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1170 Data Structures and Collections Chapter 23 23.6.1 Binary Search Tree of Integer Values The application of Fig. 23.17 and Fig. 23.18 creates a binary search tree of integers and traverses it (i.e., walks through all its nodes) in three ways using recursive inorder, preorder and postorder traversals. The program generates 10 random numbers and inserts each into the tree. Figure 23.17 defines class Tree in namespace BinaryTreeLibrary for reuse purposes. Figure 23.18 defines class TreeTest to demonstrate class Tree s functionality. Method Mainof class TreeTestinstantiates an empty Treeobject, then randomly generates 10 integers and inserts each value in the binary tree by calling Treemethod InsertNode. The program then performs preorder, inorder and postorder traversals of the tree. We will discuss these traversals shortly. Class TreeNode (lines 9 95 of Fig. 23.17) is a self-referential class containing three private data members leftNode and rightNode, of type TreeNode, and data, of type int. Initially, every TreeNodeis a leaf node, so the constructor (lines 16 20) initializes references leftNodeand rightNodeto null. Properties LeftNode(lines 23 34), Data (lines 37 48) and RightNode (lines 51 62) provide access to a ListNode s privatedata members. We discuss TreeNodemethod Insert(lines 67 93) shortly. 1 // Fig. 23.17: BinaryTreeLibrary.cs 2 // Definition of class TreeNode and class Tree. 3 4 using System; 5 6 namespace BinaryTreeLibrary 7 { 8 // class TreeNode definition 9 class TreeNode 10 { 11 private TreeNode leftNode; 12 private int data; 13 private TreeNode rightNode; 14 15 // initialize data and make this a leaf node 16 public TreeNode( int nodeData ) 17 { 18 data = nodeData; 19 leftNode = rightNode = null; // node has no children 20 } 21 22 // LeftNode property 23 public TreeNode LeftNode 24 { 25 get 26 { 27 return leftNode; 28 } 29 Fig. 23.17 Fig. 23.1FiFig. 23.17g. 23.17 Fig. 23.17 Definitions of TreeNodeand Treefor a binary search tree. (Part 1 of 5.)
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Chapter 23 Data Structures and Collections 1169 more links. This section discusses binary trees (Fig. 23.15) trees whose nodes all contain two links (none, one or both of which may be null). The root node is the first node in a tree. Each link in the root node refers to a child. The left child is the first node in the left subtree, and the right child is the first node in the right subtree. The children of a specific node are called siblings. A node with no children is called a leaf node. Computer scientists normally draw trees from the root node down exactly the opposite of the way most trees grow in nature. Common Programming Error 23.2 Not setting to null the links in leaf nodes of a tree is a common logic error. In our binary tree example, we create a special binary tree called a binary search tree. A binary search tree (with no duplicate node values) has the characteristic that the values in any left subtree are less than the value in the subtree s parent node, and the values in any right subtree are greater than the value in the subtree s parent node. Figure 23.16 illustrates a binary search tree with 12 integer values. Note that the shape of the binary search tree that corresponds to a set of data can depend on the order in which the values are inserted into the tree. A B D C Fig. 23.15 Fig. 23.1Fg. 23.FFi15ig. 23.15ig.A graphical representation of a binary tree. 23.15 47 25 77 11 43 65 93 7 17 31 44 68 Fig. 23.16 A binary search tree containing 12 values.
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1168 Data Structures and Collections Chapter 23 36 // remove items from queue 37 try 38 { 39 while ( true ) 40 { 41 removedObject = queue.Dequeue(); 42 Console.WriteLine( removedObject + ” dequeue” ); 43 queue.Print(); 44 } 45 } 46 47 // if exception occurs, print stack trace 48 catch ( EmptyListException emptyListException ) 49 { 50 Console.Error.WriteLine( 51 emptyListException.StackTrace ); 52 } 53 54 } // end method Main 55 56 } // end class QueueTest 57 } The queue is: True The queue is: True $ The queue is: True $ 34567 The queue is: True $ 34567 hello True dequeue The queue is: $ 34567 hello $ dequeue The queue is: 34567 hello 34567 dequeue The queue is: hello hello dequeue Empty queue at LinkedListLibrary.List.RemoveFromFront() in z:ch23linkedlistlibrarylinkedlistlibrary.cs:line 114 at QueueInheritanceLibrary.QueueInheritance.Dequeue() in z:ch23queueinheritancelibrary queueinheritancelibrary.cs:line 28 at QueueTest.QueueTest.Main(String[] args) in z:ch23fig23_14queuetest.cs:line 41 Fig. 23.14 Fig. 23.1FiFig. 23.14g. 23.14 Fig. 23.14 Using inheritance to create a queue. (Part 2 of 2.) 23.6 Trees Linked lists, stacks and queues are linear data structures (i.e., sequences). A tree is a nonlinear, two-dimensional data structure with special properties. Tree nodes contain two or
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Chapter 23 Data Structures and Collections 1167 30 31 } // end of QueueInheritance 32 } Fig. 23.13 Fig. 23.13Fig. 23FiFi.13g. 23.13g. 23.13QueueInheritanceextends class List. (Part 2 of 2.) An infinite while loop (lines 39 44) dequeues the elements from the queue in FIFO order. When there are no objects left to dequeue, method Dequeue throws an Empty- ListException and the program displays the exception s stack trace, which shows the program execution stack at the time the exception occurred. The program uses method Print(inherited from class List) to output the contents of the queue after each operation. Note that class QueueInheritanceTest uses namespace LinkedListLibrary (Fig. 23.4) and namespace QueueInheritanceLibrary(Fig. 23.13); thus, the solution for class QueueInheritanceTestmust have references to both class libraries. 1 // Fig. 23.14: QueueTest.cs 2 // Testing class QueueInheritance. 3 4 using System; 5 using QueueInheritanceLibrary; 6 using LinkedListLibrary; 7 8 namespace QueueTest 9 { 10 // demonstrate functionality of class QueueInheritance 11 class QueueTest 12 { 13 static void Main( string[] args ) 14 { 15 QueueInheritance queue = new QueueInheritance(); 16 17 // create objects to store in the stack 18 bool aBoolean = true; 19 char aCharacter = ‘$’; 20 int anInteger = 34567; 21 string aString = “hello”; 22 23 // use method Enqueue to add items to queue 24 queue.Enqueue( aBoolean ); 25 queue.Print(); 26 queue.Enqueue( aCharacter ); 27 queue.Print(); 28 queue.Enqueue( anInteger ); 29 queue.Print(); 30 queue.Enqueue( aString ); 31 queue.Print(); 32 33 // use method Dequeue to remove items from queue 34 object removedObject = null; 35 Fig. 23.14 Fig. 23.1FiFig. 23.14g. 23.14 Fig. 23.14 Using inheritance to create a queue. (Part 1 of 2.)
