Java Training Course/JT06: Difference between revisions

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imported>Gfis
Ratio
imported>Gfis
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     public Rational multiply(Rational rat2) { ... }
     public Rational multiply(Rational rat2) { ... }
     public Rational negate() { return new Rational(- numerator, denominator); }
     public Rational negate() { return new Rational(- numerator, denominator); }
     // public Rational reduce() is already implemented below
     public Rational reduce() is already implemented below
     // public Rational subtract(Rational rat2) is already implemented below
     public Rational subtract(Rational rat2) is already implemented below
===Starting Code===
===Implementation===
<pre>
<pre>
/* Fractions of integers
/* Fractions of integers
Line 30: Line 30:
// package name will later go here
// package name will later go here
// imports will later go here
// imports will later go here
 
/** Class <wm>Ratio</em> represents an integer fraction
/** Class <em>Ratio</em> represents an integer fraction
  *  together with the arithmetic operations on such Ratios.
  *  together with the arithmetic operations on such Ratios.
  *  The denominator is always > 0. All arithmetic operations
  *  The denominator is always &gt; 0. All arithmetic operations
  *  return reduced fractions where GCD(numerator, denominator) = 1.
  *  return reduced fractions where GCD(numerator, denominator) = 1.
  *  The methods have name, parameters and return values analogous to methods
  *  The methods have name, parameters and return values analogous to methods
Line 47: Line 47:
     /** value below the bar, after  the slash */
     /** value below the bar, after  the slash */
     public int denominator;
     public int denominator;
 
/*  Implement the following methods, and make use of basic operations.
/*  Implement the following methods, and make use of basic operations.
     All Ratio return values should be reduced.
     All Ratio return values should be reduced.
     Insert proper documentation comments.
     Insert proper documentation comments.
     Always arrange all methods of the class in alphabetical order, since there are many.
     Always arrange the public methods of the class in alphabetical order, since there are many.
*/
*/
     // public static Ratio abs(Ratio rat1) { return new Ratio(); }
     // public static Ratio abs(Ratio rat1) { return new Ratio(); }
     public static Ratio add(Ratio rat1, Ratio rat2) { return new Ratio(); }
     // public static Ratio add(Ratio rat1, Ratio rat2) { return new Ratio(); }
     // public static int compareTo(Ratio rat1, Ratio rat2) { return 0; } // return -1, 0, +1 iff this < = > rat2
     // public static int compareTo(Ratio rat1, Ratio rat2) { return 0; } // return -1, 0, +1 iff this < = > rat2
     public static Ratio divide(Ratio rat1, Ratio rat2) { return new Ratio(); }
     // public static Ratio divide(Ratio rat1, Ratio rat2) { return new Ratio(); }
     // public static boolean equals(Ratio rat1, Ratio rat2) { return rat1.compareTo(rat2) == 0; }
     // public static boolean equals(Ratio rat1, Ratio rat2) { return rat1.compareTo(rat2) == 0; }
     // public static boolean isInteger(Ratio rat1) { return false; }
     // public static boolean isInteger(Ratio rat1) { return false; }
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     // public static Ratio min(Ratio rat1, Ratio rat2) { return rat2; }
     // public static Ratio min(Ratio rat1, Ratio rat2) { return rat2; }
     // public static Ratio multiply(Ratio rat1, Ratio rat2) is already implemented below
     // public static Ratio multiply(Ratio rat1, Ratio rat2) is already implemented below
     public static Ratio negate(Ratio rat1) { return new Ratio(); }
     // public static Ratio negate(Ratio rat1) { return new Ratio(); }
     // public static Ratio reduce(Ratio rat1) is already implemented below
     // public static Ratio reduce(Ratio rat1) is already implemented below
     public static Ratio subtract(Ratio rat1, Ratio rat2) { return new Ratio(); }
     // public static Ratio subtract(Ratio rat1, Ratio rat2) { return new Ratio(); }
   
   
     //----------------
     //----------------
     // Constructors
     // Constructors
Line 76: Line 76:
         denominator = 1;
         denominator = 1;
     } // no-args constructor
     } // no-args constructor
 
     /** Constructor with numerator, creates a/1
     /** Constructor with numerator, creates a/1
     *  @param a numerator
     *  @param a numerator
Line 84: Line 84:
         denominator = 1;
         denominator = 1;
     } // constructor(int)
     } // constructor(int)
 
