package hw4;

/**
 * <b>RatTerm</b> is an immutable representation of a term in a single-variable
 * polynomial expression. The term has the form C*x^E where C is a rational
 * number and E is an integer.
 * <p>
 *
 * A RatTerm, t, can be notated by the pair (C . E), where C is the coefficient
 * of t, and E is the exponent of t.
 * <p>
 *
 * The zero RatTerm, (0 . 0), is the only RatTerm that may have a zero
 * coefficient. For example, (0 . 7) is an invalid RatTerm and an attempt to
 * construct such a RatTerm (through the constructor or arithmetic operations on
 * existing RatTerms) will return the semantically equivalent RatTerm (0 . 0).
 * For example, (1 . 7) + (-1 . 7) = (0 . 0).
 * <p>
 *
 * (0 . 0), (1 . 0), (1 . 1), (1 . 3), (3/4 . 17), (7/2 . -1), and (NaN . 74)
 * are all valid RatTerms, corresponding to the polynomial terms "0", "1", "x",
 * "x^3", "3/4*x^17", "7/2*x^-1" and "NaN*x^74", respectively.
 */
// See RatNum's documentation for a definition of "immutable".
public final class RatTerm {

  /** Coefficient of this term. */
  private final RatNum coeff;

  /** Exponent of this term. */
  private final int expt;

  // Abstraction Function:
  // For a given RatTerm t, "coefficient of t" is synonymous with
  // t.coeff, and, likewise, "exponent of t" is synonymous with t.expt.
  // All RatTerms with a zero coefficient are represented by the
  // zero RatTerm, z, which has zero for its coefficient AND exponent.
  //
  // Representation Invariant:
  // coeff != null
  // coeff.equals(RatNum.ZERO) ==> expt == 0

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

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

  /** A constant holding a one value of type RatTerm */
  private static final RatNum ONE = new RatNum(1);

  /**
   * @param c the coefficient of the RatTerm to be constructed.
   * @param e the exponent of the RatTerm to be constructed.
   * @requires c != null
   * @effects Constructs a new RatTerm t, with t.coeff = c, and if
   *          c.equals(RatNum.ZERO), then t.expt = 0, otherwise t.expt = e
   */
  public RatTerm(RatNum c, int e) {
    if (c.equals(RatNum.ZERO)) {
      // If coefficient is zero, must set exponent to zero.
      coeff = RatNum.ZERO;
      expt = 0;
    } else {
      coeff = c;
      expt = e;
    }
    checkRep();
  }

  /**
   * Gets the coefficient of this RatTerm.
   *
   * @return the coefficient of this RatTerm.
   */
  public RatNum getCoeff() {
    // TODO: Fill in this method, then remove the RuntimeException
    throw new RuntimeException("RatTerm->getCoeff() is not yet implemented");
  }

  /**
   * Gets the exponent of this RatTerm.
   *
   * @return the exponent of this RatTerm.
   */
  public int getExpt() {
    // TODO: Fill in this method, then remove the RuntimeException
    throw new RuntimeException("RatTerm->getExpt() is not yet implemented");
  }

  /**
   * Returns true if this RatTerm is not-a-number.
   *
   * @return true if and only if this has NaN as a coefficient.
   */
  public boolean isNaN() {
    // TODO: Fill in this method, then remove the RuntimeException
    throw new RuntimeException("RatTerm->isNaN() is not yet implemented");
  }

  /**
   * Returns true if this RatTerm is equal to 0.
   *
   * @return true if and only if this has zero as a coefficient.
   */
  public boolean isZero() {
    // TODO: Fill in this method, then remove the RuntimeException
    throw new RuntimeException("RatTerm->isZero() is not yet implemented");
  }

  /**
   * Returns the value of this RatTerm, evaluated at d.
   *
   * @param d The value at which to evaluate this term.
   * @return the value of this polynomial when evaluated at 'd'. For example,
   *         "3*x^2" evaluated at 2 is 12. if (this.isNaN() == true), return
   *         Double.NaN
   */
  public double eval(double d) {
    // TODO: Fill in this method, then remove the RuntimeException
    // Hint: You may find java.lang.Math's pow() method useful.
    throw new RuntimeException("RatTerm->eval() is not yet implemented");
  }

