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vb.net code to generate barcode otherwise x is not in a[]; // step 1 // step 2 // step 3 in Java
otherwise x is not in a[]; // step 1 // step 2 // step 3 EAN13 Recognizer In Java Using Barcode Control SDK for Java Control to generate, create, read, scan barcode image in Java applications. Paint UPC  13 In Java Using Barcode generator for Java Control to generate, create GTIN  13 image in Java applications. // step 4
Decode EAN / UCC  13 In Java Using Barcode scanner for Java Control to read, scan read, scan image in Java applications. Barcode Drawer In Java Using Barcode encoder for Java Control to generate, create barcode image in Java applications. The output is: Recognizing Barcode In Java Using Barcode reader for Java Control to read, scan read, scan image in Java applications. Paint EAN13 Supplement 5 In Visual C# Using Barcode printer for .NET Control to generate, create European Article Number 13 image in VS .NET applications. {22, 33, 44, 55, 66, 77, 88, 99} search(a, 44): 2 search(a, 50): 1 search(a, 77): 5 search(a, 100): 1 Making EAN / UCC  13 In VS .NET Using Barcode creator for ASP.NET Control to generate, create EAN13 image in ASP.NET applications. EAN 13 Encoder In .NET Using Barcode creator for VS .NET Control to generate, create GTIN  13 image in Visual Studio .NET applications. CHAP. 2] Paint GTIN  13 In Visual Basic .NET Using Barcode printer for VS .NET Control to generate, create EAN13 image in .NET framework applications. Draw Code 39 In Java Using Barcode generator for Java Control to generate, create Code39 image in Java applications. ARRAYS
Data Matrix ECC200 Generator In Java Using Barcode generator for Java Control to generate, create Data Matrix 2d barcode image in Java applications. Print GS1 DataBar In Java Using Barcode maker for Java Control to generate, create GS1 DataBar Expanded image in Java applications. The search() method returns the index of the target x: search(a, 44) returns 2, because a[2] = 44; search(a, 77) returns 5, because a[5] = 77. The method returns 1 when the target is not in the array: search(a, 50) returns 1, because 50 is not in the array. USS93 Generator In Java Using Barcode generator for Java Control to generate, create Uniform Symbology Specification Code 93 image in Java applications. Encode Code 128 In None Using Barcode creation for Software Control to generate, create Code 128 Code Set C image in Software applications. The sequential search is correct. This means that it works. The following argument is a proof of that fact. If n = 0, then the sequence is empty and the loop does not execute at all. Only step 4 executes, immediately returning 1. This satisfies the postconditions: x cannot equal any of the elements because there aren t any. If n = 1, then the loop iterates only once, with i = 0. On that iteration, either s0 = x or s0 x. If s0 = x, then 0 is returned and the postcondition is satisfied. If s0 x, then the loop terminates, step 4 executes, and 1 is returned, and that satisfies the postcondition because the single element of the sequence is not equal to x. Suppose n > 1. We want to apply the First Principle of Mathematical Induction to deduce that the loop invariant must be true on every iteration of the loop. (See page 321.) That requires the verification of the invariant on the first iteration and the deduction of the invariant on iteration i from the corresponding invariant on iteration i 1. On the first iteration of the loop, i = 0, and the loop invariant in step 2 is true vacuously because the subsequence {s0...si 1} is empty. Then in step 3, either s0 = x or s0 x. If s0 = x, then 0 is returned and the postcondition is satisfied. If s0 x, then the loop continues on to a second iteration. Then i = 1, and the loop invariant in step 2 is again true because the subsequence {s0...si 1} = {s0} and s0 x. Suppose now that on iteration i 1, the loop invariant is true; that is, none of the elements in the subsequence {s0..si 1} is equal to x. If the loop continues on to the next iteration, then the condition si = x at step 3 was not true. Thus, si x. Therefore, none of the elements in the subsequence {s0..si } is equal to x, which is the loop invariant on the ith iteration The sequential search runs in O(n) time. This means that, on average, the running time is proportional to the number of elements in the array. So if everything else is the same, then applying the sequential search to an array twice as long will take about twice as long, on average. The following argument is a proof of that fact. If x is in the sequence, say at x = si with i < n, then the loop will iterate i times. In that case, the running time is proportional to i, which is O(n) since i < n. If x is not in the sequence, then the loop will iterate n times, making the running time proportional to n, which is O(n). THE BINARY SEARCH ALGORITHM The binary search is the standard algorithm for searching through a sorted sequence. It is much more efficient than the sequential search, but it does require that the elements be in order. It repeatedly divides the sequence in two, each time restricting the search to the half that would contain the element. You might use the binary search to look up a word in a dictionary. Here is the binary algorithm: (Precondition: s = {s0, s1, . . ., sn 1} is a sorted sequence of n values of the same type as x.) (Postcondition: either the index i is returned where si = x, or 1 is returned.) 1. Let ss be a subsequence of the sequence s, initially set equal to s. 2. If the subsequence ss is empty, return 1. Encoding UPC  13 In Visual Studio .NET Using Barcode generator for ASP.NET Control to generate, create EAN / UCC  13 image in ASP.NET applications. Encoding GS1  13 In None Using Barcode drawer for Font Control to generate, create European Article Number 13 image in Font applications. Code 128 Reader In Visual C#.NET Using Barcode reader for Visual Studio .NET Control to read, scan read, scan image in VS .NET applications. Code 3/9 Creation In C# Using Barcode creation for Visual Studio .NET Control to generate, create Code 3/9 image in .NET applications. UPC Symbol Creator In Visual Studio .NET Using Barcode encoder for Reporting Service Control to generate, create UCC  12 image in Reporting Service applications. Creating USS128 In C# Using Barcode generator for .NET Control to generate, create UCC128 image in .NET framework applications. 
