package hw4;

/** <b>RatNum</b> represents an <b>immutable</b> rational number.
    It includes all of the elements in the set of rationals, as well
    as the special "NaN" (not-a-number) element that results from
    division by zero.
    <p>
    The "NaN" element is special in many ways.  Any arithmetic
    operation (such as addition) involving "NaN" will return "NaN".
    With respect to comparison operations, such as less-than, "NaN" is
    considered equal to itself, and larger than all other rationals.
    <p>
    Examples of RatNums include "-1/13", "53/7", "4", "NaN", and "0".
 */

// ("immutable" is a common term for which "Effective Java" (p. 63)
// provides the following definition: "An immutatable class is simply
// a class whose instances cannot be modified.  All of the information
// contained in each instance is provided when it is created and is
// fixed for the lifetime of the object.")
public final class RatNum extends Number implements Comparable<RatNum> {

  private final int numer;
  private final int denom;

  // Abstraction Function:
  //   A RatNum r is NaN if r.denom = 0, (r.numer / r.denom) otherwise.
  // (An abstraction function explains what the state of the fields in a
  // RatNum represents.  In this case, a rational number can be
  // understood as the result of dividing two integers, or not-a-number
  // if we would be dividing by zero.)

  // Representation invariant for every RatNum r:
  //   (r.denom >= 0) &&
  //   (r.denom > 0 ==> there does not exist integer i > 1 such that
  //                    r.numer mod i = 0 and r.denom mod i = 0;)
  //   In other words,
  //     * r.denom is always non-negative.
  //     * r.numer/r.denom is in reduced form (assuming r.denom is not zero).
  // (A representation invariant tells us something that is true for all
  // instances of a RatNum)

  /** A constant holding a Not-a-Number (NaN) value of type RatNum */
  public static final RatNum NaN = new RatNum(1, 0);

  /** A constant holding a zero value of type RatNum */
  public static final RatNum ZERO = new RatNum(0);

  /** @param n The value of the new RatNum.
        @effects Constructs a new RatNum = n.
   */
  public RatNum(int n) {
    numer = n;
    denom = 1;
    checkRep();
  }

  /** @param n The numerator of the new RatNum.
        @param d The denominator of the new RatNum.
        @effects If d = 0, constructs a new RatNum = NaN.  Else
         constructs a new RatNum = (n / d).
   */
  public RatNum(int n, int d) {
    // special case for zero denominator; gcd(n,d) requires d != 0
    if (d == 0) {
      numer = n;
      denom = 0;

    } else {

      // reduce ratio to lowest terms
      int g = gcd(n,d);
      n = n / g;
      d = d / g;

      if (d < 0) {
        numer = -n;
        denom = -d;
      } else {
        numer = n;
        denom = d;
      }
    }
    checkRep();
  }

  /**
   * Checks that the representation invariant holds (if any).
   **/
  private void checkRep() {
    assert (denom >= 0) : "Denominator of a RatNum cannot be less than zero";

    if (denom > 0) {
      int thisGcd = gcd(numer, denom);
      assert (thisGcd == 1 || thisGcd == -1) : "RatNum not in lowest form";
    }
  }

  /** Returns true if this is NaN
        @return true iff this is NaN (not-a-number)
   */
  public boolean isNaN() {
    return (denom == 0);
  }

  /** Returns true if this is negative.
        @return true iff this < 0. */
  public boolean isNegative() {
    return (compareTo(ZERO) < 0);
  }

  /** Returns true if this is positive.
        @return true iff this > 0. */
  public boolean isPositive() {
    return (compareTo(ZERO) > 0);
  }

  /** Compares two RatNums.
        @param rn The RatNum to be compared.
        @requires rn != null
        @return a negative number if this < rn,
        0 if this = rn,
        a positive number if this > rn.
   */
  @Override
  public int compareTo(RatNum rn) {
    if (this.isNaN() && rn.isNaN()) {
      return 0;
    } else if (this.isNaN()) {
      return 1;
    } else if (rn.isNaN()) {
      return -1;
    } else {
      RatNum diff = this.sub(rn);
      return diff.numer;
    }
  }

  /** Approximates the value of this rational.
        @return a double approximation for this.  Note that "NaN" is
        mapped to {@link Double#NaN}, and the {@link Double#NaN} value
        is treated in a special manner by several arithmetic operations,
        such as the comparison and equality operators.  See the
        <a href="http://docs.oracle.com/javase/specs/jls/se7/html/jls-4.html#jls-4.2.3">
        Java Language Specification, section 4.2.3</a>, for more details.
   */
  @Override
  public double doubleValue() {
    if (isNaN()) {
      return Double.NaN;
    } else {
      // convert int values to doubles before dividing.
      return ((double)numer) / ((double)denom);
    }
  }

  /** Returns an integer approximation for this.  The rational number
        is rounded to the nearest integer.
   */
  @Override
  public int intValue() {
    // round to nearest by adding +/- .5 before truncating division.
    // we expect the implementation to use "round half away from zero".
    // for more info, see http://en.wikipedia.org/wiki/Rounding#Round_half_away_from_zero

    // note that even though the result is guaranteed to fit in an
    // int, we need to use longs for the computation.
    if (numer >= 0) {
      return (int) (((long)numer + (denom/2)) / denom);
    } else {
      return (int) (((long)numer - (denom/2)) / denom);
    }
  }