  /**
   * Negation operation.
   *
   * @return a RatTerm equals to (-this). If this is NaN, then returns NaN.
   */
  public RatTerm negate() {
    // TODO: Fill in this method, then remove the RuntimeException
    throw new RuntimeException("RatTerm->negate() is not yet implemented");
  }

  /**
   * Addition operation.
   *
   * @param p The other value to be added.
   * @requires arg != null
   * @return a RatTerm equals to (this + arg). If either argument is NaN, then
   *         returns NaN.
   * @throws IllegalArgumentException
   *             if (this.expt != arg.expt) and neither argument is zero or
   *             NaN.
   */
  public RatTerm add(RatTerm arg) {
    // TODO: Fill in this method, then remove the RuntimeException
    throw new RuntimeException("RatTerm->add() is not yet implemented");
  }

  /**
   * Subtraction operation.
   *
   * @param p The value to be subtracted.
   * @requires arg != null
   * @return a RatTerm equals to (this - arg). If either argument is NaN, then
   *         returns NaN.
   * @throws IllegalArgumentException
   *             if (this.expt != arg.expt) and neither argument is zero or
   *             NaN.
   */
  public RatTerm sub(RatTerm arg) {
    // TODO: Fill in this method, then remove the RuntimeException
    throw new RuntimeException("RatTerm->sub() is not yet implemented");
  }

  /**
   * Multiplication operation.
   *
   * @param p The other value to be multiplied.
   * @requires arg != null
   * @return a RatTerm equals to (this * arg). If either argument is NaN, then
   *         returns NaN.
   */
  public RatTerm mul(RatTerm arg) {
    // TODO: Fill in this method, then remove the RuntimeException
    throw new RuntimeException("RatTerm->mul() is not yet implemented");
  }

  /**
   * Division operation.
   *
   * @param p The divisor.
   * @requires arg != null
   * @return a RatTerm equals to (this / arg). If arg is zero, or if either
   *         argument is NaN, then returns NaN.
   */
  public RatTerm div(RatTerm arg) {
    // TODO: Fill in this method, then remove the RuntimeException
    throw new RuntimeException("RatTerm->div() is not yet implemented");
  }

  /**
   * Return the derivative of this RatTerm.
   *
   * @return a RatTerm that, q, such that q = dy/dx, where this == y. In other
   *         words, q is the derivative of this. If this.isNaN(), then return
   *         some q such that q.isNaN()
   *         <p>
   *         Given a term, a*x^b, the derivative of the term is: (a*b)*x^(b-1)
   *         for b > 0 and 0 for b == 0 (Do not worry about the case when b <
   *         0. The caller of this function, RatPoly, contains a rep.
   *         invariant stating that b is never less than 0.)
   */
  public RatTerm differentiate() {
    // TODO: Fill in this method, then remove the RuntimeException
    throw new RuntimeException("RatTerm->differentiate() is not yet implemented");
  }

  /**
   * Returns the antiderivative of this RatTerm.
   *
   * @return a RatTerm, q, such that dq/dx = this where the constant of
   *         intergration is assumed to be 0. In other words, q is the
   *         antiderivative of this. If this.isNaN(), then return some q such
   *         that q.isNaN()
   *         <p>
   *         Given a term, a*x^b, (where b >= 0) the antiderivative of the
   *         term is: a/(b+1)*x^(b+1) (Do not worry about the case when b < 0.
   *         The caller of this function, RatPoly, contains a rep. invariant
   *         stating that b is never less than 0.)
   */
  public RatTerm antiDifferentiate() {
    // TODO: Fill in this method, then remove the RuntimeException
    throw new RuntimeException(
        "RatTerm->antiDifferentiate() unimplemented!");
  }

