I'm trying to work with fractions in Java.
I want to implement arithmetic functions. For this, I will first require a way to normalize the functions. I know I can't add 1/6 and 1/2 until I have a common denominator. I will have to add 1/6 and 3/6. A naive approach would have me add 2/12 and 6/12 and then reduce. How can I achieve a common denominator with the least performance penalty? What algorithm is best for this?
Version 8 (thanks to hstoerr):
Improvements include:
the equals() method is now consistent with the compareTo() method
final class Fraction extends Number {
private int numerator;
private int denominator;
public Fraction(int numerator, int denominator) {
if(denominator == 0) {
throw new IllegalArgumentException("denominator is zero");
}
if(denominator < 0) {
numerator *= -1;
denominator *= -1;
}
this.numerator = numerator;
this.denominator = denominator;
}
public Fraction(int numerator) {
this.numerator = numerator;
this.denominator = 1;
}
public int getNumerator() {
return this.numerator;
}
public int getDenominator() {
return this.denominator;
}
public byte byteValue() {
return (byte) this.doubleValue();
}
public double doubleValue() {
return ((double) numerator)/((double) denominator);
}
public float floatValue() {
return (float) this.doubleValue();
}
public int intValue() {
return (int) this.doubleValue();
}
public long longValue() {
return (long) this.doubleValue();
}
public short shortValue() {
return (short) this.doubleValue();
}
public boolean equals(Fraction frac) {
return this.compareTo(frac) == 0;
}
public int compareTo(Fraction frac) {
long t = this.getNumerator() * frac.getDenominator();
long f = frac.getNumerator() * this.getDenominator();
int result = 0;
if(t>f) {
result = 1;
}
else if(f>t) {
result = -1;
}
return result;
}
}
I have removed all previous versions. My thanks to:
Dave Ray
cletus
duffymo
James
Milhous
Oscar Reyes
Jason S
Francisco Canedo
Outlaw Programmer
Beska
It just so happens that I wrote a BigFraction class not too long ago, for Project Euler problems. It keeps a BigInteger numerator and denominator, so it'll never overflow. But it'll be a tad slow for a lot of operations that you know will never overflow.. anyway, use it if you want it. I've been dying to show this off somehow. :)
Edit: Latest and greatest version of this code, including unit tests is now hosted on GitHub and also available via Maven Central. I'm leaving my original code here so that this answer isn't just a link...
import java.math.*;
/**
* Arbitrary-precision fractions, utilizing BigIntegers for numerator and
* denominator. Fraction is always kept in lowest terms. Fraction is
* immutable, and guaranteed not to have a null numerator or denominator.
* Denominator will always be positive (so sign is carried by numerator,
* and a zero-denominator is impossible).
*/
public final class BigFraction extends Number implements Comparable<BigFraction>
{
private static final long serialVersionUID = 1L; //because Number is Serializable
private final BigInteger numerator;
private final BigInteger denominator;
public final static BigFraction ZERO = new BigFraction(BigInteger.ZERO, BigInteger.ONE, true);
public final static BigFraction ONE = new BigFraction(BigInteger.ONE, BigInteger.ONE, true);
/**
* Constructs a BigFraction with given numerator and denominator. Fraction
* will be reduced to lowest terms. If fraction is negative, negative sign will
* be carried on numerator, regardless of how the values were passed in.
*/
public BigFraction(BigInteger numerator, BigInteger denominator)
{
if(numerator == null)
throw new IllegalArgumentException("Numerator is null");
if(denominator == null)
throw new IllegalArgumentException("Denominator is null");
if(denominator.equals(BigInteger.ZERO))
throw new ArithmeticException("Divide by zero.");
//only numerator should be negative.
if(denominator.signum() < 0)
{
numerator = numerator.negate();
denominator = denominator.negate();
}
//create a reduced fraction
BigInteger gcd = numerator.gcd(denominator);
this.numerator = numerator.divide(gcd);
this.denominator = denominator.divide(gcd);
}
/**
* Constructs a BigFraction from a whole number.
*/
public BigFraction(BigInteger numerator)
{
this(numerator, BigInteger.ONE, true);
}
public BigFraction(long numerator, long denominator)
{
this(BigInteger.valueOf(numerator), BigInteger.valueOf(denominator));
}
public BigFraction(long numerator)
{
this(BigInteger.valueOf(numerator), BigInteger.ONE, true);
}
/**
* Constructs a BigFraction from a floating-point number.
*
* Warning: round-off error in IEEE floating point numbers can result
* in answers that are unexpected. For example,
* System.out.println(new BigFraction(1.1))
* will print:
* 2476979795053773/2251799813685248
*
* This is because 1.1 cannot be expressed exactly in binary form. The
* given fraction is exactly equal to the internal representation of
* the double-precision floating-point number. (Which, for 1.1, is:
* (-1)^0 * 2^0 * (1 + 0x199999999999aL / 0x10000000000000L).)
*
* NOTE: In many cases, BigFraction(Double.toString(d)) may give a result
* closer to what the user expects.
*/
public BigFraction(double d)
{
if(Double.isInfinite(d))
throw new IllegalArgumentException("double val is infinite");
if(Double.isNaN(d))
throw new IllegalArgumentException("double val is NaN");
//special case - math below won't work right for 0.0 or -0.0
if(d == 0)
{
numerator = BigInteger.ZERO;
denominator = BigInteger.ONE;
return;
}
final long bits = Double.doubleToLongBits(d);
final int sign = (int)(bits >> 63) & 0x1;
final int exponent = ((int)(bits >> 52) & 0x7ff) - 0x3ff;
final long mantissa = bits & 0xfffffffffffffL;
//number is (-1)^sign * 2^(exponent) * 1.mantissa
BigInteger tmpNumerator = BigInteger.valueOf(sign==0 ? 1 : -1);
BigInteger tmpDenominator = BigInteger.ONE;
//use shortcut: 2^x == 1 << x. if x is negative, shift the denominator
if(exponent >= 0)
tmpNumerator = tmpNumerator.multiply(BigInteger.ONE.shiftLeft(exponent));
else
tmpDenominator = tmpDenominator.multiply(BigInteger.ONE.shiftLeft(-exponent));
//1.mantissa == 1 + mantissa/2^52 == (2^52 + mantissa)/2^52
tmpDenominator = tmpDenominator.multiply(BigInteger.valueOf(0x10000000000000L));
tmpNumerator = tmpNumerator.multiply(BigInteger.valueOf(0x10000000000000L + mantissa));
BigInteger gcd = tmpNumerator.gcd(tmpDenominator);
numerator = tmpNumerator.divide(gcd);
denominator = tmpDenominator.divide(gcd);
}
/**
* Constructs a BigFraction from two floating-point numbers.
*
* Warning: round-off error in IEEE floating point numbers can result
* in answers that are unexpected. See BigFraction(double) for more
* information.
*
* NOTE: In many cases, BigFraction(Double.toString(numerator) + "/" + Double.toString(denominator))
* may give a result closer to what the user expects.
*/
public BigFraction(double numerator, double denominator)
{
if(denominator == 0)
throw new ArithmeticException("Divide by zero.");
BigFraction tmp = new BigFraction(numerator).divide(new BigFraction(denominator));
this.numerator = tmp.numerator;
this.denominator = tmp.denominator;
}
/**
* Constructs a new BigFraction from the given BigDecimal object.
*/
public BigFraction(BigDecimal d)
{
this(d.scale() < 0 ? d.unscaledValue().multiply(BigInteger.TEN.pow(-d.scale())) : d.unscaledValue(),
d.scale() < 0 ? BigInteger.ONE : BigInteger.TEN.pow(d.scale()));
}
public BigFraction(BigDecimal numerator, BigDecimal denominator)
{
if(denominator.equals(BigDecimal.ZERO))
throw new ArithmeticException("Divide by zero.");
BigFraction tmp = new BigFraction(numerator).divide(new BigFraction(denominator));
this.numerator = tmp.numerator;
this.denominator = tmp.denominator;
}
/**
* Constructs a BigFraction from a String. Expected format is numerator/denominator,
* but /denominator part is optional. Either numerator or denominator may be a floating-
* point decimal number, which in the same format as a parameter to the
* <code>BigDecimal(String)</code> constructor.
*
* #throws NumberFormatException if the string cannot be properly parsed.
*/
public BigFraction(String s)
{
int slashPos = s.indexOf('/');
if(slashPos < 0)
{
BigFraction res = new BigFraction(new BigDecimal(s));
this.numerator = res.numerator;
this.denominator = res.denominator;
}
else
{
BigDecimal num = new BigDecimal(s.substring(0, slashPos));
BigDecimal den = new BigDecimal(s.substring(slashPos+1, s.length()));
BigFraction res = new BigFraction(num, den);
this.numerator = res.numerator;
this.denominator = res.denominator;
}
}
/**
* Returns this + f.
