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vb.net barcode printing Problems in Java
Problems Scanning Data Matrix 2d Barcode In Java Using Barcode Control SDK for Java Control to generate, create, read, scan barcode image in Java applications. Creating DataMatrix In Java Using Barcode maker for Java Control to generate, create ECC200 image in Java applications. 13.1 Determine which of the binary trees in Figure 13.7 is a heap.
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Barcode Decoder In Java Using Barcode reader for Java Control to read, scan read, scan image in Java applications. Printing ECC200 In C#.NET Using Barcode maker for .NET framework Control to generate, create ECC200 image in .NET framework applications. 13.2 13.3 13.4 Paint Data Matrix ECC200 In Visual Studio .NET Using Barcode generation for ASP.NET Control to generate, create Data Matrix 2d barcode image in ASP.NET applications. Data Matrix ECC200 Generation In .NET Using Barcode encoder for Visual Studio .NET Control to generate, create ECC200 image in .NET applications. Determine which of the arrays in Figure 13.8 on page 251 has the heap property. Show the heap after inserting each of these keys in this order: 44, 66, 33, 88, 77, 77, 22. Show the array obtained from the natural map of each of the heaps obtained in Problem 13.3. Make ECC200 In Visual Basic .NET Using Barcode generator for .NET framework Control to generate, create Data Matrix 2d barcode image in VS .NET applications. Making GTIN  128 In Java Using Barcode generator for Java Control to generate, create GTIN  128 image in Java applications. CHAP. 13] EAN / UCC  13 Drawer In Java Using Barcode creator for Java Control to generate, create UPC  13 image in Java applications. Generate UPCA In Java Using Barcode creation for Java Control to generate, create UCC  12 image in Java applications. HEAPS AND PRIORITY QUEUES
Create Code 11 In Java Using Barcode drawer for Java Control to generate, create Code 11 image in Java applications. UPCA Recognizer In C#.NET Using Barcode reader for VS .NET Control to read, scan read, scan image in VS .NET applications. Figure 13.8 Arrays
Generate UPCA Supplement 2 In None Using Barcode drawer for Microsoft Excel Control to generate, create UPC A image in Microsoft Excel applications. Decode Code 128 In None Using Barcode reader for Software Control to read, scan read, scan image in Software applications. Write and test this method
Create Code 128 In .NET Framework Using Barcode drawer for Reporting Service Control to generate, create Code 128 Code Set B image in Reporting Service applications. Universal Product Code Version A Scanner In VB.NET Using Barcode decoder for VS .NET Control to read, scan read, scan image in .NET applications. boolean isHeap(int[] a) // returns true if and only if the specified array // has the heap property
Scan EAN128 In VB.NET Using Barcode recognizer for Visual Studio .NET Control to read, scan read, scan image in .NET applications. Draw Bar Code In VS .NET Using Barcode creation for ASP.NET Control to generate, create bar code image in ASP.NET applications. 13.6 13.7 Prove that every subtree of a heap is a heap. Show the heap after inserting each of these keys in this order: 50, 95, 70, 30, 90, 25, 35, 80, 60, 40, 20, 10, 75, 45, 35. Answers to Review Questions
13.1 13.2 13.3 13.4 Heaps are used to implement priority queues and the heap sort. (See page 266.) Insertions into and removals from a heap are very efficient; they run in O(lgn). A priority queue is a bestinfirstout container, that is, the element with the highest priority comes out first. Elements are removed from a queue in the same order in which they are inserted: firstinfirstout. Elements in a priority queue must have an ordinal key field which determines the priority order in which they are to be removed. Heaps are used to implement priority queues because they allow O(lgn) insertions and removals. This is because both the add() and the remove() methods are implemented by traversing a roottoleaf path through the heap. Such paths are no longer than the height of the tree which is at most lgn. The natural mapping starts at a[1] instead of a[0] to facilitate navigation up and down the heap tree. By numbering the root 1 and continuing sequentially with a level order traversal, the number of the parent of any node numbered k will be k/2, and the numbers of its child nodes will be 2k and 2k+1. If it takes an average of 3ms to remove an element from a priority queue with 1,000 elements, then it should take about 6ms to remove an element from a priority queue with 1,000,000 elements. The run time for a method that uses a priority queue to sort an array would be O(2n lgn) because it will make n insertions and n removals, each running in O(lgn) time. 13.7 13.8 Solutions to Problems
13.1 a. This is not a heap because the roottoleaf path {88, 44, 77} is not descending (44 < 77). b. This is a heap. c. This is not a heap because the roottoleaf path {55, 33, 44} is not descending (33 < 44) and the roottoleaf path {55, 77, 88} is not descending (55 < 77 < 88). d. This is not a heap because the binary tree is not complete. e. This is a heap. f. This is not a heap because the tree is not binary. HEAPS AND PRIORITY QUEUES
[CHAP. 13
a. This array does not have the heap property because the roottoleaf path {a[1], a[3], a[6]} = {88, 44, 77} is not descending (44 < 77). b. This array does have the heap property. c. This array does have the heap property. d. This array does not have the heap property because its data elements are not contiguous: It does not represent a complete binary tree. e. This array does have the heap property. f. This array does not have the heap property because the roottoleaf path {a[1], a[3], a[6]} = {88, 22, 55} is not descending (22 < 55) and the roottoleaf path {a[1], a[3], a[7]} = {88, 22, 66} is not descending (22 < 66). Figure 13.9 shows a trace of the insertion of the keys 44, 66, 33, 88, 77, 55, 22 into a heap. Figure 13.9 Trace of insertions into a heap
13.4 13.5 Figure 13.10 on page 253 shows the arrays for the heaps in Problem 13.3.
boolean isHeap(int[] a) { // returns true if and only if the specified array // has the heap property int n = a.length; for (int i = n/2; i < n; i++) { for (int j = i; j > 1; j /=2) { if (a[j/2] < a[j]) { return false; } } } return true; } CHAP. 13]

