CS111, Wellesley College 2006 Lab 10 Wedn/Thur, November 8/9, 2006

Iteration

The purpose of this lab is to give you practice with iteration via tail recursion and while loops. You will use iteration tables to show the sequence of values assigned to parameters and variables that are updated and/or used to meet the invariant in your method loops.

Today's plan:

• Iteration lists
• Picture this
• It's turtles all the way down

I. Iteration Using Lists (pencil and paper)

In class, you saw that tail recursion, while loops, and for loops are all equivalent in power. Which mechanism you choose depends on the particular program and is often a matter of taste.

For the problems below, draw an iteration table for the given method and then write equivalent methods using the other forms of iteration. Assume we have a list L1 = [3,1,2,4].

A.   weightedSum()

  public static int weightedSum (IntList L) {

      return weightedSumTail(L, 1, 0);
  }
   
  public static int weightedSumTail (IntList L, int weight, int total) {
   
         if (isEmpty(L)) {
             return total;
         } else {
             return weightedSumTail(tail(L), weight+1, (weight*head(L)) + total);
         }  
  }

B.   isMember()

   public static boolean isMemberWhile(int n, IntList L) {
   
       while (!isEmpty(L) && (head(L)!=n)) {
           L = tail(L);
       }
       return !isEmpty(L); // only true if n is in L
    }
   

II. Iteration in PictureWorld -- Row World

To begin this problem, download the lab10_programs folder from the cs111d account. In DrJava, open RowWorld.java in the Row folder. In this task, you will be fleshing out skeletons for various methods defined in the RowWorld class. The Test folder contains a test version so you can see what your applet should produce.

row(p,n) produces a picture with p arranged in n equally spaced columns (ie a row with n elements).
For example,

row(smile(Color.black,Color.yellow),1)	row(smile(Color.black,Color.yellow),4)

// This method returns a picture with p arranged in numberItems
// equally spaced columns (ie a row with numberItems elements).

public Picture row (Picture p, int numberItems) {

    if (numberItems<=0) { // base case: a row with no elements is empty
        return empty();
    } else { // general case: a row is a picture with a row
             // of one fewer number of elements to its right
        return beside(p, row(p, numberItems-1), 1.0/numberItems);
    }
}

Draw an iteration table for row(smile(Color.black,Color.yellow), 4). Rewrite the method in three ways:

• using tail-recursion
• using a while loop
• using a for loop

III. Iteration in Turtle World

Look in the Polygons subdirectory of the lab10_programs directory, and open PolygonWorld.java. In this task, you will be fleshing out skeletons for various methods defined in the PolygonMaker class within PolygonWorld.java. The test folder has an example of working code.

A.   Polygons

In this problem, you will program turtles to draw regular polygons. A regular polygon has sides of equal length and angles of equal length, as shown in the following images:

We will draw these polygons using the three strategies for expressing iteration:

• Tail Recursion.
• A while loop.
• A for loop.

A turtle can draw a polygon by repeatedly drawing a side and then turning by an angle of (360.0/sides), until it has drawn the specified number of sides. One strategy for encoding this iteration is to use tail recursion. Below is the skeleton for such a such a strategy. The polygon() method invokes the tail recursive polygonTail() method with the appropriate initial parameters for the state variables of the iteration.

	
public void polygon (int sides, int length) {

    double angle = 360.0/(double)sides;
    polygonTail(sides, length, angle);
}

	

public void polygonTail(int numSides, int length, double angle){

    // Flesh out this body. 

}

Flesh out the bodies of the polygonTail(), polygonWhile() and polygonFor() methods.

You can test your methods by selecting the appropriate checkbox in the Parameter window before pressing the Run button in the Turtle window.

B.   Polygon Flowers

Now that you can draw a polygon, you can use this method to draw a polygon flower. A polygon flower is defined by the number of petals and the number of sides of each petal. Each petal is a regular polygon, and the petals are rotated with respect to one another. The angle of rotation is equal to (360.0/petals). Some sample flowers are as follows:

As with the polygon, we will write methods to draw these flowers using tail recursion and while loops. Fill out the skeletons for:

• flowerTail()
• flowerWhile()
• flowerFor()

Test out your methods by executing FlowerWorld.html and selecting the checkbox corresponding to the method you want to test.

C.   Nested for loops

Now, just for practice, we will write a method to draw these flowers using a nested for loop. For this method, do not make use of the Polygon methods you wrote in the last section. Draw an iteration table for flowerNestedFor(6,4,60) and fill out the skeleton for flowerNestedFor().

Test out your method by executing FlowerWorld.html and selecting the checkbox corresponding to the flowerNestedFor method.