*/
public BigFraction add(BigFraction f)
{
if(f == null)
throw new IllegalArgumentException("Null argument");
//n1/d1 + n2/d2 = (n1*d2 + d1*n2)/(d1*d2)
return new BigFraction(numerator.multiply(f.denominator).add(denominator.multiply(f.numerator)),
denominator.multiply(f.denominator));
}
/**
* Returns this + b.
*/
public BigFraction add(BigInteger b)
{
if(b == null)
throw new IllegalArgumentException("Null argument");
//n1/d1 + n2 = (n1 + d1*n2)/d1
return new BigFraction(numerator.add(denominator.multiply(b)),
denominator, true);
}
/**
* Returns this + n.
*/
public BigFraction add(long n)
{
return add(BigInteger.valueOf(n));
}
/**
* Returns this - f.
*/
public BigFraction subtract(BigFraction f)
{
if(f == null)
throw new IllegalArgumentException("Null argument");
return new BigFraction(numerator.multiply(f.denominator).subtract(denominator.multiply(f.numerator)),
denominator.multiply(f.denominator));
}
/**
* Returns this - b.
*/
public BigFraction subtract(BigInteger b)
{
if(b == null)
throw new IllegalArgumentException("Null argument");
return new BigFraction(numerator.subtract(denominator.multiply(b)),
denominator, true);
}
/**
* Returns this - n.
*/
public BigFraction subtract(long n)
{
return subtract(BigInteger.valueOf(n));
}
/**
* Returns this * f.
*/
public BigFraction multiply(BigFraction f)
{
if(f == null)
throw new IllegalArgumentException("Null argument");
return new BigFraction(numerator.multiply(f.numerator), denominator.multiply(f.denominator));
}
/**
* Returns this * b.
*/
public BigFraction multiply(BigInteger b)
{
if(b == null)
throw new IllegalArgumentException("Null argument");
return new BigFraction(numerator.multiply(b), denominator);
}
/**
* Returns this * n.
*/
public BigFraction multiply(long n)
{
return multiply(BigInteger.valueOf(n));
}
/**
* Returns this / f.
*/
public BigFraction divide(BigFraction f)
{
if(f == null)
throw new IllegalArgumentException("Null argument");
if(f.numerator.equals(BigInteger.ZERO))
throw new ArithmeticException("Divide by zero");
return new BigFraction(numerator.multiply(f.denominator), denominator.multiply(f.numerator));
}
/**
* Returns this / b.
*/
public BigFraction divide(BigInteger b)
{
if(b == null)
throw new IllegalArgumentException("Null argument");
if(b.equals(BigInteger.ZERO))
throw new ArithmeticException("Divide by zero");
return new BigFraction(numerator, denominator.multiply(b));
}
/**
* Returns this / n.
*/
public BigFraction divide(long n)
{
return divide(BigInteger.valueOf(n));
}
/**
* Returns this^exponent.
*/
public BigFraction pow(int exponent)
{
if(exponent == 0)
return BigFraction.ONE;
else if (exponent == 1)
return this;
else if (exponent < 0)
return new BigFraction(denominator.pow(-exponent), numerator.pow(-exponent), true);
else
return new BigFraction(numerator.pow(exponent), denominator.pow(exponent), true);
}
/**
* Returns 1/this.
*/
public BigFraction reciprocal()
{
if(this.numerator.equals(BigInteger.ZERO))
throw new ArithmeticException("Divide by zero");
return new BigFraction(denominator, numerator, true);
}
/**
* Returns the complement of this fraction, which is equal to 1 - this.
* Useful for probabilities/statistics.
*/
public BigFraction complement()
{
return new BigFraction(denominator.subtract(numerator), denominator, true);
}
/**
* Returns -this.
*/
public BigFraction negate()
{
return new BigFraction(numerator.negate(), denominator, true);
}
/**
* Returns -1, 0, or 1, representing the sign of this fraction.
*/
public int signum()
{
return numerator.signum();
}
/**
* Returns the absolute value of this.
*/
public BigFraction abs()
{
return (signum() < 0 ? negate() : this);
}
/**
* Returns a string representation of this, in the form
* numerator/denominator.
*/
public String toString()
{
return numerator.toString() + "/" + denominator.toString();
}
/**
* Returns if this object is equal to another object.
*/
public boolean equals(Object o)
{
if(!(o instanceof BigFraction))
return false;
BigFraction f = (BigFraction)o;
return numerator.equals(f.numerator) && denominator.equals(f.denominator);
}
/**
* Returns a hash code for this object.
*/
public int hashCode()
{
//using the method generated by Eclipse, but streamlined a bit..
return (31 + numerator.hashCode())*31 + denominator.hashCode();
}
/**
* Returns a negative, zero, or positive number, indicating if this object
* is less than, equal to, or greater than f, respectively.
*/
public int compareTo(BigFraction f)
{
if(f == null)
throw new IllegalArgumentException("Null argument");
//easy case: this and f have different signs
if(signum() != f.signum())
return signum() - f.signum();
//next easy case: this and f have the same denominator
if(denominator.equals(f.denominator))
return numerator.compareTo(f.numerator);
//not an easy case, so first make the denominators equal then compare the numerators
return numerator.multiply(f.denominator).compareTo(denominator.multiply(f.numerator));
}
/**
* Returns the smaller of this and f.
*/
public BigFraction min(BigFraction f)
{
if(f == null)
throw new IllegalArgumentException("Null argument");
return (this.compareTo(f) <= 0 ? this : f);
}
/**
* Returns the maximum of this and f.
*/
public BigFraction max(BigFraction f)
{
if(f == null)
throw new IllegalArgumentException("Null argument");
return (this.compareTo(f) >= 0 ? this : f);
}
/**
* Returns a positive BigFraction, greater than or equal to zero, and less than one.
*/
public static BigFraction random()
{
return new BigFraction(Math.random());
}
public final BigInteger getNumerator() { return numerator; }
public final BigInteger getDenominator() { return denominator; }
//implementation of Number class. may cause overflow.
public byte byteValue() { return (byte) Math.max(Byte.MIN_VALUE, Math.min(Byte.MAX_VALUE, longValue())); }
public short shortValue() { return (short)Math.max(Short.MIN_VALUE, Math.min(Short.MAX_VALUE, longValue())); }
public int intValue() { return (int) Math.max(Integer.MIN_VALUE, Math.min(Integer.MAX_VALUE, longValue())); }
public long longValue() { return Math.round(doubleValue()); }
public float floatValue() { return (float)doubleValue(); }
public double doubleValue() { return toBigDecimal(18).doubleValue(); }
/**
* Returns a BigDecimal representation of this fraction. If possible, the
* returned value will be exactly equal to the fraction. If not, the BigDecimal
* will have a scale large enough to hold the same number of significant figures
* as both numerator and denominator, or the equivalent of a double-precision
* number, whichever is more.
*/
public BigDecimal toBigDecimal()
{
//Implementation note: A fraction can be represented exactly in base-10 iff its
//denominator is of the form 2^a * 5^b, where a and b are nonnegative integers.
//(In other words, if there are no prime factors of the denominator except for
//2 and 5, or if the denominator is 1). So to determine if this denominator is
//of this form, continually divide by 2 to get the number of 2's, and then
//continually divide by 5 to get the number of 5's. Afterward, if the denominator
//is 1 then there are no other prime factors.
//Note: number of 2's is given by the number of trailing 0 bits in the number
int twos = denominator.getLowestSetBit();
BigInteger tmpDen = denominator.shiftRight(twos); // x / 2^n === x >> n
final BigInteger FIVE = BigInteger.valueOf(5);
int fives = 0;
BigInteger[] divMod = null;
//while(tmpDen % 5 == 0) { fives++; tmpDen /= 5; }
while(BigInteger.ZERO.equals((divMod = tmpDen.divideAndRemainder(FIVE))[1]))
{
fives++;
tmpDen = divMod[0];
}
if(BigInteger.ONE.equals(tmpDen))
{
//This fraction will terminate in base 10, so it can be represented exactly as
//a BigDecimal. We would now like to make the fraction of the form
//unscaled / 10^scale. We know that 2^x * 5^x = 10^x, and our denominator is
//in the form 2^twos * 5^fives. So use max(twos, fives) as the scale, and
//multiply the numerator and deminator by the appropriate number of 2's or 5's
//such that the denominator is of the form 2^scale * 5^scale. (Of course, we
//only have to actually multiply the numerator, since all we need for the
//BigDecimal constructor is the scale.
