Graphic by Keith Ohlfs
CS111, Wellesley College, Spring 2002

Problem Set 6

Due Tuesday, March 26, at 11:59pm

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About this Problem Set

The purpose of this problem set is to give you more experience with recursion and writing recursive methods that return values. Task 1 is a pencil-and-paper problem in which you will draw an invocation tree for a recursive function. In Task 2, you will use recursion in PictureWorld to generate a recursively structured quilt. In Task 3, you will use recursion in BuggleWorld to implement the elaborate buggle bagel-harvesting ritual. The code for Tasks 2 and 3 is available in the ps6_programs folder in the cs111 download directory on nike.

There are also two optional extra credit problems. In Extra Credit Challenge 1, you can use recursion to have buggles count the number of bagels in a maze. In Extra Credit Challenge 2, you are asked to design your own recursive buggle/turtle/picture patterns. The code for the Extra Credit Challenges is available in the ps6_programs_extra folder in the cs111 download directory on nike.

How to turn in this Problem Set

You are required to turn in both a hardcopy and a softcopy. For general guidelines on problem set submission, including how to submit a softcopy and how to check if you softcopy submission was successful, click here. Please make sure to keep a copy of your work, either on a zip disk, or in your private directory (or, to play it safe, both).

Hardcopy Submission

Your hardcopy packet should consist of:
  1. The cover page;
  2. Your invocation tree diagram from Task 1;
  3. Your modified Patchwork.java file from Task 2;
  4. Your modified HarvestWorld.java file from Task 3.
  5. Your modified MazeCounterWorld.java file from Extra Credit Challenge 1 (this part is completely optional).
  6. Your modified MyBuggleWorld.java, MyTurtleWorld.java, and/or MyPictureWorld.java files from Extra Credit Challenge 2 (this part is completely optional).
Staple these together, and slide the packet under the door of Elena's office (E127, in minifocus).

Softcopy Submission

Save the modified Patchwork.java and HarvestWorld.java files in the ps6_programs folder. Submit the entire ps6_programs folder to your drop folder on the cs111 server.

If you complete any of the extra credit problems, submit the entire ps6_programs_extra folder to your drop folder on the cs111 server.

Task 1: Invocation Tree for a Recursive Function

Consider the following class method: 
    public static int f (int n) {
	if (n <= 2) {
	    return n;
	} else {
	    return n + f(n/2) + f(n/3);
	}
    }
Draw an invocation tree that summarizes the execution of the class method invocation f(30). Each node of the execution tree should have the form f(arg):result, where arg is the integer that is the argument of the invocation of f and result is the result of the invocation.

Keep in mind that dividing two integers in Java always returns an integer result. For example, (15/2) returns 7, (5/2) returns 2, and (5/3) returns 1.

Task 2: Patchwork

Your goal in this problem is to write a recursive method that draws the following Picture in PictureWorld:

This picture is specified by the following method in the file Patchwork.java within the folder Patchwork:

patchwork(6, Color.red, Color.yellow, Color.blue, Color.green);

In this problem, you are to write a recursive definition of the following method:

public Picture patchwork(int levels, Color c1, Color c2, Color c3, Color c4)
Returns a picture of the above pictured staircase pattern nested levels levels deep, using colors c1, c2, c3, and c4

To see the picture created by patchwork(n, Color.red, Color.yellow, Color.blue, Color.green) for values of n between 0 and 6, experiment with the test applet Patchwork.java within the Test subfolder of the Patchwork folder. Select patchQuiltn from the pulldown menu in the applet, where n ranges from 0 to 6.

Important Notes:

Your final definition for patchwork should be very short. You should be able to write the definition in a handful of lines without defining any auxiliary methods of your own. However, you can use any of the methods in the PictureWorld contract, as well as any of the following auxiliary methods, which we have provided for you:

public Picture patch(Color c) 
   Return a picture that consists of a solid patch of color c
    
public Picture fourPics(p1, p2, p3, p4) 
   Return a picture that consists of four pictures p1, p2, p3 and p4, with
       p1 in the upper left corner, p2 in the upper right corner, p3 in the
       lower left corner and p4 in the lower right corner. 


  
    

Task 3: Harvest World

Note: Please read this entire problem carefully. Simply generating the correct final pattern is not enough to get full credit. Each specified method must behave as described below.

