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how to make barcode in c#.net Intelligent exhaustive search in Software
91 Intelligent exhaustive search Encoding Quick Response Code In None Using Barcode printer for Software Control to generate, create Denso QR Bar Code image in Software applications. QR Code JIS X 0510 Recognizer In None Using Barcode scanner for Software Control to read, scan read, scan image in Software applications. 911 Backtracking
QR Code Generator In C#.NET Using Barcode creator for .NET Control to generate, create Denso QR Bar Code image in Visual Studio .NET applications. Generate QRCode In VS .NET Using Barcode encoder for ASP.NET Control to generate, create QRCode image in ASP.NET applications. Backtracking is based on the observation that it is often possible to reject a solution by looking at just a small portion of it For example, if an instance of SAT contains the clause (x 1 x2 ), then all assignments with x1 = x2 = 0 (ie, false) can be instantly eliminated To put it differently, by quickly checking and discrediting this partial assignment, we are able to prune a quarter of the entire search space A promising direction, but can it be systematically exploited Here s how it is done Consider the Boolean formula (w, x, y, z) speci ed by the set of clauses (w x y z), (w x), (x y), (y z), (z w), (w z) We will incrementally grow a tree of partial solutions We start by branching on any one variable, say w: Printing QRCode In VS .NET Using Barcode drawer for .NET Control to generate, create Denso QR Bar Code image in .NET framework applications. QRCode Encoder In Visual Basic .NET Using Barcode encoder for VS .NET Control to generate, create QR Code 2d barcode image in Visual Studio .NET applications. Initial formula w=0 w=1
Drawing Bar Code In None Using Barcode printer for Software Control to generate, create bar code image in Software applications. EAN / UCC  13 Creation In None Using Barcode creator for Software Control to generate, create GTIN  13 image in Software applications. Plugging w = 0 and w = 1 into , we nd that no clause is immediately violated and thus neither of these two partial assignments can be eliminated outright So we need to keep 266 Encode Data Matrix 2d Barcode In None Using Barcode generator for Software Control to generate, create DataMatrix image in Software applications. Code128 Creator In None Using Barcode encoder for Software Control to generate, create Code 128C image in Software applications. branching We can expand either of the two available nodes, and on any variable of our choice Let s try this one: Universal Product Code Version A Printer In None Using Barcode generator for Software Control to generate, create UCC  12 image in Software applications. GTIN  128 Generation In None Using Barcode creation for Software Control to generate, create EAN / UCC  13 image in Software applications. Initial formula w=0 w=1
Encoding MSI Plessey In None Using Barcode creator for Software Control to generate, create MSI Plessey image in Software applications. Bar Code Scanner In .NET Using Barcode Control SDK for ASP.NET Control to generate, create, read, scan barcode image in ASP.NET applications. This time, we are in luck The partial assignment w = 0, x = 1 violates the clause (w x) and can be terminated, thereby pruning a good chunk of the search space We backtrack out of this culdesac and continue our explorations at one of the two remaining active nodes In this manner, backtracking explores the space of assignments, growing the tree only at nodes where there is uncertainty about the outcome, and stopping if at any stage a satisfying assignment is encountered In the case of Boolean satis ability, each node of the search tree can be described either by a partial assignment or by the clauses that remain when those values are plugged into the original formula For instance, if w = 0 and x = 0 then any clause with w or x is instantly satis ed and any literal w or x is not satis ed and can be removed What s left is (y z), (y), (y z) Likewise, w = 0 and x = 1 leaves with the empty clause ( ) ruling out satis ability Thus the nodes of the search tree, representing partial assignments, are themselves SAT subproblems This alternative representation is helpful for making the two decisions that repeatedly arise: which subproblem to expand next, and which branching variable to use Since the bene t of backtracking lies in its ability to eliminate portions of the search space, and since this happens only when an empty clause is encountered, it makes sense to choose the subproblem that contains the smallest clause and to then branch on a variable in that clause If this clause happens to be a singleton, then at least one of the resulting branches will be terminated (If there is a tie in choosing subproblems, one reasonable policy is to pick the one lowest in the tree, in the hope that it is close to a satisfying assignment) See Figure 91 for the conclusion of our earlier example More abstractly, a backtracking algorithm requires a test that looks at a subproblem and quickly declares one of three outcomes: 1 Failure: the subproblem has no solution 2 Success: a solution to the subproblem is found 3 Uncertainty 267 (), (y z), Creating Bar Code In C#.NET Using Barcode generator for Visual Studio .NET Control to generate, create barcode image in VS .NET applications. Code128 Encoder In None Using Barcode maker for Microsoft Excel Control to generate, create Code 128 Code Set B image in Microsoft Excel applications. Figure 91 Backtracking reveals that is not satis able
Painting Code 3/9 In None Using Barcode generation for Online Control to generate, create Code 3 of 9 image in Online applications. Bar Code Generator In None Using Barcode maker for Font Control to generate, create bar code image in Font applications. (w x y z), (w x), (x y), (y z), (z w), (w z) w=0 (x y z), (x), (x y), (y z) x=0 (y z), (y), (y z) y=0 (z), (z) z=0 () z=1 () y=1 () x=1 (), (y z) w=1 (x y), (y z), (z), (z) z=0 (x y), () z=1 (x y), (y), () Encode Code 128 In .NET Framework Using Barcode generation for Reporting Service Control to generate, create Code 128 Code Set C image in Reporting Service applications. Code128 Reader In Visual Studio .NET Using Barcode reader for .NET framework Control to read, scan read, scan image in Visual Studio .NET applications. In the case of SAT, this test declares failure if there is an empty clause, success if there are no clauses, and uncertainty otherwise The backtracking procedure then has the following format Start with some problem P0 Let S = {P0 }, the set of active subproblems Repeat while S is nonempty: choose a subproblem P S and remove it from S expand it into smaller subproblems P 1 , P2 , , Pk For each Pi : If test(Pi ) succeeds: halt and announce this solution If test(Pi ) fails: discard Pi Otherwise: add Pi to S Announce that there is no solution For SAT, the choose procedure picks a clause, and expand picks a variable within that clause We have already discussed some reasonable ways of making such choices With the right test, expand, and choose routines, backtracking can be remarkably effective in practice The backtracking algorithm we showed for SAT is the basis of many successful satis ability programs Another sign of quality is this: if presented with a 2 SAT instance, it will always nd a satisfying assignment, if one exists, in polynomial time (Exercise 91)!

