Jhtp5 20 Datastructures

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Jhtp5 20 Datastructures

  1. 1. Chapter 20 – Data Structures Outline 20.1 Introduction 20.2 Self-Referential Classes 20.3 Dynamic Memory Allocation 20.4 Linked Lists 20.5 Stacks 20.6 Queues 20.7 Trees
  2. 2. 20.1 Introduction <ul><li>Dynamic data structures </li></ul><ul><ul><li>Grow and shrink at execution time </li></ul></ul><ul><ul><li>Several types </li></ul></ul><ul><ul><ul><li>Linked lists </li></ul></ul></ul><ul><ul><ul><li>Stacks </li></ul></ul></ul><ul><ul><ul><li>Queues </li></ul></ul></ul><ul><ul><ul><li>Binary trees </li></ul></ul></ul>
  3. 3. 20.2 Self-Referential Classes <ul><li>Self-referential class </li></ul><ul><ul><li>Contains instance variable referring to object of same class </li></ul></ul><ul><ul><ul><li>class Node { private int data; private Node nextNode; // reference to next linked node } </li></ul></ul></ul><ul><ul><ul><li>Member nextNode is a link </li></ul></ul></ul><ul><ul><ul><ul><li>nextNode “links” a Node object to another Node object </li></ul></ul></ul></ul>
  4. 4. 20.2 Self-Referential Classes (cont.) Fig 20.1 Self-referential-class objects linked together. 15 10
  5. 5. 20.3 Dynamic Memory Allocation <ul><li>Dynamic memory allocation </li></ul><ul><ul><li>Obtain more memory at execution time to store new objects </li></ul></ul><ul><ul><ul><li>Declaration and class-instance creation expression </li></ul></ul></ul><ul><ul><ul><li>Node nodeToAdd = new Node ( 10 ); </li></ul></ul></ul>
  6. 6. 20.4 Linked Lists <ul><li>Linked list </li></ul><ul><ul><li>Linear collection of self-referential classes (nodes) </li></ul></ul><ul><ul><li>Connected by reference links </li></ul></ul><ul><ul><li>Nodes can be inserted and deleted anywhere in linked list </li></ul></ul><ul><ul><li>Last node is set to null to mark end of list </li></ul></ul>
  7. 7. 20.4 Linked Lists (cont.) Fig 20.2 Linked list graphical representation. firstNode ... H D Q lastNode
  8. 8. List.java Lines 6-10 1 // Fig. 20.3: List.java 2 // ListNode and List class declarations. 3 package com.deitel.jhtp5.ch20; 4 5 // class to represent one node in a list 6 class ListNode { 7 8 // package access members; List can access these directly 9 Object data; 10 ListNode nextNode; 11 12 // create a ListNode that refers to object 13 ListNode( Object object ) 14 { 15 this ( object, null ); 16 } 17 18 // create ListNode that refers to Object and to next ListNode 19 ListNode( Object object, ListNode node ) 20 { 21 data = object; 22 nextNode = node; 23 } 24 25 // return reference to data in node 26 Object getObject() 27 { 28 return data; // return Object in this node 29 } 30 Self-referential class ListNode contains data and link to nextNode
  9. 9. List.java Line 41 Line 42 Line 55 31 // return reference to next node in list 32 ListNode getNext() 33 { 34 return nextNode; // get next node 35 } 36 37 } // end class ListNode 38 39 // class List declaration 40 public class List { 41 private ListNode firstNode; 42 private ListNode lastNode; 43 private String name; // string like &quot;list&quot; used in printing 44 45 // construct empty List with &quot;list&quot; as the name 46 public List() 47 { 48 this ( &quot;list&quot; ); 49 } 50 51 // construct an empty List with a name 52 public List( String listName ) 53 { 54 name = listName; 55 firstNode = lastNode = null ; 56 } 57 58 // insert Object at front of List 59 public synchronized void insertAtFront( Object insertItem ) 60 { Reference to first node in linked list Reference to last node in linked list First and last nodes in empty list are null