  /** Returns a float approximation for this.  This method is
        specified by our superclass, Number.
   */
  @Override
  public float floatValue() {
    return (float) doubleValue();
  }


  /** Returns a long approximation for this.  This method is
        specified by our superclass, Number.  The value returned
        is rounded to the nearest long.
   */
  @Override
  public long longValue() {
    return intValue();
  }


  // in the implementation comments for the following methods, <this>
  // is notated as "a/b" and <arg> likewise as "x/y"

  /** Returns the additive inverse of this RatNum.
        @return a Rational equal to (0 - this).
   */
  public RatNum negate() {
    return new RatNum(- this.numer, this.denom);
  }

  /** Addition operation.
        @param arg The other value to be added.
        @requires arg != null
        @return a RatNum equal to (this + arg).
        If either argument is NaN, then returns NaN.
   */
  public RatNum add(RatNum arg) {
    // a/b + x/y = ay/by + bx/by = (ay + bx)/by
    return new RatNum((this.numer*arg.denom) + (arg.numer*this.denom),
        this.denom*arg.denom);
  }

  /** Subtraction operation.
        @param arg The value to be subtracted.
        @requires arg != null
        @return a RatNum equal to (this - arg).
        If either argument is NaN, then returns NaN.
   */
  public RatNum sub(RatNum arg) {
    // a/b - x/y = a/b + -x/y
    return this.add(arg.negate());
  }

  /** Multiplication operation.
        @param arg The other value to be multiplied.
        @requires arg != null
        @return a RatNum equal to (this * arg).
        If either argument is NaN, then returns NaN.
   */
  public RatNum mul(RatNum arg) {
    // (a/b) * (x/y) = ax/by
    return new RatNum(this.numer*arg.numer,
        this.denom*arg.denom );
  }

  /** Division operation.
        @param arg The divisor.
        @requires arg != null
        @return a RatNum equal to (this / arg).
        If arg is zero, or if either argument is NaN, then returns NaN.
   */
  public RatNum div(RatNum arg) {
    // (a/b) / (x/y) = ay/bx
    if (arg.isNaN()) {
      return arg;
    } else {
      return new RatNum(this.numer*arg.denom,
          this.denom*arg.numer);
    }
  }

  /** Returns the greatest common divisor of 'a' and 'b'.
        @param a, b The numbers for which to find the GCD.
        @requires b != 0
        @return d such that a % d = 0 and b % d = 0
   */
  private static int gcd(int a, int b) {
    // Euclid's method
    if (b == 0) {
      return 0;
    }
    while (b != 0) {
      int tmp = b;
      b = a % b;
      a = tmp;
    }
    return a;
  }

  /** Standard hashCode function.
        @return an int that all objects equal to this will also
        return.
   */
  @Override
  public int hashCode() {
    // all instances that are NaN must return the same hashcode;
    if (this.isNaN()) {
      return 0;
    }
    return (this.numer*2) + (this.denom*3);
  }

  /** Standard equality operation.
        @param obj The object to be compared for equality.
        @return true if and only if 'obj' is an instance of a RatNum
        and 'this' and 'obj' represent the same rational number.  Note
        that NaN = NaN for RatNums.
   */
  @Override
  public boolean equals(/*@Nullable*/ Object obj) {
    if (obj instanceof RatNum) {
      RatNum rn = (RatNum) obj;

      // special case: check if both are NaN
      if (this.isNaN() && rn.isNaN()) {
        return true;
      } else {
        return (this.numer == rn.numer) && (this.denom == rn.denom);
      }
    } else {
      return false;
    }
  }

  /** @return a String representing this, in reduced terms.
        The returned string will either be "NaN", or it will take on
        either of the forms "N" or "N/M", where N and M are both
        integers in decimal notation and M != 0.
   */
  @Override
  public String toString() {
    // using '+' as String concatenation operator in this method
    if (isNaN()) {
      return "NaN";
    } else if (denom != 1) {
      return numer + "/" + denom;
    } else {
      return Integer.toString(numer);
    }
  }

  /** Makes a RatNum from a string describing it.
        @param ratStr A string of the format described in the @requires clause.
        @requires 'ratStr' is an instance of a string, with no spaces,
        of the form: <UL>
        <LI> "NaN"
        <LI> "N/M", where N and M are both integers in
        decimal notation, and M != 0, or
        <LI> "N", where N is an integer in decimal
        notation.
        </UL>
        @returns NaN if ratStr = "NaN".  Else returns a
        RatNum r = ( N / M ), letting M be 1 in the case
        where only "N" is passed in.
   */
  public static RatNum valueOf(String ratStr) {
    int slashLoc = ratStr.indexOf('/');
    if (ratStr.equals("NaN")) {
      return new RatNum(1,0);
    } else if (slashLoc == -1) {
      // not NaN, and no slash, must be an Integer
      return new RatNum( Integer.parseInt( ratStr ) );
    } else {
      // slash, need to parse the two parts separately
      int n = Integer.parseInt(ratStr.substring(0, slashLoc));
      int d = Integer.parseInt(ratStr.substring(slashLoc+1,
          ratStr.length()));
      return new RatNum(n, d);
    }
  }

  /**
   * Declare a serialization version number. This field is necessary because
   * our parent class (Number) implements Serializable; see the api docs for
   * java.lang.Serializable for more details.
   */
  private static final long serialVersionUID = -8593953691277016262L;
}