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 BoundedGrid object made up of rows and columns.‡ A BoundedGrid object models a bounded rectangular grid that contains objects at various grid locations. Each cell contains zero or one objects.  In this program, cells that are not empty will contain color blocks (objects of the ColorBlock class).

  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 (3, 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 a grid steps through all the locations in the grid.  There are many different ways to traverse through a grid.  One common type of traversal is a row-major traversal, which steps through the grid 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 grid 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 RowMajorGridIterator iterator, which steps through a grid in row-major order.

    RowMajorGridIterator it = new RowMajorGridIterator(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 grid 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 grid 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 Grid Iterator Lab (GridIterator.zip) and unzip it. You will see the following files and folders.
    • The Instructions folder contains this write-up (GridIterator.shtml).
    • The grid.jar Java archive (jar) file contains a library of classes that can be used to model a two-dimensional grid as described above.
      • BoundedGrid (class that represents the two-dimensional grid)‡
      • Location (class that represents the row and column positions of a location in the grid)‡
      • ColorBlock (class whose objects represent blocks of color put in a grid)
    • The GridPkgClassDocumentation folder contains the class documentation for the classes in the grid.jar library.
    • The JavaSourceFiles folder contains the source files for the Grid Plotter program in which we can draw pictures by placing (plotting) color blocks in a grid.
      • IteratorLab (contains the main method)
      • GridIterator class (the abstract iterator class you will be extending)
        • RowMajorGridIterator (an iterator class that implements a row-major traversal; you can use this as a template for other iterator classes)
        • ColMajorGridIterator (a skeleton iterator class that you fill in)
      • IteratorGUI (a class that implements the program's graphical user interface; you are not expected to read or understand this class)
      • IterationController (a class used by the program's graphical user interface to control the traversals; you are not expected to read or understand this class)
    • You can find documentation for these files in the GridIteratorClassDocumentation folder.

    Note: All of the classes in the JavaSourceFiles folder and the grid.jar Java archive file are covered by the GNU General Public License.

  2. Compile and run the program. As the program starts up you will be asked for the dimensions (number of rows and columns) of the grid in which you will be drawing. For now you can go with the default values, since your purpose for this exercise is just to experiment with the user interface. Once you have chosen the grid dimensions, 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. Experiment with the speed adjustment slider while the program is drawing color blocks.

  3. Experiment with the program to discover what the "Create New Grid" and "Clear" buttons and the "Background Color" and "Drawing Color" menus do. What happens if you press the "Row-Major Order" button twice in a row?

  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 Grid Iterator application is the IteratorLab class, which contains the main method.  Look over the class.   It defines two constants that define the size of the window containing the graphical user interface and two more that define the extreme values for the speed adjustment slider.  The class's main method establishes what traversal algorithms are supported and then creates the graphical user interface and makes it visible on the screen. The IterationController.register method is a class method that associates an algorithm name (which becomes the 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 a grid?  How do ColorBlock objects get added to a grid?  Is the ColorBlock class needed?  Couldn't we just put Color objects in a grid?

 

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 a grid, as in the code example in the Introduction section of this lab.  The GridIterator abstract class partially implements the standard Java Iterator interface; the RowMajorGridIterator class is one example of a concrete subclass of GridIterator 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 GridIterator 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 GridIterator, such as RowMajorGridIterator.  The way findNextLocation is implemented in each concrete subclass determines how the iterator traverses the grid.  Each concrete subclass of GridIterator must also provide a constructor that takes a BoundedGrid 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 grid is empty?

  2. Can you create an Iterator instance?  A GridIterator instance?  A RowMajorGridIterator instance?

  3. Looking at the GridIterator 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 RowMajorGridIterator 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 ColMajorGridIterator class, using RowMajorGridIterator 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 ReverseRowMajorGridIterator class, using RowMajorGridIterator 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 GridIterator must provide a constructor that takes a BoundedGrid as a parameter.  That constructor could use either of the constructors in GridIterator: the one that takes only a bounded grid as a parameter, or the one that takes both a bounded grid and a starting location.

  3. Create a ReverseColMajorGridIterator class, using ColMajorGridIterator 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 ColMajorGridIterator. 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 grid.  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 grid 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 grid is higher than it is wide or wider than it is high. The diagrams below show the behavior for a 5 x 5 grid, a 3 x 5 grid, a 5 x 3 grid, and a 1 x 1 grid.

  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 grid 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 grid, a 3 x 5 grid, a 5 x 3 grid, and a 1 x 1 grid.

  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 grid 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 grid is square.)  The diagrams below show the behavior for a 5 x 5 grid, a 4 x 5 grid, a 5 x 4 grid, and a 1 x 1 grid.

    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 grid, but not the interior cells. This is actually a traversal of the grid's perimeter rather than of the grid as a whole, because you will not be visiting every location in the grid.   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 grid, a 2 x 5 grid, a 3 x 1 grid, and a 1 x 1 grid.

  8. Create a SpiralTraversal class. This algorithm should highlight the cells along the perimeter of the grid, 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 grid.   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 grids.)  The diagrams below show the behavior for a 5 x 5 grid, a 4 x 5 grid, a 5 x 4 grid, and a 1 x 1 grid.