  10. 10. List.java Lines 61-62 Line 65 Lines 71-72 Line 74 Lines 81-82 61 if ( isEmpty() ) // firstNode and lastNode refer to same object 62 firstNode = lastNode = new ListNode( insertItem ); 63 64 else // firstNode refers to new node 65 firstNode = new ListNode( insertItem, firstNode ); 66 } 67 68 // insert Object at end of List 69 public synchronized void insertAtBack( Object insertItem ) 70 { 71 if ( isEmpty() ) // firstNode and lastNode refer to same Object 72 firstNode = lastNode = new ListNode( insertItem ); 73 74 else // lastNode's nextNode refers to new node 75 lastNode = lastNode.nextNode = new ListNode( insertItem ); 76 } 77 78 // remove first node from List 79 public synchronized Object removeFromFront() throws EmptyListException 80 { 81 if ( isEmpty() ) // throw exception if List is empty 82 throw new EmptyListException( name ); 83 84 Object removedItem = firstNode.data; // retrieve data being removed 85 86 // update references firstNode and lastNode 87 if ( firstNode == lastNode ) 88 firstNode = lastNode = null ; 89 else 90 firstNode = firstNode.nextNode; If list is not empty, the first node should refer to the newly inserted node If list is empty, the first and last node should refer to the newly inserted node If list is not empty, the last node should refer to the newly inserted node If list is empty, removing a node causes an exception If list is empty, the first and last node should refer to the newly inserted node
  11. 11. List.java Line 100 Lines 112-117 91 92 return removedItem; // return removed node data 93 94 } // end method removeFromFront 95 96 // remove last node from List 97 public synchronized Object removeFromBack() throws EmptyListException 98 { 99 if ( isEmpty() ) // throw exception if List is empty 100 throw new EmptyListException( name ); 101 102 Object removedItem = lastNode.data; // retrieve data being removed 103 104 // update references firstNode and lastNode 105 if ( firstNode == lastNode ) 106 firstNode = lastNode = null ; 107 108 else { // locate new last node 109 ListNode current = firstNode; 110 111 // loop while current node does not refer to lastNode 112 while ( current.nextNode != lastNode ) 113 current = current.nextNode; 114 115 lastNode = current; // current is new lastNode 116 current.nextNode = null ; 117 } 118 119 return removedItem; // return removed node data 120 121 } // end method removeFromBack If list is not empty, the second-to-last node becomes the last node If list is empty, removing a node causes an exception
  12. 12. List.java Lines 141-144 122 123 // determine whether list is empty 124 public synchronized boolean isEmpty() 125 { 126 return firstNode == null ; // return true if List is empty 127 } 128 129 // output List contents 130 public synchronized void print() 131 { 132 if ( isEmpty() ) { 133 System.out.println( &quot;Empty &quot; + name ); 134 return ; 135 } 136 137 System.out.print( &quot;The &quot; + name + &quot; is: &quot; ); 138 ListNode current = firstNode; 139 140 // while not at end of list, output current node's data 141 while ( current != null ) { 142 System.out.print( current.data.toString() + &quot; &quot; ); 143 current = current.nextNode; 144 } 145 146 System.out.println( &quot; &quot; ); 147 } 148 149 } // end class List Traverse list and print node values
  13. 13. EmptyListException.java Lines 5-19 1 // Fig. 20.4: EmptyListException.java 2 // Class EmptyListException declaration. 3 package com.deitel.jhtp5.ch20; 4 5 public class EmptyListException extends RuntimeException { 6 7 // no-argument constructor 8 public EmptyListException() 9 { 10 this ( &quot;List&quot; ); // call other EmptyListException constructor 11 } 12 13 // constructor 14 public EmptyListException( String name ) 15 { 16 super ( name + &quot; is empty&quot; ); // call superclass constructor 17 } 18 19 } // end class EmptyListException Exception thrown when program attempts to remove node from empty list
  14. 14. ListTest.java Line 10 Lines 13-16 Lines 19-26 1 // Fig. 20.5: ListTest.java 2 // ListTest class to demonstrate List capabilities. 3 import com.deitel.jhtp5.ch20.List; 4 import com.deitel.jhtp5.ch20.EmptyListException; 5 6 public class ListTest { 7 8 public static void main( String args[] ) 9 { 10 List list = new List(); // create the List container 11 12 // objects to store in list 13 Boolean bool = Boolean. TRUE ; 14 Character character = new Character( '$' ); 15 Integer integer = new Integer( 34567 ); 16 String string = &quot;hello&quot; ; 17 18 // insert references to objects in list 19 list.insertAtFront( bool ); 20 list.print(); 21 list.insertAtFront( character ); 22 list.print(); 23 list.insertAtBack( integer ); 24 list.print(); 25 list.insertAtBack( string ); 26 list.print(); 27 Create linked list Create values ( Object s) to store in linked-list nodes Insert values in linked list