BigInteger unscaled = numerator;
int scale = Math.max(twos, fives);
if(twos < fives)
unscaled = unscaled.shiftLeft(fives - twos); //x * 2^n === x << n
else if (fives < twos)
unscaled = unscaled.multiply(FIVE.pow(twos - fives));
return new BigDecimal(unscaled, scale);
}
//else: this number will repeat infinitely in base-10. So try to figure out
//a good number of significant digits. Start with the number of digits required
//to represent the numerator and denominator in base-10, which is given by
//bitLength / log[2](10). (bitLenth is the number of digits in base-2).
final double LG10 = 3.321928094887362; //Precomputed ln(10)/ln(2), a.k.a. log[2](10)
int precision = Math.max(numerator.bitLength(), denominator.bitLength());
precision = (int)Math.ceil(precision / LG10);
//If the precision is less than 18 digits, use 18 digits so that the number
//will be at least as accurate as a cast to a double. For example, with
//the fraction 1/3, precision will be 1, giving a result of 0.3. This is
//quite a bit different from what a user would expect.
if(precision < 18)
precision = 18;
return toBigDecimal(precision);
}
/**
* Returns a BigDecimal representation of this fraction, with a given precision.
* #param precision the number of significant figures to be used in the result.
*/
public BigDecimal toBigDecimal(int precision)
{
return new BigDecimal(numerator).divide(new BigDecimal(denominator), new MathContext(precision, RoundingMode.HALF_EVEN));
}
//--------------------------------------------------------------------------
// PRIVATE FUNCTIONS
//--------------------------------------------------------------------------
/**
* Private constructor, used when you can be certain that the fraction is already in
* lowest terms. No check is done to reduce numerator/denominator. A check is still
* done to maintain a positive denominator.
*
* #param throwaway unused variable, only here to signal to the compiler that this
* constructor should be used.
*/
private BigFraction(BigInteger numerator, BigInteger denominator, boolean throwaway)
{
if(denominator.signum() < 0)
{
this.numerator = numerator.negate();
this.denominator = denominator.negate();
}
else
{
this.numerator = numerator;
this.denominator = denominator;
}
}
}
Make it immutable;
Make it canonical, meaning 6/4 becomes 3/2 (greatest common divisor algorithm is useful for this);
Call it Rational, since what you're representing is a rational number;
You could use BigInteger to store arbitrarilyy-precise values. If not that then long, which has an easier implementation;
Make the denominator always positive. Sign should be carried by the numerator;
Extend Number;
Implement Comparable<T>;
Implement equals() and hashCode();
Add factory method for a number represented by a String;
Add some convenience factory methods;
Add a toString(); and
Make it Serializable.
In fact, try this on for size. It runs but may have some issues:
public class BigRational extends Number implements Comparable<BigRational>, Serializable {
public final static BigRational ZERO = new BigRational(BigInteger.ZERO, BigInteger.ONE);
private final static long serialVersionUID = 1099377265582986378L;
private final BigInteger numerator, denominator;
private BigRational(BigInteger numerator, BigInteger denominator) {
this.numerator = numerator;
this.denominator = denominator;
}
private static BigRational canonical(BigInteger numerator, BigInteger denominator, boolean checkGcd) {
if (denominator.signum() == 0) {
throw new IllegalArgumentException("denominator is zero");
}
if (numerator.signum() == 0) {
return ZERO;
}
if (denominator.signum() < 0) {
numerator = numerator.negate();
denominator = denominator.negate();
}
if (checkGcd) {
BigInteger gcd = numerator.gcd(denominator);
if (!gcd.equals(BigInteger.ONE)) {
numerator = numerator.divide(gcd);
denominator = denominator.divide(gcd);
}
}
return new BigRational(numerator, denominator);
}
public static BigRational getInstance(BigInteger numerator, BigInteger denominator) {
return canonical(numerator, denominator, true);
}
public static BigRational getInstance(long numerator, long denominator) {
return canonical(new BigInteger("" + numerator), new BigInteger("" + denominator), true);
}
public static BigRational getInstance(String numerator, String denominator) {
return canonical(new BigInteger(numerator), new BigInteger(denominator), true);
}
public static BigRational valueOf(String s) {
Pattern p = Pattern.compile("(-?\\d+)(?:.(\\d+)?)?0*(?:e(-?\\d+))?");
Matcher m = p.matcher(s);
if (!m.matches()) {
throw new IllegalArgumentException("Unknown format '" + s + "'");
}
// this translates 23.123e5 to 25,123 / 1000 * 10^5 = 2,512,300 / 1 (GCD)
String whole = m.group(1);
String decimal = m.group(2);
String exponent = m.group(3);
String n = whole;
// 23.123 => 23123
if (decimal != null) {
n += decimal;
}
BigInteger numerator = new BigInteger(n);
// exponent is an int because BigInteger.pow() takes an int argument
// it gets more difficult if exponent needs to be outside {-2 billion,2 billion}
int exp = exponent == null ? 0 : Integer.valueOf(exponent);
int decimalPlaces = decimal == null ? 0 : decimal.length();
exp -= decimalPlaces;
BigInteger denominator;
if (exp < 0) {
denominator = BigInteger.TEN.pow(-exp);
} else {
numerator = numerator.multiply(BigInteger.TEN.pow(exp));
denominator = BigInteger.ONE;
}
// done
return canonical(numerator, denominator, true);
}
// Comparable
public int compareTo(BigRational o) {
// note: this is a bit of cheat, relying on BigInteger.compareTo() returning
// -1, 0 or 1. For the more general contract of compareTo(), you'd need to do
// more checking
if (numerator.signum() != o.numerator.signum()) {
return numerator.signum() - o.numerator.signum();
} else {
// oddly BigInteger has gcd() but no lcm()
BigInteger i1 = numerator.multiply(o.denominator);
BigInteger i2 = o.numerator.multiply(denominator);
return i1.compareTo(i2); // expensive!
}
}
public BigRational add(BigRational o) {
if (o.numerator.signum() == 0) {
return this;
} else if (numerator.signum() == 0) {
return o;
} else if (denominator.equals(o.denominator)) {
return new BigRational(numerator.add(o.numerator), denominator);
} else {
return canonical(numerator.multiply(o.denominator).add(o.numerator.multiply(denominator)), denominator.multiply(o.denominator), true);
}
}
public BigRational multiply(BigRational o) {
if (numerator.signum() == 0 || o.numerator.signum( )== 0) {
return ZERO;
} else if (numerator.equals(o.denominator)) {
return canonical(o.numerator, denominator, true);
} else if (o.numerator.equals(denominator)) {
return canonical(numerator, o.denominator, true);
} else if (numerator.negate().equals(o.denominator)) {
return canonical(o.numerator.negate(), denominator, true);
} else if (o.numerator.negate().equals(denominator)) {
return canonical(numerator.negate(), o.denominator, true);
} else {
return canonical(numerator.multiply(o.numerator), denominator.multiply(o.denominator), true);
}
}
public BigInteger getNumerator() { return numerator; }
public BigInteger getDenominator() { return denominator; }
public boolean isInteger() { return numerator.signum() == 0 || denominator.equals(BigInteger.ONE); }
public BigRational negate() { return new BigRational(numerator.negate(), denominator); }
public BigRational invert() { return canonical(denominator, numerator, false); }
public BigRational abs() { return numerator.signum() < 0 ? negate() : this; }
public BigRational pow(int exp) { return canonical(numerator.pow(exp), denominator.pow(exp), true); }
public BigRational subtract(BigRational o) { return add(o.negate()); }
public BigRational divide(BigRational o) { return multiply(o.invert()); }
public BigRational min(BigRational o) { return compareTo(o) <= 0 ? this : o; }
public BigRational max(BigRational o) { return compareTo(o) >= 0 ? this : o; }
public BigDecimal toBigDecimal(int scale, RoundingMode roundingMode) {
return isInteger() ? new BigDecimal(numerator) : new BigDecimal(numerator).divide(new BigDecimal(denominator), scale, roundingMode);
}
// Number
public int intValue() { return isInteger() ? numerator.intValue() : numerator.divide(denominator).intValue(); }
public long longValue() { return isInteger() ? numerator.longValue() : numerator.divide(denominator).longValue(); }
public float floatValue() { return (float)doubleValue(); }
public double doubleValue() { return isInteger() ? numerator.doubleValue() : numerator.doubleValue() / denominator.doubleValue(); }
#Override
public String toString() { return isInteger() ? String.format("%,d", numerator) : String.format("%,d / %,d", numerator, denominator); }
#Override
public boolean equals(Object o) {
if (this == o) return true;
if (o == null || getClass() != o.getClass()) return false;
BigRational that = (BigRational) o;
if (denominator != null ? !denominator.equals(that.denominator) : that.denominator != null) return false;
if (numerator != null ? !numerator.equals(that.numerator) : that.numerator != null) return false;
return true;
}
#Override
public int hashCode() {
int result = numerator != null ? numerator.hashCode() : 0;
result = 31 * result + (denominator != null ? denominator.hashCode() : 0);
return result;
}
public static void main(String args[]) {
