Sample Final Questions
CS 2010
Fall 2003

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  Answers are between dashed lines, like this.
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A radar center must track flying objects. Every flying object has a
position, which is expressed as three numbers for latitude, longitude,
and altitude. Known objects also have an identifying string, while
unknown objects have no identifier.

Provide a data definition (suitable for use with Scheme) for
radar-tracked flying objects.

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  ;; A FO is either
  ;;  - (make-identified string num num num)
  ;;  - (make-ufo num num num)
  (define-struct identified (id lat long alt))
  (define-struct ufo (lat long alt))
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----------------------------------------

Provide a Java version of your data definition for radar-tracked
flying objects.

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  abstract class FO {
    double lat;
    double lng;
    double alt;
  }
  
  class Identified extends FO {
    String id;
    ...
  }                             
  
  class UFO extends FO {
    ...
  }
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----------------------------------------

A data definition:

   ; A blue is either
   ;  - (make-small num num)
   ;  - (make-medium num blue)
   (define-struct small (x y))
   (define-struct medium (w z))

Provide enough examples to cover each case of data definition.

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  (make-small 12 89)
  
  (make-medium 87 (make-small 1 2))
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----------------------------------------

Provide a Scheme template for the above data definition

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  (define (func-for-blue b)
    (cond
      [(small? b) .. (small-x b) .... (small-y b) ...]
      [(medium? b) ... (medium-w b) 
                    .... (func-for-blue (medium-z b)) ...]))
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----------------------------------------

Translate the preceding data definition to Java, and include template
methods. You can omit class constructors.

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  abstract class Blue {
     abstract ... method(...);
  }

  class Small extends Blue {
     int x;
     int y;
     ... method(..) {
       this.x ... this.y ...
     }
  }

  class Medium extends Blue {
     int w;
     Blue z;
     ... method(...) {
        ... this.w ... this.z.method(...) ...
     }
  }
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----------------------------------------

Translate your Scheme examples to Java examples.

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  new Small(12, 89)
  new Medium(87, new Small(1, 2))
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----------------------------------------

Suppose we add a new variant to blue:

   ; A blue is either
   ;  ...
   ;  - (make-large blue blue num)
   ...
   (define-struct large (p q r))

Explain breifly but completely how the Scheme template changes.

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  Add a condition whose question is (large? b)
  and add a recursive call for the firt two pieces
  (large-p b) and (large-q b), and also extract (large-r b)
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----------------------------------------

Here's a new data definition:

 ; A purple is either
 ;  - num
 ;  - (make-light purple)
 ;  - (make-heavy purple purple)
 (define light (next))
 (define heavy (left right))

Here's a broken function:

 ; purple-nums : purple -> list-of-num
 ;  Returns a list of all numbers in p
 (define (purple-nums p)
  (cond
   [(light? p) (purple-nums (light-next p))]
   [else (cond
           [(number? (heavy-left p))
            (cons (heavy-left p) (purple-nums (heavy-right p)))]
           [else (cons
                  (purple-nums p)
                  (purple-nums (heavy-right p)))])]))

Because the implementation fails to follow the data definition in two
essential ways, "purple-nums" doesn't work.

 - What are the two ways in which the function is broken?

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    - no num case at the top "cond"
    - no recursive call on (heavy-left p) in the last case
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 - Provide two example purples, one to expose each problem:

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    7
    (make-heavy (make-light 8) 10)
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----------------------------------------

The following Java code implements the same data structure and
function:

   // Assume a NList class for lists of numbers:
   abstract class NList {
     ...
     abstract NList scaleNums(int factor);
   }
   class NEmpty extends NList { NEmpty() {} ... }
   class NCons extends NList { 
      NCons(int first, NList rest) { ...} 
      ...
   }
  

   abstract class Purple {
     // Sums all of the numbers in this purple
     abstract NList nums();
   }
  
   class NumPurple extends Purple {
     int n;
     NumPurple(int n) {
       this.n = n;
     }
     NList nums() {
       return this.n;
     }
   }
  
   class LightPurple extends Purple {
     private Purple next;
     LightPurple(Purple next) {
       this.next = next;
     }
     NList nums() {
       return this.next.nums();
     }
   }
  
   class HeavyPurple extends Purple {
     Purple left;
     Purple right;
     HeavyPurple(Purple left, Purple right) {
       this.left = left;
       this.right = right;
     }
     NList nums() {
       return new NCons(this.left.nums(), this.right.nums());
    }
  }
  

 - The code has two contract violations (so that it will not execute
   at all). What are the two problems?

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     a. NumPurple's nums() returns a num instead of a NList
     b. HeavryPurple's nums() conses a NList instead of a num
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 - Suggest a way to fix the contract violations and also make the
   method meet its purpose.

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     a. new NCons(this.n, new NEmpty())
     b. need append in NList:
           NList append(NList l);
        and use it:
          return this.left.nums().append(this.right.nums());
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----------------------------------------

Extend the LightPurple class to implement ScaleLightPurple:

 - A ScaleLightPurple has a Purple (like all LightPurples) but also
   an integer that scales all of the ints in the next purple.

 - Clearly, the ScaleLightPurple class must override the nums()
   method. Note that the next field in LightPurple is private.

 - Include also a setScale() method in ScaleLightPurple for setting
   the scale of the purple. The setScale() method changes the
   purple, rather than producing a new purple (so it returns void).

   
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   class ScaleLightPurple extends LightPurple {
      int scale;
      ScaleLightPurple(Purple next, int scale) {
        super(next);
        this.scale = scale;
      }

      NList nums() {
        return super.nums().scale(this.scale);
      }

      void setScale(int s) {
        this.scale = s;
      }
   }
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----------------------------------------

  Purple p1 = new ScaleLightPurple(new NumPurple(12), 2);
  ScaleLightPurple p2 = p1;
  p1.setScale(1);
  p2.setScale(3);
  p2.nums()

The contracts don't match in this code. In what two places must a
cast be inserted to make the contracts match?

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  In decl p2 = p1:  p2 = (ScaleLightPurple)p1;

  In p1.setScale:   ((ScaleLightPurple)p1).setScale(1);
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What is the result of the last expression?

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  new Cons(36, new Empty())
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----------------------------------------

Suppose that we drop ScaleLightPurple, but we add a Combiner interface
declaration to the above program and a combine method as follows:

   interface Combiner {
     Object combine(int n, Object o);
   }

   abstract class Purple {
     ...
     abstract Object combineNums(Combiner c, Object base);
   }
  
   class NumPurple extends Purple {
     ...
     Object combine(Combiner c, Object base) {
       return c.combine(this.n, base);
     }
   }
  
   class LightPurple extends Purple {
     ...
     Object combine(Combiner c, Object base) {
       return this.next.combine(c, base);
     }
   }
  
   class HeavyPurple extends Purple {
     ...
     Object combine(Combiner c, Object base) {
       this.left.combine(c, this.right.combine(c, base));
    }
  }
  
Note that, given

   class Conser implements Combiner {
     Object combine(int n, Object l) {
       return new NCons(n, (NList)l);
     }
   }
  
then for any Purple p,

  p.combine(new Conser(), new NEmpty())

is the same as

  p.nums()


Define a class MaxFinder that implements Combiner for finding the
maximum positive integer in a Purple (or 0 if the Purple contains no
positive integers). Use

  class Integer {
    int i;
    Integer(int i) { this.i = i; }
    int intValue() { return this.i; }
  }

and the result of

  p.combine(new MaxFinder(), new Integer(0))

should be an instance of Integer.

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  class MaxFinder implement Combiner {
    Object combine(int n, Object o) {
       if (n > ((Integer)o).intValue())
        return new Integer(n);
       else
        return o;
    }
  }
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