/**
 * A class to create, add, and multiply polynomials. A polynomial is defined
 * as a sum of terms where each term has variable x, an int coefficient, and
 * a nonnegative int exponent
 */
public class Polynomial
{
   private Node head ;   // points to the first Node of a Polynomial

   /**
    * Default constructor creates a Polynomial with no terms
    */
   public Polynomial()  // DO NOT MODIFY THIS CONSTRUCTOR
   {
      head = null ;
   }
   
   /**
    * "Copy" constructor. Creates a "deep copy" of a given Polynomial. 
    * I.e. a new Polynomial with identical terms
    * @param p the Polynomial to be copied
    */
   public Polynomial(Polynomial p) 
   {
      // TO DO: write body of this method
   }
   
   /**
    * Creates a new Term and Node containing it and inserts it in its proper
    * place in this Polynomial (i.e. in ascending order by exponent) 
    * @param coeff the coefficient of the new Term
    * @param expo the exponent of the new Term
    */
   public void addTerm(int coeff, int expo)
   {
      // TO DO: write body of this method 
   }      
  
   /**
    * Returns a polynomial as a String in this form: x + 3x^2 + 7x^3 + x^5
    * @return the polynomial as a String
    */
   public String toString()
   {
       // TO DO: write body of this method
       // temporary return so class skeleton will compile and run
       return "Hi Mom!" ;
   }
   
   // collect terms of a Polynomial object. I.e. replace all terms having the 
   // same exponent with a single term which is their sum
   private void collectTerms()
   {
       // TO DO: write body of this method
   }
   
   /**
    * Multiply this Polynomial by another Polynomial
    * @param p the other Polynomial
    * @return the product of the two Polynomials
    */
   public Polynomial polyMultiply(Polynomial p)
   {
       // TO DO: write body of this method
       // temporary return so class skeleton will compile and run
       return null ;
   }
   
   /**
    * Add this Polynomial and another Polynomial
    * @param p the other Polynomial
    * @return the sum of the two Polynomials
    */
   public Polynomial polyAdd(Polynomial p)
   {      
       // TO DO: write body of this method
       // temporary return so class skeleton will compile and run
       return null ;
   }
   
   // Node class definition - DO NOT MODIFY!
   class Node <E extends Term>
   {
      private E info ;     // each node stores an object of the 
                           // type-parameter class...
      private Node next ;  // ...and a pointer to another node

      // Node Constructor 
      // parameter x is an object of the type-parameter class
      Node(E x)         
      {
         info = x;	// set info portion to parameter passed
         next = null;	// not pointing to another Node yet
      }
   } // end of Node class definition ============================
} // end of Polynomial class definition =========================