Homework J5: Triangulation Due: Friday, 1 April 2005 by 10 a.m.

Introduction

For this homework, you will develop a program that will count types of triangles.  There are two files that need to be submitted: Triangle.java and TriangleCount.java.  No skeleton code is being provided. 

There are two parts to this assignment.  The first, developing the Triangle class, reviews creating classes and using if and switch statements (your program can use one, the other, or both types of statements).  The second, developing the TriangleCount.java file, uses for and while loops.

Background

Recall that there are many types of triangles:

Right triangle	Isosceles triangle	Equilateral triangle	Scalene triangle

• Right triangle: where one of the angles is a right angle (90°).  The sides of a right triangle fulfills Pythagorean's theorem: a²+b²=c², where c is the length of the diagonal side, and a and b are the lengths of the two sides adjacent to the right angle
• Isosceles triangle: where two of the sides are equal in length
• Equilateral triangle: where all three sides are equal in length
• Scalene triangle: where all three sides are of different lengths

Note that there are other types of triangles (obtuse, acute, etc.), but we are ignoring those for this assignment.

Triangle class

For the first part of this assignment, you will need to develop a Triangle class to represent a triangle.  For the triangles in this assignment, all the lengths of the sides are all of type int. 

The class should thus include three private int variables, to hold the sides of the triangle.  We will call them a, b, and c in this assignment (although you can name them to something else).

The class should include the following methods.

• public Triangle()
  The default constructor, it sets the triangle's sides to 3, 4, and 5.  Note that because there are no required mutators for this homework, the constructor can set the fields directly (you can also add a mutator, if you want - but there won't be a bonus or penalty for either way of doing this).
   
• public Triangle (int x, int y, int z)
  The specific constructor, it sets the sides a, b, and c of the triangle respectively to the values of parameters x, y, and z. The parameters x, y, and z should have the property that x < y < z. If they are not in sorted order, then assign the value 1 to a, b, and c (as that is a valid triangle).  Note that because there are no required mutators for this homework, the constructor can set the fields directly (you can also add a mutator, if you want - but there won't be a bonus or penalty for either way of doing this).
   
• public boolean isTriangle()
  This method will return true or false, depending on whether the values in the three sides make up a valid triangle.  Given that a, b, and c are in sorted order (the specific constructor only accepts them in sorted order), the sides represent a valid triangle only if a + b > c.
   
• public boolean isRight()
  This method returns true or false, depending on whether the triangle is a right triangle or not.  Specifically, it will return true if the sides form a valid triangle (via a call to the isTriangle() method) AND the sides fulfill the formula a²+b²=c².
   
• public boolean isIsosceles()
  This method returns true or false, depending on whether the triangle is a isosceles triangle or not.  Specifically, it will return true if the sides form a valid triangle AND two of the sides are equal (it can be any two).  Please make sure to spell this method right!  It will cause issues if you misspell isosceles.
   
• public boolean isScalene()
  This method returns true or false, depending on whether the triangle is a scalene triangle or not.  Specifically, it will return true if the sides form a valid triangle AND none of the sides are equal to each other.
   
• public boolean isEquilateral()
  This method returns true or false, depending on whether the triangle is a equilateral triangle or not.  Specifically, it will return true if the sides form a valid triangle AND all the sides are of equal length.
   
• public String toString()
  This method will allow you to print out the triangle.  Specifically, it returns a String representation of the triangle.  If the triangle has side lengths of 3, 4, and 5, then this method will return the String "(3,4,5)" (without the quotes, of course).

TriangleCount

The second part of this assignment is to write the TriangleCount class.  This class will just have the main() method.

First, the main method should initialize a Scanner object, and ask the user to enter n (an int).

The program will test triangles of all possible sizes x, y, and z from (1,1,1) to (n,n,n).  Thus, if n is 5, then there are 5*5*5 or 125 possible triangles that must be checked.  This will most likely require three nested loops.  For each of the triangles, the following steps must be done:

• Check if the sides are in sorted order (i.e. x < y < z).  If not, then no output should be provided for that collection of side lengths.  This check (to see if they are in sorted order) should be done in the nested loops, not in the Triangle class (as the Triangle class will assign the values (1,1,1)).
• Create a new Triangle object using the current side lengths
• Check if it is a valid triangle - if it is not, then no output should be provided for that collection of side lengths.
• Otherwise, indicate which properties the triangle possesses (i.e., indicate whether it is a right, isosceles, equilateral, and scalene triangle). Some side length values will correspond to more than 1 triangle (e.g., (3, 3, 3) is both isosceles and equilateral), so do not assume that once a property is present, the others are not.

Sample Run

The following is a sample run of the program.  The red number 5 was supplied by the user.

Enter n: 5

(1,1,1) isosceles equilateral
(1,2,2) isosceles
(1,3,3) isosceles
(1,4,4) isosceles
(1,5,5) isosceles
(2,2,2) isosceles equilateral
(2,2,3) isosceles
(2,3,3) isosceles
(2,3,4) scalene
(2,4,4) isosceles
(2,4,5) scalene
(2,5,5) isosceles
(3,3,3) isosceles equilateral
(3,3,4) isosceles
(3,3,5) isosceles
(3,4,4) isosceles
(3,4,5) right scalene
(3,5,5) isosceles
(4,4,4) isosceles equilateral
(4,4,5) isosceles
(4,5,5) isosceles
(5,5,5) isosceles equilateral

Note that a number of the possible combinations of numbers were not printed.  Any three numbers that are not ordered were not printed (such as 4,3,2).  And any values that are not valid triangles (such as 1,2,3) are also not printed.  The main() method should not print these combinations, as described above.  Also note that each possible triangle will print a triangle type: either all sides are equal (equilateral/isosceles), 2 sides are equal (isosceles), or no sides are equal (scalene).

Submission

When you are finished, submit Triangle.java and TriangleCount.java.