BigRational r1 = BigRational.valueOf("3.14e4");
BigRational r2 = BigRational.getInstance(111, 7);
dump("r1", r1);
dump("r2", r2);
dump("r1 + r2", r1.add(r2));
dump("r1 - r2", r1.subtract(r2));
dump("r1 * r2", r1.multiply(r2));
dump("r1 / r2", r1.divide(r2));
dump("r2 ^ 2", r2.pow(2));
}
public static void dump(String name, BigRational r) {
System.out.printf("%s = %s%n", name, r);
System.out.printf("%s.negate() = %s%n", name, r.negate());
System.out.printf("%s.invert() = %s%n", name, r.invert());
System.out.printf("%s.intValue() = %,d%n", name, r.intValue());
System.out.printf("%s.longValue() = %,d%n", name, r.longValue());
System.out.printf("%s.floatValue() = %,f%n", name, r.floatValue());
System.out.printf("%s.doubleValue() = %,f%n", name, r.doubleValue());
System.out.println();
}
}
Output is:
r1 = 31,400
r1.negate() = -31,400
r1.invert() = 1 / 31,400
r1.intValue() = 31,400
r1.longValue() = 31,400
r1.floatValue() = 31,400.000000
r1.doubleValue() = 31,400.000000
r2 = 111 / 7
r2.negate() = -111 / 7
r2.invert() = 7 / 111
r2.intValue() = 15
r2.longValue() = 15
r2.floatValue() = 15.857142
r2.doubleValue() = 15.857143
r1 + r2 = 219,911 / 7
r1 + r2.negate() = -219,911 / 7
r1 + r2.invert() = 7 / 219,911
r1 + r2.intValue() = 31,415
r1 + r2.longValue() = 31,415
r1 + r2.floatValue() = 31,415.857422
r1 + r2.doubleValue() = 31,415.857143
r1 - r2 = 219,689 / 7
r1 - r2.negate() = -219,689 / 7
r1 - r2.invert() = 7 / 219,689
r1 - r2.intValue() = 31,384
r1 - r2.longValue() = 31,384
r1 - r2.floatValue() = 31,384.142578
r1 - r2.doubleValue() = 31,384.142857
r1 * r2 = 3,485,400 / 7
r1 * r2.negate() = -3,485,400 / 7
r1 * r2.invert() = 7 / 3,485,400
r1 * r2.intValue() = 497,914
r1 * r2.longValue() = 497,914
r1 * r2.floatValue() = 497,914.281250
r1 * r2.doubleValue() = 497,914.285714
r1 / r2 = 219,800 / 111
r1 / r2.negate() = -219,800 / 111
r1 / r2.invert() = 111 / 219,800
r1 / r2.intValue() = 1,980
r1 / r2.longValue() = 1,980
r1 / r2.floatValue() = 1,980.180176
r1 / r2.doubleValue() = 1,980.180180
r2 ^ 2 = 12,321 / 49
r2 ^ 2.negate() = -12,321 / 49
r2 ^ 2.invert() = 49 / 12,321
r2 ^ 2.intValue() = 251
r2 ^ 2.longValue() = 251
r2 ^ 2.floatValue() = 251.448975
r2 ^ 2.doubleValue() = 251.448980
I'm trying to work with proper fractions in Java.
Apache Commons Math has had a Fraction class for quite some time. Most times the answer to, "Boy I wish Java had something like X in the core library!" can be found under the umbrella of the Apache Commons library.
Please make it an immutable type! The value of a fraction doesn't change - a half doesn't become a third, for example. Instead of setDenominator, you could have withDenominator which returns a new fraction which has the same numerator but the specified denominator.
Life is much easier with immutable types.
Overriding equals and hashcode would be sensible too, so it can be used in maps and sets. Outlaw Programmer's points about arithmetic operators and string formatting are good too.
As a general guide, have a look at BigInteger and BigDecimal. They're not doing the same thing, but they're similar enough to give you good ideas.
Well, for one, I'd get rid of the setters and make Fractions immutable.
You'll probably also want methods to add, subtract, etc., and maybe some way to get the representation in various String formats.
EDIT: I'd probably mark the fields as 'final' to signal my intent but I guess it's not a big deal...
It's kinda pointless without arithmetic methods like add() and multiply(), etc.
You should definitely override equals() and hashCode().
You should either add a method to normalize the fraction, or do it automatically. Think about whether you want 1/2 and 2/4 to be considered the same or not - this has implications for the equals(), hashCode() and compareTo() methods.
I will need to order them from smallest to largest,
so eventually I will need to represent them as a double also
Not strictly necessary. (In fact if you want to handle equality correctly, don't rely on double to work properly.) If b*d is positive, a/b < c/d if ad < bc. If there are negative integers involved, that can be handled appropriately...
I might rewrite as:
public int compareTo(Fraction frac)
{
// we are comparing this=a/b with frac=c/d
// by multiplying both sides by bd.
// If bd is positive, then a/b < c/d <=> ad < bc.
// If bd is negative, then a/b < c/d <=> ad > bc.
// If bd is 0, then you've got other problems (either b=0 or d=0)
int d = frac.getDenominator();
long ad = (long)this.numerator * d;
long bc = (long)this.denominator * frac.getNumerator();
long diff = ((long)d*this.denominator > 0) ? (ad-bc) : (bc-ad);
return (diff > 0 ? 1 : (diff < 0 ? -1 : 0));
}
The use of long here is to ensure there's not an overflow if you multiply two large ints. handle If you can guarantee that the denominator is always nonnegative (if it's negative, just negate both numerator and denominator), then you can get rid of having to check whether b*d is positive and save a few steps. I'm not sure what behavior you're looking for with zero denominator.
Not sure how performance compares to using doubles to compare. (that is, if you care about performance that much) Here's a test method I used to check. (Appears to work properly.)
public static void main(String[] args)
{
int a = Integer.parseInt(args[0]);
int b = Integer.parseInt(args[1]);
int c = Integer.parseInt(args[2]);
int d = Integer.parseInt(args[3]);
Fraction f1 = new Fraction(a,b);
Fraction f2 = new Fraction(c,d);
int rel = f1.compareTo(f2);
String relstr = "<=>";
System.out.println(a+"/"+b+" "+relstr.charAt(rel+1)+" "+c+"/"+d);
}
(p.s. you might consider restructuring to implement Comparable or Comparator for your class.)
One very minor improvement could potentially be to save the double value that you're computing so that you only compute it on the first access. This won't be a big win unless you're accessing this number a lot, but it's not overly difficult to do, either.
One additional point might be the error checking you do in the denominator...you automatically change 0 to 1. Not sure if this is correct for your particular application, but in general if someone is trying to divide by 0, something is very wrong. I'd let this throw an exception (a specialized exception if you feel it's needed) rather than change the value in a seemingly arbitrary way that isn't known to the user.
In constrast with some other comments, about adding methods to add subtract, etc...since you didn't mention needing them, I'm assuming you don't. And unless you're building a library that is really going to be used in many places or by other people, go with YAGNI (you ain't going to need it, so it shouldn't be there.)
There are several ways to improve this or any value type:
Make your class immutable, including making numerator and denominator final
Automatically convert fractions to a canonical form, e.g. 2/4 -> 1/2
Implement toString()
Implement "public static Fraction valueOf(String s)" to convert from strings to fractions. Implement similar factory methods for converting from int, double, etc.
Implement addition, multiplication, etc
Add constructor from whole numbers
Override equals/hashCode
Consider making Fraction an interface with an implementation that switches to BigInteger as necessary
Consider sub-classing Number
Consider including named constants for common values like 0 and 1
Consider making it serializable
Test for division by zero
Document your API
Basically, take a look at the API for other value classes like Double, Integer and do what they do :)
If you multiply the numerator and denominator of one Fraction with the denominator of the other and vice versa, you end up with two fractions (that are still the same values) with the same denominator and you can compare the numerators directly. Therefore you wouldn't need to calculate the double value:
public int compareTo(Fraction frac) {
int t = this.numerator * frac.getDenominator();
int f = frac.getNumerator() * this.denominator;
if(t>f) return 1;
if(f>t) return -1;
return 0;
}
how I would improve that code:
a constructor based on String Fraction(String s) //expect "number/number"
a copy constructor Fraction(Fraction copy)
override the clone method
implements the equals, toString and hashcode methods
implements the interface java.io.Serializable, Comparable
a method "double getDoubleValue()"
a method add/divide/etc...
I would make that class as immutable (no setters)
You have a compareTo function already ... I would implement the Comparable interface.
May not really matter for whatever you're going to do with it though.
If you're feeling adventurous, take a look at JScience. It has a Rational class that represents fractions.
Specifically: Is there a better way to handle being passed a zero denominator? Setting the denominator to 1 is feels mighty arbitrary. How can I do this right?
I would say throw a ArithmeticException for divide by zero, since that's really what's happening:
public Fraction(int numerator, int denominator) {
if(denominator == 0)
throw new ArithmeticException("Divide by zero.");
this.numerator = numerator;
this.denominator = denominator;
}
Instead of "Divide by zero.", you might want to make the message say "Divide by zero: Denominator for Fraction is zero."