     /** Constructor with numerator and denominator, creates a/b
     /** Constructor with numerator and denominator, creates a/b
     *  @param a numerator
     *  @param a numerator
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         denominator = b;
         denominator = b;
     } // constructor(int, int)
     } // constructor(int, int)
 
     /** Constructor from a String representation, creates a/b
     /** Constructor from a String representation, creates a/b
     *  @param str String of the form "a/b"
     *  @param str String of the form "a/b"
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             slashPos = str.length() - 2;
             slashPos = str.length() - 2;
         }
         }
         numerator   = Integer.parseInt(str.substring(0, slashPos));
         numerator   = Integer.parseInt(str.substring(0, slashPos));
         denominator = Integer.parseInt(str.substring(slashPos + 1));
         denominator = Integer.parseInt(str.substring(slashPos + 1));
     } // constructor(String)
     } // constructor(String)
 
     //----------------
     //----------------
     // Internal getters
     // Internal getters
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         return numerator;
         return numerator;
     } // getNum()
     } // getNum()
 
     /** Gets the denominator
     /** Gets the denominator
     *  @return the denominator of this Ratio
     *  @return the denominator of this Ratio
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         return denominator;
         return denominator;
     } // getDen()
     } // getDen()
 
     //----------------
     //----------------
     // Public methods
     // Public methods
     //----------------
     //----------------
    /** Returns the sum of one Ratio and a second.
    *  @param rat1 1st Ratio
    *  @param rat2 2nd Ratio
    *  @return (rat1 + rat2)
    */
    public static Ratio add(Ratio rat1, Ratio rat2) {
        int denom  = Ratio.lcm(rat1.denominator, rat2.denominator);
        int fact1  = denom / rat1.denominator;
        int fact2  = denom / rat2.denominator;
        int numSum = rat1.numerator * fact1
                    + rat2.numerator * fact2;
        return Ratio.reduce(new Ratio(numSum, denom));
    } // add(Ratio)
    /** Returns the quotient of one Ratio and a second.
    *  @param rat1 1st Ratio
    *  @param rat2 2nd Ratio
    *  @return (rat1 / rat2)
    */
    public static Ratio divide(Ratio rat1, Ratio rat2) {
        return Ratio.reduce(new Ratio
                ( rat1.numerator  * rat2.denominator
                , rat1.denominator * rat2.numerator    )
                );
    } // divide(Ratio)
     /** Returns the greatest common divisor of 2 integers.
     /** Returns the greatest common divisor of 2 integers.
     *  @param a 1st integer
     *  @param a 1st integer
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     */
     */
     public static int gcd(int a, int b) {
     public static int gcd(int a, int b) {
         int result = 0;
         int result = Math.abs(a);
         // not yet implemented
        if (result != 1) {
         return result;
            int p = result;
     } // gcd(int,int)
            int q = Math.abs(b);
            while (q != 0) {
                int temp = q;
                q = p % q;
                p = temp;
            }
            result = p;
         } // if > 1
         return Math.abs(result);
     } // gcd(a, b)
   
     /** Returns the least common multiple of 2 integers.
     /** Returns the least common multiple of 2 integers.
     *  @param a 1st integer
     *  @param a 1st integer
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         return result / gcd(a, b);
         return result / gcd(a, b);
     } // lcm(int,int)
     } // lcm(int,int)
 
     /** Returns the product of one Ratio and a second.
     /** Returns the product of one Ratio and a second.
     *  @param rat1 1st Ratio
     *  @param rat1 1st Ratio
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                 );
                 );
     } // multiply(Ratio)
     } // multiply(Ratio)
   
 
    /** Returns the negative of a Ratio.
    * @param rat1  Ratio to be negated
    *  @return (- rat1)
    */
    public static Ratio negate(Ratio rat1) {
        return Ratio.reduce(new Ratio( - rat1.numerator, rat1.denominator));
    } // negate(Ratio)
 
