## Thursday, 22 December 2016

### Chapter 13 Exercise 18, Introduction to Java Programming, Tenth Edition Y. Daniel LiangY.

13.18 (Use the Rational class)
Write a program that computes the following
summation series using the Rational class:

You will discover that the output is incorrect because of integer overflow (too large).
To fix this problem, see Programming Exercise 13.15.

import java.math.BigDecimal;
import java.math.RoundingMode;

public class BigRational extends Number implements Comparable<BigRational> {
// Data fields for numerator and denominator
private BigDecimal numerator = BigDecimal.ZERO;
private BigDecimal denominator = BigDecimal.ONE;

/** Construct a rational with default properties */
public BigRational() {
this(BigDecimal.ZERO, BigDecimal.ONE);
}

/** Construct a rational with specified numerator and denominator */
public BigRational(BigDecimal numerator, BigDecimal denominator) {
BigDecimal gcd = gcd(numerator, denominator);
this.numerator = ((denominator.compareTo(BigDecimal.ZERO) > 0) ? BigDecimal.ONE : new BigDecimal(-1)).multiply(numerator).divide(gcd);
this.denominator = denominator.abs().divide(gcd);
}

public BigRational(String decimal) {

int index = (decimal.contains(".")) ? decimal.indexOf('.') : decimal.indexOf('/');
BigDecimal d;
BigDecimal n;
// if string is in decimal form
if (decimal.contains(".")) {
int power = decimal.substring(index + 1, decimal.length()).length();
d = new BigDecimal(Math.pow(10,power));
n = new BigDecimal(new StringBuilder(decimal).deleteCharAt(index).toString());
} else {
// if string contains '/'
n = new BigDecimal(decimal.substring(0, index));
d = new BigDecimal(decimal.substring(index + 1, decimal.length()));
}

BigDecimal gcd = gcd(n, d);
this.numerator = ((d.compareTo(BigDecimal.ZERO) > 0) ? BigDecimal.ONE : new BigDecimal(-1)).multiply(n).divide(gcd);
this.denominator = d.abs().divide(gcd);

}

/** Find GCD of two numbers */
private static BigDecimal gcd(BigDecimal n, BigDecimal d) {
BigDecimal n1 = n.abs();
BigDecimal n2 = d.abs();

BigDecimal remainder = n1.remainder(n2);
while (remainder.compareTo(BigDecimal.ZERO) > 0) {
n1 = n2;
n2 = remainder;
remainder = n1.remainder(n2);
}

return n2;
}

/** Return numerator */
public BigDecimal getNumerator() {
return numerator;
}

/** Return denominator */
public BigDecimal getDenominator() {
return denominator;
}

/** Add a rational number to this rational */
BigDecimal n1 = numerator.multiply(secondBigRational.getDenominator());
BigDecimal n2 = denominator.multiply(secondBigRational.getNumerator());

BigDecimal d = denominator.multiply(secondBigRational.getDenominator());
return new BigRational(n, d);
}

/** Subtract a rational number from this rational */
public BigRational subtract(BigRational secondBigRational) {
BigDecimal n1 = numerator.multiply(secondBigRational.getDenominator());
BigDecimal n2 = denominator.multiply(secondBigRational.getNumerator());
BigDecimal n = n1.subtract(n2);

BigDecimal d = denominator.multiply(secondBigRational.getDenominator());
return new BigRational(n, d);
}

/** Multiply a rational number to this rational */
public BigRational multiply(BigRational secondBigRational) {
BigDecimal n = numerator.multiply(secondBigRational.getNumerator());
BigDecimal d = denominator.multiply(secondBigRational.getDenominator());
return new BigRational(n, d);
}

/** Divide a rational number from this rational */
public BigRational divide(BigRational secondBigRational) {
BigDecimal n = numerator.multiply(secondBigRational.getDenominator());
BigDecimal d = denominator.multiply(secondBigRational.numerator);
return new BigRational(n, d);
}

@Override
public String toString() {
if (denominator.equals(BigDecimal.ONE))
return numerator + "";
else
return numerator + "/" + denominator;
}

@Override // Override the equals method in the Object class
public boolean equals(Object other) {
if ((this.subtract((BigRational)(other))).getNumerator().equals(BigDecimal.ZERO))
return true;
else
return false;
}

@Override // Implement the abstract intValue method in Number
public int intValue() {
return (int)doubleValue();
}

@Override // Implement the abstract floatValue method in Number
public float floatValue() {
return (float)doubleValue();
}

@Override // Implement the doubleValue method in Number
public double doubleValue() {
return numerator.divide(denominator).doubleValue();
}

public BigDecimal bigDecimalDouble() {
return numerator.divide(denominator, 100, RoundingMode.HALF_DOWN);
}