Once you've created a fraction object why would you want to allow other objects to set the numerator or the denominator? I would think these should be read only. It makes the object immutable...
Also...setting the denominator to zero should throw an invalid argument exception (I don't know what it is in Java)
Timothy Budd has a fine implementation of a Rational class in his "Data Structures in C++". Different language, of course, but it ports over to Java very nicely.
I'd recommend more constructors. A default constructor would have numerator 0, denominator 1. A single arg constructor would assume a denominator of 1. Think how your users might use this class.
No check for zero denominator? Programming by contract would have you add it.
I'll third or fifth or whatever the recommendation for making your fraction immutable. I'd also recommend that you have it extend the Number class. I'd probably look at the Double class, since you're probably going to want to implement many of the same methods.
You should probably also implement Comparable and Serializable since this behavior will probably be expected. Thus, you will need to implement compareTo(). You will also need to override equals() and I cannot stress strongly enough that you also override hashCode(). This might be one of the few cases though where you don't want compareTo() and equals() to be consistent since fractions reducable to each other are not necessarily equal.
A clean up practice that I like is to only have only one return.
public int compareTo(Fraction frac) {
int result = 0
double t = this.doubleValue();
double f = frac.doubleValue();
if(t>f)
result = 1;
else if(f>t)
result -1;
return result;
}
Use Rational class from JScience library. It's the best thing for fractional arithmetic I seen in Java.
I cleaned up cletus' answer:
Added Javadoc for all methods.
Added checks for method preconditions.
Replaced custom parsing in valueOf(String) with the BigInteger(String) which is both more flexible and faster.
import com.google.common.base.Splitter;
import java.math.BigDecimal;
import java.math.BigInteger;
import java.math.RoundingMode;
import java.util.List;
import java.util.Objects;
import org.bitbucket.cowwoc.preconditions.Preconditions;
/**
* A rational fraction, represented by {#code numerator / denominator}.
* <p>
* This implementation is based on <a
* href="https://stackoverflow.com/a/474577/14731">https://stackoverflow.com/a/474577/14731</a>
* <p>
* #author Gili Tzabari
*/
public final class BigRational extends Number implements Comparable<BigRational>
{
private static final long serialVersionUID = 0L;
public static final BigRational ZERO = new BigRational(BigInteger.ZERO, BigInteger.ONE);
public static final BigRational ONE = new BigRational(BigInteger.ONE, BigInteger.ONE);
/**
* Ensures the fraction the denominator is positive and optionally divides the numerator and
* denominator by the greatest common factor.
* <p>
* #param numerator a numerator
* #param denominator a denominator
* #param checkGcd true if the numerator and denominator should be divided by the greatest
* common factor
* #return the canonical representation of the rational fraction
*/
private static BigRational canonical(BigInteger numerator, BigInteger denominator,
boolean checkGcd)
{
assert (numerator != null);
assert (denominator != null);
if (denominator.signum() == 0)
throw new IllegalArgumentException("denominator is zero");
if (numerator.signum() == 0)
return ZERO;
BigInteger newNumerator = numerator;
BigInteger newDenominator = denominator;
if (newDenominator.signum() < 0)
{
newNumerator = newNumerator.negate();
newDenominator = newDenominator.negate();
}
if (checkGcd)
{
BigInteger gcd = newNumerator.gcd(newDenominator);
if (!gcd.equals(BigInteger.ONE))
{
newNumerator = newNumerator.divide(gcd);
newDenominator = newDenominator.divide(gcd);
}
}
return new BigRational(newNumerator, newDenominator);
}
/**
* #param numerator a numerator
* #param denominator a denominator
* #return a BigRational having value {#code numerator / denominator}
* #throws NullPointerException if numerator or denominator are null
*/
public static BigRational valueOf(BigInteger numerator, BigInteger denominator)
{
Preconditions.requireThat(numerator, "numerator").isNotNull();
Preconditions.requireThat(denominator, "denominator").isNotNull();
return canonical(numerator, denominator, true);
}
/**
* #param numerator a numerator
* #param denominator a denominator
* #return a BigRational having value {#code numerator / denominator}
*/
public static BigRational valueOf(long numerator, long denominator)
{
BigInteger bigNumerator = BigInteger.valueOf(numerator);
BigInteger bigDenominator = BigInteger.valueOf(denominator);
return canonical(bigNumerator, bigDenominator, true);
}
/**
* #param value the parameter value
* #param name the parameter name
* #return the BigInteger representation of the parameter
* #throws NumberFormatException if value is not a valid representation of BigInteger
*/
private static BigInteger requireBigInteger(String value, String name)
throws NumberFormatException
{
try
{
return new BigInteger(value);
}
catch (NumberFormatException e)
{
throw (NumberFormatException) new NumberFormatException("Invalid " + name + ": " + value).
initCause(e);
}
}
/**
* #param numerator a numerator
* #param denominator a denominator
* #return a BigRational having value {#code numerator / denominator}
* #throws NullPointerException if numerator or denominator are null
* #throws IllegalArgumentException if numerator or denominator are empty
* #throws NumberFormatException if numerator or denominator are not a valid representation of
* BigDecimal
*/
public static BigRational valueOf(String numerator, String denominator)
throws NullPointerException, IllegalArgumentException, NumberFormatException
{
Preconditions.requireThat(numerator, "numerator").isNotNull().isNotEmpty();
Preconditions.requireThat(denominator, "denominator").isNotNull().isNotEmpty();
BigInteger bigNumerator = requireBigInteger(numerator, "numerator");
BigInteger bigDenominator = requireBigInteger(denominator, "denominator");
return canonical(bigNumerator, bigDenominator, true);
}
/**
* #param value a string representation of a rational fraction (e.g. "12.34e5" or "3/4")
* #return a BigRational representation of the String
* #throws NullPointerException if value is null
* #throws IllegalArgumentException if value is empty
* #throws NumberFormatException if numerator or denominator are not a valid representation of
* BigDecimal
*/
public static BigRational valueOf(String value)
throws NullPointerException, IllegalArgumentException, NumberFormatException
{
Preconditions.requireThat(value, "value").isNotNull().isNotEmpty();
List<String> fractionParts = Splitter.on('/').splitToList(value);
if (fractionParts.size() == 1)
return valueOfRational(value);
if (fractionParts.size() == 2)
return BigRational.valueOf(fractionParts.get(0), fractionParts.get(1));
throw new IllegalArgumentException("Too many slashes: " + value);
}
/**
* #param value a string representation of a rational fraction (e.g. "12.34e5")
* #return a BigRational representation of the String
* #throws NullPointerException if value is null
* #throws IllegalArgumentException if value is empty
* #throws NumberFormatException if numerator or denominator are not a valid representation of
* BigDecimal
*/
private static BigRational valueOfRational(String value)
throws NullPointerException, IllegalArgumentException, NumberFormatException
{
Preconditions.requireThat(value, "value").isNotNull().isNotEmpty();
BigDecimal bigDecimal = new BigDecimal(value);
int scale = bigDecimal.scale();
BigInteger numerator = bigDecimal.unscaledValue();
BigInteger denominator;
if (scale > 0)
denominator = BigInteger.TEN.pow(scale);
else
{
numerator = numerator.multiply(BigInteger.TEN.pow(-scale));
denominator = BigInteger.ONE;
}
return canonical(numerator, denominator, true);
}
private final BigInteger numerator;
private final BigInteger denominator;
/**
* #param numerator the numerator
* #param denominator the denominator
* #throws NullPointerException if numerator or denominator are null
*/
private BigRational(BigInteger numerator, BigInteger denominator)
{
Preconditions.requireThat(numerator, "numerator").isNotNull();
Preconditions.requireThat(denominator, "denominator").isNotNull();
this.numerator = numerator;
this.denominator = denominator;
}
/**
* #return the numerator
*/
public BigInteger getNumerator()
{
return numerator;
}
/**
* #return the denominator
*/
public BigInteger getDenominator()
{
return denominator;
}
#Override
#SuppressWarnings("AccessingNonPublicFieldOfAnotherObject")
public int compareTo(BigRational other)
{
Preconditions.requireThat(other, "other").isNotNull();
// canonical() ensures denominator is positive
if (numerator.signum() != other.numerator.signum())
return numerator.signum() - other.numerator.signum();
// Set the denominator to a common multiple before comparing the numerators
BigInteger first = numerator.multiply(other.denominator);
BigInteger second = other.numerator.multiply(denominator);
return first.compareTo(second);
}
/**
* #param other another rational fraction
* #return the result of adding this object to {#code other}
* #throws NullPointerException if other is null
*/
#SuppressWarnings("AccessingNonPublicFieldOfAnotherObject")
public BigRational add(BigRational other)
{
Preconditions.requireThat(other, "other").isNotNull();
if (other.numerator.signum() == 0)
return this;
if (numerator.signum() == 0)
return other;
if (denominator.equals(other.denominator))
return new BigRational(numerator.add(other.numerator), denominator);
return canonical(numerator.multiply(other.denominator).