     /** Reduces and normalizes the fraction, that means:  
     /** Reduces and normalizes the fraction, that means:  
     *  <ul>
     *  (1) divides the numerator and the denominator by
    *  <li>divides the numerator and the denominator by
     *  their greatest common divisor, if that is &gt; 1,
     *  their greatest common divisor, if that is &gt; 1,</li>
     *  (2) makes the denominator always positive,  
     *  <li>makes the denominator always positive,</li>
     *  (3) normalizes the denominator to 1 if the numerator is 0.
     *  <li>normalizes the denominator to 1 if the numerator is 0.</li>
     *  @param rat1 the Ratio to be reduced
     *  </ul>
    *  @return the reduced Ratio
     */
     */
     public static Ratio reduce(Ratio rat1) {
     public static Ratio reduce(Ratio rat1) {
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         return result;
         return result;
     } // reduce(Ratio)
     } // reduce(Ratio)
 
    /** Returns the difference of one Ratio and a second.
    *  @param rat1 1st Ratio
    *  @param rat2 2nd Ratio
    *  @return (rat1 - rat2)
    */
    public static Ratio subtract(Ratio rat1, Ratio rat2) {
        return Ratio.add(rat1, Ratio.negate(rat2));
    } // subtract(Ratio)
 
     /** Returns this Ratio as a String.
     /** Returns this Ratio as a String.
     *  @return a String of the form "a/b", or only "a" if b is 1.
     *  @return a String of the form "a/b", or only "a" if b is 1.
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         return result;
         return result;
     } // toString()
     } // toString()
 
 
     //================
     //================
     /** Test program, shows a series of fixed operations
     /** Test program, shows a series of fixed operations
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             String  str1 = args[iarg];
             String  str1 = args[iarg];
             Ratio rat1 = new Ratio(str1);
             Ratio rat1 = new Ratio(str1);
             System.out.println(str0 + " + " + str1 + " = " + Ratio.add       (rat0, rat1).toString());
             System.out.println(str0 + " + " + str1 + " = " + Ratio.add     (rat0, rat1).toString());
             System.out.println(str0 + " - " + str1 + " = " + Ratio.subtract(rat0, rat1).toString());
             System.out.println(str0 + " - " + str1 + " = " + Ratio.subtract(rat0, rat1).toString());
             System.out.println(str0 + " * " + str1 + " = " + Ratio.multiply(rat0, rat1).toString());
             System.out.println(str0 + " * " + str1 + " = " + Ratio.multiply(rat0, rat1).toString());
             System.out.println(str0 + " / " + str1 + " = " + Ratio.divide     (rat0, rat1).toString());
             System.out.println(str0 + " / " + str1 + " = " + Ratio.divide (rat0, rat1).toString());
             System.out.println();
             System.out.println();
             str0 = str1;
             str0 = str1;
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     } // main
     } // main
} // Ratio
} // Ratio
</ore>
</pre>
[[Java Training Course/JT05|&lt; Previous: JT05]] Control Structures: The Greatest Common Divisor<br />
[[Java Training Course/JT05|&lt; Previous: JT05]] Control Structures: The Greatest Common Divisor<br />
[[Java Training Course/JT07|&gt; Next: JT07]] Class ''Rational''
[[Java Training Course/JT07|&gt; Next: JT07]] Class ''Rational''

Latest revision as of 15:25, 7 November 2017

Preliminary Class Ratio

As a preparation we implement a Java class which represents fractions and arithmetic operations thereon, but the operations (methods in Java terminology) are all static. They are implemented in a rather straight-forward way, and they are not yet really object-oriented.

Below you will find a skeleton for the code. The task of this session is

  • Fill in the bodies of the following methods if necessary.
  • Thereby make as much use of other methods as possible.
  • Insert proper documentation comments.
  • Arrange the methods of the class in alphabetical order (since there are many).

Desired Methods

    public Rational abs() { return new Rational((numerator < 0 ? - numerator : numerator), denominator) }
    public Rational add(Rational rat2) { ... }
    public int compareTo(Rational rat2) { /* return -1, 0, +1 iff this < = > rat2 */ ... }
    public Rational divide(Rational rat2) { ... }
    public boolean equals(Rational rat2) { return this.compareTo(rat2) == 0; }
    public boolean isInteger() { return denominator == 1; }
    public int intValue() { return numerator / denominator; }
    public Rational max(Rational rat2) { return this.compareTo(rat2) > 0 ? this : rat2 }
    public Rational min(Rational rat2) { return this.compareTo(rat2) < 0 ? this : rat2 }
    public Rational multiply(Rational rat2) { ... }
    public Rational negate() { return new Rational(- numerator, denominator); }
    public Rational reduce() is already implemented below
    public Rational subtract(Rational rat2) is already implemented below