  /**
   * Returns a string representation of this RatTerm.
   *
   * @return A String representation of the expression represented by this.
   *         <p>
   *         There is no whitespace in the returned string.
   *         <p>
   *         If the term is itself zero, the returned string will just be "0".
   *         <p>
   *         If this.isNaN(), then the returned string will be just "NaN"
   *         <p>
   *
   * The string for a non-zero, non-NaN RatTerm is in the form "C*x^E" where C
   * is a valid string representation of a RatNum (see {@link hw4.RatNum}'s
   * toString method) and E is an integer. UNLESS: (1) the exponent E is zero,
   * in which case T takes the form "C" (2) the exponent E is one, in which
   * case T takes the form "C*x" (3) the coefficient C is one, in which case T
   * takes the form "x^E" or "x" (if E is one) or "1" (if E is zero).
   * <p>
   * Valid example outputs include "3/2*x^2", "-1/2", "0", and "NaN".
   */
  @Override
  public String toString() {
    if (this.isNaN()) {
      return "NaN";
    }
    StringBuilder output = new StringBuilder();
    RatNum c = coeff;
    int e = expt;
    if (c.isNegative()) {
      output.append("-");
      c = c.negate();
    }
    if (c.equals(ONE) && (e == 1)) {
      output.append("x");
    } else if (e == 0) {
      output.append(c.toString());
    } else if (c.equals(ONE)) {
      output.append("x^" + e);
    } else if (e == 1) {
      output.append(c.toString() + "*x");
    } else {
      output.append(c.toString() + "*x^" + e);
    }
    return output.toString();
  }

  /**
   * Builds a new RatTerm, given a descriptive String.
   *
   * @param ratStr A string of the format described in the @requires clause.
   * @requires 'termStr' is an instance of a string with no spaces that
   *           expresses a RatTerm in the form defined in the toString()
   *           method.
   *           <p>
   *
   * Valid inputs include "0", "x", and "-5/3*x^3", and "NaN".
   *
   * @return a RatTerm t such that t.toString() = termStr
   */
  public static RatTerm valueOf(String termStr) {

    if (termStr.equals("NaN")) {
      return NaN;
    }

    // Term is: "R" or "R*x" or "R*x^N" or "x^N" or "x",
    // where R is a rational num and N is an integer.

    // First we parse the coefficient
    int multIndex = termStr.indexOf("*");
    RatNum coeff = null;
    if (multIndex == -1) {
      // "R" or "x^N" or "x"
      int xIndex = termStr.indexOf("x");
      if (xIndex == -1) {
        // "R"
        coeff = RatNum.valueOf(termStr);
      } else {
        int negIndex = termStr.indexOf("-");
        // "x^N" or "x" ==> coeff = 1
        if (negIndex == -1) {
          coeff = new RatNum(1);
        }
        // "-x^N" or "-x" ==> coeff = -1
        else if (negIndex == 0) {
          coeff = new RatNum(-1);
        } else {
          throw new RuntimeException(
              "Minus sign, '-', not allowed in the middle of input string: "
                  + termStr);
        }
      }
    } else {
      // "R*x" or "R*x^N"
      coeff = RatNum.valueOf(termStr.substring(0, multIndex));
    }

    // Second we parse the exponent
    int powIndex = termStr.indexOf("^");
    int expt;
    if (powIndex == -1) {
      // "R" or "R*x" or "x"
      int xIndex = termStr.indexOf("x");
      if (xIndex == -1) {
        // "R"
        expt = 0;
      } else {
        // "R*x" or "x"
        expt = 1;
      }
    } else {
      // "R*x^N" or "x^N"
      expt = Integer.parseInt(termStr.substring(powIndex + 1));
    }
    return new RatTerm(coeff, expt);
  }

  /**
   * Standard hashCode function.
   *
   * @return an int that all objects equal to this will also.
   */
  @Override
  public int hashCode() {
    if (this.isNaN()) {
      return 0;
    }
    return (coeff.hashCode() * 7) + (expt * 43);
  }

  /**
   * Standard equality operation.
   *
   * @param obj The object to be compared for equality.
   * @return true iff 'obj' is an instance of a RatTerm and 'this' and 'obj'
   *         represent the same RatTerm. Note that all NaN RatTerms are equal.
   */
  @Override
  public boolean equals(/*@Nullable*/ Object obj) {
    if (obj instanceof RatTerm) {
      RatTerm rt = (RatTerm) obj;
      if (this.isNaN() && rt.isNaN()) {
        return true;
      } else {
        return (this.expt == rt.expt) && this.coeff.equals(rt.coeff);
      }
    } else {
      return false;
    }
  }

  /**
   * Checks that the representation invariant holds (if any).
   */
  private void checkRep() {
    assert (coeff != null) : "coeff == null";
    assert (!coeff.equals(RatNum.ZERO) || expt == 0) : "coeff is zero while expt == " + expt;
  }
}