add(other.numerator.multiply(denominator)),
denominator.multiply(other.denominator), true);
}
/**
* #param other another rational fraction
* #return the result of subtracting {#code other} from this object
* #throws NullPointerException if other is null
*/
#SuppressWarnings("AccessingNonPublicFieldOfAnotherObject")
public BigRational subtract(BigRational other)
{
return add(other.negate());
}
/**
* #param other another rational fraction
* #return the result of multiplying this object by {#code other}
* #throws NullPointerException if other is null
*/
#SuppressWarnings("AccessingNonPublicFieldOfAnotherObject")
public BigRational multiply(BigRational other)
{
Preconditions.requireThat(other, "other").isNotNull();
if (numerator.signum() == 0 || other.numerator.signum() == 0)
return ZERO;
if (numerator.equals(other.denominator))
return canonical(other.numerator, denominator, true);
if (other.numerator.equals(denominator))
return canonical(numerator, other.denominator, true);
if (numerator.negate().equals(other.denominator))
return canonical(other.numerator.negate(), denominator, true);
if (other.numerator.negate().equals(denominator))
return canonical(numerator.negate(), other.denominator, true);
return canonical(numerator.multiply(other.numerator), denominator.multiply(other.denominator),
true);
}
/**
* #param other another rational fraction
* #return the result of dividing this object by {#code other}
* #throws NullPointerException if other is null
*/
public BigRational divide(BigRational other)
{
return multiply(other.invert());
}
/**
* #return true if the object is a whole number
*/
public boolean isInteger()
{
return numerator.signum() == 0 || denominator.equals(BigInteger.ONE);
}
/**
* Returns a BigRational whose value is (-this).
* <p>
* #return -this
*/
public BigRational negate()
{
return new BigRational(numerator.negate(), denominator);
}
/**
* #return a rational fraction with the numerator and denominator swapped
*/
public BigRational invert()
{
return canonical(denominator, numerator, false);
}
/**
* #return the absolute value of this {#code BigRational}
*/
public BigRational abs()
{
if (numerator.signum() < 0)
return negate();
return this;
}
/**
* #param exponent exponent to which both numerator and denominator is to be raised.
* #return a BigRational whose value is (this<sup>exponent</sup>).
*/
public BigRational pow(int exponent)
{
return canonical(numerator.pow(exponent), denominator.pow(exponent), true);
}
/**
* #param other another rational fraction
* #return the minimum of this object and the other fraction
*/
public BigRational min(BigRational other)
{
if (compareTo(other) <= 0)
return this;
return other;
}
/**
* #param other another rational fraction
* #return the maximum of this object and the other fraction
*/
public BigRational max(BigRational other)
{
if (compareTo(other) >= 0)
return this;
return other;
}
/**
* #param scale scale of the BigDecimal quotient to be returned
* #param roundingMode the rounding mode to apply
* #return a BigDecimal representation of this object
* #throws NullPointerException if roundingMode is null
*/
public BigDecimal toBigDecimal(int scale, RoundingMode roundingMode)
{
Preconditions.requireThat(roundingMode, "roundingMode").isNotNull();
if (isInteger())
return new BigDecimal(numerator);
return new BigDecimal(numerator).divide(new BigDecimal(denominator), scale, roundingMode);
}
#Override
public int intValue()
{
return (int) longValue();
}
#Override
public long longValue()
{
if (isInteger())
return numerator.longValue();
return numerator.divide(denominator).longValue();
}
#Override
public float floatValue()
{
return (float) doubleValue();
}
#Override
public double doubleValue()
{
if (isInteger())
return numerator.doubleValue();
return numerator.doubleValue() / denominator.doubleValue();
}
#Override
#SuppressWarnings("AccessingNonPublicFieldOfAnotherObject")
public boolean equals(Object o)
{
if (this == o)
return true;
if (!(o instanceof BigRational))
return false;
BigRational other = (BigRational) o;
return numerator.equals(other.denominator) && Objects.equals(denominator, other.denominator);
}
#Override
public int hashCode()
{
return Objects.hash(numerator, denominator);
}
/**
* Returns the String representation: {#code numerator / denominator}.
*/
#Override
public String toString()
{
if (isInteger())
return String.format("%,d", numerator);
return String.format("%,d / %,d", numerator, denominator);
}
}
Initial remark:
Never write this:
if ( condition ) statement;
This is much better
if ( condition ) { statement };
Just create to create a good habit.
By making the class immutable as suggested, you can also take advantage of the double to perform the equals and hashCode and compareTo operations
Here's my quick dirty version:
public final class Fraction implements Comparable {
private final int numerator;
private final int denominator;
private final Double internal;
public static Fraction createFraction( int numerator, int denominator ) {
return new Fraction( numerator, denominator );
}
private Fraction(int numerator, int denominator) {
this.numerator = numerator;
this.denominator = denominator;
this.internal = ((double) numerator)/((double) denominator);
}
public int getNumerator() {
return this.numerator;
}
public int getDenominator() {
return this.denominator;
}
private double doubleValue() {
return internal;
}
public int compareTo( Object o ) {
if ( o instanceof Fraction ) {
return internal.compareTo( ((Fraction)o).internal );
}
return 1;
}
public boolean equals( Object o ) {
if ( o instanceof Fraction ) {
return this.internal.equals( ((Fraction)o).internal );
}
return false;
}
public int hashCode() {
return internal.hashCode();
}
public String toString() {
return String.format("%d/%d", numerator, denominator );
}
public static void main( String [] args ) {
System.out.println( Fraction.createFraction( 1 , 2 ) ) ;
System.out.println( Fraction.createFraction( 1 , 2 ).hashCode() ) ;
System.out.println( Fraction.createFraction( 1 , 2 ).compareTo( Fraction.createFraction(2,4) ) ) ;
System.out.println( Fraction.createFraction( 1 , 2 ).equals( Fraction.createFraction(4,8) ) ) ;
System.out.println( Fraction.createFraction( 3 , 9 ).equals( Fraction.createFraction(1,3) ) ) ;
}
}
About the static factory method, it may be useful later, if you subclass the Fraction to handle more complex things, or if you decide to use a pool for the most frequently used objects.
It may not be the case, I just wanted to point it out. :)
See Effective Java first item.
Might be useful to add simple things like reciprocate, get remainder and get whole.
Even though you have the methods compareTo(), if you want to make use of utilities like Collections.sort(), then you should also implement Comparable.
public class Fraction extends Number implements Comparable<Fraction> {
...
}
Also, for pretty display I recommend overriding toString()
public String toString() {
return this.getNumerator() + "/" + this.getDenominator();
}
And finally, I'd make the class public so that you can use it from different packages.
This function simplify using the eucledian algorithm is quite useful when defining fractions
public Fraction simplify(){
int safe;
int h= Math.max(numerator, denominator);
int h2 = Math.min(denominator, numerator);
if (h == 0){
return new Fraction(1,1);
}
while (h>h2 && h2>0){
h = h - h2;
if (h>h2){
safe = h;
h = h2;
h2 = safe;
}
}
return new Fraction(numerator/h,denominator/h);
}
For industry-grade Fraction/Rational implementation, I would implement it so it can represent NaN, positive infinity, negative infinity, and optionally negative zero with operational semantics exactly the same as the IEEE 754 standard states for floating point arithmetics (it also eases the conversion to/from floating point values). Plus, since comparison to zero, one, and the special values above only needs simple, but combined comparison of the numerator and denominator against 0 and 1 - i would add several isXXX and compareToXXX methods for ease of use (eg. eq0() would use numerator == 0 && denominator != 0 behind the scenes instead of letting the client to compare against a zero valued instance). Some statically predefined values (ZERO, ONE, TWO, TEN, ONE_TENTH, NAN, etc.) are also useful, since they appear at several places as constant values. This is the best way IMHO.
Class Fraction:
public class Fraction {
private int num; // numerator
private int denom; // denominator
// default constructor
public Fraction() {}
// constructor
public Fraction( int a, int b ) {
num = a;
if ( b == 0 )
throw new ZeroDenomException();
else
denom = b;
}
// return string representation of ComplexNumber
#Override
public String toString() {
return "( " + num + " / " + denom + " )";
}
// the addition operation
public Fraction add(Fraction x){
return new Fraction(
x.num * denom + x.denom * num, x.denom * denom );
}
// the multiplication operation
public Fraction multiply(Fraction x) {
return new Fraction(x.num * num, x.denom * denom);
}
}
The main program:
static void main(String[] args){
Scanner input = new Scanner(System.in);
System.out.println("Enter numerator and denominator of first fraction");
int num1 =input.nextInt();
int denom1 =input.nextInt();
Fraction x = new Fraction(num1, denom1);
System.out.println("Enter numerator and denominator of second fraction");
int num2 =input.nextInt();
int denom2 =input.nextInt();
Fraction y = new Fraction(num2, denom2);
Fraction result = new Fraction();
System.out.println("Enter required operation: A (Add), M (Multiply)");
char op = input.next().charAt(0);
if(op == 'A') {
result = x.add(y);
System.out.println(x + " + " + y + " = " + result);
}
Related
I'm trying to use Junit for the first time but I'm facing some unexpected failure.
