 Home
 Products
 Integration
 Tutorial
 Barcode FAQ
 Purchase
 Company
how to generate a barcode using asp.net c# Recursion No, thanks in Software
Recursion No, thanks Printing QR Code ISO/IEC18004 In None Using Barcode creator for Software Control to generate, create QR Code JIS X 0510 image in Software applications. QR Code JIS X 0510 Recognizer In None Using Barcode recognizer for Software Control to read, scan read, scan image in Software applications. Returning to our discussion of longest increasing subsequences: the formula for L(j) also suggests an alternative, recursive algorithm Wouldn t that be even simpler Actually, recursion is a very bad idea: the resulting procedure would require exponential time! To see why, suppose that the dag contains edges (i, j) for all i < j that is, the given sequence of numbers a1 , a2 , , an is sorted In that case, the formula for subproblem L(j) becomes L(j) = 1 + max{L(1), L(2), , L(j 1)} QR Code Creation In Visual C#.NET Using Barcode encoder for VS .NET Control to generate, create QR Code image in Visual Studio .NET applications. QR Code ISO/IEC18004 Generation In VS .NET Using Barcode creation for ASP.NET Control to generate, create QR Code image in ASP.NET applications. The following gure unravels the recursion for L(5) Notice that the same subproblems get solved over and over again! Generating QR Code In .NET Using Barcode creator for .NET framework Control to generate, create QR Code JIS X 0510 image in Visual Studio .NET applications. Creating QR Code In VB.NET Using Barcode encoder for VS .NET Control to generate, create QR image in .NET applications. L(5) EAN13 Maker In None Using Barcode creator for Software Control to generate, create EAN13 image in Software applications. Barcode Encoder In None Using Barcode drawer for Software Control to generate, create bar code image in Software applications. L(1) Draw UPC Symbol In None Using Barcode creator for Software Control to generate, create UPCA image in Software applications. Encoding Code 3 Of 9 In None Using Barcode maker for Software Control to generate, create USS Code 39 image in Software applications. L(2) L(1) USS Code 128 Encoder In None Using Barcode maker for Software Control to generate, create Code 128A image in Software applications. Paint DataMatrix In None Using Barcode printer for Software Control to generate, create Data Matrix 2d barcode image in Software applications. L(3) L(1) L(2) L(1) L(1) L(2) L(1) Drawing Standard 2 Of 5 In None Using Barcode encoder for Software Control to generate, create 2/5 Industrial image in Software applications. Print EAN 13 In VB.NET Using Barcode generator for VS .NET Control to generate, create EAN / UCC  13 image in .NET framework applications. L(4) L(3) L(1) L(2) L(1) ECC200 Generation In ObjectiveC Using Barcode generator for iPad Control to generate, create Data Matrix ECC200 image in iPad applications. Creating GS1  13 In None Using Barcode creator for Online Control to generate, create EAN13 image in Online applications. For L(n) this tree has exponentially many nodes (can you bound it ), and so a recursive solution is disastrous Then why did recursion work so well with divideandconquer The key point is that in divideandconquer, a problem is expressed in terms of subproblems that are substantially smaller, say half the size For instance, mergesort sorts an array of size n by recursively sorting two subarrays of size n/2 Because of this sharp drop in problem size, the full recursion tree has only logarithmic depth and a polynomial number of nodes In contrast, in a typical dynamic programming formulation, a problem is reduced to subproblems that are only slightly smaller for instance, L(j) relies on L(j 1) Thus the full recursion tree generally has polynomial depth and an exponential number of nodes However, it turns out that most of these nodes are repeats, that there are not too many distinct subproblems among them Ef ciency is therefore obtained by explicitly enumerating the distinct subproblems and solving them in the right order Recognize ANSI/AIM Code 39 In Visual C# Using Barcode decoder for VS .NET Control to read, scan read, scan image in .NET applications. Generating Matrix 2D Barcode In Visual Basic .NET Using Barcode maker for .NET framework Control to generate, create 2D Barcode image in .NET applications. Programming
Barcode Recognizer In VB.NET Using Barcode reader for Visual Studio .NET Control to read, scan read, scan image in Visual Studio .NET applications. GS1  12 Encoder In Visual C#.NET Using Barcode maker for VS .NET Control to generate, create UPC Symbol image in .NET applications. The origin of the term dynamic programming has very little to do with writing code It was rst coined by Richard Bellman in the 1950s, a time when computer programming was an esoteric activity practiced by so few people as to not even merit a name Back then programming meant planning, and dynamic programming was conceived to optimally plan multistage processes The dag of Figure 62 can be thought of as describing the possible ways in which such a process can evolve: each node denotes a state, the leftmost node is the starting point, and the edges leaving a state represent possible actions, leading to different states in the next unit of time The etymology of linear programming, the subject of 7, is similar 63 Edit distance
When a spell checker encounters a possible misspelling, it looks in its dictionary for other words that are close by What is the appropriate notion of closeness in this case A natural measure of the distance between two strings is the extent to which they can be aligned, or matched up Technically, an alignment is simply a way of writing the strings one above the other For instance, here are two possible alignments of SNOWY and SUNNY: S S U N O W N N Cost: 3 Y Y S S U N O W N Cost: 5 N Y Y The indicates a gap ; any number of these can be placed in either string The cost of an alignment is the number of columns in which the letters differ And the edit distance between two strings is the cost of their best possible alignment Do you see that there is no better alignment of SNOWY and SUNNY than the one shown here with a cost of 3 Edit distance is so named because it can also be thought of as the minimum number of edits insertions, deletions, and substitutions of characters needed to transform the rst string into the second For instance, the alignment shown on the left corresponds to three edits: insert U, substitute O N, and delete W In general, there are so many possible alignments between two strings that it would be terribly inef cient to search through all of them for the best one Instead we turn to dynamic programming A dynamic programming solution When solving a problem by dynamic programming, the most crucial question is, What are the subproblems As long as they are chosen so as to have the property (*) from page 159 it is an easy matter to write down the algorithm: iteratively solve one subproblem after the other, in order of increasing size Our goal is to nd the edit distance between two strings x[1 m] and y[1 n] What is a good subproblem Well, it should go part of the way toward solving the whole problem; so how about looking at the edit distance between some pre x of the rst string, x[1 i], and some pre x of the second, y[1 j] Call this subproblem E(i, j) (see Figure 63) Our nal objective, then, is to compute E(m, n) 161 Figure 63 The subproblem E(7, 5)

