Classes Chapter 6 Spring 2007 CS 101 Aaron Bloomfield The Car class More on classes vs.

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Transcript Classes Chapter 6 Spring 2007 CS 101 Aaron Bloomfield The Car class More on classes vs.

Classes

Chapter 6 Spring 2007 CS 101 Aaron Bloomfield 1

The Car class

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More on classes vs. objects

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A new example: creating a Car class

 What properties does a car have in the real world?

 Color   Position (x,y) Fuel in tank  We will implement these properties in our Car class public class Car { private Color color; private int xpos; private int ypos; private int fuel; //...

} 4

Car’s instance variables

public class Car { private Color color; private int xpos; private int ypos; private int fuel; //...

} - color - fuel + … Car - xpos - ypos 5

Instance variables and attributes

 Default initialization  If the variable is within a method, Java does NOT initialize it  If the variable is within a class, Java initializes it as follows: Car  Numeric instance variables initialized to 0 - color = null - xpos = 0  Logical instance variables initialized to false - fuel = 0 + … - ypos = 0  Object instance variables initialized to null 6

Car behaviors or methods

 What can a car do? And what can you do to a car?

 Move it    Change it’s x and y positions Change it’s color Fill it up with fuel  For our computer simulation, what else do we want the Car class to do?

 Create a new Car  Plot itself on the screen  Each of these behaviors will be written as a method 7

Creating a new car

 To create a new Car, we call:  Car c = new Car();  Notice this looks like a method  You are calling a special method called a constructor  A constructor is used to create (or construct) an object  It sets the instance variables to initial values  The constructor: public Car() { fuel = 1000; color = Color.BLUE; } 8

Constructors

No return type!

For now, all constructors are public EXACT same name as class

public Car() { fuel = 1000; color = Color.BLUE; } 9

Our Car class so far

public class Car { private Color color; private int xpos; private int ypos; private int fuel; public Car() { fuel = 1000; color = Color.BLUE; } } public class Car { private Color color = Color.BLUE

; private int xpos; private int ypos; private int fuel = 1000 ; public Car() { } } 10

Our Car class so far

public class Car { private Color color = Color.BLUE; private int xpos = 0 ; private int ypos = 0 ; private int fuel = 1000; Car - color = Color.BLUE

- fuel = 1000

+ Car()

+ … - xpos = 0 - ypos = 0 public Car() { } }  Called the default constructor   The default constructor has no parameters If you don’t include one, Java will SOMETIMES put one there automatically 11

Alien Song

AlienSong.mpg

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Another constructor

 Another constructor: public Car (Color c, int x, int y, int f) { color = c; xpos = x; ypos = y; fuel = f; }    This constructor takes in four parameters The instance variables in the object are set to those parameters This is called a specific constructor  An constructor you provide that takes in parameters is called a specific constructor 13

}

Our Car class so far

public class Car { private Color color = Color.BLUE; private int xpos = 0; private int ypos = 0; private int fuel = 1000; public Car() { } Car - color = Color.BLUE

- fuel = 1000 - xpos = 0 - ypos = 0 + Car()

+ Car (Color, int, int, int)

+ … public Car (Color c, int x, int y, int f) { color = c; xpos = x; ypos = y; fuel = f; } 14

Using our Car class

 Now we can use both our constructors: Car c1 = new Car(); Car c2 = new Car (Color.BLACK, 1, 2, 500); c1 c2 Car - color = Color.BLUE

- fuel = 1000 + Car() + Car (Color, int, int, int) + … - xpos = 0 - ypos = 0 Car - color = Color.BLACK

- fuel = 500 - xpos = 1 - ypos = 2 + Car() + Car (Color, int, int, int) + … 15

So what does private mean?

 Consider the following code

Note that it’s a different class!

public class CarSimulation { public static void main (String[] args) { Car c = new Car(); System.out.println (c.fuel); } }    Recall that fuel is a private instance variable in the Car class Private means that code outside the class CANNOT access the variable  For either reading or writing Java will not compile the above code  If fuel were public, the above code would work 16

So how do we get the fuel of a Car?

 Via accessor methods in the Car class: public int getFuel() { } return fuel; public Color getColor() { return color; } public int getYPos() { return ypos; } public int getXPos() { } return xpos;   As these methods are within the Car class, they can read the private instance variables As the methods are public, anybody can call them 18

So how do we

set

the fuel of a Car?

 Via mutator methods in the Car class: public void setFuel (int f) { } fuel = f; public void setColor (Color c) { color = c; } public void setXPos (int x) { xpos = x; } public void setYPos (int y) { ypos = y; }   As these methods are within the Car class, they can read the private instance variables As the methods are public, anybody can call them 19

Why use all this?

 These methods are called a get/set pair  Used with private variables  We’ll see why one uses these later in this slide set  Our Car so far: Car - color = Color.BLUE

- fuel = 1000 - xpos = 0 - ypos = 0 + Car() + Car (Color, int, int, int)

+ void setXPos (int x) + void setYPos (int y) + void setColor (Color c) + void setFuel (int f) + int getFuel() + int getXPos() + int getYPos() + Color getColor()

+ … 20

Back to our specific constructor

public class Car { private Color color = Color.BLUE; private int xpos = 0; private int ypos = 0; private int fuel = 1000; public class Car { private Color color = Color.BLUE; private int xpos = 0; private int ypos = 0; private int fuel = 1000; } } public Car (Color c, int x, int y, int f) { color = c; xpos = x; ypos = y; fuel = f; } } public Car (Color c, int x, int y, int f) { setColor (c); setXPos (x); setYPos (y); setFuel (f); 21

Back to our specific constructor

 Using the mutator methods (i.e. the ‘set’ methods) is the preferred way to modify instance variables in a constructor  We’ll see why later 22

Today’s demotivators

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So what’s left to add to our Car class?

 What else we should add:  A mutator that sets both the x and y positions at the same time  A means to “use” the Car’s fuel  A method to paint itself on the screen  Let’s do the first: public void setPos (int x, int y) { setXPos (x); setYPos (y); }  Notice that it calls the mutator methods 24

Using the Car’s fuel

 Whenever the Car moves, it should burn some of the fuel  For each pixel it moves, it uses one unit of fuel  We could make this more realistic, but this is simpler  Math.abs() returns the absolute value public void setXPos (int x) { xpos = x; } public void setXPos (int x) { fuel -= Math.abs

(getXPos()-x); xpos = x; } public void setYPos (int y) { ypos = y; } public void setYPos (int y) { fuel -= Math.abs

(getYPos()-y); 25 ypos = y; }

Setting both positions at once

public void setPos (int x, int y) { setXPos(x); setYPos(y); }  Notice that to modify the instance variables, the mutator methods are used 26

Drawing the Car

 The simple way to have the Car draw itself: } public void paint (Graphics g) { g.setColor (color); g.fillRect (xpos-50, ypos-100, 100, 200);  This draws a single rectangle that is 100 by 200 pixels in size  Lets use constants for the car’s height and width...

