementing 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 treepublic class BinaryTree extends Object{// … methodsprivate BinaryTreeNode myRoot;private int mySize;}
visualizing a binarytree
Visualizing a BinaryTree

aBTree

myRootmySize

3

46

63

17

binary search trees
Binary Search Trees

Search Algorithm

  • Initialize a handle currentNode to the node containing the root
  • Repeatedly do the following:

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

If target_item > currentNode.myValueset currentNode = currentNode.rightChild

Else

terminate repetition because target_item has been found

tree traversals
Tree Traversals
  • A traversal is moving through the binary tree, visiting each node exactly once
    • for now order not important
  • Traverse Algorithm
    • Visit the root and process its contents
    • Traverse the left subtree
      • visit its root, process
      • traverse left sub-sub tree
      • traverse right sub-sub tree
    • Traverse the right subtree
tree traversal is recursive

The "anchor"

The inductive step

Tree Traversal is Recursive

If the binary tree is empty thendo nothing

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

traversal order
Traversal Order

Three possibilities for inductive step …

  • Left subtree, Node, Right subtreethe inorder traversal
  • Node, Left subtree, Right subtreethe preorder traversal
  • Left subtree, Right subtree, Nodethe postorder traversal
constructing binary search trees
Constructing Binary Search Trees
  • 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 a polygonsketcher
12.6 Graphical/Internet Java:A PolygonSketcher
  • 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
behavior
Behavior

PolygonSketcher

Undo

Clear

Complete

Quit

design
Design
  • 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
coding
Coding
  • 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 sketchpanel class
The SketchPanel Class
  • 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

polygonsketcher class
PolygonSketcher Class
  • Builds the GUI
    • including a central SketchPanel
  • Listens for mouse button clicks
  • When button click events happen
    • actionPerformed() method sends appropriate messages to the SketchPanel
  • Note source code, Figure 12.13
part of the picture data structures
Part of the Picture:Data 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 structures
Other 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