  15. 15. ListTest.java Lines 30-44 28 // remove objects from list; print after each removal 29 try { 30 Object removedObject = list.removeFromFront(); 31 System.out.println( removedObject.toString() + &quot; removed&quot; ); 32 list.print(); 33 34 removedObject = list.removeFromFront(); 35 System.out.println( removedObject.toString() + &quot; removed&quot; ); 36 list.print(); 37 38 removedObject = list.removeFromBack(); 39 System.out.println( removedObject.toString() + &quot; removed&quot; ); 40 list.print(); 41 42 removedObject = list.removeFromBack(); 43 System.out.println( removedObject.toString() + &quot; removed&quot; ); 44 list.print(); 45 46 } // end try block 47 48 // catch exception if remove is attempted on an empty List 49 catch ( EmptyListException emptyListException ) { 50 emptyListException.printStackTrace(); 51 } 52 } 53 54 } // end class ListTest Remove values from linked list
  16. 16. ListTest.java Program Output The list is: true   The list is: $ true   The list is: $ true 34567   The list is: $ true 34567 hello $ removed The list is: true 34567 hello   true removed The list is: 34567 hello   hello removed The list is: 34567   34567 removed Empty list
  17. 17. 20.4 Linked Lists (cont.) Fig 20.6 Graphical representation of operation insertAtFront . firstNode 7 11 12 7 11 12 new Listnode firstNode new Listnode (a) (b)
  18. 18. 20.4 Linked Lists (cont.) Fig 20.7 Graphical representation of operation insertAtBack . firstNode 12 new Listnode (a) (b) firstNode new Listnode lastNode lastNode 7 11 5 12 7 11 5
  19. 19. 20.4 Linked Lists (cont.) Fig 20.8 Graphical representation of operation removeFromFront . firstNode 12 (a) (b) 7 11 5 lastNode lastNode firstNode removeItem 12 7 11 5
  20. 20. 20.4 Linked Lists (cont.) Fig 20.9 Graphical representation of operation removeFromBack . 12 (a) (b) lastNode 7 11 5 lastNode firstNode removeItem firstNode current 12 7 11 5
  21. 21. 20.5 Stacks <ul><li>Stack </li></ul><ul><ul><li>Constrained version of a linked list </li></ul></ul><ul><ul><ul><li>Add and remove nodes only to and from the top of the stack </li></ul></ul></ul><ul><ul><ul><ul><li>Push method adds node to top of stack </li></ul></ul></ul></ul><ul><ul><ul><ul><li>Pop method removes node from top of stack </li></ul></ul></ul></ul>
  22. 22. StackInheritance.java Line 5 Lines 14-17 Lines 20-23 1 // Fig. 20.10: StackInheritance.java 2 // Derived from class List. 3 package com.deitel.jhtp5.ch20; 4 5 public class StackInheritance extends List { 6 7 // construct stack 8 public StackInheritance() 9 { 10 super ( &quot;stack&quot; ); 11 } 12 13 // add object to stack 14 public synchronized void push( Object object ) 15 { 16 insertAtFront( object ); 17 } 18 19 // remove object from stack 20 public synchronized Object pop() throws EmptyListException 21 { 22 return removeFromFront(); 23 } 24 25 } // end class StackInheritance StackInheritance extends List , because a stack is a constrained version of a linked list Method push adds node to top of stack Method pop removes node from top of stack
  23. 23. StackInheritanceTest.java Line 10 Lines 13-16 Lines 19-26 1 // Fig. 20.11: StackInheritanceTest.java 2 // Class StackInheritanceTest. 3 import com.deitel.jhtp5.ch20.StackInheritance; 4 import com.deitel.jhtp5.ch20.EmptyListException; 5 6 public class StackInheritanceTest { 7 8 public static void main( String args[] ) 9 { 10 StackInheritance stack = new StackInheritance(); 11 12 // create objects to store in the stack 13 Boolean bool = Boolean. TRUE ; 14 Character character = new Character( '$' ); 15 Integer integer = new Integer( 34567 ); 16 String string = &quot;hello&quot; ; 17 18 // use push method 19 stack.push( bool ); 20 stack.print(); 21 stack.push( character ); 22 stack.print(); 23 stack.push( integer ); 24 stack.print(); 25 stack.push( string ); 26 stack.print(); Create stack Create values ( Object s) to store in stack Insert values in stack