@Override // Implement the abstract longValue method in Number
public long longValue() {
return (long)doubleValue();
}

@Override // Implement the compareTo method in Comparable
public int compareTo(BigRational o) {
if (this.subtract(o).getNumerator().compareTo(BigDecimal.ZERO) > 0)
return 1;
else if (this.subtract(o).getNumerator().compareTo(BigDecimal.ZERO) < 0)
return -1;
else
return 0;
}
}


public class Rational extends Number implements Comparable<Rational> {
// Data fields for numerator and denominator
private long[] r = new long[2];
private static int NUMERATOR = 0;
private static int DENOMINATOR = 1;

/** Default constructor */
public Rational() {
this(0, 1);
}

/** Construct a rational with specified numerator and denominator */
public Rational(long numerator, long denominator) {
long gcd = gcd(numerator, denominator);
r[NUMERATOR] = ((denominator > 0) ? 1 : -1) * numerator / gcd;
r[DENOMINATOR] = Math.abs(denominator) / gcd;
}

/** Find GCD of two numbers */
private long gcd(long n, long d) {
long t1 = Math.abs(n);
long t2 = Math.abs(d);
long remainder = t1 % t2;

while (remainder != 0) {
t1 = t2;
t2 = remainder;
remainder = t1%t2;
}

return t2;
}

/** Return numerator */
public long getNumerator() {
return r[NUMERATOR];
}

/** Return denominator */
public long getDenominator() {
return r[DENOMINATOR];
}

/** Add a rational number to this rational */
long n = r[NUMERATOR] * secondRational.getDenominator() +
r[DENOMINATOR] * secondRational.getNumerator();
long d = r[DENOMINATOR] * secondRational.getDenominator();
return new Rational(n, d);
}

/** Subtract a rational number from this rational */
public Rational subtract(Rational secondRational) {
long n = r[NUMERATOR] * secondRational.getDenominator()
- r[DENOMINATOR] * secondRational.getNumerator();
long d = r[DENOMINATOR] * secondRational.getDenominator();
return new Rational(n, d);
}

/** Multiply a rational number to this rational */
public Rational multiply(Rational secondRational) {
long n = r[NUMERATOR] * secondRational.getNumerator();
long d = r[DENOMINATOR] * secondRational.getDenominator();
return new Rational(n, d);
}

/** Divide a rational number from this rational */
public Rational divide(Rational secondRational) {
long n = r[NUMERATOR] * secondRational.getDenominator();
long d = r[DENOMINATOR] * secondRational.r[NUMERATOR];
return new Rational(n, d);
}

@Override
public String toString() {
if (r[DENOMINATOR] == 1)
return r[NUMERATOR] + "";
else
return r[NUMERATOR] + "/" + r[DENOMINATOR];
}

/** Override the equals method in the Object class */
public boolean equals(Object parm1) {
return (this.subtract((Rational) (parm1))).getNumerator() == 0;
}

/** Override the hashCode method in the Object class */
public int hashCode() {
return new Double(this.doubleValue()).hashCode();
}

/** Override the abstract intValue method in java.lang.Number */
public int intValue() {
return (int)doubleValue();
}

/** Override the abstract floatValue method in java.lang.Number */
public float floatValue() {
return (float)doubleValue();
}

/** Override the doubleValue method in java.lang.Number */
public double doubleValue() {
return r[NUMERATOR] * 1.0 / r[DENOMINATOR];
}

/** Override the abstract longValue method in java.lang.Number */
public long longValue() {
return (long)doubleValue();
}

@Override
public int compareTo(Rational o) {
if ((this.subtract(o)).getNumerator() > 0)
return 1;
else if ((this.subtract(o)).getNumerator() < 0)
return -1;
else
return 0;
}
}


import java.math.BigDecimal;

public class Exercise_18 {

public static void main(String[] args) {

// using rational class
Rational total = new Rational();
for (int i = 1; i < 100; i++) {
total = total.add(new Rational(i, i + 1));
if (i < 10) {
System.out.println("total = " + total);
}

}
System.out.println(total + " = " + total.doubleValue());

// using BigRational class
BigRational r = new BigRational( BigDecimal.ZERO, new BigDecimal(1));

for (int i = 1; i < 100; i++) {
r = r.add(new BigRational(new BigDecimal(i), new BigDecimal(i + 1)));
if (i < 10) {
System.out.println("r = " + r);
}

}
System.out.println("BigRational total = " + r);
System.out.println("BigRational decimal form = " + r.bigDecimalDouble());
}

}