public class Point
{
   private double x;
   private double y;
   // suppose a constructor and other useful methods are here too!
}

public class Student {
   private int id;
   private String name;
   private double gpa;
   public Student(int id, String name) {
      this.id= id;
      this.name= name;
      this.gpa= 0.0;
   }
   public boolean qualifiesForScholarship() {
      return gpa >= 3.0;
   }
   public double getGpa() {
      return gpa;
   }
   public void setGpa(double gpa) {
      this.gpa= gpa;
   }
   public String toString() {
      return name + " (" + id + ") " + gpa;
   }
}

1. (4 pts) Some students participate in athletics and for those students we need to be able to store a code for which sport they play (0=soccer, 1=basketball, 2=track) and the number of years they have participated. Create a new class called StudentAthlete that inherits from Student and provides these attributes.

2. (4 pts) In the new StudentAthlete class create a constructor that accepts as parameters an id, name, and sport code. The years of participation should be 0. The constructor should invoke the constructor of it's super class.

3. (4 pts) Suppose that student athletes have different rules when qualifying for scholarships. Student athletes can qualify for a scholarship if their GPA is at least 3.0 as for other students. They can also qualify if they have participated in a sport for at least one year and their GPA is at least 2.75. Override the qualifiesForScholarship method in the new StudentAthlete class accordingly.

4. (6 pts) Draw a UML diagram depicting these two classes. When depicting attributes you should specify their type. When depicting methods you should specify their return type, name, and parameters. Be sure to show the inheritance relationship.

5. (6 pts) Write a stand-alone method (not inside either of the classes) that will accept as a parameter a full array of student objects (some of which might be of type Student and others which might be of type StudentAthlete. The method should list all students who qualify for a scholarship according to their various requirements.

We have bunnies standing in a line, numbered 1, 2, .... The odd bunnies (1, 3, ...) have the normal 2 ears. The even bunnies (2, 4, ...) we'll say have 3 ears, because they each have a raised foot. Write a method that accepts a value for n and recursively calculates and returns the number of “ears” in the bunny line 1, 2, ... (without loops or multiplication).

public static double fun(double [] a, int b, int c) {
   double d,e;
   if (b>c) return 0;
   if (b==c) return a[b];

   d= fun(a,b,(b+c)/2);
   e= fun(a,(b+c)/2+1,c);

   if (d >=e)
      return d;
   else
      return e;
}

1. (6 pts) What value is returned by this method if invoked with fun(cool,0,4) assuming cool is declared and initialized as follows. REMEMBER: An int divided by an int is always an int.

   	double [] cool= {12,45,22,15,32};
   

2. (2 pts) Does this method utilize indirect recursion?

[fontsize=\small]
class GameToken {
   public boolean isSolid;
   public boolean isSlidable;
   public boolean isMobile;
   public GameToken(boolean isSolid, boolean isSlidable, boolean isMobile) {
      this.isSolid= isSolid;
      this.isSlidable= isSlidable;
      this.isMobile= isMobile;
   }
}
class GameBoard {
   private GameToken [][] board;
   private GameToken player, blank;
   public GameBoard(int rows, int cols) {
      player= new GameToken(true, false, true);
      blank= new GameToken(false, false, false);
      // your code here
   }
}

In this game each position in the 2d grid contains a reference to some GameToken object. A wall/barrier is solid and cannot be pushed into another cell (i.e., it is not slidable), and cannot move on its own (i.e., not mobile). An open space (containing air or water) is not solid, not slidable, and not mobile. A person/character is solid, not slidable, but is mobile. An inanimate object (desk, chair, barrel, etc.) is solid and slidable, but not mobile.

1. Modify the constructor for the GameBoard class by adding code following the “your code here” comment to accomplish the following:
   1. (4 pts) Reserve memory for the board (based on the parameters provided) and have all board positions refer to the blank attribute.
   2. (2 pts) Put the player in the top, left corner of the board.

2. (6 pts) Write a method for the GameBoard class called countCharacters that will look at an existing (initialized) board and return the number of animated person/characters on the board. The attribute “player” may or may not be positioned on the board when this method is called.