 Home
 Products
 Integration
 Tutorial
 Barcode FAQ
 Purchase
 Company
vb.net code to generate barcode Building a Binary Search Tree in Java
EXAMPLE 12.5 Building a Binary Search Tree Decoding EAN13 In Java Using Barcode Control SDK for Java Control to generate, create, read, scan barcode image in Java applications. Encoding GS1  13 In Java Using Barcode printer for Java Control to generate, create GS1  13 image in Java applications. Figure 12.9 on page 236 shows the binary search tree that is built by inserting the input sequence 44, 22, 77, 55, 99, 88, 33. EAN13 Scanner In Java Using Barcode scanner for Java Control to read, scan read, scan image in Java applications. Bar Code Generator In Java Using Barcode maker for Java Control to generate, create bar code image in Java applications. If a binary search tree is balanced, it allows for very efficient searching. As with the binary search, it takes O(lgn) steps to find an element in a balanced binary search tree. But without further restrictions, a binary search tree may grow to be very unbalanced. The worst case is when the elements are inserted in sorted order. In that case the tree degrades to a linear list, thereby making the search algorithm an O(n) sequential search. EXAMPLE 12.6 An Unbalanced Binary Search Tree Bar Code Recognizer In Java Using Barcode decoder for Java Control to read, scan read, scan image in Java applications. EAN / UCC  13 Drawer In C#.NET Using Barcode generator for .NET Control to generate, create UPC  13 image in Visual Studio .NET applications. This is the same input data as in Example 12.5, but in a different order: 99, 22, 88, 33, 77, 55, 44. The resulting binary search tree is shown in Figure 12.10 on page 236. This shows that the same input in different order produces a different tree. But more important, it shows that it is not unlikely for the binary search tree to be linear, or nearly linear. EAN13 Creator In VS .NET Using Barcode creator for ASP.NET Control to generate, create EAN13 Supplement 5 image in ASP.NET applications. Draw EAN / UCC  13 In Visual Studio .NET Using Barcode generator for .NET framework Control to generate, create GTIN  13 image in VS .NET applications. SEARCH TREES
GTIN  13 Drawer In Visual Basic .NET Using Barcode encoder for .NET Control to generate, create EAN13 image in .NET framework applications. Code 3 Of 9 Maker In Java Using Barcode generator for Java Control to generate, create USS Code 39 image in Java applications. [CHAP. 12
Make EAN13 In Java Using Barcode printer for Java Control to generate, create European Article Number 13 image in Java applications. ECC200 Printer In Java Using Barcode creator for Java Control to generate, create DataMatrix image in Java applications. Figure 12.9 Inserting into a binary search tree
British Royal Mail 4State Customer Barcode Encoder In Java Using Barcode creation for Java Control to generate, create RM4SCC image in Java applications. GS1128 Encoder In Visual C#.NET Using Barcode encoder for Visual Studio .NET Control to generate, create UCC.EAN  128 image in .NET framework applications. PERFORMANCE OF BINARY SEARCH TREES Both the insert() and the search() functions begin at the root of the tree and proceed down toward the leaves, making one comparison at each level of the tree. Therefore the time required to execute either algorithm is proportional to h + 1, where h is the height of the tree. The search() function may terminate before reaching a leaf, but h + 1 is still an upper bound on the number of comparisons that it can make. Theorem 12.2 In a binary search tree of size n, the insert() and the search() functions each require O(lgn) comparisons in the best case. In the best case, the binary tree is completely balanced and nearly full, so by Corollary 11.2 on page 202, h = lg(n+1) 1 = O(lgn). Theorem 12.3 In a binary search tree of size n, the insert() and the search() functions each require O(n) comparisons in the worst case. In the worst case the tree is linear, so h + 1 = n = O(n). Linear 1D Barcode Creation In C#.NET Using Barcode drawer for .NET Control to generate, create Linear Barcode image in .NET applications. EAN13 Supplement 5 Decoder In None Using Barcode scanner for Software Control to read, scan read, scan image in Software applications. Figure 12.10 A BST
Painting Barcode In None Using Barcode creation for Software Control to generate, create bar code image in Software applications. Generating Bar Code In VS .NET Using Barcode creation for Reporting Service Control to generate, create bar code image in Reporting Service applications. Theorem 12.4 In a binary search tree of size n, the insert() and the search() functions each require O(2lnn) O(1.39lgn) comparisons in the average case. The proof of this result is beyond the scope of this outline. Decoding UCC  12 In Java Using Barcode recognizer for Java Control to read, scan read, scan image in Java applications. Making GS1128 In ObjectiveC Using Barcode drawer for iPad Control to generate, create UCC  12 image in iPad applications. CHAP. 12] AVL TREES
SEARCH TREES
The imbalance problem illustrated in Example 12.6 can be avoided by imposing balance constraints on the nodes of the binary search tree. Define the balance number at any node of a tree to be the difference between the height of its left subtree and the height of its right subtree. An AVL tree is a binary search tree where the balance number at each node is either 1, 0, or 1. The name comes from the two inventors of this method: G.M. Adel sonVelskii and Y.M. Landis. The tree in Figure 12.12 is not an AVL tree because it is imbalanced at node C. Its balance number there is 2, which is outside the allowable range. It is also imbalanced at node G. The tree in Figure 12.11 is an AVL tree: Every balance number is either 1, 0 or 1. EXAMPLE 12.7 An AVLTree CLASS This class for AVL trees extends the
BinaryTree class defined in Example 11.20
Figure 12.11 An AVL tree
Figure 12.12 Not an AVL tree
on page 212: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 public class AVLTree extends BinaryTree { protected AVLTree left, right; protected int balance; protected java.util.Comparator comp; public AVLTree(java.util.Comparator comp){ this.comp = comp; } public AVLTree(Object root, java.util.Comparator comp) { this.root = root; this.comp = comp; } public boolean add(Object object) { AVLTree temp = attach(object); if (temp != this) { left = temp.left; right = temp.right; balance = temp.balance; } return true; }

