Lab: Traversing 2D Data Structures
Using Iterators

Alyce Brady
Kalamazoo College

 

Introduction

In this lab you will implement the iterators for several algorithms that step through (traverse) a two-dimensional data structure made up of rows and columns. These algorithms are useful for many different kinds of two-dimensional data structures.†

The two-dimensional data structure used in this lab is represented by a BoundedEnv object.‡ A BoundedEnv object models a bounded rectangular grid that contains objects at various grid locations. Each cell contains zero or one objects.

  0 1 2 3 4 5 6 7 8
0
     
obj1
          
 
obj2
              
   
obj3
  
obj4
        
               
obj5
1
2
3

We refer to locations in the grid by their row and column numbers in parentheses, such as location (2, 7). Row and column numbers start at 0 rather than 1, so location (0, 0) refers to the first row and first column. Object obj1 in the grid shown above is in the first row and fourth column, or at location (0, 3). Object obj5 is at location (4, 8). (This is similar to the way Java array and ArrayList indices are numbered.)

A traversal through a two-dimensional data structure is an algorithm that steps through all the elements of the data structure, visiting each element exactly once.  A traversal through an environment steps through all the locations in the environment.  There are many different ways to traverse through an environment.  One common type of traversal is a row-major traversal, which steps through the environment row-by-row.  It first visits all the locations in row 0, then all the locations in row 1, and so on.  Another common traversal is a column-major traversal, which steps through the environment column-by-column.  It first visits all the locations in column 0, then all the locations in column 1, and so on.

In this lab you will define iterator classes that implement various traversal algorithms.  For example, the following simple code uses the RowMajorEnvIterator iterator, which steps through an environment in row-major order.

    RowMajorEnvIterator it = new RowMajorEnvIterator(env);
    while ( it.hasNext() )
    {
        Location nextLoc = (Location) it.next();
        new ColorBlock(highlightColor, env, nextLoc);
    }

The iterator classes you define will be used in a program that defines buttons for the various traversal algorithms and then illustrates each algorithm by placing color block objects in the environment in the order of the traversal.  Not all of them will be true traversals, in which every location is visited exactly once, but all will step through environment locations in some specific pattern.

Getting Started

In this lab you will be implementing new iterator classes and adding them to the list of iterators used by the IteratorLab application. The first thing to do, therefore, is to download the existing code for this application.

Exercise Set 1

  1. Download the zip file that contains the starting code files for the Iterator Lab (IteratorLab.zip) and unzip it. When you unzip the file and look in the Code folder, you will see several files that contain classes you will be viewing and modifying, a class (TraversalGUI) that you do not have to read but that the program needs in order to run, and two jar files (mbsbb.jar and genericEnv.jar) that contain additional classes the program needs in order to run. You will also find a Documentation folder that contains documentation for the classes you will use in this lab.  The core classes in the application are:
    • IteratorLab (contains the main method)
    • EnvIterator class (the abstract iterator class you will be extending)
      • RowMajorEnvIterator (an iterator class that implements a row-major traversal; you can use this as a template for other iterator classes)
      • ColMajorEnvIterator (a skeleton iterator class that you fill in)
    • ColorBlock class (the traversal puts color blocks in the environment to illustrate the traversal algorithm; this class is provided in one of the jar files and is documented in the Documentation folder.)
    • BoundedEnv and Location from the AP® Marine Biology Simulation case study.‡ (These classes are provided in the jar files and are documented in the Documentation folder.)
    All classes are covered by the GNU General Public License.

  2. Compile and run the program. If you click on the Row-Major Order button, you should see color blocks filling the locations of the grid in row-major (top-down, left-to-right) order.

  3. Experiment with the program to discover what the "Row-Major Order," "Stop," "Reset," and "Open a New Window" buttons do.

  4. Experiment with the "Column-Major Order" button.  What is printed to System.out?  What happens if you click on the "Stop" button after a couple of iterations?  What happens if you let the traversal run indefinitely?

