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Barcode Decoder In Java Using Barcode decoder for Java Control to read, scan read, scan image in Java applications. Encoding EAN13 In C#.NET Using Barcode generation for VS .NET Control to generate, create EAN 13 image in Visual Studio .NET applications. By using the divideandconquer strategy, the merge sort obtains an O(n lgn) run time, a significant improvement over the O(n2) times spent by the previous sorting algorithms. The strategy is 1. Split the sequence into two subsequences. 2. Sort each subsequence separately. 3. Merge the two subsequences back together. The merge sort does the first step in the simplest balanced way possible: It splits the sequence at its middle. If the first step is done in other ways, we obtain different sorting algorithms. The divideandconquer strategy is also used in the binary search (page 31). The simplest unbalanced way to split the sequence is to put all but the last element in the first subsequence, leaving only the last element in the second subsequence. This produces the recursive version of the insertion sort. (See Problem 14.22 on page 277.) Another unbalanced way to split the sequence is to put the largest element alone in the second subsequence, leaving all the other elements in the first subsequence. This produces the recursive version of the selection sort. (See Problem 14.18 on page 276.) Not that this makes the merge step 3 trivial: Merely append the largest element to the end of the first subsequence. A fourth way to split the sequence is to partition it so that every element in the first subsequence is less than every the element in the second subsequence. This condition of course is true in the previous case that led to the recursive selection sort. However, if we can obtain this property together with having the two subsequences the same size, then we obtain a new O(n lgn) algorithm, called the quick sort. THE QUICK SORT The quick sort is like the merge sort: It is recursive, it requires an auxiliary function with several loops, and it runs in O(n lg n) time. But in most cases it is quicker than the merge sort. The quick sort works by partitioning the array into two pieces separated by a single element x that is greater than or equal to every element in the left piece and less than or equal to every element in the right piece. This guarantees that the single element x, called the pivot element, is in its correct position. Then the algorithm proceeds, applying the same method to the two pieces separately. This is naturally recursive and very quick. Algorithm 14.6 The Quick Sort (Precondition: s = {sp . . . sq 1} is a sequence of q p ordinal values.) (Postcondition: The entire sequence s is sorted.) 1. If q p > 1, do steps 2 5. 2. Apply Algorithm 14.7 to s, obtaining the pivot index m. 3. (Invariant: the pivot element sm is in its correct sorted position.) 4. Apply the quick sort to {s0, s1, . . . , sm 1}. 5. Apply the quick sort to {sm+1, si+2, . . . , sn 1}. Algorithm 14.7 Partition (Precondition: s = {sp . . . sq 1} is a sequence of q p ordinal values.) (Postcondition: Return m, where p m < q and si sm sj for p i 1. Set x = s p (the pivot element). 2. Set i = p and j = q. Printing UPC  13 In .NET Using Barcode generator for ASP.NET Control to generate, create EAN 13 image in ASP.NET applications. UPC  13 Maker In Visual Studio .NET Using Barcode drawer for .NET Control to generate, create EAN / UCC  13 image in .NET applications. j < q.) Creating UPC  13 In Visual Basic .NET Using Barcode generation for Visual Studio .NET Control to generate, create EAN13 Supplement 5 image in .NET applications. Making GTIN  128 In Java Using Barcode maker for Java Control to generate, create UCC  12 image in Java applications. 3. 4. 5. 6. 7. 8. Creating Data Matrix In Java Using Barcode printer for Java Control to generate, create Data Matrix ECC200 image in Java applications. Barcode Creator In Java Using Barcode creation for Java Control to generate, create bar code image in Java applications. SORTING
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