Here is the failure message:
org.opentest4j.AssertionFailedError: expected: <2> but was: <19>.
It would be great if someone will be able to help me understand where is my error.
I spend more than 30 minutes in trying to understand the reason behind it and I can't. I guess I need to do a minor change somewhere.
public class Fraction {
private int numerator;
private int denominator;
public int getNumerator() {
return numerator;
}
public int getDenomonator() {
return denominator;
}
public Fraction(int n, int d) {
numerator = n;
denominator = d;
}
/**
* This method is adding other fraction
* to our current(this) fraction
* #param otherFraction
*/
public void add(Fraction otherFraction) {
int a = numerator;
int b = denominator;
int c = otherFraction.getNumerator();
int d = otherFraction.getDenomonator();
numerator = a * d + b * c;
denominator = b * d;
int min = denominator;
if (numerator < denominator) {
min = numerator;
}
int commonDiv = 1;
for (int i = 1; i <= min; i++) {
if ((numerator % i == 0) && (denominator % 1 == 0)) {
commonDiv = i;
}
}
numerator = numerator / commonDiv;
denominator = denominator / commonDiv;
if (numerator == 0) denominator = 1;
}
}
Test:
class FreactionTest {
#Test
void test() {
Fraction f1 = new Fraction(3,4);
Fraction f2 = new Fraction(5,6);
f1.add(f2);
assertEquals(f1.getNumerator(),19);
assertEquals(f1.getDenomonator(),12);
}
#Test
void testAddNegative() {
Fraction f1 = new Fraction(3,4);
Fraction f2 = new Fraction(-3,4);
f1.add(f2);
assertEquals(f1.getNumerator(),0);
assertEquals(f1.getDenomonator(),1);
}
}
I expected the code to run successfully.
It looks like you have your expected/actual backwards in the call to assertEquals(). According to the docs here, the first argument is the expected value, and the second argument is the actual value. So you need to switch your arguments, since right now you're hard-coding the actual result to be 19. The call you're trying to test should be the second argument, and the value you expect to be returned should be the first argument. You're doing it in all your other assertEquals() calls also, so be sure to change those as well.
I am learning how to code and I am having trouble with my class methods and testing these methods. Here is the problem:
In this lab, we will create a Fraction class. This class is used to represent a ratio of two integers. The main method of the FractionDriver class will contain the code that tests your Fraction class. I recommend that you test your Fraction class incrementally.
Your Fraction class should have two private integer instance variables, numerator and denominator. Initially, the value of numerator should be 0 and the value of denominator should be 1.
Write two mutator methods, setNumerator() and setDenominator(), that allow the user to set the numerator and the denominator to an integer value. Your code should not allow the denominator to be set to 0. If the user tries to set the denominator to 0, the value should not be changed.
Also, include a method named getValue() that returns the value of the numerator divided by the denominator as a double.
Add a toString() method that returns a String representation of the fraction in the form numerator/denominator, for example 5/3.
Finally, add an equals method that determines whether two objects of type Fraction are equal. Note that 3/5 and 6/10 should be considered equal.
Here is my code for my Fraction class:
public class Fraction {
private int numerator = 0;
private int denominator = 1;
private double divide;
//setting numerator and denominator
public void setNumerator(int numerator) {
this.numerator = numerator;
}
public void setDenominator(int denominator) {
if (denominator == 0) {
return;
}
this.denominator = denominator;
}
//returning value of the numerator divided by a denominator as a double
public void getValue() {
divide = numerator / denominator;
this.divide = divide;
System.out.println("The value of this fraction in decimal form is: " + divide);
}
//returning the fraction as a string #/#
public String toString() {
return "Your fraction is: " + numerator + "/" + denominator;
}
public boolean equals(Fraction other) {
if(other.divide == divide) {
return true;
}
return false;
}
}
Here is the code for my driver so far:
public class FractionDriver {
public static void main(String[] args) {
Fraction fract1 = new Fraction();
Fraction fract2 = new Fraction();
//initialize variables
fract1.setNumerator(1);
fract1.setDenominator(2);
fract2.setNumerator(5);
fract2.setDenominator(10);
for(int i = 0; i < 1; i++) {
//testing toString method
System.out.println(fract1.toString());
System.out.println(fract2.toString());
fract1.getValue();
fract2.getValue();
}
}
}
When I test my getValue() method for both fractions, each have the result of 0.0 and I am not sure what I am doing wrong in my class method.
Also, how do I test my equals method?
Dividing an int by an int gives another int. You don't get halves etc.
See Why is the result of 1/3 == 0?
Your method to get value is VOID... so that's your problem.
It should be
//returning value of the numerator divided by a denominator as a double
public double getValue() {
divide = numerator / denominator;
this.divide = divide;
return this.divide;
}
But better to make it
public double getValue() {
return numerator / denominator;
}
I'm having trouble figuring out when to use int, double and long.
I'm working on calculating the power of an integer and return the result as long as the power provided is not a negative number.
For the assignment, I'm required to use the following code to start:
public static long powerN(int number, int power) {
Here's what I came up with:
public class PowerCalculator
{
/**
* Calculate the non-negative power of an integer number. If a negative power is input, the method returns 1.
*
* #param number The number to take power.
* #param power The power factor to be taken to.
* #return The calculation result after taking power of the integer number.
*/
public static long powerN(int number, int power) {
if (power > 0)
{
double result = (Math.pow(number, power));
return result;
}
else
{
return 1;
}
}
}
I know I'm messing up the use of int, double or long but I don't know how to fix it.
Wait! If you're doing it yourself, use a faster algorithm like Exponentiation by squaring, something like this:
long powerN(long number, int power){
long res = 1;
long sq = number;
while(power > 0){
if(power % 2 == 1){
res *= sq;
}
sq = sq * sq;
power /= 2;
}
return res;
}
You could do it by yourself:
public static long powerN(
int number,
int power
) {
if(power == 0) return 1;
int result = number;
while(power > 1) {
result*=number;
power--;
}
return (long)result;
}
PS: This does not handle negative powers.
In case you'd like to use Math.pow:
public static long powerN(int number, int power) {
return (long) Math.pow(number, power);
}
Option 1: Cast result of Math.pow to long:
public class PowerCalculator{
/**
* Calculate the non-negative power of an integer number. If a negative power is input, the method returns 1.
*
* #param number The number to take power.
* #param power The power factor to be taken to.
* #return The calculation result after taking power of the integer number.
*/
public static long powerN(int number, int power) {
// write your code after this line
if (power < 0){
return 1;
} else{
return (long) Math.pow(number, power);
}
Option 2: without using Math.pow
public class PowerCalculator{
/**
* Calculate the non-negative power of an integer number. If a negative power is input, the method returns 1.
*
* #param number The number to take power.
* #param power The power factor to be taken to.
* #return The calculation result after taking power of the integer number.
*/
public static long powerN(int number, int power) {
// write your code after this line
long result = 1;
while (power > 0) {
result *= number;
power--;
}
return result;
}
I am trying to print the contents of a of my object Fraction(), but it keeps giving me a lot of errors and referring me back to where my print statements start. I have a toString() method that I created, but that does not seem to work either. Here is my class and tester class:
package fraction;
public class Fraction
{
/**
* The numerator and denominator.
