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ssrs 2d barcode SEARCH TREES in Java
SEARCH TREES Data Matrix Recognizer In Java Using Barcode Control SDK for Java Control to generate, create, read, scan barcode image in Java applications. Generating Data Matrix ECC200 In Java Using Barcode printer for Java Control to generate, create DataMatrix image in Java applications. Figure 12.15 Binary trees
Recognizing Data Matrix ECC200 In Java Using Barcode reader for Java Control to read, scan read, scan image in Java applications. Barcode Printer In Java Using Barcode encoder for Java Control to generate, create bar code image in Java applications. Answers to Review Questions
Bar Code Recognizer In Java Using Barcode recognizer for Java Control to read, scan read, scan image in Java applications. Printing Data Matrix ECC200 In Visual C#.NET Using Barcode creation for .NET framework Control to generate, create DataMatrix image in .NET applications. 12.1 The disadvantage of a binary search tree is that it may become very unbalanced, in which case searching degenerates into an O(n) algorithm. The advantage is the efficiency that a binary tree provides for insertions and deletions. The advantage of an AVL tree is that it is always balanced, guaranteeing the O(lgn) speed of the binary search algorithm. The disadvantages the complex rotations used by the insertion and removal algorithms needed to maintain the tree s balance. Data Matrix 2d Barcode Creator In Visual Studio .NET Using Barcode encoder for ASP.NET Control to generate, create ECC200 image in ASP.NET applications. Draw ECC200 In VS .NET Using Barcode maker for VS .NET Control to generate, create Data Matrix image in Visual Studio .NET applications. Solutions to Problems
Print Data Matrix ECC200 In Visual Basic .NET Using Barcode printer for Visual Studio .NET Control to generate, create DataMatrix image in .NET framework applications. UPC A Maker In Java Using Barcode generation for Java Control to generate, create UPC Code image in Java applications. 12.1 To insert a new record with key 16 into the tree shown in Figure 12.16, the initial search would lead to the first leaf node. Since that is a fiveway search tree, that first leaf node has overflowed, causing it to be split into two leaf nodes and moving its middle key 19 up to its parent node, as shown in Figure 12.17. But now that parent node has overflowed. So it also gets split, moving its middle key up to its parent node, as shown in Figure 12.18. Two other ordering of the seven keys in Example 12.5 on page 235 that will produce the same BST: a. 44, 22, 33, 77, 55, 99, 88 b. 44, 22, 77, 33, 55, 99, 88 An array of objects could be sorted by inserting their objects into a binary search tree and then using an inorder traversal to copy them back into the array. The BST property guarantees that the inorder traversal will visit the elements in order. If an AVL tree is used, then each insertion runs in O(lgn) time, so building the tree with n elements will require O(n lgn) time. The subsequent inorder traversal also has O(n lgn) complexity, so the entire algorithm sorts the array in O(n lgn) time. All except a are binary search trees. UCC128 Printer In Java Using Barcode generator for Java Control to generate, create EAN / UCC  13 image in Java applications. Printing Code 128 Code Set A In Java Using Barcode creation for Java Control to generate, create Code 128 Code Set C image in Java applications. SEARCH TREES
Print MSI Plessey In Java Using Barcode generator for Java Control to generate, create MSI Plessey image in Java applications. Recognizing USS Code 39 In VB.NET Using Barcode scanner for VS .NET Control to read, scan read, scan image in .NET applications. [CHAP. 12
Read Code128 In Visual C# Using Barcode decoder for .NET framework Control to read, scan read, scan image in Visual Studio .NET applications. Barcode Encoder In ObjectiveC Using Barcode printer for iPhone Control to generate, create bar code image in iPhone applications. Figure 12.16 Inserting the key 16 in a fiveway search tree
Bar Code Encoder In Visual Basic .NET Using Barcode generator for VS .NET Control to generate, create barcode image in VS .NET applications. Draw Bar Code In Java Using Barcode generation for Android Control to generate, create bar code image in Android applications. Figure 12.17 Inserting the key 16 in a fiveway search tree
Make Universal Product Code Version A In None Using Barcode generator for Word Control to generate, create UPCA image in Office Word applications. Scanning UCC  12 In VB.NET Using Barcode scanner for Visual Studio .NET Control to read, scan read, scan image in .NET framework applications. Figure 12.18 Inserting the key 16 in a fiveway search tree
private AVLTree rotateRight() { AVLTree x = this, y = left, z = y.left; x.left = z; y.left = x; int xb = x.balance; int yb = y.balance; CHAP. 12] SEARCH TREES
if (yb > 1) { ++x.balance; y.balance = ( xb<0 yb+1 : xb+yb+2 ); } else if (yb > xb) { x.balance += yb1; ++y.balance; } else { y.balance = xb+2; } return y; } Theorem. Every subtree of a binary search tree is a binary search tree. Proof: Let T be a binary search tree, and let S be a subtree of T. Let x be any element in S, and let L and R be the left and right subtrees of x in S. Then, since S is a subtree of T, x is also an element of T, and L and R are the left and right subtrees of x in T. Therefore, y x z for every y L and every z R because T has the BST property. Thus, S also has the BST property. Theorem. Every subtree of an AVL tree is an AVL tree. Proof: The proof that every subtree of a binary search tree is a binary search tree is given in Problem 12.6. If a S is a subtree of an AVL tree T, then every node is S is also in T. Therefore, the balance number at every node in S is 1, 0, or 1. The solution is shown in Figure 12.19.
Figure 12.19 AVL tree insertions
SEARCH TREES
[CHAP. 12
Figure 12.19 (continued) AVL tree insertions
Heaps and Priority Queues
HEAPS A heap is a complete binary tree whose elements have keys that satisfy the following heap property: the keys along any path from root to leaf are descending (i.e., nonincreasing). EXAMPLE 13.1 A Heap Figure 13.1 shows a heap. Note that the keys along each of its roottoleaf paths are descending: 77 66 44 22; 77 66 44 41; 77 66 60 58; 77 66 60 25; 77 55 33 29; 77 55 55.

