CS 313 - Homework 5 - Object-oriented programming

Part 1 due: Monday 3/16 in class

Part 2 due: Friday 3/20 in class

The other two problems are due Friday before break. You may work on problems 2 and 3 only in groups of two, or by yourself.

As usual, on the first page of your printouts for either problem, write your name(s), the names of the students with whom you collaborated, and how much time it took you. There is no electronic submission for either part of this homework.

Here's a quick review on how to start Smalltalk/X. First, edit the file ".bashrc" in your home directory and add the line

export STX_LIBDIR=/home/share/smalltalkX/stx/projects/smalltalk

You should do all your work in the same directory (e.g. ~/cs313/smalltalk) since smalltalk save large image files. To start Smalltalk/X, move your terminal window to the left bottom corner of your screen, go to your smalltalk directory and type "smalltalk". The first time you do this, accept the license conditions and close the "Hello" window. Move the "Launcher" window to the top left, and open a new Workspace window (from the Tools menu). Move the Workspace window underneath the launcher, making sure you can still see your console window below (that's where your print output will appear). In the Launcher window, select "Exit Smalltalk" from the File menu, and click on "Exit & Save". This saves the current image "st.img" in your smalltalk directory. The next time you start smalltalk, you'll be right where you left off!

1. Implement a new method primesUpTo for the class Integer that returns an OrderedCollection of all prime numbers less or equal to the receiver.

   Sample output:

       29 primesUpTo.
   
       OrderedCollection(2 3 5 7 11 13 17 19 23 29)
   

   Specific instructions:
   • Implement the sieve of Eratosthenes as discussed in class.

   • Use an object of class OrderedCollection to return the list of primes. Use "OrderedCollection new" to create an empty collection, and use the message "add: anObject" to add new elements to the collection.

   • Use an object of class Array to hold an array of booleans that represent whether the number at the current index is prime or not. Supposing that N is an integer, use "Array new: N" to create an array with N elements (indexed from 1 to N). Use the messages "at: i" to get the element at index i, "at: i put: x" to set the element at index i to x, and "atAllPut: x" to set all elements to x.
   For printing, cut and paste your method definition into a text file. Don't forget to document your method, and to include sample output (which you can cut and paste from a workspace window). Also, don't forget to include your name, names of collaborators, and how much time it took you.

2. Implement a binary search tree in an object-oriented fashion in Smalltalk. This is similar to Sethi, p. 296, problem 7.6, where you can find some code to get started. However, your "Node" class should also have an instance variable "data" (which will hold an integer), and members of the "Tree" class should understand the messages "insert:" and "member:" (just like in homeworks 2 and 3). "Tree" objects should also understand the message "values", which should return an OrderedCollection of all the values in the tree, collected using an in-order traversal. Here is some sample output:

         |t| t:= Tree new. t insert: 3. t insert: 1. t insert: 2.
   
         t member: 1.      -> true
         t member: 4.      -> false
         t values.         -> OrderedCollection(1 2 3)
   

   Tips: In my sample solution, I use the following instance methods:
   • for class Tree: "member: anInt", "insert: anInt", "values", as well as "isEmpty" and "do: aBlock".
   • for class Node: accessor methods for all 3 instance variables, as well as "do: aBlock".
   The "do:" methods are used to perform a block on each data element in the tree using an in-order traversal. Once you have those, writing "values" is easy. I also define my own class method "new" for one of the two classes (I won't tell you which), to make sure everything is properly initialized.

3. Implement a Fraction class in Python to represent numbers such as 2/3 and -4/5. Your class should support creating new fractions with given integer numerators and denominators, the operators +, -, *, /, and conversion to float and to string. Fractions should always be stored in reduced form, i.e. 1/4 instead of 2/8. I suggest you proceed in three stages:
   1. Implement a first version with methods add, mul, toFloat, and toString, and without reducing. Given the sample testing code

      a = Fraction(6,8)
      b = Fraction(5,4)
      c = a.add(b)
      print a.toString(), "+", b.toString(), "=", c.toString(), "=", c.toFloat()
      d = c.mul(a)
      print c.toString(), "*", a.toString(), "=", d.toString(), "=", d.toFloat()
      

      your program should produce the following output:

      6/8 + 5/4 = 64/32 = 2.0
      64/32 * 6/8 = 384/256 = 1.5
      

   2. Add code to ensure that fractions are always reduced. Hint: a GCD function might come in handy here. Also omit denominators of 1 when converting to strings. The code above should now produce the following output:

      3/4 + 5/4 = 2 = 2.0
      2 * 3/4 = 3/2 = 1.5
      

   3. Add "sub" and "div" methods that implement the operations - and /, and make sure everything works for negative fractions. Also allow omitting the denominator of 1 when constructing integer fractions, e.g., a = Fraction(3). Finally, define the operators +, -, *, / to work directly with Fraction objects. This is easily accomplished in Python by renaming your "add" method into "__add__" (i.e., add two leading and two trailing underscores). Do the same for "mul", "sub", "div". Also rename "toFloat" into "__float__" and "toString" into "__str__". (See the Python documentation on special method names for more information on why this works.) Now you should be able to run code like this:

      a = Fraction(2)
      b = Fraction(13, 4)
      c = a-b
      print a, "-", b, "=", c, "=", float(c)
      
      a = Fraction(2, -3)
      b = Fraction(-5, 6)
      c = a/b
      print a, "/", b, "=", c, "=", float(c)
      

      which should produce the following output:

      2 - 13/4 = -5/4 = -1.25
      -2/3 / -5/6 = 4/5 = 0.8
      

   You are allowed to work in groups of two on problems 2 and 3. Hand in one printout per group. To print Smalltalk code, create a text file containing your class and method definitions. You can start by selecting "FileOut -> as" from the System Browser's "Category" menu. But don't just hand in the resulting file, but clean it up and organize it nicely! (See my IntList file for an example.)

   For both Smalltalk and Python, don't forget to document your methods, to include your name(s), names of collaborators, and how much time it took you. Please include testing code and sample output! The IntList file is also an example for good sample output. In any case, give me more than just the testing code included above.