Implementation

/* Fractions of integers
 * @(#) $Id$
 * 2017-11-07: revised in Bekasi
 * 2017-09-23, Georg Fischer
 */
// package name will later go here
// imports will later go here

/** Class <em>Ratio</em> represents an integer fraction
 *  together with the arithmetic operations on such Ratios.
 *  The denominator is always > 0. All arithmetic operations
 *  return reduced fractions where GCD(numerator, denominator) = 1.
 *  The methods have name, parameters and return values analogous to methods
 *  of the Java object type BigInteger, see
 *  https://docs.oracle.com/javase/7/docs/api/java/math/BigInteger.html
 */
public class Ratio {
    //----------------
    // Internal Properties
    //----------------
    /** value above the bar, before the slash */
    public int numerator;
    /** value below the bar, after  the slash */
    public int denominator;

/*  Implement the following methods, and make use of basic operations.
    All Ratio return values should be reduced.
    Insert proper documentation comments.
    Always arrange the public methods of the class in alphabetical order, since there are many.
*/
    // public static Ratio abs(Ratio rat1) { return new Ratio(); }
    // public static Ratio add(Ratio rat1, Ratio rat2) { return new Ratio(); }
    // public static int compareTo(Ratio rat1, Ratio rat2) { return 0; } // return -1, 0, +1 iff this < = > rat2
    // public static Ratio divide(Ratio rat1, Ratio rat2) { return new Ratio(); }
    // public static boolean equals(Ratio rat1, Ratio rat2) { return rat1.compareTo(rat2) == 0; }
    // public static boolean isInteger(Ratio rat1) { return false; }
    // public static int intValue(Ratio rat1) { return 0; }
    // public static Ratio max(Ratio rat1, Ratio rat2) { return rat1; }
    // public static Ratio min(Ratio rat1, Ratio rat2) { return rat2; }
    // public static Ratio multiply(Ratio rat1, Ratio rat2) is already implemented below
    // public static Ratio negate(Ratio rat1) { return new Ratio(); }
    // public static Ratio reduce(Ratio rat1) is already implemented below
    // public static Ratio subtract(Ratio rat1, Ratio rat2) { return new Ratio(); }
    
    //----------------
    // Constructors
    //----------------
    /** No-args constructor, creates 1/1
     */
    public Ratio() {
        numerator   = 1;
        denominator = 1;
    } // no-args constructor

    /** Constructor with numerator, creates a/1
     *  @param a numerator
     */
    public Ratio(int a) {
        numerator   = a;
        denominator = 1;
    } // constructor(int)

    /** Constructor with numerator and denominator, creates a/b
     *  @param a numerator
     *  @param b denominator
     */
    public Ratio(int a, int b) {
        numerator   = a;
        denominator = b;
    } // constructor(int, int)

    /** Constructor from a String representation, creates a/b
     *  @param str String of the form "a/b"
     */
    public Ratio(String str) {
        int slashPos = str.indexOf("/");
        if (slashPos < 0) {
            str += "/1";
            slashPos = str.length() - 2;
        }
        numerator    = Integer.parseInt(str.substring(0, slashPos));
        denominator = Integer.parseInt(str.substring(slashPos + 1));
    } // constructor(String)

    //----------------
    // Internal getters
    //----------------
    /** Gets the numerator
     *  @return the numerator   of this Ratio
     */
    private int getNum() {
        return numerator;
    } // getNum()

    /** Gets the denominator
     *  @return the denominator of this Ratio
     */
    private int getDen() {
        return denominator;
    } // getDen()

    //----------------
    // Public methods
    //----------------

    /** Returns the sum of one Ratio and a second.
     *  @param rat1 1st Ratio
     *  @param rat2 2nd Ratio
     *  @return (rat1 + rat2)
     */
    public static Ratio add(Ratio rat1, Ratio rat2) {
         int denom  = Ratio.lcm(rat1.denominator, rat2.denominator);
         int fact1  = denom / rat1.denominator;
         int fact2  = denom / rat2.denominator;
         int numSum = rat1.numerator * fact1
                    + rat2.numerator * fact2;
         return Ratio.reduce(new Ratio(numSum, denom));
    } // add(Ratio)

