Graphic by Keith Ohlfs

CS111, Wellesley College, Spring 2000 Problem Set 9 Due: Friday, May 5, by 4:00 p.m.

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Reading Assignment:

• Notes on permutations
• SampleGUI.java (code covered in lecture on Thursday, April 27). This can be found in lec23_programs in the CS111 download folder.

About this Problem Set

The purpose of this problem set is to give you experience with lists of lists (Task 1) and with graphical user interfaces (Task 2). In Task 2, you will also get experience writing a complete program almost entirely from scratch.

How to turn in this Problem Set

Homework Problems :

• Task 1: Save your modified ChangeMaker.java file in the ps9_programs folder. Turn in a hardcopy of the ChangeMaker.java file.
• Task 2: Save your modified GuessTheColor.java file in the ps9_programs folder. Turn in a hardcopy of the GuessTheColor.java file.

Turn in only one package of hardcopy materials. Staple your files together with the cover page, and submit your hardcopy package by placing it in the box outside of Stanzi's office (SCI E106).

Reminders

1. Pay careful attention to upper and lower case letters in the filenames.
2. Once you have used Fetch to upload a file to the cs111 server, you should be sure to doublecheck that the file was actually uploaded. You can do this in Fetch by verifying that the file is now listed in your directory. Not only should you check that the file is listed, but you should check that it does not have a size of 0K. If the file isn't listed or if the size for the document is 0K, this means that there was an error in transferring it via Fetch and you must re-upload the document. When transferring a folder, you should check that its contents have been uploaded correctly. That is, you should be sure to check that every single file that you wish to submit has been uploaded correctly. Often times, although not always, you will see a message "Connection Failed" when there is an error in transferring your files.
3. If you have trouble uploading files, it may be because you have reached the limits of your Nike file system quota. You will get an error message informing you that this is the problem. In this case, you need to delete some of your old files, either from your home directory or your drop folders (which are also counted toward your quota). To delete a file in Fetch, just drag it to the Trash.

• It is your responsibility to keep a personal back-up of every file that you submit electronically until you have received a grade for the assignment.

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Task 1: Making Change

Lists of lists are useful data structures for holding lists of possibilities. For example, as seen in lecture and lab, we can use them to hold the list of all permutations and subsequences of a list of numbers.

In this problem, we will use lists of lists to represent all the possible ways of making change for a given amount of money using an unlimited number of coins from a given list of denominations. You may assume that the amount of money is a non-negative integer, and that the list of coin denominations is a list of distinct positive integers ordered in decreasing order. When making change for the given amount, you may use any number of "copies" of the coins in the denomination list.

In the resulting list of lists, each element (which we shall call a change list) should be a list of coin values sorted in order of decreasing value whose sum is the given amount of money. These change lists should be ordered in reverse lexicographic order (i.e., reverse dictionary order). That is, change lists with a larger first coin come before change lists with a smaller first coin. If two change lists have the same first coin, the one with the largest second coin goes first. And so on.

Here are a few simple examples:

Amount of money	Denominations	Ways to Make Change
5	[5,1]	[[5], [1,1,1,1,1] ] 1 nickel or 5 pennies
16	[10,5,1]	[[10, 5, 1], [10, 1, 1, 1, 1, 1, 1], [5, 5, 5, 1], [5, 5, 1, 1, 1, 1, 1, 1], [5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] ]
16	[10,5]	[]
21	[10,5,1]	[[10, 10, 1], [10, 5, 5, 1], [10, 5, 1, 1, 1, 1, 1, 1], [10, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [5, 5, 5, 5, 1], [5, 5, 5, 1, 1, 1, 1, 1, 1], [5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] ]

Your goal is to formulate a strategy that will list all the possible ways to make change for a given amount of money with a list of possible denominations provided in descending order of value. To do this, you will flesh out the makeChange() method in the ChangeMaker.java file within the ChangeMaker folder of ps9_programs. The contract for the method is as follows:

public static IntListList makeChange (int amount, IntList coins)
Assume that amount is a non-negative integer and that coins is a list of distinct positive integers in descending order. Returns a list of all possible change lists, where a change list is a list of denominations taken from coins (potentially with duplicates) whose sum is amount. The denominations in a change list should be in descending order. The change lists themselves should be ordered in reverse lexicographic order.

Notes

• Modify the ChangeMaker.java file. Test your solutions by running ChangeMakerTest.html. The correct output for the test cases is provided at the end of this problem description.
• Since makeChange involves working with IntList and IntListList lists, we can no longer just use list methods and operators without the class name because Java won't know which method we want (i.e. do we want the one that applies to the IntList or the IntListList class?). Instead, we must specify the name of the class with the method (e.g. IntList.prepend or IntListList.prepend). However, specifying the full name of the class makes the code harder to read so we have provided you with the following "shortcut" way to refer to IntList and IntListList methods and operators for doing this problem.