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Drawing the Car

 A better version: private final int CAR_WIDTH = 100; private final int CAR_HEIGHT = 200; public void paint (Graphics g) { g.setColor (color); g.fillRect (getXPos() CAR_WIDTH/2 , getYPos() CAR_HEIGHT/2 , CAR_WIDTH , CAR_HEIGHT ); }   This makes it easier to change the car size  We could have made the car size instance variables and set them via mutators 28 Lets add tires!

Drawing the Car

private final int CAR_WIDTH = 100; private final int CAR_HEIGHT = 200; private final int TIRE_WIDTH = 20; private final int TIRE_HEIGHT = 40; private final int TIRE_OFFSET = 20; public void paint (Graphics g) { g.setColor (color); g.fillRect (getXPos()-CAR_WIDTH/2, getYPos()-CAR_HEIGHT/2, CAR_WIDTH, CAR_HEIGHT); // Draw the tires g.setColor (Color.BLACK); g.fillRect (getXPos()-(CAR_WIDTH/2+TIRE_WIDTH), getYPos()-(CAR_HEIGHT/2-TIRE_OFFSET), TIRE_WIDTH, TIRE_HEIGHT); g.fillRect (getXPos()-(CAR_WIDTH/2+TIRE_WIDTH), getYPos()+(CAR_HEIGHT/2-TIRE_OFFSET-TIRE_HEIGHT), TIRE_WIDTH, TIRE_HEIGHT); g.fillRect (getXPos()+(CAR_WIDTH/2), getYPos()+(CAR_HEIGHT/2-TIRE_OFFSET-TIRE_HEIGHT), TIRE_WIDTH, TIRE_HEIGHT); g.fillRect (getXPos()+(CAR_WIDTH/2),

Don’t worry about this – just know that it draws four tires

getYPos()-(CAR_HEIGHT/2-TIRE_OFFSET), TIRE_WIDTH, TIRE_HEIGHT); } 29

What happens when the car runs out of fuel?

 We could do a number of things:  Not allow the car to move anymore  Print out a message saying, “fill me up!”  We’ll color the car red  We’ll insert the following code at the beginning of the paint() method: if ( fuel < 0 ) { color = Color.RED; } 30

Drawing the Car

private final int CAR_WIDTH = 100; private final int CAR_HEIGHT = 200; private final int TIRE_WIDTH = 20; private final int TIRE_HEIGHT = 40; private final int TIRE_OFFSET = 20; public void paint (Graphics g) { if ( fuel < 0 ) { color = Color.RED; } g.setColor (color); g.fillRect (getXPos()-CAR_WIDTH/2, getYPos()-CAR_HEIGHT/2, CAR_WIDTH, CAR_HEIGHT); // Draw the tires g.setColor (Color.BLACK); g.fillRect (getXPos()-(CAR_WIDTH/2+TIRE_WIDTH), getYPos()-(CAR_HEIGHT/2-TIRE_OFFSET), TIRE_WIDTH, TIRE_HEIGHT); g.fillRect (getXPos()-(CAR_WIDTH/2+TIRE_WIDTH), getYPos()+(CAR_HEIGHT/2-TIRE_OFFSET-TIRE_HEIGHT), TIRE_WIDTH, TIRE_HEIGHT); g.fillRect (getXPos()+(CAR_WIDTH/2), getYPos()+(CAR_HEIGHT/2-TIRE_OFFSET-TIRE_HEIGHT), TIRE_WIDTH, TIRE_HEIGHT); g.fillRect (getXPos()+(CAR_WIDTH/2), getYPos()-(CAR_HEIGHT/2-TIRE_OFFSET), TIRE_WIDTH, TIRE_HEIGHT); } 31

Our car in action

CarGUI.java

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How well do you feel you understand the Car class?

Very well! This stuff is easy!

Fairly well – with a little review, I’ll be good Okay. It’s not great, but it’s not horrible, either Not well. I’m kinda confused Not at all. I’m soooooo lost.

20% 20% 20% 20% 20% V er y w el l! T hi F s ai st rly uf w f i el ...

l – O w ka y.

ith I a t’s li n tt.

ot N .

g ot re w at el , b l. I’ u.

m N ..

k ot in a da t a c ll.

...

I ’m s oo oo o.

..

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Cubic Tragedy

Cubic_tragedy_m640.mov

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Miscellaneous Stuff

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What I’m not expecting you to know yet…

 What the static keyword means  And why the main() method is  And why other methods are not  Why you should always call the mutator methods, instead of setting the field directly  Just know that it’s a good programming practice, and follow it  We’ll see why later  Why instance variables are supposed to be private  Just know that it’s a good programming practice, and follow it  Again, we’ll see why soon 36

Terminology

 An attribute of a class can be called:  Instance variable or class variable  We’ll see the difference later  Static variable (or static field)  Synonymous with class variable     Field  Generally means either type Variable  Also means either type Attribute Property  Argh!

 I will generally use the terms variable or field when I am not differentiating between the two  And instance variable/field and class variable/field when I am 37

The main() method

 Consider a class with many methods: public class WhereToStart { public static void foo (int x) { // ...

} public static void bar () { // ...

} public static void main (String[] args) { // ...

} }  Where does Java start executing the program?

 Always at the beginning of the main() method!

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Running a class without a main() method

 Consider the Car class  It had no main() method!

 The main() method was in the CarSimulation (or CarGUI) class  So let’s try running it… 39

Car.java

Program Demo

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Variable initialization

 A local variable is NOT initialized to a default value  This is any variable declared within a method   Or within a block within a method This is pretty stupid, in my opinion  Parameters are initialized to whatever value they are passed  Instance and class variables are initialized to default values   Numbers to zero, booleans to false, references to null This means any field in a class  Either class variables or instance variables 41

1.

2.

3.

4.

5.

How well do you feel you understand creating classes so far?

Very well! This stuff is easy!