    /** Returns the quotient of one Ratio and a second.
     *  @param rat1 1st Ratio
     *  @param rat2 2nd Ratio
     *  @return (rat1 / rat2)
     */
    public static Ratio divide(Ratio rat1, Ratio rat2) {
        return Ratio.reduce(new Ratio
                ( rat1.numerator   * rat2.denominator
                , rat1.denominator * rat2.numerator    )
                );
    } // divide(Ratio)

    /** Returns the greatest common divisor of 2 integers.
     *  @param a 1st integer
     *  @param b 2nd integer
     *  @return gcd(a,b), which is always positive
     */
    public static int gcd(int a, int b) {
        int result = Math.abs(a);
        if (result != 1) {
            int p = result;
            int q = Math.abs(b);
            while (q != 0) {
                int temp = q;
                q = p % q;
                p = temp;
            }
            result = p;
        } // if > 1
        return Math.abs(result);
    } // gcd(a, b)
    
    /** Returns the least common multiple of 2 integers.
     *  @param a 1st integer
     *  @param b 2nd integer
     *  @return lcm(a,b)
     */
    public static int lcm(int a, int b) {
        int result = a * b;
        if (result < 0) { // absolute, make positive
            result = - result;
        } // abs
        return result / gcd(a, b);
    } // lcm(int,int)

    /** Returns the product of one Ratio and a second.
     *  @param rat1 1st Ratio
     *  @param rat2 2nd Ratio
     *  @return (rat1 * rat2)
     */
    public static Ratio multiply(Ratio rat1, Ratio rat2) {
        return Ratio.reduce(new Ratio
                ( rat1.numerator   * rat2.numerator
                , rat1.denominator * rat2.denominator)
                );
    } // multiply(Ratio)

    /** Returns the negative of a Ratio.
     *  @param rat1  Ratio to be negated
     *  @return (- rat1)
     */
    public static Ratio negate(Ratio rat1) {
        return Ratio.reduce(new Ratio( - rat1.numerator, rat1.denominator));
    } // negate(Ratio)

    /** Reduces and normalizes the fraction, that means: 
     *  (1) divides the numerator and the denominator by
     *  their greatest common divisor, if that is > 1,
     *  (2) makes the denominator always positive, 
     *  (3) normalizes the denominator to 1 if the numerator is 0.
     *  @param rat1 the Ratio to be reduced
     *  @return the reduced Ratio
     */
    public static Ratio reduce(Ratio rat1) {
        Ratio result = new Ratio(rat1.numerator, rat1.denominator);
        int common = gcd(rat1.numerator, rat1.denominator);
        if (common > 1) {
            result.numerator   /= common;
            result.denominator /= common;
        }
        if (result.numerator == 0) {
            result.denominator = 1;
        } else if (result.denominator < 0) {
            result.numerator   = - result.numerator;
            result.denominator = - result.denominator;
        }
        return result;
    } // reduce(Ratio)
 
    /** Returns the difference of one Ratio and a second.
     *  @param rat1 1st Ratio
     *  @param rat2 2nd Ratio
     *  @return (rat1 - rat2)
     */
    public static Ratio subtract(Ratio rat1, Ratio rat2) {
        return Ratio.add(rat1, Ratio.negate(rat2));
    } // subtract(Ratio)

    /** Returns this Ratio as a String.
     *  @return a String of the form "a/b", or only "a" if b is 1.
     */
    public String toString() {
        String result = String.valueOf(numerator);
        if (denominator != 1) {
            result += "/" + String.valueOf(denominator);
        }
        return result;
    } // toString()

    //================
    /** Test program, shows a series of fixed operations
     *  @param args String array of commandline arguments
     */
    public static void main(String[] args) {
        int iarg = 0;
        String   str0 = "0/1";
        Ratio rat0 = new Ratio(str0);
        while (iarg < args.length) {
            String   str1 = args[iarg];
            Ratio rat1 = new Ratio(str1);
            System.out.println(str0 + " + " + str1 + " = " + Ratio.add     (rat0, rat1).toString());
            System.out.println(str0 + " - " + str1 + " = " + Ratio.subtract(rat0, rat1).toString());
            System.out.println(str0 + " * " + str1 + " = " + Ratio.multiply(rat0, rat1).toString());
            System.out.println(str0 + " / " + str1 + " = " + Ratio.divide  (rat0, rat1).toString());
            System.out.println();
            str0 = str1;
            rat0 = rat1;
            iarg ++;
        } // while iarg
    } // main
} // Ratio

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