Bagels in BuggleWorld grow in fields (you knew that, didn't you?). Twice a year the Harvester buggles go out and harvest bagels so that buggles in BuggleWorld will have bagels to eat and play with throughout the year. Bagels are the most important commodity in BuggleWorld. Therefore, their harvesting procedure is quite complex and elaborate. It is described below:

Each Harvester is assigned a field of bagels to harvest. The buggle does not know the width or height of the bagel field. The buggle starts in the bottom left corner of the field and harvests bagels one row at a time (a row is a vertical column on the BuggleWorld grid). It doesn't matter if the buggle chooses to harvest the closest row first and work down to the end of the field or to walk to the end of the field and harvest rows on the way back to the beginning. Note that there are no bagels planted in the bottom horizontal row of the field. Instead, that is the path that buggles walk on to get from row to row.

Each row is harvested according to the following procedure:

The buggle harvests the bagels in the row by picking them up and counting them. It doesn't matter if the buggle picks up bagels on the way to the end of the row or picks them up coming back from the end.

The buggle stacks the bagels in a row near the path (starting from the second cell up) so that they will be able to dry (dried bagels are the best and keep fresh all year long).

The rest of the field needs to be covered with tarp (black) which preserves the field from bad weather during the non-growing season. The tarp is at the far end of the row (i.e. at the top of the BuggleWorld grid). The buggle needs to go to the end of the row and pull the tarp up to the point where the bagels are stacked. The buggle should count the number of empty spaces left in each row (spaces covered by the tarp).

While the Harvester buggles do all the work, their supervisors want to be able to quickly look at the field and see how it did. It's a bit difficult to see the entire field, so the Harvester buggle must mark each row indicating whether or not the row did well. Bad rows (fewer bagels than blank spaces) are marked red and will get more fertilizer and attention in the next growing season. Good rows (more bagels than blank spaces) are marked green. Fair rows (same number of bagels as blank spaces) are left uncolored. Each row is also tagged with the number of empty spaces (i.e. spaces covered with black tarp). See the pictures below for clarification.

Finally, the Harvester buggle must count the number of bagels harvested in the field and report that to her supervisor.

The following two pictures show the state of a field before and after the buggle has harvested it.


Your task is to write the methods that will make the Harvester buggle do its job. You are free to write any auxiliary methods needed. At a minimum, you must define the following methods for the Harvester class. The complete specifications for each method are given in HarvestWorld.java (as usual, you can download the program files from the download directory). Each method must satisfy the specification in the code file. The descriptions below are intended to supplement and clarify the specifications in the code file.

In addition to their specificaitons, all the methods described below must also meet the following invariant:

The buggle's state (position, heading, color, and brush state) will not be changed by execution of this method. Assumes the buggle's brush is initially up.

public int harvestField()
This method assumes that the buggle is starting in the lower left corner of a field facing EAST. When this method is invoked, the buggle will harvest the field of bagels to its front and left (up to the walls in front of and to the left of the buggle) and return the number of bagels harvested in this field.

public int harvestRow()
When this method is invoked, the buggle will harvest the row of bagels to its left (i.e. the vertical column above the buggle). The number of bagels harvested in this row is returned. This method should be invoked when the buggle is facing EAST and in the bottom row (the clear path) of the field.

public int harvestBagels()
When this method is invoked, the buggle will pick up all the bagels between it and the wall and return the number of bagels picked up. This method should be invoked when the buggle is facing NORTH and in the bottom row (the clear path) of the field.

public void stackBagels(int numberBagels)
When this method is invoked, the buggle will create a stack of the specified number of bagels in front of itself. This method assumes that there will always be at least enough space in front of the buggle for the bagel stack. This method should be invoked when the buggle is facing NORTH and in the bottom row (the clear path) of the field.

public int pullTarp()
When this method is invoked, the buggle should draw a black line from the wall in front of the buggle to the current cell in front of the buggle (i.e. do not color the cell the buggle is on when the method is invoked). This method returns the number of cells colored. This method should be invoked when the buggle is facing NORTH and at the end of its bagel stack (i.e. right where the tarp should start).

public void markRow(int numberBagels, int numberSpaces)
This method paints the current cell green if numberBagels is greater than numberSpaces. The current cell is painted red if numberBagels is less than numberSpaces. The current cell is not painted if the numberBagels is equal to numberSpaces. The buggle also marks the cell with the numberSpaces (using dropInt());

Notes:

Use paintCell to color cells:
public void paintCell (Color c)
Paints the cell under this buggle with the color c

Use dropInt to drop an integer into a particular cell:
public int dropInt (int n)
Drops the integer n into the current cell and returns the integer dropped.

