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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.

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Presentation on theme: "Data Structures Chapter 12. Chapter Contents Chapter Objectives 12.1 Introductory Example: Counting Internet Addresses 12.2 The ArrayList and LinkedList."— Presentation transcript:

1 Data Structures Chapter 12

2 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 Part of the Picture: Data Structures 12.6 Graphical/Internet Java: A PolygonSketcher Class

3 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

4 Review Arrays An array stores a sequence of values type [] 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

5 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

6 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

7 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

8 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

9 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 size array 0

10 Adding to addressSequence The command addressSequence.add(anAddressCounter); – appends anAddressCounter object to the sequence The system will then … AddressSeqeunce size array 0 [0] [1] [2]... [m-1] Allocate the array Make first element point to the AddressCounter 1 Update size attribute of the ArrayList

11 Updating addressSequence Consider the command ((AddressCounter) addressSequence.get(index)).incrementCount(); // assume index == 1 AddressSeqeunce size array 2 [0] [1] [2]... [m-1], 1, 1 Gets this object Cast it as an AddressCounter object, 2 Increment the count attribute

12 123.111.345.444, 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 size array 2 [0] [1] [2]... [n-1], 1, 1

13 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

14 The LinkedList Class Given LinkedList alist = new LinkedList();... aList.add(new(integer(88)); aList.add(new(integer(77)); aList.add(new(integer(66)); Resulting object shown at left aList head size tail 3 668877

15 Linked List Containers aList head size tail 3 668877 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

16 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

17 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

18 Using a LinkedList Given the command LinkedList addressSequence = new LinkedList(); Uses the LinkedList constructor to build an empty list head size tail 0 addressSequence

19 Adding to the Linked List Results of command for first add addressSequence.add(anAddressCounter); head size tail 0 addressSequence 123.111.345.444, 1 Successive adds create more nodes and data values adjust links

20 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()

21 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)); 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

22 Accessing Values in a Linked List An alternative, more efficient access algorithm ListIterator it = addressSequence.listIterator(); while (it.hasNext()) System.out.println(; 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 object 2. advances iterator to next node using successor attribute 3. returns handle saved in step 1, so object pointed to can be output

23 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 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 n th item in the list – allocates memory for the data item

24 Choosing the Proper List Algorithm 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)

25 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

26 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

27 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 95 ten to base eight: Use repeated division by eight, taking remainders in reverse order 1 3 7 eight

28 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 7 3 1 1 3 7

29 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

30 Number Base Conversion Algorithm 1. Create an empty stack to hold numbers 2. Repeat following while number != 0 a) Calculate remainder = number % base b) Push remainder onto stack of remainders c) Replace number = number / base 3. Declare result as an empty String 4. While stack not empty do the following: a) Remove remainder from top of stack b) Convert remainder to base equivalent c) Concatenate base equivalent to result 5. Return result

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

32 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

33 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

34 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

35 Implementing a Queue Class LinkedList Implement as a LinkedList attribute value – insertions and deletions from either end are efficient, occur in constant O(1) time – good choice ArrayList Implement as an ArrayList attribute – poor choice – adding values at one end, removing at other end require multiple shifts

36 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

37 Queue Structure myHead mySize myTail n aQueue... value 0 value 1 value n-1

38 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

39 Queue Class 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

40 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

41 Visualize Binary Search 13 28 35 49 62 66 80 Drawn as a binary tree 49 28 1335 66 62 80

42 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 1335 66 62 80 Leaf nodes Sibling nodes Parent and child nodes

43 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 )

44 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

45 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 Value myValue myRightChild myLeftChild

46 Implementing Binary Trees Declaration of BinaryTreeNode class public class BinaryTreeNode { // … methods go here // Attributes private BinaryTreeNode myLeftChild, myRightChild; private Object myValue; } Pointers to succeeding nodes Handle to stored value

47 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 tree public class BinaryTree extends Object { // … methods private BinaryTreeNode myRoot; private int mySize; }

48 Visualizing a BinaryTree 46 63 17 3 myRoot mySize aBTree

49 Binary Search Trees Search Algorithm 1. Initialize a handle currentNode to the node containing the root 2. Repeatedly do the following: If target_item < currentNode.myValue set currentNode = currentNode.leftChild If target_item > currentNode.myValue set currentNode = currentNode.rightChild Else terminate repetition because target_item has been found

50 Tree 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 contents 2. Traverse the left subtree 1.visit its root, process 2.traverse left sub-sub tree 3.traverse right sub-sub tree 3. Traverse the right subtree 1. …

51 Tree Traversal is Recursive If the binary tree is empty then do nothing Else L: Traverse the left subtree N: Visit the root R: Traverse the right subtree The "anchor" The inductive step

52 Traversal Order Three possibilities for inductive step … Left subtree, Node, Right subtree the inorder traversal Node, Left subtree, Right subtree the preorder traversal Left subtree, Right subtree, Node the postorder traversal

53 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

54 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

55 Behavior PolygonSketcher UndoClearCompleteQuit

56 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

57 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

58 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

59 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

60 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

61 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

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