  24. 24. StackInheritanceTest.java Line 33 27 28 // remove items from stack 29 try { 30 Object removedObject = null ; 31 32 while ( true ) { 33 removedObject = stack.pop(); // use pop method 34 System.out.println( removedObject.toString() + &quot; popped&quot; ); 35 stack.print(); 36 } 37 } 38 39 // catch exception if stack is empty when item popped 40 catch ( EmptyListException emptyListException ) { 41 emptyListException.printStackTrace(); 42 } 43 } 44 45 } // end class StackInheritanceTest Remove object from stack
  25. 25. StackInheritanceTest.java Program Output The stack is: true   The stack is: $ true   The stack is: 34567 $ true   The stack is: hello 34567 $ true   hello popped The stack is: 34567 $ true   34567 popped The stack is: $ true   $ popped The stack is: true   true popped Empty stack com.deitel.jhtp5.ch20.EmptyListException: stack is empty at com.deitel.jhtp5.ch20.List.removeFromFront(List.java:82) at com.deitel.jhtp5.ch20.StackInheritance.pop( StackInheritance.java:22) at StackInheritanceTest.main(StackInheritanceTest.java:33)
  26. 26. StackComposition.java Lines 15-18 Lines 21-24 1 // Fig. 20.12: StackComposition.java 2 // Class StackComposition declaration with composed List object. 3 package com.deitel.jhtp5.ch20; 4 5 public class StackComposition { 6 private List stackList; 7 8 // construct stack 9 public StackComposition() 10 { 11 stackList = new List( &quot;stack&quot; ); 12 } 13 14 // add object to stack 15 public synchronized void push( Object object ) 16 { 17 stackList.insertAtFront( object ); 18 } 19 20 // remove object from stack 21 public synchronized Object pop() throws EmptyListException 22 { 23 return stackList.removeFromFront(); 24 } 25 Method push adds node to top of stack Method pop removes node from top of stack
  27. 27. StackComposition.java 26 // determine if stack is empty 27 public synchronized boolean isEmpty() 28 { 29 return stackList.isEmpty(); 30 } 31 32 // output stack contents 33 public synchronized void print() 34 { 35 stackList.print(); 36 } 37 38 } // end class StackComposition
  28. 28. 20.6 Queues <ul><li>Queue </li></ul><ul><ul><li>Similar to a supermarket checkout line </li></ul></ul><ul><ul><li>Nodes inserted only at tail (back) </li></ul></ul><ul><ul><ul><li>Method enqueue </li></ul></ul></ul><ul><ul><li>Nodes removed only from head (front) </li></ul></ul><ul><ul><ul><li>Method dequeue </li></ul></ul></ul>
  29. 29. Queue.java Lines 15-18 Lines 21-24 1 // Fig. 20.13: Queue.java 2 // Class Queue. 3 package com.deitel.jhtp5.ch20; 4 5 public class Queue { 6 private List queueList; 7 8 // construct queue 9 public Queue() 10 { 11 queueList = new List( &quot;queue&quot; ); 12 } 13 14 // add object to queue 15 public synchronized void enqueue( Object object ) 16 { 17 queueList.insertAtBack( object ); 18 } 19 20 // remove object from queue 21 public synchronized Object dequeue() throws EmptyListException 22 { 23 return queueList.removeFromFront(); 24 } 25 Method enqueue adds node to top of stack Method dequeue removes node from top of stack
  30. 30. Queue.java 26 // determine if queue is empty 27 public synchronized boolean isEmpty() 28 { 29 return queueList.isEmpty(); 30 } 31 32 // output queue contents 33 public synchronized void print() 34 { 35 queueList.print(); 36 } 37 38 } // end class Queue
  31. 31. QueueTest.java Line 10 Lines 13-16 Lines 19-26 1 // Fig. 20.14: QueueTest.java 2 // Class QueueTest. 3 import com.deitel.jhtp5.ch20.Queue; 4 import com.deitel.jhtp5.ch20.EmptyListException; 5 6 public class QueueTest { 7 8 public static void main( String args[] ) 9 { 10 Queue queue = new Queue(); 11 12 // create objects to store in queue 13 Boolean bool = Boolean. TRUE ; 14 Character character = new Character( '$' ); 15 Integer integer = new Integer( 34567 ); 16 String string = &quot;hello&quot; ; 17 18 // use enqueue method 19 queue.enqueue( bool ); 20 queue.print(); 21 queue.enqueue( character ); 22 queue.print(); 23 queue.enqueue( integer ); 24 queue.print(); 25 queue.enqueue( string ); 26 queue.print(); Create queue Create values ( Object s) to store in queue Insert values in queue
