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vb.net barcode printing SORTING in Java
SORTING Data Matrix 2d Barcode Recognizer In Java Using Barcode Control SDK for Java Control to generate, create, read, scan barcode image in Java applications. Encode Data Matrix 2d Barcode In Java Using Barcode generator for Java Control to generate, create Data Matrix ECC200 image in Java applications. 3 4 5 6 7 8 9 10 11 Data Matrix ECC200 Reader In Java Using Barcode decoder for Java Control to read, scan read, scan image in Java applications. Print Bar Code In Java Using Barcode maker for Java Control to generate, create bar code image in Java applications. for (int i = 1; i < a.length; i++) { // int ai = a[i], j; // for (j = i; j > 0 && a[j1] > ai; j) { // a[j] = a[j1]; // } a[j] = ai; // // INVARIANT: a[0] <= a[1] <= ... <= a[i]; } } Read Bar Code In Java Using Barcode scanner for Java Control to read, scan read, scan image in Java applications. Make DataMatrix In Visual C# Using Barcode maker for VS .NET Control to generate, create Data Matrix ECC200 image in Visual Studio .NET applications. step step step step
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Painting ECC200 In Java Using Barcode generation for Java Control to generate, create DataMatrix image in Java applications. Paint EAN / UCC  13 In Java Using Barcode maker for Java Control to generate, create UCC  12 image in Java applications. Theorem 14.5 The insertion sort is correct. See the solution to Problem 14.23 on page 277 for a proof of this theorem. Theorem 14.6 The insertion sort runs in O(n2) time. See the solution to Problem 14.24 on page 277 for a proof of this theorem. Theorem 14.7 The insertion sort runs in O(n) time on a sorted sequence. See the solution to Problem 14.25 on page 283 for a proof of this theorem. THE SHELL SORT Theorem 14.7 suggests that if the sequence is nearly sorted, then the insertion sort will run nearly in O(n) time. That is true. The shell sort exploits that fact to obtain an algorithm that in general runs in better than O(n1.5) time. It applies the insertion sort repeatedly to skip subsequences such as {s0, s3, s6, s9, . . . , sn 2} and {s1, s4, s7, s10, . . . , sn 1}. These are two of the three skip3subsequences. Algorithm 14.4 The Shell Sort (Precondition: s = {s0 . . . sn 1} is a sequence of n ordinal values.) (Postcondition: The entire sequence s is sorted.) 1. Set d = 1. 2. Repeat step 3 until 9d > n. 3. Set d = 3d + 1. 4. Do steps 5 6 until d = 0. 5. Apply the insertion sort to each of the d skipdsubsequences of s. 6. Set d = d/3. Suppose that s has n = 200 elements. Then the loop at step 2 would iterate three times, increasing d from 1 to d = 4, 13, and 40. The first iteration of the loop at step 4 would apply the insertion sort to each of the 40 skip40subsequences {s0, s40, s80, s120, s160}, {s1, s41, s81, s121, s161}, {s2, s42, s82, s122, s162}, . . . , {s39, s79, s119, s159, s199}. Then step 6 would reduce d to 13, and then the second iteration of the loop at step 4 would apply the insertion sort to each of the thirteen skip13subsequences {s0, s13, s26, s39, s52, s65, . . . , s194}, {s1, s14, s27, s40, s53, s66, . . . , s195}, . . . , {s12, s25, s38, s51, s64, s77, . . . , s193}. Then step 6 would reduce d to 4, and the third iteration of the loop at step 4 would apply the insertion sort to each of the four skip4subsequences {s0, s4, s8, s12, . . ., s196}, {s1, s5, s9, s13, . . . , s197}, {s2, s6, s10, s14, . . . , s198}, and {s3, s7, s11, s15, . . . , s199}. Then step 6 would reduce d to 1, and, and the fourth Identcode Generation In Java Using Barcode printer for Java Control to generate, create Identcode image in Java applications. EAN13 Recognizer In C# Using Barcode recognizer for .NET framework Control to read, scan read, scan image in .NET framework applications. SORTING
Scan EAN13 In Visual Studio .NET Using Barcode decoder for .NET framework Control to read, scan read, scan image in .NET framework applications. 1D Barcode Encoder In .NET Framework Using Barcode creator for ASP.NET Control to generate, create Linear Barcode image in ASP.NET applications. [CHAP. 14
Making EAN 13 In None Using Barcode generator for Excel Control to generate, create European Article Number 13 image in Microsoft Excel applications. Code 128 Code Set C Decoder In Visual C#.NET Using Barcode reader for VS .NET Control to read, scan read, scan image in .NET applications. iteration of the loop at step 4 would apply the insertion sort to the entire sequence. This entire process would apply the insertion sort 58 times: 40 times to subsequences of size n1 = 5, 13 times to subsequences of size n2 = 15, 4 times to subsequences of size n3 = 50, and once to the entire sequence of size n4 = n = 200. At first glance, the repeated use of the insertion sort within the shell sort would seem to take longer than simply applying the insertion sort directly just once to the entire sequence. Indeed, a direct calculation of the total number of comparisons, using the complexity function n2, yields 40(n12) + 13(n22) + 4(n32) + 1(n42) = 40(52) + 13(152) + 4(502) + 1(2002) = 53,925 which is quite a bit worse than the single n2 = 2002 = 40,000 But after the first iteration of step 4, the subsequent subsequences are nearly sorted. So the actual number of comparisons needed there is closer to n. Thus, the actual number of comparisons is more like 40(n12) + 13(n2) + 4(n3) + 1(n4) = 40(52) + 13(15) + 4(50) + 1(200) = 1,595 which is quite a bit better than 40,000. Theorem 14.8 The shell sort runs in O(n1.5) time. Note that, for n = 200, n1.5 = 2001.5 = 2,829, which is a lot better than n2 = 2002 = 40,000. EXAMPLE 14.7 The Shell Sort Code 39 Extended Drawer In None Using Barcode printer for Software Control to generate, create USS Code 39 image in Software applications. Encoding GTIN  12 In .NET Using Barcode maker for .NET Control to generate, create UPC Code image in VS .NET applications. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 public static void sort(int[] a) { // POSTCONDITION: a[0] <= a[1] <= ... <= a[a.length1]; int d = 1, j, n = a.length; // step 1 while (9*d < n) { // step 2 d = 3*d + 1; // step 3 } while (d > 0) { // step 4 for (int i = d; i < n; i++) { // step 5 int ai = a[i]; j = i; while (j >= d && a[jd] > ai) { a[j] = a[jd]; j = d; } a[j] = ai; } d /= 3; // step 6 } } THE MERGE SORT The merge sort applies the divideandconquer strategy to sort a sequence. First it subdivides the sequence into subsequences of singletons. Then it successively merges the subsequences pairwise until a single sequence is reformed. Each merge preserves order, so each merged subsequence is sorted. When the final merge is finished, the complete sequence is sorted. Although it can be implemented iteratively, the merge sort is naturally recursive: Split the sequence in two, sort each half, and then merge them back together preserving their order. The basis occurs when the subsequence contains only a single element. CHAP. 14]

