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barcode in ssrs 2008 Figure 14.3 The natural mapping for the heap sort in Java
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MSI Plessey Generator In Java Using Barcode generation for Java Control to generate, create MSI Plessey image in Java applications. Making GS1  12 In None Using Barcode printer for Excel Control to generate, create UCC  12 image in Office Excel applications. Theorem 14.15 The heap sort is correct. See Problem 14.31 on page 277. Theorem 14.16 The heap sort runs in O(n lgn) time. Each call to the heapify() function takes at most lg n steps because it iterates only along a path from the current element down to a leaf. The longest such path for a complete binary tree of n elements is lg n. The heapify() function is called n/2 times in the first for loop and n 1 times in the second for loop. That comes to less than (3n/2) lg n, which is proportional to n lg n. If we regard a sorting algorithm as a stream process wherein elements stream into an array in random order and then stream out in sorted order, then the heap sort can be regarded as an efficient mean between the extremes of the selection sort and the insertion sort. The selection sort does all its sorting during the removal stage of the process, having stored the elements in the unsorted order in which they arrived. The insertion sort does all its sorting during the insertion stage of the process so that the elements can stream out of the array in the sorted order in which they were stored. But the heap sort does a partial sorting by inserting the elements into a heap and then finishes the sorting as the elements are removed from the heap. The payoff from this mean between the extremes is greater efficiency: O(n lg n) instead of O(n2). THE SPEED LIMIT FOR COMPARISON SORTS Theorem 14.17 No sorting algorithm that rearranges the array by comparing its elements can have a worstcase complexity function better than O(n lg n). Consider the decision tree that covers all possible outcomes of the algorithm on an array of size n. Since the algorithm rearranges the array by comparing its elements, each node in the decision tree represents a condition of the form (a[i] < a[j]). Each such condition has two possible outcomes (true or false), so the decision tree is a binary tree. And since the tree must cover all possible arrangements, it must have at least n! leaves. Therefore, by Corollary 11.3 on page 203, the height of the decision tree must be at least lg(n!). In the worst case, the number of comparisons that the algorithm makes is the same as the height of the decision tree. Therefore, the algorithm s worstcase complexity function must be O(lg(n!)). Now by Stirling s Formula (outlined on page 325), n! so log n! log 2n n e Making Data Matrix ECC200 In Visual C#.NET Using Barcode generation for Visual Studio .NET Control to generate, create ECC200 image in VS .NET applications. Print EAN13 In Java Using Barcode creation for Eclipse BIRT Control to generate, create UPC  13 image in BIRT reports applications. Bar Code Recognizer In VS .NET Using Barcode reader for .NET Control to read, scan read, scan image in .NET applications. ANSI/AIM Code 39 Creation In None Using Barcode printer for Excel Control to generate, create Code39 image in Office Excel applications. Read Data Matrix ECC200 In None Using Barcode decoder for Software Control to read, scan read, scan image in Software applications. Scan Bar Code In VS .NET Using Barcode Control SDK for ASP.NET Control to generate, create, read, scan barcode image in ASP.NET applications. 