  32. 32. QueueTest.java Line 33 27 28 // remove objects from queue 29 try { 30 Object removedObject = null ; 31 32 while ( true ) { 33 removedObject = queue.dequeue(); // use dequeue method 34 System.out.println( removedObject.toString() + &quot; dequeued&quot; ); 35 queue.print(); 36 } 37 } 38 39 // process exception if queue is empty when item removed 40 catch ( EmptyListException emptyListException ) { 41 emptyListException.printStackTrace(); 42 } 43 } 44 45 } // end class QueueCompositionTest Remove value from queue
  33. 33. QueueTest.java The queue is: true   The queue is: true $   The queue is: true $ 34567   The queue is: true $ 34567 hello   true dequeued The queue is: $ 34567 hello $ dequeued The queue is: 34567 hello   34567 dequeued The queue is: hello   hello dequeued Empty queue com.deitel.jhtp5.ch20.EmptyListException: queue is empty at com.deitel.jhtp5.ch20.List.removeFromFront(List.java:88) at com.deitel.jhtp5.ch20.Queue.dequeue(Queue.java:23) at QueueTest.main(QueueTest.java:33)
  34. 34. 20.7 Trees <ul><li>Tree </li></ul><ul><ul><li>Non-linear, two-dimensional data structure </li></ul></ul><ul><ul><ul><li>(unlike linked lists, stacks and queues) </li></ul></ul></ul><ul><ul><li>Nodes contain two or more links </li></ul></ul><ul><ul><li>Root node is the first node </li></ul></ul><ul><ul><li>Each link refers to a child </li></ul></ul><ul><ul><ul><li>Left child is the first node in left subtree </li></ul></ul></ul><ul><ul><ul><li>Right child is the first node in right subtree </li></ul></ul></ul><ul><ul><ul><li>Children of a specific node are siblings </li></ul></ul></ul><ul><ul><ul><li>Nodes with no children are leaf nodes </li></ul></ul></ul>
  35. 35. 20.7 Trees (cont.) <ul><li>Binary search tree </li></ul><ul><ul><li>Special ordering of nodes </li></ul></ul><ul><ul><ul><li>Values in left subtrees are less than values in right subtrees </li></ul></ul></ul><ul><ul><li>Inorder traversal </li></ul></ul><ul><ul><ul><li>Traverse left subtree, obtain node value, traverse right subtree </li></ul></ul></ul><ul><ul><li>Preorder traversal </li></ul></ul><ul><ul><ul><li>Obtain node value, traverse left subtree, traverse right subtree </li></ul></ul></ul><ul><ul><li>Postorder traversal </li></ul></ul><ul><ul><ul><li>Traverse left subtree, traverse right subtree, obtain node value </li></ul></ul></ul>
  36. 36. 20.7 Trees (cont.) Fig 20.15 Binary tree graphical representation. B A D C
  37. 37. 20.7 Trees (cont.) Fig 20.16 Binary search tree containing 12 values. 47 11 43 65 93 25 77 7 17 31 44 68
  38. 38. Tree.java Lines 9 and 11 Lines 24-32 1 // Fig. 20.17: Tree.java 2 // Declaration of class TreeNode and class Tree. 3 package com.deitel.jhtp5.ch20; 4 5 // class TreeNode declaration 6 class TreeNode { 7 8 // package access members 9 TreeNode leftNode; 10 int data; 11 TreeNode rightNode; 12 13 // initialize data and make this a leaf node 14 public TreeNode( int nodeData ) 15 { 16 data = nodeData; 17 leftNode = rightNode = null ; // node has no children 18 } 19 20 // locate insertion point and insert new node; ignore duplicate values 21 public synchronized void insert( int insertValue ) 22 { 23 // insert in left subtree 24 if ( insertValue < data ) { 25 26 // insert new TreeNode 27 if ( leftNode == null ) 28 leftNode = new TreeNode( insertValue ); 29 Left and right children If value of inserted node is less than value of tree node, insert node in left subtree