  IntList Methods (IL)	IntListList Methods (ILL)
  IL.empty IL.prepend IL.head IL.tail IL.isEmpty IL.length IL.append IL.postpend	ILL.empty ILL.prepend ILL.head ILL.tail ILL.isEmpty ILL.length ILL.append ILL.postpend

• You may find it useful to use the following mapPrepend() method, which was used in both lecture and lab. It has been included in the ChangeMaker class for your convenience:

  public static IntListList mapPrepend (int n, IntListList L) {
      if (ILL.isEmpty(L)) { 
          return L;
      } else {
        return ILL.prepend (IL.prepend(n, ILL.head(L)), 
  			           mapPrepend(n, ILL.tail(L)));
      }
    }

• Hint for the general case(s) of your recursion: when making change for a given amount, if the first coin in the denomination list isn't too big, you can either use it in the resulting change lists or not. Consider a particular example, such as making change for 21 cents using the denominations [10, 5, 1]. What change lists do you get if you use the 10? What change lists do you get if you don't use the 10. Do you see a pattern? Use wishful thinking!
• Think about the following carefully for the base case(s) of the recursion: What does it mean to make change from an empty list of coins? What does it mean to make change for zero money? (Depending on how you approach the problem, you might also need to consider making change for a negative amount of money.)
• It is possible to write a definition for makeChange() in very few lines. If your solution is longer than 15 lines or so, you are probably on the wrong track!

   

Correct Test Case Answers

----------------------------------------------------
There are 2 ways to make change for 5 cents using [10, 5, 1]:
[[5],
 [1, 1, 1, 1, 1]
 ]
----------------------------------------------------
There are 6 ways to make change for 16 cents using [10, 5, 1]:
[[10, 5, 1],
 [10, 1, 1, 1, 1, 1, 1],
 [5, 5, 5, 1],
 [5, 5, 1, 1, 1, 1, 1, 1],
 [5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
 [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
 ]
----------------------------------------------------
There are 9 ways to make change for 21 cents using [25, 10, 5, 1]:
[[10, 10, 1],
 [10, 5, 5, 1],
 [10, 5, 1, 1, 1, 1, 1, 1],
 [10, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
 [5, 5, 5, 5, 1],
 [5, 5, 5, 1, 1, 1, 1, 1, 1],
 [5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
 [5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
 [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
 ]
----------------------------------------------------
There are 13 ways to make change for 26 cents using [25, 10, 5, 1]:
[[25, 1],
 [10, 10, 5, 1],
 [10, 10, 1, 1, 1, 1, 1, 1],
 [10, 5, 5, 5, 1],
 [10, 5, 5, 1, 1, 1, 1, 1, 1],
 [10, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
 [10, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
 [5, 5, 5, 5, 5, 1],
 [5, 5, 5, 5, 1, 1, 1, 1, 1, 1],
 [5, 5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
 [5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
 [5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
 [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
 ]
----------------------------------------------------
There are 60 ways to make change for 56 cents using [25, 10, 5, 1]:
[[25, 25, 5, 1],
 [25, 25, 1, 1, 1, 1, 1, 1],
 [25, 10, 10, 10, 1],
 [25, 10, 10, 5, 5, 1],
 [25, 10, 10, 5, 1, 1, 1, 1, 1, 1],
 [25, 10, 10, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
 [25, 10, 5, 5, 5, 5, 1],
 [25, 10, 5, 5, 5, 1, 1, 1, 1, 1, 1],
 [25, 10, 5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
 [25, 10, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
 [25, 10, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
 [25, 5, 5, 5, 5, 5, 5, 1],
 [25, 5, 5, 5, 5, 5, 1, 1, 1, 1, 1, 1],
 [25, 5, 5, 5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
 [25, 5, 5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
 [25, 5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
 [25, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
 [25, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
 [10, 10, 10, 10, 10, 5, 1],
 [10, 10, 10, 10, 10, 1, 1, 1, 1, 1, 1],
 [10, 10, 10, 10, 5, 5, 5, 1],
 [10, 10, 10, 10, 5, 5, 1, 1, 1, 1, 1, 1],
 [10, 10, 10, 10, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
 [10, 10, 10, 10, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
 [10, 10, 10, 5, 5, 5, 5, 5, 1],
 [10, 10, 10, 5, 5, 5, 5, 1, 1, 1, 1, 1, 1],
 [10, 10, 10, 5, 5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
 [10, 10, 10, 5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
 [10, 10, 10, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
 [10, 10, 10, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
 [10, 10, 5, 5, 5, 5, 5, 5, 5, 1],
 [10, 10, 5, 5, 5, 5, 5, 5, 1, 1, 1, 1, 1, 1],
 [10, 10, 5, 5, 5, 5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
 [10, 10, 5, 5, 5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
 [10, 10, 5, 5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
 [10, 10, 5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
 [10, 10, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
 [10, 10, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
 [10, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1],
 [10, 5, 5, 5, 5, 5, 5, 5, 5, 1, 1, 1, 1, 1, 1],
 [10, 5, 5, 5, 5, 5, 5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
 [10, 5, 5, 5, 5, 5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
 [10, 5, 5, 5, 5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
 [10, 5, 5, 5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
 [10, 5, 5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
 [10, 5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
 [10, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
 [10, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
 [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1],
 [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1, 1, 1, 1, 1, 1],
 [5, 5, 5, 5, 5, 5, 5, 5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
 [5, 5, 5, 5, 5, 5, 5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
 [5, 5, 5, 5, 5, 5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
 [5, 5, 5, 5, 5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
 [5, 5, 5, 5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
 [5, 5, 5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
 [5, 5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
 [5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
 [5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
 [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
 ]
----------------------------------------------------
There are 2 ways to make change for 15 cents using [10, 5]:
[[10, 5],
 [5, 5, 5]
 ]
----------------------------------------------------
There are 0 ways to make change for 16 cents using [10, 5]:
[ ]
----------------------------------------------------