Fairly well – with a little review, I’ll be good Okay. It’s not great, but it’s not horrible, either Not well. I’m kinda confused Not at all. I’m soooooo lost.

20% 20% 20% 20% 20% V er y w el l! T hi F s ai st rly uf w f i el ...

l – O w ka y.

ith I a t’s li n tt.

ot N .

g ot re w at el , b l. I’ u.

m N ..

k ot in a da t a c ll.

...

I ’m s oo oo o.

..

42

The Circle class

Introducing static-ness, visibilities, etc.

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A Circle class

 We are going to develop a Circle class  Perhaps for use in a graphics program  Why?

 Partly to review creating classes   Go over some topics that were a bit fuzzy  Constructors and creating objects Show why one uses the get/set methods instead of directly modifying the instance variables   Discuss visibilities (public, private, etc.) Discuss the static keyword 45

Circle class properties

 What properties does a circle have?

 Radius  PI = 3.141592653589793234

  Color (if plotting in a graphics program) (x,y) location  These properties will become instance variables  We are only going to play with the first two (radius and PI) in this example  Thus, we are ignoring the color and location 46

Our Circle class

Circle c = new Circle(); c public class Circle { double radius; Note the radius field is not initialized by us double PI = 3.1415926536; } Circle - radius = 0.0

PI = 3.14159… … + … We’re ignoring the public for now Note the fields are not static 47

Accessing our Circle object

 Any variable or method in an object can be accessed by using a period  The period means ‘follow the reference’ c  Example: System.in

 Example: System.out.println

(c.radius);  Example: c.PI = 4; This is bad – PI should have been declared final (this will be done later) Circle - radius = 0.0

PI = 3.14159… … + … 48

What’s the output?

public class Circle { double radius; double PI = 3.1415926536; } public class CircleTest { public static void main (String[] args) { int x; Circle c = new Circle(); System.out.println (x); } } Java will give a “variable not initialized” error  When a variable is declared as part of a method, Java does not initialize it to a default value 49

What’s the output now?

public class Circle { double radius; double PI = 3.1415926536; } public class CircleTest { public static void main (String[] args) { int x; Circle c = new Circle(); System.out.println (c.radius); Java outputs 0.0!

} }  When a variable is declared as part of a class, Java does initialize it to a default value 50

What’s going on?

   A (method) variable needs to be initialized before it is used  Usually called a local variable A instance variable is automatically initialized by Java  All numbers are initialized to 0, booleans to false, etc.

This is a bit counter-intuitive… 51

Circle class behaviors

 What do we want to do with (and to) our Circle class?

 Create circles  Modify circles (mutators)     Find out about our circles’ properties (accessors) Find the area of the circle Plot it on the screen (or printer) A few others…  These will be implemented as methods 52

Calling the Circle constructor

 To create a Circle object: c1 Circle c1 = new Circle();  This does four things:  Creates the c1 reference  Creates the Circle object   Makes the c1 reference point to the Circle object Calls the constructor with no parameters (the ‘default’ constructor) Circle - radius = 0.0

PI = 3.14159… … + Circle() + Circle (double r) + …  The constructor is always the first method called when creating (or ‘constructing’) an object 53

Calling the Circle constructor

 To create a Circle object: c1 Circle c1 = new Circle( 2.0

);  This does four things:  Creates the c1 reference  Creates the Circle object   Makes the c1 reference point to the Circle object Calls the constructor with 1 double parameters (the ‘specific’ constructor) Circle - radius = 0.0

PI = 3.14159… … + Circle() + Circle (double r) + …  The constructor is always the first method called when creating (or ‘constructing’) an object 54

Constructors

 Remember, the purpose of the constructor is to initialize the instance variables  PI is already set, so only radius needs setting public Circle() { } radius = 1.0; Note there is no return type for constructors public Circle (double r) { radius = r; } Note that the constructor name is the EXACT same as the class name Note that there are two “methods” with the same name!

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What happens in memory

   Consider: Circle c = new Circle(); A double takes up 8 bytes in memory Thus, a Circle object takes up 16 bytes of memory  As it contains two doubles Circle Shorthand representation c c - radius = 1.0

- PI = 3.1415926536

… + Circle() + Circle (double r) + … Circle - radius = 1.0

- PI = 3.14159

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}

Circle class: our class so far

public class Circle { double radius; double PI = 3.1415926536; public Circle() { radius = 1.0; } public Circle (double r) { radius = r; } 57

1.

2.

3.

4.

5.

How well do you feel you understand the constructors?

Very well! This stuff is easy!

Fairly well – with a little review, I’ll be good Okay. It’s not great, but it’s not horrible, either Not well. I’m kinda confused Not at all. I’m soooooo lost.

20% 20% 20% 20% 20% V er y w el l! T hi F s ai st rly uf w f i el ...

l – O w ka y.

ith I a t’s li n tt.

ot N .

g ot re w at el , b l. I’ u.

m N ..

k ot in a da t a c ll.

...

I ’m s oo oo o.

..

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New 2005 demotivatiors!

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}

Circle class: our class so far

public class Circle { double radius; double PI = 3.1415926536; public Circle() { radius = 1.0; } public Circle (double r) { radius = r; } 60

Consider the following code

public class CircleTest { public static void main (String[] args) { Circle c1 = new Circle(); Circle c2 = new Circle(); Circle c3 = new Circle(); Circle c4 = new Circle(); } } 61

What happens in memory

 There are 4 Circle objects in memory  Taking up a total of 4*16 = 64 bytes of memory c1 Circle - radius = 1.0

- PI = 3.14159

c2 Circle - radius = 1.0

- PI = 3.14159

c3 Circle - radius = 1.0

- PI = 3.14159

c4 Circle - radius = 1.0

- PI = 3.14159

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Consider the following code

public class CircleTest { public static void main (String[] args) { Circle c1 = new Circle(); //...

Circle c1000000 = new Circle(); } } public class CircleTest { public static void main (String[] args) { Vector v = new Vector(); for ( int i = 0; i < 1000000; i++ ) v.add (new Circle()); } } These programs create 1 million Circle objects!

