Preface

This lab is quite different from others. You will not be writing any lines of code, and you will not be turning in any printouts. Instead, you will be required to solve a few puzzles and to demonstrate your success in person with one of the course TAs. (Don't worry - you will be writing plenty of code other weeks!)

Overview

The textbook discusses performing an Euler Tour on a tree as a unified, recursive framework for a variety of common tree traversals. Our goal in this lab is to make sure you get a very well grounded understanding of this general concept, and the various things you might accomplish by customizing the process.

Actually, to be specific, the book only discusses the concept of an Eulur Tour in the context of binary trees. The three common traversal orders are generaly known as "preorder," "inorder," and "postorder", depending on when you consider "visiting" a node, relative to its children. In this context, the Eulur tour can be implemented as:

EulerTour (Tree T, Position p) {

  // consider this the time when p is visited  "on the left"

  if (T.isInternal(p))
    EulerTour(T, T.leftChild(p));

  // consider this the time when p is visited  "from below"

  if (T.isInternal(p))
    EulerTour(T, T.rightChild(p));

  // consider this the time when p is visited  "on the right"
}

The same concept can be applied to general trees as well (though the concept of "inorder" is not quite well defined). In this context, the pseudocode might appear as:

EulerTour (Tree T, Position p) {

  // consider this the time when p is visited  "on the left"

  Iterator children = T.children(p);
  while (children.hasNext()) {
     Position child = (Position) children.nextObject();
     EulerTour(T, child);

     // if there are still more children to come,
     // consider this a time when p is visited  "from below"
  }

  // consider this the time when p is visited  "on the right"
}

The Applet

• Starting The Applet

  You will need to view this Applet using the appletviewer program rather than a browser. The reason is that the program will need to read input from the file system, and by default this is prohibited for security reasons, when running an Applet in a web browser.

  The Applet can be viewed from a DOS window using the appletviewer program which is part of Sun's JDK. To do this from the department labs, open a DOS window from the "Programming (java) --> jdk (dos)" menu, and do the following:

  DOSprompt>  e:
  DOSprompt>  cd prof_pub\mhg\comp271\labs\eulertour\
  DOSprompt>  appletviewer EulerTour.html
  

• Using The Applet

  A sample screenshot of the Applet is given below (you may click to enlarge it).

  

  • Loading a sample tree
    The first issue when using the Applet is selecting the tree which will be used. Several example trees have been saved in appropriately formatted files in the same directory as the sourcecode (e.g., "binary.txt" and "disk.txt"). To (re)load a tree, you should type the full filename into the box to the left of the "input file" button. After entering the name, a click on the button should result in the tree being loaded from the file and a picture of the tree being displayed by the Applet.

  • Animating the Euler Tour
    The main function of this applet is to animate a Euler Tour on the given tree. You can (re)start such an animation by clicking on the "start euler" button. By default, the animation walks continously through the entire tour. The speed of the animation can be altered by changing the value in the box to the left of the "sleep time" button and then clicking on the button to enact the change. A larger sleep time will result in a slower animation. While the tour is running, you can manually "pause" and "resume" the animation with the appropriately labeled buttons. You can also "abort" the current tour at any point (for example, if it is taking way too long with the current sleep value).

  • Optional Features
    Based on the terminology from our text, each node of a tree is "visited" by the Euler tour three or more times, once on the "left," once on the "right," and one or more times from the "bottom."

    To the right side of the screen, the Applet contains three columns of buttons which effect the behavior of the software during a tour. Essentially these buttons allow you to turn on or off features of the animation which get triggered with each such type of "visit" of a node.

    • Graphics: With the default settings, the progress of the tour is animated graphically with a series of lines and curves surrounding the original tree. Specifically, just before a node is visited on the left, a red line is drawn near the edge leading from the parent to that node; a black curve is drawn below each node as it is visited from below; just after a node is visited on the right, a magenta line will be drawn near the edge leading to the parent.

      You could choose to turn off some or all of the graphics, but for the purpose of this lab, we recommend that you leave the graphics on.
      A note about "refreshing" the graphics: If the window is obscured while the Euler tour is being animated, the obscured lines which may have previously been drawn are not automatically refreshed when the window becomes visible again.

    • Pause: By default, the animation runs continously, pausing only if you hit the "pause euler" button. However, it may be convenient to have the applet automatically pause the tour whenever a visit of a particular type or types occurs. By turning on one or more of these selections, these pauses will happen. Note: after each such pause, the animation will only continue when you click on the "resume euler" button.

    • Print: There is a text area in the center of the screen which can be used to display additional output. Specifically, the applet can be instructed to print the text associated with each node whenever a visit of a particular type or types occurs. Generally, you will get more recognizable outputs when only one button is selected, but you may certainly choose to select multiple buttons if you wish.

Your Task

Please answer the following questions and turn in your answers to the TA.

1. Load the tree "binary.txt" and begin an Euler tour with pauses turned on for visits "on the right."
   What node is the tour at when the first pause occurs?
   When the second pause occurs?
   When the third pause occurs?
   
   
   

2. Using "binary.txt" turn off all pauses and turn on the print option "from bottom." Run the entire Euler tour and report the output generated by this tour.
   
   
   

3. When running an Euler Tour on the "disk.txt" tree, what are the respective second to last and last two nodes to be visited "on the left"?

   "from the bottom"?

   "on the right"?

   Note: To get these, you can either use pauses (time consuming), look at the last two pieces of output (easier), or answer the question on your own without using the software (are you right?).
   
   
   

4. If using the "simple.txt" tree, what print button(s) would you need to turn on to get output which is in alphabetical order?
   
   
   

5. If using the "simple.txt" tree, what output do you get if all three print buttons are turned on.
   
   
   

6. If using the "paper.txt" tree, what print button(s) would you need to turn on to get output which is essentially a Table of Contents?
   
   
   

7. Returning to "simple.txt" what combination of print buttons should be turned on in order to get the output:
   MDAAGFFKKGDTPPWWTM.
   
   
   

Acknowledgment

We are grateful to Min Wang, a former Loyola student, for developing the original version of this software as an independent project in 2000.