  39. 39. Tree.java Lines 35-43 30 else // continue traversing left subtree 31 leftNode.insert( insertValue ); 32 } 33 34 // insert in right subtree 35 else if ( insertValue > data ) { 36 37 // insert new TreeNode 38 if ( rightNode == null ) 39 rightNode = new TreeNode( insertValue ); 40 41 else // continue traversing right subtree 42 rightNode.insert( insertValue ); 43 } 44 45 } // end method insert 46 47 } // end class TreeNode 48 49 // class Tree declaration 50 public class Tree { 51 private TreeNode root; 52 53 // construct an empty Tree of integers 54 public Tree() 55 { 56 root = null ; 57 } 58 59 // insert a new node in the binary search tree 60 public synchronized void insertNode( int insertValue ) 61 { If value of inserted node is greater than value of tree node, insert node in right subtree
  40. 40. Tree.java Lines 81-93 62 if ( root == null ) 63 root = new TreeNode( insertValue ); // create the root node here 64 65 else 66 root.insert( insertValue ); // call the insert method 67 } 68 69 // begin preorder traversal 70 public synchronized void preorderTraversal() 71 { 72 preorderHelper( root ); 73 } 74 75 // recursive method to perform preorder traversal 76 private void preorderHelper( TreeNode node ) 77 { 78 if ( node == null ) 79 return ; 80 81 System.out.print( node.data + &quot; &quot; ); // output node data 82 preorderHelper( node.leftNode ); // traverse left subtree 83 preorderHelper( node.rightNode ); // traverse right subtree 84 } 85 86 // begin inorder traversal 87 public synchronized void inorderTraversal() 88 { 89 inorderHelper( root ); 90 } 91 Preorder traversal – obtain data, traverse left subtree, then traverse right subtree
  41. 41. Tree.java Lines 98-100 Lines 115-117 92 // recursive method to perform inorder traversal 93 private void inorderHelper( TreeNode node ) 94 { 95 if ( node == null ) 96 return ; 97 98 inorderHelper( node.leftNode ); // traverse left subtree 99 System.out.print( node.data + &quot; &quot; ); // output node data 100 inorderHelper( node.rightNode ); // traverse right subtree 101 } 102 103 // begin postorder traversal 104 public synchronized void postorderTraversal() 105 { 106 postorderHelper( root ); 107 } 108 109 // recursive method to perform postorder traversal 110 private void postorderHelper( TreeNode node ) 111 { 112 if ( node == null ) 113 return ; 114 115 postorderHelper( node.leftNode ); // traverse left subtree 116 postorderHelper( node.rightNode ); // traverse right subtree 117 System.out.print( node.data + &quot; &quot; ); // output node data 118 } 119 120 } // end class Tree Inorder traversal – traverse left subtree, obtain data, then traverse right subtree Postorder traversal – traverse left subtree, traverse right subtree, then obtain data
  42. 42. TreeTest.java Lines 15-19 Line 22 Line 25 1 // Fig. 20.18: TreeTest.java 2 // This program tests class Tree. 3 import com.deitel.jhtp5.ch20.Tree; 4 5 public class TreeTest { 6 7 public static void main( String args[] ) 8 { 9 Tree tree = new Tree(); 10 int value; 11 12 System.out.println( &quot;Inserting the following values: &quot; ); 13 14 // insert 10 random integers from 0-99 in tree 15 for ( int i = 1 ; i <= 10 ; i++ ) { 16 value = ( int ) ( Math.random() * 100 ); 17 System.out.print( value + &quot; &quot; ); 18 tree.insertNode( value ); 19 } 20 21 System.out.println ( &quot; Preorder traversal&quot; ); 22 tree.preorderTraversal(); // perform preorder traversal of tree 23 24 System.out.println ( &quot; Inorder traversal&quot; ); 25 tree.inorderTraversal(); // perform inorder traversal of tree Insert 10 random integers in tree Traverse binary tree via preorder algorithm Traverse binary tree via inorder algorithm
  43. 43. TreeTest.java Line 28 26 27 System.out.println ( &quot; Postorder traversal&quot; ); 28 tree.postorderTraversal(); // perform postorder traversal of tree 29 System.out.println(); 30 } 31 32 } // end class TreeTest Inserting the following values: 39 69 94 47 50 72 55 41 97 73   Preorder traversal 39 69 47 41 50 55 94 72 73 97   Inorder traversal 39 41 47 50 55 69 72 73 94 97   Postorder traversal 41 55 50 47 73 72 97 94 69 39 Traverse binary tree via postorder algorithm
  44. 44. 20.7 Trees (cont.) Fig 20.19 Binary search tree with seven values. 27 6 17 33 48 13 42

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