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Task 2: Color Guessing

The "Guess The Color" Game

This problem involves a simple game in which a player guesses the red, green, and blue components of a randomly chosen color. The game is played using an applet whose initial appearance is as follows:

The applet has the following parts:

• A message line at the top of the applet which displays directions and feedback. Initially this says "Press the New Game button to start a game".
• A collection of three text fields on the left of the applet, labelled "Red", "Green", and "Blue", where the user may type in numbers for the RGB components of a color.
• A set of four buttons at the bottom of the applet, labelled "New Game", "Guess", "Hint", and "I Give Up!" .
• A "canvas" area, initially white, that takes up most of the real estate in the applet.

Pressing the New Game button starts a new game. Starting a new game zeroes out the three text fields and displays a randomly chosen color on the canvas, which we will refer to as the secret color. It also displays the message "Press Guess to make a guess; Hint for a hint." in the message line.

The goal of the game is to guess the RGB (Red/Green/Blue) components of the secret color. Recall that RGB components are numbers between 0 and 255. A guess is entered by typing numbers into the three text fields and pressing the Guess button. Here is the result of a first guess:

Whenever a guess is made, the canvas is changed to show a rectangular "ring" with the guessed color. In this example, the guessed color is a light purple while the secret color is a darker purple. The area outside the ring and the the "hole" inside the ring both show the secret color. Showing secret color both outside and inside makes it easier to compare the guessed color to the secret one. The "thickness" of the ring segments are one-fifth the size of the canvas in each dimension.

Since it is surprisingly difficult to get the colors to match, a "hint" option is provided. Pressing the Hint button indicates for each color component whether it needs to be made larger, smaller, or kept the same. (In this respect, the game is like the classical game of Hi/Lo, except that it is played with three secret numbers at once.) As with guesses, hints are numbered. For example, pressing the Hint button in our running game yields.

Play continues with the player making more guesses and optionally choosing to see hints. Below are some snapshots from a running game.

As indicated by the last of the above pictures, the differences between the guessed color and the secret color can be so small as to be almost undetectable by the human eye. Human vision is not the only problem; some computer screens/and or color mapping software don't accurately display all subtle color differences. In this case, the hint information is extremely helpful for getting the "correct" answer!

When the correct RGB value has been guessed, the message line displays a message indicating this fact, along with the number of guesses and hints that were used in the process.

Using binary search in conjunction with hints, it is possible to guess the components of any secret color in no more than 8 guesses. But you can achieve this result even if you don't see the secret color! With enough practice, you can do better than 8 guesses if you use the feedback provided by the color in the canvas. (If there is sufficient interest, we can hold a contest to see who can reliably guess colors with the fewest number of guesses.)