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What happens in memory

 There are 1 million Circle objects in memory  Taking up a total of 1,000,000*16 ≈ 16 Mb of memory c1 Circle - radius = 1.0

- PI = 3.14159

c2 Circle - radius = 1.0

- PI = 3.14159

… c1000000 Circle - radius = 1.0

- PI = 3.14159

Note that the final PI field is repeated 1 million times 64

The use of static for fields

 If a variable is static , then there is only ONE of that variable for ALL the objects  That variable is shared by all the objects c1 Circle - radius = 1.0

c2 Circle - radius = 1.0

c3 … - radius = 1.0

Circle - radius = 1.0

PI 3.1415926536

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More on static fields

 What does the following print  Note that PI is not final Circle c1 = new Circle(); Circle c2 = new Circle(); Circle c3 = new Circle(); Circle c4 = new Circle(); c1.PI = 4.3; System.out.println (c2.PI);  It prints 4.3

Note you can refer to static fields by object.variable

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Even more on static fields

 There is only one copy of a static many objects are declared in memory  field no matter how Even if there are zero objects declared!

 The one field is “common” to all the objects  Static variables are called class variables  As there is one such variable for all the objects of the class  Whereas non-static variables are called instance variables  Thus, you can refer to a static field by using the class name:  Circle.PI

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Even even more on static fields

 This program also prints 4.3: Circle c1 = new Circle(); Circle c2 = new Circle(); Circle c3 = new Circle(); Circle c4 = new Circle(); Circle.PI = 4.3; System.out.println (c2.PI); 68

Even even even more on static fields

 We’ve seen static fields used with their class names:  System.in

(type: InputStream)     System.out

Math.PI

Integer.MAX_VALUE

Game.BOARD_X_COORD

(type: OutputStream) (type: double) (type: int) (in HW J6) 69

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4.

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How well do you feel you understand static-ness?

Very well! This stuff is easy!

Fairly well – with a little review, I’ll be good Okay. It’s not great, but it’s not horrible, either Not well. I’m kinda confused Not at all. I’m soooooo lost.

20% 20% 20% 20% 20% V er y w el l! T hi F s ai st rly uf w f i el ...

l – O w ka y.

ith I a t’s li n tt.

ot N .

g ot re w at el , b l. I’ u.

m N ..

k ot in a da t a c ll.

...

I ’m s oo oo o.

..

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Hand Paintings

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Back to our Circle class

public class Circle { double radius; final static double PI = 3.1415926536; public Circle() { radius = 1.0; } Note that PI is now final and static public Circle (double r) { radius = r; } }  But it doesn’t do much!

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Adding a method

public class Circle { double radius; final static double PI = 3.1415926536; // Constructors...

double computeArea () { return PI*radius*radius; } } Note that a (non-static) method can use both instance and class variables 73

Using that method

public class CircleTest { public static void main (String[] args) { Circle c = new Circle(); c.radius = 2.0; double area = c.computeArea(); System.out.println (area); } } Prints 12.566370614356

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What happens when that method is called

public class Circle { double radius; final static double PI = 3.1415926536; public Circle() { radius = 1.0; } area 12.566

// other constructor double computeArea () { return PI*radius*radius; } } public class CircleTest { public static void main (String[] args) { Circle c = new Circle(); c.radius = 2.0; double area = c.computeArea(); System.out.println (area); } } c - radius = 2.0

PI = 3.14159… … + Circle() + Circle (double r) + computeArea() + … 75

}

Review of our Circle class

public class Circle { double radius; final static double PI = 3.1415926536; public Circle() { } Slight change from before public Circle (double r) { radius = r; } double computeArea () { return PI*radius*radius; } 76

A note about methods/variable order

 Within a method, a variable must be declared before it is used  In a class, methods and variables can be declared in any order  This is different than C++ 77

Review of static for fields

 If a variable is static , then there is only ONE of that variable for ALL the objects  That variable is shared by all the objects c1 Circle - radius = 1.0

c2 Circle - radius = 1.0

c3 … - radius = 1.0

Circle - radius = 1.0

PI 3.1415926536

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Adding another method

double oneOverRadius() { return 1.0/radius; }  I couldn’t think of a good reason to divide something by the radius… 80

What happens now?

 Code in class CircleTest’s main() method Circle c = new Circle(); // c.radius is now 0.0

System.out.println (c.oneOverRadius());  Java won’t crash, but many other programming languages (C and C++, in particular) will  So we’ll call this a ‘crash’ for the sake of this lecture  Java prints “Infinity”  Not what we wanted, though!

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One way to fix this…

public class Circle { double radius = 1.0; final static double PI = 3.1415926536; // Constructors...

double computeArea () { return PI*radius*radius; } double oneOverRadius() { return 1.0/radius; } } Note that the radius variable is now initialized to 1.0

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Back to our program…

 This code will now run properly: Circle c = new Circle(); // c.radius = 1.0

System.out.println (c.oneOverRadius());  But this code will “crash”: Circle c = new Circle(); // c.radius = 1.0

c.radius = 0.0; System.out.println (c.oneOverRadius()); 83

Where the “crash” occurs

public class CircleTest { public static void main (String[] args) { Circle c = new Circle(); // c.radius = 1.0

public class Circle { double radius = 1.0; final static double PI = 3.1415926536; c.radius = 0.0; } double computeArea () { return PI*radius*radius; } } System.out.println

(c.oneOverRadius()); double oneOverRadius() { } return 1.0/radius; Here is the badly written code Here is where the “crash” occurs 84

Motivation for private fields

 Problem: We do not want people using our Circle class to be able to modify the fields on their own  Solution: Don’t allow other code to modify the radius field  Give it private visibility  private field means that only code within the class can modify the 85

One way to fix this…

public class Circle { private double radius = 1.0; final static double PI = 3.1415926536; // Constructors...

double computeArea () { return PI*radius*radius; } double oneOverRadius() { return 1.0/radius; } } Note that the radius variable is now private 86

Today’s demotivators

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Back to our program…

 This code will now not compile: Circle c = new Circle(); // c.radius = 1.0

c.radius = 0.0; System.out.println (c.oneOverRadius());  Java will give a compile-time error:  radius has private access in Circle 88

Back to our program…

 This code will also not compile: Circle c = new Circle(); // c.radius = 1.0

System.out.println (c.radius);  Java will give the same compile-time error:  radius has private access in Circle 89

The problem now…

 But now you can’t modify a Circle’s radius!

 Or find out what it is  Solution: Use a get/set methods in Circle:  A mutator method: void setRadius (double r) { radius = r; }  An accessor method: double getRadius () { return radius; } 90

Our Circle class so far

public class Circle { private double radius = 1.0; final static double PI = 3.1415926536; // Constructors...

