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In their historical overview of minimum spanning tree algorithms, Ronald L. Graham and Pavol Hell outline three algorithms that they consider especially important and that have played a central role in the history of the problem. The first two are the algorithms that are commonly attributed to Kruskal and Prim (although the second one was originally formulated by Vojt ch Jarn k in 1930), while the third is the one initially described by Bor vka. Graham and Hell succinctly explain the algorithms as follows. A partial solution is a spanning forest, consisting of a set of fragments (components, trees). Initially, each node is a fragment. In each iteration, edges are added, joining fragments, until we have a spanning tree. Algorithm 1: Add a shortest edge that joins two different fragments. Algorithm 2: Add a shortest edge that joins the fragment containing the root to another fragment. Algorithm 3: For every fragment, add the shortest edge that joins it to another fragment. For algorithm 2, the root is chosen arbitrarily at the beginning. For algorithm 3, it is assumed that all edge weights are different to ensure that no cycles can occur. As you can see, all three algorithms are based on the same fundamental fact that the shortest edge over a cut is safe. Also, in order to implement them efficiently, you need to be able to find shortest edges, detect whether two nodes belong to the same fragment, and so forth (as explained for algorithms 1 and 2 in the main text). Still, these brief explanations can be useful as a memory aid or to get the bird s-eye perspective on what s going on.



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In the code example above, we used a System.out.println() to display the database information. This prints directly to the console. If you ve done much development with Java, you probably know the problem that can happen with this. You ll have so many System.out.println() commands, that what is printed scrolls right off the screen, or is lost among the hundreds of lines of debug. The DriverManager class provides a method that can be used to redirect debug output, and a method to send strings to the output through the driver manager. These methods are:

s Note Before you start developing a web application using JSF, you need a JSF implementation library. You

public static void setLogWriter(PrintWriter) public static void println(String)





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Although induction is generally used to show that a greedy algorithm is correct, there are some extra tricks that can be employed. I ve already used some in this chapter, but here I ll try to give you an overview, using some simple problems involving time intervals. It turns out there are many problems of this type that can be solved by greedy algorithms. I m not including code for these; the implementations are pretty straightforward (although it might be a useful exercise to actually implement them).

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can download JSF Reference Implementation (JSF-RI) 1.2 from https://javaserverfaces.dev.java. net/. After downloading it, extract the ZIP file into a directory of your choice and then copy jsf-api.jar and jsf-impl.jar (located in the lib directory of the JSF-RI installation) to your WEB-INF/lib directory. JSF-RI depends on JSTL, so you also have to copy jstl.jar (located in the lib/j2ee directory of the Spring installation).

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This is what Kleinberg and Tardos (in Algorithm Design) call staying ahead. The idea is to show that as you build your solution, one step at a time, the greedy algorithm will always have gotten at least as far as a hypothetical optimal algorithm would have. Once you reach the finish line, you ve shown that greed is optimal. This technique can be useful in solving a very common example of greed: resource scheduling. The problem involves select a set of compatible intervals. Normally, we think of these intervals as time intervals. Compatibility simply means that none of them should overlap, so this could be used to model requests for using a resource, such as a lecture hall, for certain time periods. Another example would be to let you be the resource and to let the intervals be various activities you d like to participate

Using setLogWriter(), you can direct the DriverManager object s debug statements to an instance of PrintWriter. The PrintWriter can be a wrapper for any Writer or OutputStream, such as a file, a stream, or a PipedWriter. You can also send your own debug statements to the log by calling the println() method. Here is a snippet of code showing how we could have used this feature in the example above:

// At the top of the try block FileWriter fw = new FileWriter("mydebug.log"); PrintWriter pw = new PrintWriter(fw); DriverManager.setLogWriter(pw); // After getting the Connection and the DatabaseMetaData objects DriverManager.println("db name is " + dbmd.getDatabaseProductName());

city/ WEB-INF/ classes/ lib/ commons-logging.jar jsf-api.jar jsf-impl.jar jstl.jar spring.jar applicationContext.xml faces-config.xml web.xml distance.jsp In the web deployment descriptor (i.e., web.xml) of a JSF application, you have to register the JSF servlet FacesServlet to handle web requests. You can map this servlet to the URL pattern *.faces. To load Spring s application context at startup, you also have to register the servlet listener ContextLoaderListener. <web-app version="2.4" xmlns="http://java.sun.com/xml/ns/j2ee" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://java.sun.com/xml/ns/j2ee http://java.sun.com/xml/ns/j2ee/web-app_2_4.xsd"> <listener> <listener-class> org.springframework.web.context.ContextLoaderListener </listener-class> </listener> <servlet> <servlet-name>faces</servlet-name> <servlet-class>javax.faces.webapp.FacesServlet</servlet-class> </servlet> <servlet-mapping> <servlet-name>faces</servlet-name> <url-pattern>*.faces</url-pattern> </servlet-mapping> </web-app> The basic idea of JSF is to separate presentation logic from UIs by encapsulating it in one or more JSF managed beans. For your distance-finding function, you can create the following DistanceBean class for a JSF managed bean: package com.apress.springrecipes.city.jsf; ... public class DistanceBean {

CHAPTER 7 GREED IS GOOD PROVE IT!

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