*/
private int top;
private int bottom;
/**
* Creates the fraction 0/1
*/
public Fraction()
{
top = 0;
bottom = 1;
}
/**
* Creates the fraction n/1
* #param n an integer
*/
public Fraction(int n)
{
top = n;
bottom = 1;
}
/**
* Creates a fraction with the specified numerator and denominator
* #param n the numerator
* #param d the denominator
*/
public Fraction(int n, int d)
{
top = n;
bottom = d;
if (bottom == 0) {
throw new IllegalArgumentException();
}
}
/**
* Computes the sum of this fraction and the specified fraction
* #param f a fraction
* #return the fraction obtained by adding this fraction from the specified fraction
*/
public Fraction add(Fraction f)
{
return new Fraction(this.numerator() * f.denominator() + f.numerator() * this.denominator());
}
/**
* Compares this fraction and the specified fraction
* #param f a fraction
* #return 0 when this fraction is equal to the specified fraction; 1 when this fraction is greater than the specified
* fraction; -1 otherwise
*/
public int compareTo(Fraction f)
{
if (top > f.numerator())
return 1;
else if (top < f.numerator())
return -1;
else if (bottom > f.denominator())
return 1;
else if (bottom < f.denominator())
return -1;
else
return 0;
}
/**
* Gives the denominator of this fraction
* #return the denominator of this fraction
*/
public int denominator()
{
return bottom;
}
/**
* Gives the quotient of this fraction and the specified fraction
* #param f a fraction
* #return the fraction obtained by dividing this fraction by the specified fraction
* #throws IllegalArgumentException when the numerator equals 0
*/
public Fraction divide(Fraction f)
{
if (f.numerator() == 0) {
throw new IllegalArgumentException();
}
else
{
return new Fraction(this.numerator() * f.numerator(), this.denominator() * f.denominator());
}
}
/**
* Determines whether this fraction is equal to the specified fraction
* #param f a fraction
* #return true when this fraction is equal to the specified fraction; otherwise, false
*/
public boolean equals(Fraction f)
{
return top == f.numerator() && bottom == f.denominator();
}
/**
* Computes the greatest common divisor of the specified numbers
* #param num1 an integer
* #param num2 an integer
* #return the greatest common divisor of the specified parameters
*/
private int gcd(int num1, int num2)
{
if (num2 == 0) {
return num1;
}
else
{
return gcd(num2, num1%num2);
}
}
/**
* Calculates the product of this fraction and the specified fraction
* #param f a fraction
* #return the product of this fraction and the specified fraction
*/
public Fraction multiply(Fraction f)
{
return new Fraction(this.numerator() * f.numerator(), this.denominator() * f.denominator());
}
/**
* Simplifies this fraction by expressing its numerator and denominator in standard form:
* the denominator is positive and the numerator and denominator are relative primes
*/
public void normalize()
{
int gcd = gcd(top,bottom);
top /= gcd;
bottom /= gcd;
}
/**
* Gives the numerator of this fraction
* #return the numerator of this fraction
*/
public int numerator()
{
return top;
}
/**
* Computes the reciprocal of this fraction
* #return the reciprocal of this fraction
* #throws IllegalArgumentException when the numerator is equal to 0
*/
public Fraction reciprocal()
{
if (top == 0) {
throw new IllegalArgumentException();
}
int temp;
temp = numerator();
top = denominator();
bottom = temp;
return new Fraction(top, bottom);
}
/**
* Modifies this fraction
* #param n the new numerator of this fraction
* #param d the new denominator of this fraction
* #throws IllegalArgumentException when the denominator equals 0
*/
public void setFraction(int n, int d)
{
if (d == 0) {
throw new IllegalArgumentException();
}
top = n;
bottom = d;
}
/**
* Computes the difference of this fraction and the specified fraction
* #param f a fraction
* #return the fraction obtained by subtracting this fraction from the specified fraction
*/
public Fraction subtract(Fraction f)
{
return new Fraction(this.numerator() * f.denominator() - f.numerator() * this.denominator(), this.denominator() * f.denominator());
}
/**
* Gives a string representing this fraction in in-line notation, numerator/denominator
* #return a string representing this fraction in in-line notation, numerator/denominator
*/
#Override public String toString()
{
return String.format("%d/%d",top,bottom);
}
}
package fraction;
import java.util.Scanner;
public class FractionTester
{
public static void main(String[] args)
{
Scanner in = new Scanner(System.in);
System.out.print("Enter the numerator and denominator of f1 > ");
int n1 = in.nextInt(), d1 = in.nextInt();
System.out.print("Enter the numerator and denominator of f2 > ");
int n2 = in.nextInt(), d2 = in.nextInt();
System.out.print("Enter the numerator and denominator of f3 > ");
int n3 = in.nextInt(), d3 = in.nextInt();
System.out.print("Enter the numerator and denominator of f4 > ");
int n4 = in.nextInt(), d4 = in.nextInt();
System.out.println();
Fraction f1 = new Fraction(n1, d1);
Fraction f2 = new Fraction(n2, d2);
Fraction f3 = new Fraction(n3, d3);
Fraction f4 = new Fraction(n4, d4);
System.out.printf("f1 = %d", f1);
System.out.printf("f2 = %d", f2);
System.out.printf("f3 = %d", f3);
System.out.printf("f4 = %d", f4);
if (f1.compareTo(f2) == 0) {
System.out.println("f1 = f2");
}
else if (f1.compareTo(f2) < 0) {
System.out.println("f1 < f2");
}
else {
System.out.println("f1 > f2");
}
if (f3.compareTo(f4) == 0) {
System.out.println("f1 = f2");
}
else if (f3.compareTo(f4) < 0) {
System.out.println("f1 < f2");
}
else {
System.out.println("f1 > f2");
}
System.out.println();
}
}
I am trying to print the contents of the objects f1, f2, f3, and f4. It says my error is on the first print statement (System.out.printf("f1 = %d", f1);).
Your fraction is not a number (%d) but an Object of which the toString() method should be called. Change %d to %s and it will work, i.e.
System.out.printf("f1 = %s", f1);
That's not how toString() works, change:
System.out.printf("f1 = %d", f1)
to:
System.out.println("f1 = "+ f1)
When you print an object its toString() will be called, which will return a String, while you where trying to print %d (a digit).
For some reason, I'm getting the correct result, but my negative sign is having issues.
For example, if I do 1/4 - (-2/4), I get (-3/4).
Here is my minus method for subtracting fractions.
/**
Subtracts a fraction from another fraction.
#param toUse, the fraction to subtract.
#return minusFraction, the result after subtraction.
*/
public Fraction minus(Fraction toUse)
{
int newNum = ((toUse.numerator * denominator)
- (numerator * toUse.denominator));
int newDen = denominator * toUse.denominator;
Fraction minusFraction = new Fraction(newNum, newDen);
return minusFraction;
}
Here is my reduce() method, just in case...
/**
Reduces the fraction, if possible, to it's simplest form.
Converts negative fractions to the form -x/y, or if -x/-y --> x/y
*/
private void reduce()
{
int lowest = Math.abs(numerator);
int highest = Math.abs(denominator);
if (lowest > highest)
{
int temp = highest;
highest = lowest;
lowest = temp;
}
while (lowest != 0)
{
int temp = lowest;
lowest = highest % lowest;
highest = temp;
}
numerator /= highest;
denominator /= highest;
if (denominator < 0)
{
numerator *= -1;
denominator *= -1;
}
}
I only switched an operator from my previous addition method, given here as well. I think only switching the + to a - may have caused my issue.
/**
Adds two fractions together.
#param toUse, the fraction to be added.
#return plusFraction, the sum of the two fractions.
*/
public Fraction plus(Fraction toUse)
{
int newNum = ((toUse.numerator * denominator)
+ (numerator * toUse.denominator));
int newDen = denominator * toUse.denominator;
Fraction plusFraction = new Fraction(newNum, newDen);
return plusFraction;
}
i think the problem is in your Fraction Minus function:
public Fraction minus(Fraction toUse)
{
int newNum = ( (numerator * toUse.denominator)-
(toUse.numerator * denominator)
);
int newDen = denominator * toUse.denominator;
Fraction minusFraction = new Fraction(newNum, newDen);
return minusFraction;
}
ex:
1/4-(-2/4).....
here the toUse.numerator is -2 and toUseDenominator is 4
what your code was doing it made your toUse fraction(-2/4) as base fraction and was getting subtracted from the original base Fraction(1/4) i.e (-2/4)-(1/4)...hence the result -3/4
hopefully it works
Two problems:
You are subtracting in the wrong order.
Your javadoc says:
/**
Subtracts a fraction from another fraction.
#param toUse, the fraction to subtract.
#return minusFraction, the result after subtraction.
*/
Which implies this.numerator - toUse.numerator
But here you do the opposite:
int newNum = ((toUse.numerator * denominator)
- (numerator * toUse.denominator));
Which, when you call 1/4.minus(-2/4) ends up computing:
int newNum = (-2*4) - (1*4) = -9
int newDen = 4 * -4 = -16
// Your new fraction will have -9/-16 which you reduce to -3/-4
// (which is how you hold -3/4)
Just switch the code to:
/**
Subtracts a fraction from another fraction.
#param toUse, the fraction to subtract.
#return minusFraction, the result after subtraction.
*/
public Fraction minus(Fraction toUse)
{
int newNum = ((numerator * toUse.denominator)
- (toUse.numerator * denominator));
int newDen = denominator * toUse.denominator;
Fraction minusFraction = new Fraction(newNum, newDen);
return minusFraction;
}
Now when
int newNum = (1*4) - (-2*4) = 9
int newDen = 4 * -4 = -16
This brings us to the second problem. Your reduce method relies on the denominator to determine if the number is negative or positive. But it is the numerator that should really carry the sign because you do the subtraction on the numerator.