Test your methods by executing the HarvestWorld.html applet. When you first load the applet, the BuggleWorld grid is empty. Hit Reset to generate a bagel field. Every time you Run this applet, the number of bagels reported by the Harvester buggle will appear in the cyan box within the parameter frame window.

A working applet can be found in the test subfolder of the HarvestWorld folder. You should experiment with this test applet to better understand the behavior of Harvester buggles.

Hint: It may be easier to write the methods in the reverse order from the order listed above. That is, you might want to start by writing the markRow() method.

 

Extra Credit Challenge 1: MazeCounter

This is a completely optional problem. You should only attempt it after completing the required parts of the assignment.

Before starting this problem, you should read over the notes on the PathfinderWorld example.

Maisy Buggle comes from a long line of maze-navigating buggles. But unlike other buggles, she is not satisifed with stopping when she finds the first bagel in a maze. She wants to explore the world and find out how many bagels there are in the entire maze! For instance, suppose Maisy starts at "home" (facing eastward at point (1,1)) in the following maze:

Using the same maze-navigating strategy followed by the PathFinder buggle described in the the PathfinderWorld notes, Maisy can traverse the entire maze and determine that it contains 17 bagels. Suppose that, after exploring the submaze accessible from a given cell, Maisy writes in the cell the number of bagels in that submaze. Then after she returns to her home position, the maze would be annotated as follows.

Note that the number in each cell is the number of bagels to the left, right, in front of, and under Maisy when she is in a cell (assuming she is facing the direction in which she entered the cell).

To get a better sense for how the above numbers are generated, you should experiment with the test applet MazeCounterWorld.html within the Test subfolder of the MazeCounter folder of ps5_programs. This applet has a parameter window that look like this:

The numbers in yellow control the side length of the maze and the number of bagels placed randomly in the maze. If you change these and press the Reset button, a new maze will be created with these parameters. The cyan-colored box labelled result is where Maisy writes the total number of bagels in the maze when she returns home. For example, after Maisy has explored the maze depicted above, the parameter window changes to:

Before proceeding with this problem, you should play with the test applet and study the above pictures until you understand how the numbers for each cell are determined.

Maisy is a member of the MazeCounter class of buggles. Your goal in this problem is to define a collection of methods in the MazeCounter class that direct Maisy to count the number of bagels in any maze, also annotating the cells with numbers, as shown above. You should flesh out the skeleton of the MazeCounter class in the MazeCounter folder of ps5_programs. This skeleton contains a "stub" version of a method with the following contract.

public int countBagels()
Counts the number of bagels to the left, right, in front of, and under this buggle.Drops this number in the cell under this buggle, and then returns it.Leaves the state of this buggle unchanged.

You should replace the stub with a method that works. As part of your solution, you should define any auxiliary methods that you find helpful. It is strongly recommended that you use a decomposition similar to the one used in for the PathFinder buggle. Your solution should work for any maze size and any number of bagels. (Warning: do not attempt to place more bagels in the maze than there are grid cells. This situation is not handled gracefully, and will cause your machine to crash.)

In order to drop an integer in a cell, you will need to invoke the following Buggle primitive:

public int dropInt (int n)
"Drops" the integer n in the cell of this buggle. The cell shows the most recently dropped integer. This method returns the integer that was dropped.

Extra Credit Challenge 2: Create Your Own Recursive Patterns

This is a completely optional problem. You should only attempt it after completing the rest of the assignment.

We have seen that fascinating recursive patterns can be created in BuggleWorld, TurtleWorld, and PictureWorld. In this problem, we ask you to create your own recursive patterns in one or more of these worlds.

Start with the folders MyBuggleWorld, MyTurtleWorld, and MyPictureWorld in the ps6_problems_extra folder. Feel free to define any methods you desire to create your patterns.

Some notes:

  • This is the only problem on this problem set in which you may collaborate with others in the class. Feel free to collaborate with as many people as you want.
  • There will be no prizes for designs in this challenge. But all extra credit assignments submitted will be posted on an "exhibition page" so that you can share your designs with the class.
  • If you need help to do something fancy, please talk to the instructors and/or TAs.
  • Extra credit will be given on this problem in proportion to the creativity and artistry in your designs, as well as the level of technical challenge.