Studying the Algorithms

The starting point of the IteratorLab application is the IteratorLab class, which contains the main method.  Look over the class.   It defines a number of constants that affect the size of the environment and the look of the graphical user interface.  The first thing the class's main method does is to create the environment through which the traversal algorithms will step.  The last thing it does is to define the graphical user interface that provides the buttons for running the traversal algorithms, and that displays them as they run.  Before creating the graphical user interface, though, the main method establishes how objects in the environment can be displayed, and what traversal algorithms are supported.  The DisplayMap class‡ provides class methods that associate objects that can be put in an environment with the objects that know how to display them.  The TraversalGUI class provides class methods that associate an algorithm name (actually a label on a button) with the iterator class that implements that algorithm.

Exercise Set 2

  1. Experiment with the constants defined at the top of the IteratorLab class to see how changing them affects the application.

 

Next, look at the ColorBlock class, which pairs a color and location together. The Color class is a standard Java class found in java.awt. You can create a color by specifying amounts of red, green, and blue (values between 0 and 255), or you can use one of the predefined colors provided in the class, such as Color.red. The Location class comes from the AP® Marine Biology Case Study.‡

java.awt.Color Class (Selected Constants and Methods)

black, blue, cyan, gray, green, magenta, orange, pink, red, white, yellow

Color(int r, int g, int b)

 

Exercise Set 3

  1. What aspects of the ColorBlock class allow its objects to be put in an environment?  How do ColorBlock objects get added to an environment?  Is the ColorBlock class needed?  Couldn't we just put Color objects in an environment?

 

Finally, we get to the heart of the IteratorLab application, the set of traversal algorithms it supports.  These are implemented using iterators that step through an environment, as in the code example in the Introduction section of this lab.  The EnvIterator abstract class partially implements the standard Java Iterator interface; the RowMajorEnvIterator class is one example of a concrete subclass of EnvIterator that completes the implementation.  In particular, the Iterator interface specifies that all iterator classes need to define hasNext and next methods (used in the code example in the Introduction).  The abstract EnvIterator class implements these methods, but the implementation of the next method makes use of a protected, unimplemented findNextLocation method.  This method must be implemented in concrete subclasses of EnvIterator, such as RowMajorEnvIterator.  The way findNextLocation is implemented in each concrete subclass determines how the iterator traverses the environment.  Each concrete subclass of EnvIterator must also provide a constructor that takes a BoundedEnv as a parameter, since that is what the TraversalGUI object assumes is available when it tries to construct a concrete iterator object.

 

Exercise Set 4

  1. Does the code example in the Introduction section behave correctly if the environment is empty?

  2. Can you create an Iterator instance?  An EnvIterator instance?  A RowMajorEnvIterator instance?

  3. Looking at the EnvIterator class, what is the first location returned by the next method?  Does this depend on the specific implementation of findNextLocation used by an iterator object?

  4. How do the statements in the findNextLocation method of the RowMajorEnvIterator class ensure that the order in which the application highlights cells will be row-major order?

 

Adding New Algorithms

Now it's time to write some iterators for traversal algorithms of your own.

Exercise Set 5

  1. Complete the ColMajorEnvIterator class, using RowMajorEnvIterator as a guide. Test your class by running the program and watching the traversal. Are the cells highlighted left-to-right, going down each column?

  2. Create a ReverseRowMajorEnvIterator class, using RowMajorEnvIterator as a guide. This algorithm should highlight cells bottom-up, going left-to-right across each row. In other words, the row order is reversed, but the column order is not. Edit the main method in the IteratorLab class to register your new class with an appropriate name.  Test your new class by running the program and watching the traversal.   Remember that each concrete subclass of EnvIterator must provide a constructor that takes a BoundedEnv as a parameter.  That constructor could use either of the constructors in EnvIterator: the one that takes only a bounded environment as a parameter, or the one that takes both a bounded environment and a starting location.

