The class Fraction:
Putting all we have seen together
Bruce Eckel, Thinking in Java, 4th edition,
PrenticeHall, New Jersey, cf.
http://mindview.net/Books/TIJ4
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José Valente de Oliveira
4-1
The class Fraction
„
Problem: Develop a class Fraction representing rational
numbers.
„
Representation:
n – numerator
d – denominator
d>0
mdc (|n| , d ) = 1
„
Class invariant
(condição invariante de instância)
(máximo divisor comum – gcd in English) Ex. 2/4 == 1/2
Operations
n1/d1 + n2/d2 = (n1d2 + n2d1) / (d1 * d2);
n1/d1 – n2/d2 = (n1d2 - n2d1) / (d1 * d2);
n1/d1 * n2/d2 = n1 * n2 / (d1 * d2);
(n1/d1) / (n2/d2) = n1* d2 / (n2* d1); with n2 ≠ 0
(n1/d1) == (n2/d2) <=> n1 == n2 and d1 == d2
n1/d1 < n2/d2 <=> n1d2 < n2d1
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A possible client
class Main {
public static void main(String [] args) {
Fraction f = new Fraction(4, 6);
Fraction g = new Fraction(1, -2);
Fraction s = new Fraction();
s = f.add(g);
boolean b = f.less(g);
System.out.println(s);
WeSystem.out.println(b);
would like to use operators
} such as +, < but Java does not
}
support operator overloading (yet)
Class invariants
„
Where to enforce class invariants?
‰
„
right when the object is created: in the constructor
Additionally any method that modifies instance variables
directly should not be defined
public int setNumerator (int n) { num = n; }
If such methods must be implement (avoid them if
possible) they must also enforce class invariants, when
modifying instance variables.
2
/** @version 1.0 */
public class Fraction {
private int num, den;
public Fraction() { this(0); }
public Fraction(int n) { num= n; den = 1; }
public Fraction (int n, int d) {
if (d == 0) {
System.err.print("Fraction.denominator() cannot be zero");
System.exit(1);
// We will have to improve this later
}
if (d < 0) {
this.num = -n;
this.den = -d;
} else {
num = n;
// same as this.num =n;
den = d;
}
int k =mdc(Math.abs(num), den);
mdc (|n| , d ) = 1
num /= k;
den /= k;
eg.: 8/16 == 1/2,
}
/** @version 1.0 */
public class Fraction {
private int num, den;
public Fraction() { this(0); }
public Fraction(int n) { num= n; den = 1; }
public Fraction (int n, int d) {
if (d ==0) {
System.err.print("Fraction.denominator() cannot be zero");
System.exit(1);
// We will have to improve this later
}
Referencing the receiver
if (d<0) {
this.num = -n;
this.den = -d;
} else {
num = n;
// same as this.num =n;
den = d;
}
int k =mdc(Math.abs(num), den);
num /= k;
den /= k;
}
d>0
k=8
with this
3
/**
Calcula o máximo divisor comum dos seus parâmetros
@param m
inteiro positivo
@param n
inteiro positivo
@pre-condition: m >0 e n >0
@return
inteiro com o máximo divisor comum entre m e n
*/
private int mdc( int m , int n ){
int r;
while (( r = m % n ) != 0 ) {
m = n;
n = r;
}
return n;
}
} // end of class
/** retorna uma nova instância da classe com o resultado da
multiplicação do recetor this pelo argumento that
@param that uma Fraction
@return n1/d1 * n2/d2 = n1n2 / (d1 * d2);
@version 1.0
*/
By creating a new
public Fraction mult(Fraction that) {
object, the class
int n = this.num * that.num;
invariant is enforced
// ou int n = num * that.num;
int d = this.den * that.den;
return new Fraction(n, d);
}
class Main {
public static void main(String [] args) {
//..
Fraction s = f.mult(g);
}
}
[email protected]
José Valente de Oliveira
3-8
4
Where are we so far?
„
Java
‰
‰
‰
‰
A little bit of History
Goals and characteristics
First programs
First classes
„ Control of visibility
„ Sintaxe
„ Assignment semantics
„ Initialization of objects: constructors
„ References
„ Method overloading
„ Acessing the receiver: the reference this
[email protected]
José Valente de Oliveira
3-9
Check point: what’s the output?
class Point {
private int x,y;
public void setX(int nx)
public int getX()
//…
}
{ x = nx; }
{ return x; }
public class Check{
public static void main(String[] args) {
Point origin = new Point();
Point B = origin;
B.setX(1);
System.out.println(origin.getX());
}
}
[email protected]
José Valente de Oliveira
3-10
5
Scope
„
Each program element has a scope — the context
where it can be referred to using its simple name.
{
„
Elements can have the
same name when their
scope does not overlap.
int k = 0;
// ...
}
for (int k = 0; k< 3; k++) {
// OK! No problem!
}
Scope
„
„
Each program element has a scope — the context
where it can be referred to using its simple name.
{
If the scopes of two
int k = 0;
variables overlap, the
// ...
variable defined in the
inner scope takes
for (int k = 0; k< 3; k++) {
precedence over the
// loop k hides outer k
variable with the same
}
name in the outer scope. }
6
Scope
„
The Scope of an element is determined by the place
where the element is defined.
„
Variables with the same name but different scope
are different variables.
„
Possible scopes in Java:
‰
‰
‰
‰
‰
‰
Local
Function
File
Class
Prototype
Package
class Point {
private int x, y;
public Point(int x, int y) {
// x, y: the same name
// in a different scope
}
// …
}
Scope
„
The Scope of an element is determined by the place
where the element is defined.
„
Variables with the same name but different scope
are different variables.
„
Possible scopes in Java:
‰
‰
‰
‰
‰
‰
Local
Function
File
Class
Prototype
Package
class Point {
private int x, y;
public Point(int x, int y) {
this.x = x;
this.y = y;
}
// …
}
7
Questions to address next
„
Given a problem, how to find the objects that
will provide the solution?
„
What are the rules in an object society?
‰
‰
How are they organized?
How they communicate between which other?
[email protected]
José Valente de Oliveira
4-15
8