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1166 Data Structures and Collections Chapter 23 Of course, the list class contains other methods (such as InsertAtFrontand Remove- FromBack) that we would rather not make accessible through the public interface to the queue class. Remember that all methods in the publicinterface of the Listclass are also publicmethods of the derived class QueueInheritance. When we implement the queue s methods, we have each QueueInheritance method call the appropriate List method method Enqueue calls InsertAtBack, method Dequeuecalls RemoveFromFront, and IsEmptyand Printcalls invoke their base-class versions. Class QueueInheritance does not define methods IsEmpty and Print, because QueueInheritance inherits these methods from class List into QueueInheritance s public interface. Also, the methods in class QueueInheritancedo not use lockstatements. Each of the methods in this class calls a method from class List that uses lock. Note that class QueueInheritance uses namespace LinkedListLibrary (Fig. 23.4); thus, the solution for the class library that defines QueueInheritancemust have a reference to the LinkedListLibraryclass library. Class QueueInheritanceTest s Main method (Fig. 23.14) uses class QueueInheritance to instantiate a queue of objects called queue. Lines 18 21 define four objects that will be enqueued and dequeued. The program enqueues (lines 24, 26, 28 and 30) a boolcontaining true, a charcontaining $, an intcontaining 34567 and a stringcontaining hello. 1 // Fig. 23.13: QueueInheritanceLibrary.cs 2 // Implementing a queue by inheriting from class List. 3 4 using System; 5 using LinkedListLibrary; 6 7 namespace QueueInheritanceLibrary 8 { 9 // class QueueInheritance inherits List’s capabilities 10 public class QueueInheritance : List 11 { 12 // pass name “queue” to List constructor 13 public QueueInheritance() : base( “queue” ) 14 { 15 } 16 17 // place dataValue at end of queue by inserting 18 // dataValue at end of linked list 19 public void Enqueue( object dataValue ) 20 { 21 InsertAtBack( dataValue ); 22 } 23 24 // remove item from front of queue by removing 25 // item at front of linked list 26 public object Dequeue( ) 27 { 28 return RemoveFromFront(); 29 } Fig. 23.13 Fig. 23.13Fig. 23FiFi.13g. 23.13g. 23.13QueueInheritanceextends class List. (Part 1 of 2.)
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Chapter 23 Data Structures and Collections 1165 26 // remove object from stack 27 public object Pop() 28 { 29 return stack.RemoveFromFront(); 30 } 31 32 // determine whether stack is empty 33 public bool IsEmpty() 34 { 35 return stack.IsEmpty(); 36 } 37 38 // output stack contents 39 public void Print() 40 { 41 stack.Print(); 42 } 43 44 } // end class StackComposition 45 } Fig. 23.12 Fig. 23.12Fig. 23FiFi.12g. 23.12g. 23.12StackCompositionclass encapsulates functionality of class List. (Part 2 of 2.) 23.5 Queues Another common data structure is the queue. A queue is similar to a checkout line in a supermarket the first person in line is served first; customers enter the line only at the end, and they wait to be served. Queue nodes are removed only from the head of the queue and are inserted only at the tail of the queue. For this reason, a queue is a first-in, first-out (FIFO) data structure. The insert and remove operations are known as enqueue and dequeue. Queues have many applications in computer systems. Most computers have only a single processor, so they can only serve one user at a time. Entries for the other users are placed in a queue. The entry at the front of the queue receives the first available service. Each entry gradually advances to the front of the queue as users receive service. Queues also support print spooling. A multiuser environment may have only one printer. Several users may send output to the printer. If the printer is busy, users may still generate other outputs, which are spooled to disk (much as thread is wound onto a spool), where they wait in a queue until the printer becomes available. Information packets also wait in queues in computer networks. Each time a packet arrives at a network node, the routing node must route it to the next node on the network along the path to the packet s final destination. The routing node routes one packet at a time, so additional packets are enqueued until the router can route them. A file server in a computer network handles file access requests from many clients throughout the network. Servers have a limited capacity to service requests from clients. When client requests exceed that capacity, the requests wait in queues. The program of Fig. 23.13 and Fig. 23.14 creates a queue class through inheritance from a list class. We want the QueueInheritanceclass (Fig. 23.13) to have methods Enqueue, Dequeue, IsEmptyand Print. Note that these methods are essentially the InsertAtBack, RemoveFromFront, IsEmptyand Printmethods of class List.
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