Computer Science APEA 15-100, Summer 2009
Homework 7
Due:  Fri 10-Jul-2009 at 8:59am (email copy only)
(no late submissions accepted).

Read these instructions first!

• Now you are not given a file to start from!  Based on previous hw's, create your own Hw7.java file.  Be sure to name it exactly correctly, to include a main method that calls checkAssertsAreEnabled and testAll, and to have testAll call suitable test methods for all the methods you create.  Also, be sure that every method you write has exactly the right name and the right signature.
   
• Be sure to include your name, your Andrew ID, and your section clearly on the top of each file in your assignment.
   
• For non-programming problems:
  • Place all your solutions to the non-programming problems in a single file named Hw7 (with whatever extension is appropriate for the format you choose, such as Hw7.txt or Hw7.html, etc).  You must use one of these file formats: plain text (txt), or RTF, or HTML, or Word (doc, not docx), or PDF.  No other file formats will be accepted.
  • Show your work.  Correct answers without supporting calculations will not receive full credit.
     
• For programming problems:
  • Try to use well-named variables, proper indenting, reasonable commenting, etc.
  • Note:  You may not use Java concepts we have not yet covered, including loops (do/while/for), conditionals ("if" statements or tertiary operators (?:)), arrays, or methods from any classes in java.util.* (besides Scanner or others we explicitly use) to solve these problems (which isn't a problem for most of you, seeing as we have not yet covered these!).  While they may be helpful, every problem here is solvable without them, and they are not permitted for now.
     
• What to submit
  • Create a submission directory like this:  "koz-hw7"  (replace "koz" with your andrew id)
  • Place all the files you are submitting in that directory, zip that directory, and submit the zipped directory
     
• How to submit
  • Send an email with the zipped submission directory as an attachment to your CA by the submission deadline.  Do not miss the deadline, even by one minute!  Email problems are not a valid excuse for late submissions.
  • It is recommended that you "cc" yourself in that email, too, just to confirm that you properly sent the email.
     
• Note:
  • Improper submissions will be penalized up to 10 points and may be rejected.
  • Late submissions will be rejected.

1. Reading
2. Finish Lab 7
3. ch5Exercises
4. isInteger
5. nthPerfectNumber
6. Flag of Greece

• Note:  Conditionals and Loops are allowed from this assignment onwards.

1. Reading
   Continue reading the material for the next quiz, which covers 3.1, 3.2, 3.4, 3.5, 3.6 (just printf), 3.8, 5.1, 5,2, 5.3, 5.5, 5.7, and 5.8.  You will have time tomorrow and over the weekend to finish this reading.
    
2. Finish Lab 7
   Finish all the examples from lab 7.  Include the solutions in your submission, all in one file named Lab7.java.  Note: the lab collaboration policy continues to apply to the lab problems.  So you can collaborate at will to solve these problems.  This only applies to the lab problems -- all other problems in this assignment are subject to the usual homework collaboration policy.
    
3. ch5Exercises
   Do the following Exercises from Chapter 5 (pp 281-283):
   Exercises 5.7,  5.8,  5.9,  5.10
    
4. isInteger
   Write the following method:
      public static boolean isInteger(String s)
   This method takes a (possibly-null) string s and returns true if and only if that string represents an integer value.  That is, if the string is non-null, non-empty, and only contains digits (0 through 9), with an optional leading + or - sign.  Note that just a sign is not allowed, nor two or more signs, so neither "+" nor "++3" are legal.  Also, extra leading zeros are allowed, so "00032" is legal.  Finally, do not worry about overflow, so "12345678987654321" is legal.  Write your own test method.
    
5. nthPerfectNumber
   Write the following method:
      public static int nthPerfectNumber(int n)
   This method takes an integer "n" and returns the nth perfect number, where a perfect number is an integer that is the sum of its proper divisors (that is, the numbers less than it that evenly divide it). For example, the proper divisors of 6 are 1, 2, and 3, and 6 = 1 + 2 + 3, so 6 is a perfect number.  Conversely, the proper divisors of 8 are 1, 2, and 4, and 8 != 1 + 2 + 4, so 8 is not a perfect number.  If n is less than 1, the method should return -1.  And, as usual, do not worry about overflow.  Here is a test method for you:

     public static void testNthPerfectNumber() {
       System.out.print("Testing nthPerfectNumber... ");
       assert(nthPerfectNumber(-5) == -1);
       assert(nthPerfectNumber(0) == -1);
       assert(nthPerfectNumber(1) == 6);
       assert(nthPerfectNumber(2) == 28);
       assert(nthPerfectNumber(3) == 496);
       System.out.println("Passed all tests!");
     }

   Helper Method:  unspecified (but required!)
   
   Again, in writing your nthPerfectNumber method, you must use a well-conceived helper method.  You must also include a test method for your helper method (and, again, you will be graded, in part, on the quality of the test cases in that test method).
   
   Note:  As should be apparent, decomposition into helper methods is a great way to design your programs.  You are expected to use this approach in all future programming assignments.
    

6. Flag of Greece
   In the file Hw7FlagOfGreece.java, write a program that displays the flag of Greece::
     (larger image with details)
   Note:  Your program must use one well-chosen loop to draw the wide stripes.  However, you do not need to use a loop to draw any portion of the top-left inset.  You must also handle the "thin white line" problem -- remember, for each stripe, compute its top edge and bottom edge the same way, then take the difference for the stripe height.  You must also color match.

Carpe diem!