} double computeArea () { return PI*radius*radius; } double oneOverRadius() { return 1.0/radius; } void setRadius (double r) { radius = r; } double getRadius () { return radius; } 91

Using the get/set methods

public class CircleTest { public static void main (String[] args) { Circle c = new Circle(); c.setRadius (1.0); System.out.println

(c.computeArea()); System.out.println

(c.getRadius()); } } Here a method is invoked public class Circle { private double radius = 1.0; final static double PI = 3.1415926536; double computeArea () { return PI*radius*radius; } double oneOverRadius() { return 1.0/radius; } void setRadius (double r) { radius = r; } } double getRadius () { return radius; }

Wait! Another problem!

public class CircleTest { public static void main (String[] args) { Circle c = new Circle(); c.setRadius (0.0); Here is the problem now… System.out.println (c.oneOverRadius()); } } 93

This problem is easily fixed

 Change the setRadius() method to the following void setRadius (double r) { if ( r > 0.0 ) radius = r; else radius = 1.0; }  Now there is (almost) no way for code outside the Circle class to change the radius to zero  This is the purpose of mutators  To prevent changing the fields to a “bad” value  We’ll see another motivation in a bit 94

Visibilities in Java

 There are four visibilities:  private : Only code within the same class can access the field or method  Note: “access” means reading or writing the field, or invoking the method  public : Any code, anywhere, can access the field or method  protected : Used with inheritance  We won’t get to that this semester  default : Almost the same as public    This is the default (duh!) Note that it can’t be specified like the others Also called ‘package’ 95

A few notes on visibilities

 You can  NOT specify visibilities for method variables Any method variable can only be accessed within that method  Think of it as public within the method (after it’s defined) and private outside the method  You can also specify visibilities for methods and classes  We will see this a bit in this course 96

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3.

4.

5.

How well do you feel you understand visibilities?

Very well! This stuff is easy!

Fairly well – with a little review, I’ll be good Okay. It’s not great, but it’s not horrible, either Not well. I’m kinda confused Not at all. I’m soooooo lost.

20% 20% 20% 20% 20% V er y w el l! T hi F s ai st rly uf w f i el ...

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97

DeCSS: The program

#include typedef unsigned int uint; char ctb[512]="33733b2663236b763e7e362b6e2e667bd393db0643034b96de9ed60b4e0e4\ 69b57175f82c787cf125a1a528fca8ac21fd999d10049094190d898d001480840913d7d35246\ d2d65743c7c34256c2c6475dd9dd5044d0d4594dc9cd4054c0c449559195180c989c11058185\ 081c888c011d797df0247074f92da9ad20f4a0a429f53135b86c383cb165e1e568bce8ec61bb\ 3f3bba6e3a3ebf6befeb6abeeaee6fb37773f2267276f723a7a322f6a2a627fb9f9b1a0e9a9e\ 1f0b8f8b0a1e8a8e0f15d1d5584cd8dc5145c1c5485cc8cc415bdfdb5a4edade5f4bcfcb4a5e\ cace4f539793120692961703878302168286071b7f7bfa2e7a7eff2bafab2afeaaae2ff"; typedef unsigned char uchar;uint tb0[11]={5,0,1,2,3,4,0,1,2,3,4};uchar* F=NULL; uint lf0,lf1,out;void ReadKey(uchar* key){int i;char hst[3]; hst[2]=0;if(F==\ NULL){F=malloc(256);for(i=0;i<256;i++){hst[0]=ctb[2*i];hst[1]=ctb[2*i+1];F[i]=\ strtol(hst,NULL,16);}}out=0;lf0=(key[1]<<9)|key[0]|0x100;lf1=(key[4]<<16)|(key\ [3]<<8)|key[2];lf1=((lf1&0xfffff8)<<1)|(lf1&0x7)|0x8;}uchar Cipher(int sw1,\ int sw2){int i,a,b,x=0,y=0;for(i=0;i<8;i++){a=((lf0>>2)^(lf0>>16))&1;b=((lf1\ >>12)^(lf1>>20)^(lf1>>21)^(lf1>>24))&1;lf0=(lf0<<1)|a;lf1=(lf1<<1)|b;x=(x>>1)\ |(a<<7);y=(y>>1)|(b<<7);}x^=sw1;y^=sw2;return out=(out>>8)+x+y;} void \ CSSdescramble(uchar *sec,uchar *key){uint i;uchar *end=sec+0x800;uchar KEY[5]; for(i=0;i<5;i++)KEY[i]=key[i]^sec[0x54+i];ReadKey(KEY);sec+=0x80;while(sec!=\ end)*sec++=F[*sec]^Cipher(255,0);}void CSStitlekey1(uchar *key,uchar *im) {uchar k[5];int i; ReadKey(im);for(i=0;i<5;i++)k[i]=Cipher(0,0);for(i=9;i>=0;\ i- )key[tb0[i+1]]=k[tb0[i+1]]^F[key[tb0[i+1]]]^key[tb0[i]];}void CSStitlekey2\ (uchar *key,uchar *im){uchar k[5];int i;ReadKey(im);for(i=0;i<5;i++)k[i]=\ Cipher(0,255);for(i=9;i>=0;i- )key[tb0[i+1]]=k[tb0[i+1]]^F[key[tb0[i+1]]]^key\ [tb0[i]];}void CSSdecrypttitlekey(uchar *tkey,uchar *dkey){int i;uchar im1[6]; uchar im2[6]={0x51,0x67,0x67,0xc5,0xe0,0x00};for(i=0;i<6;i++)im1[i]=dkey[i]; CSStitlekey1(im1,im2);CSStitlekey2(tkey,im1);} 98

DeCSS: The shirt (and tie!)

99

How to decrypt a DVD: in haiku form.

(Thanks, Prof. D. S. T.) ----------------------- (I abandon my exclusive rights to make or perform copies of this work, U. S. Code Title Seventeen, section One Hundred and Six.) Muse! When we learned to count, little did we know all the things we could do some day by shuffling those numbers: Pythagoras said "All is number" long before he saw computers and their effects, or what they could do

DeCSS: The poem

Table Zero is: Five, zero, one, two, three, four, oh, one, two, three, four.

Table One is long: two to the eighth power bytes.

