Fraction.java

$/**$

Fractions

A unit fraction is a fraction of the form $1/$r$,$ where r is a positive non$-$zero integer.

An Egyptian fraction is a sum of distinct positive unit fractions, so called

because this is the manner in which ancient Egyptians expressed fractions in general.

For example, they would have written $3/5$ as $1/2+1/10.$

Complete the following program that, given a set of pseudo$-$Egyptian fractions

$($i$.$e$.,$ a set of distinct positive or negative unit fractions$),$ calculates the

sum and expresses it in its simplest $($i$.$e$.,$ reduced$)$ form by finding the greatest

common denominator.

This is not the same as taking a fraction and determining the set of unit fractions.

Each line of data will contain a set of numbers each of which is separated by whitespace.

They consist of a sequence of m distinct positive or negative integers which are

to be interpreted as representing the denominators of the Egyptian fraction.

For example,

Input Output

$2103/5$

$535223/70$

$981212937/588$

$*/$

import java.util.Scanner;

public class Fraction $\{$

private int numerator;

private int denominator;

~

public Fraction$()\{$

numerator $=0$;

denominator $=1$;

$\}$

public Fraction$($int denominator$)\{$

this$(1,$ denominator$)$;

$\}$

public Fraction$($int numerator, int denominator$)\{$

$\}$

public Fraction add$($Fraction other$)\{$

$\}$

public String toString$()\{$

$//$ Return a string in the form numerator$/$denominator

$\}$

public static void main$($String$[]$ args$)\{$

int denominator;

Fraction fraction $=$ new Fraction$()$; $//$ Create a zero fraction

String data;

Scanner scanner $=$ new Scanner$($

System.in$)$;

data $=$ scanner.nextLine$()$;

Scanner stream $=$ new Scanner$($data$)$;

while $($stream$.$hasNext$())\{$

denominator $=$ stream.nextInt$()$;

fraction.add$($new Fraction$($denominator$))$;

$\}$

System.out.println$($fraction$.$toString$())$;

$\}$

$\}$