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FromFile(@"C:\Temp\Junk\Sample tif document 5 pages. tiff "); PdfDocument doc = new PdfDocument(); for (int PageIndex = 0; PageIndex ...

The algorithmic complexity of enumerating all subsequences of a length-n sequence is (2n), which, as we ve seen, makes the problem impossible to solve in practice for inputs of even modest size. Fortunately, not long before I encountered this problem, so had two talented mathematics, David Aldous and Persi Diaconis. Better yet, they had published their ndings in the Bulletin of the American Mathematical Society in 1999: Longest increasing subsequences: from patience sorting to the Baik-Deift-Johansson theorem. Aldous and Diaconis described an O(n log n) algorithm to solve the problem. Algorithms with (n log n) complexity are practical to use, but it helps if they are also simple to implement. This one turns out to be.



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Assembly names affect how an assembly can be used. Private assemblies have a name that is unique among the assemblies that make up the application. Shared assemblies have a strong name, which consists of the assembly name, the version, and culture information and relies on public key cryptography to ensure that the strong name is globally unique. Strong names incorporate a digital signature to ensure that the contents of an assembly cannot be modified after creation. When an application loads an assembly, the common language runtime (CLR) checks the contents of the file to ensure that no changes have occurred. Creating a strong name is a simple process; the first step is to create a file containing a key pair that will be used to sign the assembly. (Existing key files can be used if available.) The following command uses the Strong Name Tool (sn.exe) to generate a key file named myKey.snk in the local directory:





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Let X = (x 1, x 2, . . ., x n) be a sequence of n real numbers. The length of the longest increasing subsequence of X is the length of the list L generated by the following procedure. 1. Let k = 1, and let L be an empty list of numbers. 2. While k n: 3. Inspect L for numbers greater than or equal to ak. If one exists, replace the rst (and smallest) of them with ak. Otherwise (when ak is greater than every number in L), insert ak into the list L. Increase k by 1.

Execute the code in Listing 5-1 to create the tables Locations and Readings and ll them with sample data.

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In the following example, we'll use the C# compiler to build a single-file assembly, so we'll create a file named AssemblyInfo.cs that contains the global attributes required to generate the strong name. The contents of the file are listed here:

5

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USE tempdb; GO IF OBJECT_ID('dbo.Locations') IS NOT NULL DROP TABLE dbo.Locations; CREATE TABLE dbo.Locations ( ID INT NOT NULL PRIMARY KEY, name VARCHAR(12) NOT NULL ); INSERT INTO dbo.Locations VALUES (1, 'Uptown'), (2, 'Midtown'); IF OBJECT_ID('dbo.Readings') IS NOT NULL DROP TABLE dbo.Readings; CREATE TABLE dbo.Readings ( locID INT REFERENCES dbo.Locations(ID), readingNum INT, ppb DECIMAL(6,3), PRIMARY KEY (locID,readingNum) ); INSERT INTO dbo.Readings VALUES (1,1,3.968), (1,2,3.773), (1,3,3.994), (1,4,3.889), (1,5,4.015), (1,6,4.002), (1,7,4.043), (1,8,3.932), (1,9,4.072), (1,10,4.088), (1,11,3.952), (1,12,3.992), (1,13,3.980), (1,14,4.062), (1,15,4.074), (2,1,3.894), (2,2,4.184), (2,3,3.939), (2,4,4.050), (2,5,3.940), (2,6,4.140), (2,7,3.914), (2,8,4.156), (2,9,4.143), (2,10,4.035), (2,11,4.097), (2,12,4.086), (2,13,4.093), (2,14,3.932), (2,15,4.046); GO

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using System.Reflection; using System.Runtime.CompilerServices; [assembly: AssemblyCulture("")] [assembly: AssemblyVersion("1.0.0.0")] [assembly: AssemblyKeyFile("myKey.snk")]

The pseudocode described how to implement the algorithm for a single sequence X, and the Readings table contains two sequences of readings, one for each of two locations. Therefore, with the code in Listing 5-2, we ll create a user-de ned function dbo.LISL that returns the longest increasing subsequence length for a single sequence, given a location ID as input.

IF OBJECT_ID('dbo.LISL') IS NOT NULL DROP FUNCTION dbo.LISL; CREATE FUNCTION dbo.LISL(@locID INT) RETURNS INT AS BEGIN DECLARE @Solitaire TABLE ( pos int IDENTITY(1,1) PRIMARY KEY, ppb decimal(6,3), UNIQUE (ppb,pos) );

Our metadata specifies that the assembly can be used by any culture (the assembly is said to be culture-neutral), that this is version 1.0.0.0 of the assembly, and that the key pair can be found in the myKey.snk file. Our shared assembly will contain the StringPrinter class, stored in a file named StringPrinter.cs, the contents of which are listed here:

to this:

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