Ready? Here they are: Fifty one; then one hundred fifteen; fifty nine; thirty eight; ninety nine; thirty five; one hundred seven; one hundred eighteen; sixty two; one hundred twenty six; fifty four; forty three; one hundred ten; then 100

DeCSS: The number

The world’s first illegal prime number:

4856507896573978293098418946942861377074420873513579240196520736686985134010472 3744696879743992611751097377770102744752804905883138403754970998790965395522701 1712157025974666993240226834596619606034851742497735846851885567457025712547499 9648219418465571008411908625971694797079915200486670997592359606132072597379799 3618860631691447358830024533697278181391479795551339994939488289984691783610018 2597890103160196183503434489568705384520853804584241565482488933380474758711283 3959896852232544608408971119771276941207958624405471613210050064598201769617718 0947811362200272344827224932325954723468800292777649790614812984042834572014634 8968547169082354737835661972186224969431622716663939055430241564732924855248991 2257394665486271404821171381243882177176029841255244647445055834628144883356319 0272531959043928387376407391689125792405501562088978716337599910788708490815909 7548019285768451988596305323823490558092032999603234471140776019847163531161713 0785760848622363702835701049612595681846785965333100770179916146744725492728334 8691600064758591746278121269007351830924153010630289329566584366200080047677896 7984382090797619859493646309380586336721469695975027968771205724996666980561453 3820741203159337703099491527469183565937621022200681267982734457609380203044791 2277498091795593838712100058876668925844870047077255249706044465212713040432118 2610103591186476662963858495087448497373476861420880529443 101

DeCSS: The images

102

DeCSS: The recordings

 All this info from http://www-2.cs.cmu.edu/~dst/DeCSS/Gallery/  Or do a Google search for “decss gallery” 103

DeCSS: The movie

104

Overriding methods (and constructors)

 Consider the following code: Creates a Circle of radius 1.0

 Circle c1 = new Circle (); Circle c2 = new Circle (2.0); Creates a Circle of radius 2.0

Java knows which constructor to call by the list of parameters   This is called “overloading” Meaning it means multiple things, depending on the context  We’ve seen overloading before:  3+4 Performs integer addition   3.0+4.0

“3”+”4” Performs floating-point addition Performs string concatenation  The ‘+’ operator is overloaded 105

Overriding methods (and constructors), take 2

 The following Circle constructors would not be allowed:  We are assuming PI is not final for this example public Circle() { radius = 1.0; } public Circle (double r) { radius = r; } public Circle (double p) { PI = p; } When Circle(1.0) is called, which one is meant?

106

Using mutators in the constructor

 Our second constructor has a problem: public Circle (double r) { radius = r; }  Consider the following code: Circle c = new Circle (0.0); System.out.println ( c.oneOverRadius() ); The method is dividing by zero (again) 107

Using mutators in the constructor

 This is easily fixed!

 Our revised constructors: public Circle() { setRadius (1.0); } public Circle (double r) { setRadius (r); }  The mutator will properly set the radius (and won’t set it to zero) 108

Why we always use the mutators

 Consider a modified version of our circle class: class Circle { double radius; double diameter; String size; // ...

 Our mutator now looks like this:  That’s a lot of code to copy if you decide not to call the mutator!

void setRadius (double r) { if ( radius <= 0.0 ) radius = 1.0; else radius = r; diameter = 2*radius; if ( radius < 1.0 ) size = “small”; else if ( radius < 5.0 ) size = “medium”; else if ( radius < 10.0 ) size = “large”; else size = “huge”; } 109

Google April Fools Day Jokes (2007)

http://www.google.com/tisp/

http://mail.google.com/mail/help/paper/

111

An aside: scoping issues

 Consider this class: class Foo { int x = 0; public Foo (int x) { x = x; } }    Which x is being referred to in the constructor?

Remember that Java will use the most recent x So this doesn’t set the instance variable!

 Instead, it sets the parameter equal to itself 113

An aside: scoping issues

 Let’s modify that class:  Another solution: class Foo { int x = 0; public Foo (int x) { this.x = x; } } class Foo { int x = 0; public Foo ( int y ) { x = y; } }   The ‘this.x’ means instance variable x  the And the ‘x’ means the parameter Now this does the right thing   By renaming the parameter, we achieve the same effect This very relevant to HW 7!

114

Back to the static discussion

 Remember that there is one (and only one) static PI field, regardless of how many objects are declared  Consider the following method: double getPI() { return PI; }  It doesn’t read or modify the “state” of any object  In this example, it doesn’t read/write the radius  In fact, that particular method doesn’t care anything about the objects declared  It’s only accessing a static field 115

Make getPI() static

 Consider the following: static double getPI() { return PI; }  As the method is static, it can ONLY access static fields  A static method does not care about the “state” of an object  Examples: Math.sin(), Math.tan(), Math.cos()  They don’t care about the state of any Math object  They only perform the computation 116

Invoking static methods

 As with static fields, they can be called using either an object or the class name: Circle c = new Circle(); System.out.println (c.getPI()); System.out.println (Circle.getPI());  Static methods are also called class methods 117

static methods and non static fields

 Consider the following (illegal) Circle method: static double getRadius() { return radius; }  And the code to invoke it: public static void main (String[] args) { Circle c1 = new Circle(); Circle c2 = new Circle(); Circle c3 = new Circle(); Circle c4 = new Circle(); System.out.println (Circle.getRadius()); } 118

What happening in memory

 Which radius field does Circle.getRadius() want?

c1 Circle - radius = 1.0

c2 Circle - radius = 1.0

c3 … - radius = 1.0

Circle - radius = 1.0

PI 3.1415926536

119

The main static lesson

 A static method cannot access or modify the state of the object it is a part of  If you remember nothing else about static methods, remember this!

120

static and non static rules

    Non-static fields and methods can object name Static fields and methods can be accessed by class name or the object name Non-static methods can refer to fields ONLY BOTH be accessed by the EITHER the static and non-static Static methods can are part of ONLY access static fields of the class they 121

1.

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3.

4.

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How well do you feel you understand static-ness?

Very well! This stuff is easy!

Fairly well – with a little review, I’ll be good Okay. It’s not great, but it’s not horrible, either Not well. I’m kinda confused Not at all. I’m soooooo lost.

20% 20% 20% 20% 20% V er y w el l! T hi F s ai st rly uf w f i el ...

l – O w ka y.

ith I a t’s li n tt.

ot N .

g ot re w at el , b l. I’ u.

m N ..

k ot in a da t a c ll.

...

I ’m s oo oo o.