In some cases, a player may just want to surrender and be shown the answer. To do this, the player presses the I Give Up! button. Here is the result of doing this in a different game:

The Guess, Hint, and I Give Up buttons only work when there is a game in progress. Pressing these buttons when one game has finished but a new one has not yet begun (by pressing the New Game button) results in the following error message in the message line:

Your Task

Your task is to implement the "Guess the Color" game described above. You will be writing the program almost entirely from scratch. All you are given is a rather empty skeleton file GuessTheColor.java, which you must flesh out to have the appearance and behavior of the applet described above. Here are some notes/hints on how to proceed:

• As a first step, it is strongly recommended that you spend some time playing with the test version of the game, which you can run by executing the applet Test/GuessTheColor.html in the ps9_programs folder. This will make you familiar with the "look and feel" of the game, as well as with its behavior.
• Before writing any code, carefully study the SampleGUI.java program presented in lecture. (This is available from lec23_programs in the CS111 download folder.) The SampleGUI program contains almost all the components and techniques you need to successfully implement the color guessing game.
• First concentrate on getting the layout of the applet to be correct, without worrying at all about its behavior. To specify the layout, you will need to flesh out the init() method within the GuessTheColor class.
  • Following the style SampleGUI.java, use a top-down, divide-and-conquer strategy with lots of auxiliary methods to specify the layout.
  • Keep the number of instance variables you use to a minimum. As a general rule, the only user interface components that should be instance variables are ones that you need to refer to later in the behavior part of the applet.
  • You need not worry about getting the fonts and font sizes to be exactly like those in the test applet. But the colors and placement of your components should be approximately the same.
  • If you have any questions about the contracts of any components used in the layout, you should consult the Java AWT documentation at: http://cs111.wellesley.edu/~cs111/JDK-1.0.2-API/api/Package-java.awt.html
  • We strongly recommend that you get the layout of the applet right before starting to implement the behavior.
• Once the layout is correct, you should implement the behavior of the game.
  • Following the example in SampleGUI, flesh out the action() method to dispatch to auxiliary methods according to the name of the button pressed.
  • In addition to instance variables for some user interface components, you will need some extra instance variables that keep track of the state of the game. Think carefully about what these should be.
  • In order to create the secret color, you will need to pick random numbers between 0 and 255. The GuessTheColor class comes equipped with the following method for this purpose:

    	// Returns a randomly chosen integer between LO and HI, inclusive, 
    	// with approximately uniform distribution. 
    	private int intBetween (int lo, int hi) {
    		return lo + (int) (Math.random() * (hi + 1 - lo));
    	}

  • All drawing in the canvas can be done using the fillRect() method of the Graphics class. To make rectangles of the right size, you will need to know the width and height of the canvas. These can be determined using the size() method of a component. To find out details about these and other components and methods, consult the Java AWT documentation at http://cs111.wellesley.edu/~cs111/JDK-1.0.2-API/api/Package-java.awt.html.
  • The SampleGUI example contains many idioms that are relevant to the color guessing game, such as how to turn the contents of TextFields into integers and how to print out strings composed out of many pieces.

Extra Credit

The Guess the Color game can be improved in many ways. Below are some improvements you might want to implement for extra credit. Feel free to extend the game in other ways you find interesting.

• The program does not gracefully handle errors in the text fields. What happens if numbers in the text fields are outside the range 0 to 255? What happens if non-numbers are entered into the text fields. Modify the program to handle these errors by displaying an appropriate error message in the message line.
• When the guess is close to correct but not exactly right, it can be impossible to visually distinguish the secret color from the guess. For this reason, it might be reasonable to consider a guess "correct" if it is "close enough" to the secret color. Develop and a notion of "close enough" and change the implementation so that the player wins with a guess that is "close enough".
• In the game described above, the hints are very crude: make a component "larger" or "smaller". Alternatively, the game could provide more fine grained hints. E.g., make a component "a lot larger" or "a little bit larger".
• It is cumbersome to have to type in numbers for colors. It would be more natural to use a scroll bar to select a number in the appropriate range and to see the guess dynamically updated as the scrollbar moves. (For an example of this sort of interface, see the color applet on the color contracts page).Modify the game to use scroll bars instead of text fields. With the new interface, you may want to modify the notion of what counts as a "guess".
• The applet does not repaint itself correctly when it is resized or when it is covered by other windows that are later removed. Modify it to have the correct repainting behavior. You will need to read up on how components repaint themselves in order to to this. Try looking at Java books in E101 or various Java sites on the web.

To submit extra credit, create a copy of the GuessTheColor folder named ExtraCredit that contains all of your modified code. For your softcopy, upload your ExtraCredit folder to the ps9 drop folder. For your hardcopy submission, submit (1) a description of what modificiations you made to the program and (2) your final version of GuessTheColor.java.