  3. Create a ReverseColMajorEnvIterator class, using ColMajorEnvIterator as a guide. This algorithm should highlight cells right-to-left, going up each column from the bottom. In other words, both the row and column orders should be the reverse of ColMajorEnvIterator. Test your new class.

  4. Create a Diagonal class. This algorithm should highlight cells along the diagonal from the upper-left corner to the lower-right corner.** Again, it is not a true traversal of the environment.  Before you attempt to write the code, list the locations that you want the iterator to visit. When you're done with the implementation, test your new class.
    **The diagonal algorithm goes to exactly the lower-right corner only if the environment is square.  If it is not square, the algorithm traverses down and to the right until it comes to the last column or the last row, depending on whether the environment is higher than it is wide or wider than it is high. The diagrams below show the behavior for a 5 x 5 environment, a 3 x 5 environment, a 5 x 3 environment, and a 1 x 1 environment.

  5. Create a Triangle class. This algorithm should highlight (fill in) all the cells below the diagonal you produced in the preceding exercise. (It will form a true triangle only if there are at least as many columns in the environment as there are rows.)  Before you attempt to write the code, list the locations that you want the iterator to visit. When you're done with the implementation, test your new class. The diagrams below show the behavior for a 5 x 5 environment, a 3 x 5 environment, a 5 x 3 environment, and a 1 x 1 environment.

  6. Create a DoubleDiagonal class. This algorithm should highlight the cells along the two diagonals, from the upper-left corner to the lower-right corner** and from the upper-right corner to the lower-left corner.** If the environment has an odd number of columns, the two diagonals will cross at a single location, but your "iterator" should not return that location twice.  Before you attempt to write the code, list the locations that you want the iterator to visit. When you're done with the implementation, test your new class. (**Again, whether the algorithm goes exactly to the opposite corner depends on whether the environment is square.)  The diagrams below show the behavior for a 5 x 5 environment, a 4 x 5 environment, a 5 x 4 environment, and a 1 x 1 environment.

    Hints: You can draw the double diagonal by drawing a line from the upper-left corner down and to the right and drawing a line from the upper-right corner down and to the left.  OR, you can visit both locations in the first row, followed by both locations in the 2nd row, etc.  This algorithm may be easier.  You know one of the two locations in each row from your implementation of the Diagonal class, and you can calculate the other from it, given the number of columns in each row.   You'll need a way of recognizing whether you're visiting the first location in a row, in which case the next location should be the other location in the row, or visiting the second location, in which case the next location will be on the next row.  If both locations are the same location (single cross-over point), then you do not want to visit it twice.

  7. Create a PerimeterTraversal class. This algorithm should highlight the cells along the four sides of the environment, but not the interior cells. This is actually a traversal of the environment's perimeter rather than of the environment as a whole, because you will not be visiting every location in the environment.   Before you attempt to write the code, list the locations that you want the iterator to visit in order to find a pattern. When you're done with the implementation, test your new class.  The diagrams below show the behavior for a 5 x 5 environment, a 2 x 5 environment, a 3 x 1 environment, and a 1 x 1 environment.

  8. Create a SpiralTraversal class. This algorithm should highlight the cells along the perimeter of the environment, then spiral in and highlight the cells along the perimeter of the unhighlighted cells, then spiral in again and highlight the next perimeter of unhighlighted cells.  Continue in this way until you have visited every location in the environment.   Before you attempt to write the code, list the locations that you want the iterator to visit in order to find a pattern. When you're done with the implementation, test your new class.

  9. Create a Butterfly class. This algorithm should highlight the cells in the left and right side quadrants formed by the double diagonal you produced in Exercise 6. Before you attempt to write the code, list the locations that you want the iterator to visit. When you're done with the implementation, test your new class. (See previous exercises to read more about square and non-square environments.)  The diagrams below show the behavior for a 5 x 5 environment, a 4 x 5 environment, a 5 x 4 environment, and a 1 x 1 environment.