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122

Very unofficial demotivators

123

Back to our main() method

public static void main (String[] args) We’ll learn about arrays in chapter 8 The method does not return a value Any code anywhere can call this method It’s a static method: •Can’t access non-static fields or methods directly •Can be called only by the class name 124

Implications of main() being static

 It can call other static methods within the same class class StaticMethods { static void method1() { System.out.println

(“hi!”) ; } public static void main (String args[]) { method1(); } }  Note that we didn’t have to prefix method1() with a object  Java assumes that it is in the same class 125

Another use of static methods

 Let’s say we want each Circle object to have a unique identifier  The identifier will be a positive integer  So in the Circle class, we add a  int id = 0;  instance variable: Thus, each Circle object will have it’s own id number  To keep track of the last assigned id number, we will use a class variable  static int lastAssignedID = 0;  Thus, for all Circle objects created, we will have a lastAssignedID field single 126

Circle ID numbers

 We can then create a method to obtain a unique ID number: public static int getID() { return ++lastAssignedID; }  This method is static, and only can access static fields  In our Circle constructors, we put the following line:  id = getID(); 127

Today’s demotivators

128

Debugging Java Code

129

Debugging Java code

 In Main.java:  In Error1.java: public class Main { public static void main (String args[]) { Error1 e1 = new Error1(); e1.foo(); e1.bar(); } }

This will cause a null pointer exception!

public class Error1 { public Error1() { } public void foo() { String s = null; System.out.println

(s.substring(5)); } } public void bar() { foo(); } 130

Program Demo

Errors/Main.java

131

What the error output means

 The error output: Exception in thread "main" java.lang.NullPointerException

at Error1.foo(Error1.java:6) at Main.main(Main.java:4)  This means that:    A null point exception happened In the Error1.foo() method on line 6 of Error1.java

And that was called from Main.main() on line 4 of Main.java

 Note that the top two lines tell the most useful information  So we comment out the e1.foo() call in main() 132

Debugging Java code

 In Main.java:  In Error1.java: public class Main { public static void main (String args[]) { Error1 e1 = new Error1(); //e1.foo(); e1.bar(); } } public class Error1 { public Error1() { } public void foo() { String s = null; System.out.println

(s.substring(5)); } } public void bar() { foo(); } 133

Program Demo

Errors/Main.java

134

What the error output means

 The error output: Exception in thread "main" java.lang.NullPointerException

at Error1.foo(Error1.java:6) at Error1.bar(Error1.java:10) at Main.main(Main.java:5)  This means that:  A null point exception happened    In the Error1.foo() method on line 6 of Error1.java

And that was called from Error1.bar() on line 10 of Error.java

And that was called from Main.main() on line 5 of Main.java

 Again, note that the top two lines tell the most useful information 135

Honda’s best commercial

cog.mov

136

More on methods

137

Calling a method

 Consider two Strings: String s = String t = “foo” ; “bar” ;  Calling s.substring(2) is different than calling t.substring(2)  Why?

  Because of the  object it is being called out of The method works the same in both cases (returns the substring)  But it returns different results Whenever we are calling a method, we also need to know which object we are calling it out of 138

Return values

 Many methods return a value  Math.cos()  String.valueOf()  Consider: double d = Math.cos (90 * Math.PI/180.0);  Let’s consider the Math.cos() method public double cos (double a) { double c = 0.0; // compute cos somehow into a variable c return c ; }  The value c in the cos() method is copied into d 139

The return keyword

 The return keyword does a few things:  Immediately terminate the current method  Pass the value back to whoever called the method  You can have a return anywhere you want  Inside loops, ifs, etc.

 You can have as may returns as you want as well: public String foo (int x) { if ( x == 1 ) return “one” ; else if ( x == 2 ) return else return “other” ; “two” ; } 140

More on returns

 Consider this class: public class Foo { // Default constructor omitted on this slide public String bar (String s) { String t = return t; “CS 101 ” + “ ” + s; } }  And the code to invoke it: Foo w = new Foo(); String x = “rules” ; String y = foo.bar (x); System.out.println (y);  What happens in memory?

141

“rules” ; w this Foo + Foo() + bar (String s): String + … } t y x s 101 ” “rules" “CS 101 rules" 142

Returning an object from a method

 We could rewrite our bar() method a number of ways: public String bar (String s) { String t = “CS 101 ” + “ ” + s; return t; } public String bar (String s) { return new String (“CS 101 ” + } “ ” + s); public String bar (String s) { return “CS 101 ” + “ ” + s; } 143

Returning a non-object from a method

 In other words, returning a primitive type from a method public foo () { // ...

return x + y; }  This method evaluates x+y, then returns that value to the caller 144

Chapter 2: Computer bugs

145

Off to arrays….

146

Yale vs. Harvard

147

Rational class

148

What we’ve seen so far

 An example of creating a class  Car  Up next: another example  Rational    Represents rational numbers A rational number is any number that can be expressed as a fraction Both the numerator and denominator must be integers!

 Discussed in section 4.8 of the textbook 149

What properties should our Rational class have?

 The numerator (top part of the fraction)  The denominator (bottom part of the fraction)  Not much else… 150

What do we want our Rational class to do?

 Obviously, the ability to create new Rational objects  Setting the numerator and denominator  Getting the values of the numerator and denominator  Perform basic operations with rational numbers: + - * /  Ability to print to the screen 151

Our first take at our Rational class

 Our first take Rational - numerator = 0 - denominator = 0 public class Rational { private int numerator; private int denominator; //...

} + …  This does not represent a valid Rational number!

 Why not?

 Java initializes instance variables to zero   Both the numerator and denominator are thus set to zero 0/0 is not a valid number!

152

Our next take at our Rational class

 Our next take public class Rational { private int numerator = 0 ; private int denominator = 1 ; //...

} Rational - numerator = 0 - denominator = 1  We’ve defined the attributes of our class + …  Next up: the behaviors 153

The default constructor

 Ready?

public Rational() { } Rational - numerator = 0 - denominator = 1 + Rational() + …  Yawn!

   Note that we could have initialized the instance variables here instead The default constructor is called that because, if you don’t specify ANY constructors, then Java includes one by default Default constructors do not take parameters 154

The specific constructor

 Called the specific constructor because it is one that the user specifies  They take one or more parameters public Rational (int num, int denom) { setNumerator (num); setDenominator (denom); Rational } - numerator = 0 - denominator = 1  Note that the specific constructor calls the mutator methods instead of setting the instance variables directly  We’ll see why later + Rational() + Rational (int num, int denom) + … 155

Accessor methods

 Our two accessor methods: public int getNumerator () { return numerator; } public int getDenominator () { return denominator; } Rational - numerator = 0 - denominator = 1 + Rational() + Rational (int num, int denom) + int getNumerator() + int getDemonimator() + … 156

Mutator methods

 Our two mutator methods: public void setNumerator (int towhat) { numerator = towhat; } public void setDenominator (int towhat) { denominator = towhat; } 157

Rational addition

 How to do Rational addition:

a b

c d

ad

bc bd

 Our add() method: public Rational add (Rational other) { } 158

The this keyword

this

Returns:

Rational - numerator = 5 - denominator = 6 + Rational () + Rational (int n, int d) + Rational add (Rational other) + … + Rational add (Rational other) + … Rational - numerator = 1 - denominator = 3 + Rational () + Rational (int n, int d) + Rational add (Rational other) + … 159

The this keyword

 this is a reference to whatever object we are currently in  Will not work in static methods   We’ll see why later Note that the main() method is a static method  While we’re at it, when defining a class, note that NONE of the methods so far were static 160

Rational addition

 How to do Rational addition:

a b

c d

ad

bc bd

 Our add() method: public Rational add (Rational other) { int a = this.getNumerator(); int b = this.getDenominator(); int c = other.getNumerator(); int d = other.getDenominator(); return new Rational (a*d+b*c, b*d); } 161

Rational addition

 The following method is equivalent:  Our add() method: public Rational add (Rational other) { int a = getNumerator(); int b = getDenominator(); int c = other.getNumerator(); int d = other.getDenominator(); return new Rational (a*d+b*c, b*d); } 162

Rational addition

 The following method is equivalent, but not preferred:  Our add() method: public Rational add (Rational other) { int a = numerator; int b = denominator; int c = other.numerator; int d = other.nenominator; return new Rational (a*d+b*c, b*d); } 163

Rational addition

 The following method is equivalent, but not preferred:  Our add() method: public Rational add (Rational other) { int a = this.

numerator; int b = this.

denominator; int c = other.numerator; int d = other.nenominator; return new Rational (a*d+b*c, b*d); } 164

Rational subtraction

 How to do Rational subtraction:

a b

c d

ad

bc bd

 Our subtract() method: public Rational subtract (Rational other) { int a = this.getNumerator(); int b = this.getDenominator(); int c = other.getNumerator(); int d = other.getDenominator(); return new Rational ( a*d-b*c, b*d ); } 165

Rational multiplication

 How to do Rational multiplication:

a b c

*

d

ac bd

 Our multiply() method: public Rational multiply (Rational other) { int a = this.getNumerator(); int b = this.getDenominator(); int c = other.getNumerator(); int d = other.getDenominator(); return new Rational ( a*c, b*d ); } 166

Rational division

 How to do Rational division:

a b

c d

ad bc

 Our divide() method: public Rational divide (Rational other) { int a = this.getNumerator(); int b = this.getDenominator(); int c = other.getNumerator(); int d = other.getDenominator(); return new Rational ( a*d, b*c ); } 167

Printing it to the screen

 If we try printing a Rational object to the screen: Rational r = new Rational (1,2); System.out.println (r);  We get the following: Rational@82ba41  Ideally, we’d like something more informative printed to the screen  The question is: how does Java know how to print a custom class to the screen?

168

The toString() method

 When an object is put into a print statement: Rational r = new Rational (1,2); System.out.println (r);  Java will try to call the toString() method to covert the object to a String  If the toString() method is not found, a default one is included  Hence the Rational@82ba41 from the previous slide  So let’s include our own toString() method 169

The toString() method

 Our toString() method is defined as follows: public String toString () { return getNumerator() + "/" + getDenominator(); }  Note that the prototype must ALWAYS be defined as shown  The prototype is the ‘ public String toString() ’ 170

Printing it to the screen

 Now, when we try printing a Rational object to the screen: Rational r = new Rational (1,2); System.out.println (r);  We get the following: 1/2  Which is what we wanted!

 Note that the following two lines are (mostly) equivalent: System.out.println (r); System.out.println (r.toString()); 171

Our full Rational class

Rational - numerator = 0 - denominator = 1 + Rational() + Rational (int num, int denom) + int getNumerator() + int getDemonimator() + void setNumerator (int num) + void setDenominator (int denom) + Rational add (Rational other) + Rational subtract (Rational other) + Rational multiply (Rational other) + Rational divide (Rational other) + String toString() 172

Our Rational class in use, part 1 of 4

  This code is in a main() method of a RationalDemo class First, we extract the values for our first Rational object: Scanner stdin = new Scanner(System.in); System.out.println(); // extract values for rationals r and s Rational r = new Rational(); System.out.print("Enter numerator of a rational number: "); int a = stdin.nextInt(); System.out.print("Enter denominator of a rational number: "); int b = stdin.nextInt(); r.setNumerator(a); r.setDenominator(b); 173

Our Rational class in use, part 2 of 4

 Next, we extract the values for our second Rational object: Rational s = new Rational(); System.out.print("Enter numerator of a rational number: "); int c = stdin.nextInt(); System.out.print("Enter denominator of a rational number: “) ; int d = stdin.nextInt(); s.setNumerator(c); s.setDenominator(d);  Notice that I didn’t create another Scanner object!

  Doing so would be bad I used the same one 174

Our Rational class in use, part 3 of 4

 Next, we do the arithmetic: // operate on r and s Rational sum = r.add(s); Rational difference = r.subtract(s); Rational product = r.multiply(s); Rational quotient = r.divide(s); 175

Our Rational class in use, part 4 of 4

 Lastly, we print the results // display operation results System.out.println("For r = " + r.toString() + " and s = " System.out.println(" + s.toString()); r + s = " + sum.toString()); System.out.println(" System.out.println(" System.out.println(" System.out.println(); r - s = " + difference.toString()); r * s = " + product.toString()); r / s = " + quotient.toString()); 176

A demo of our Rational class

RationalDemo.java

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Other things we might want to add to our Rational class

 The ability to reduce the fraction  So that 2/4 becomes 1/2  Not as easy as it sounds!

 More complicated arithmetic  Such as exponents, etc.

 Invert  Switches the numerator and denominator  Negate  Changes the rational number into its (additive) negation  We won’t see any of that here 178

a) b) c) d) e)

How well do you feel you understand the Rational class?

Very well! This stuff is so easy.

With a little review, I’ll be good.

Not very well at all.

I’m so lost. What’s a class again?

I’d rather not answer this question, thanks.

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