//  Polynomial class, version 1.  Publically, this version and the
//  other have the same interface.  The class represents an individual
//  polynomial.  It provides member functions to read a polynomial,
//  evaluate a polynomial, assign one polynomial to another, add two
//  polynomials, multiply two polynomials, and output a polynomial.
//
//  The internal implementation of the two versions are different.
//  This one represents coeffients of all terms, even those that are
//  zero, up to a highest degree.  This degree can be increased by the
//  assign_coefficient function.  The various operators are designed
//  to make use of this representation.
//
//  The implementation given here goes beyond the design given in the
//  text.  One important way is that there is no artificial limit on
//  the size of the exponent.
//

#ifndef POLYNOMIAL_H
#define POLYNOMIAL_H

#include <vector>
using namespace std;

class Polynomial {
public:
  // Constructors and destructors.
  Polynomial( );
  Polynomial( double a0 );        // convert a constant to a polynomial
  Polynomial( const Polynomial & old );
  ~Polynomial( );

  //  Assignment operator.
  const Polynomial & operator = ( const Polynomial& right );

  //  Evaluate the polynomial at the given value.
  double operator() ( double x ) const;

  //  Access 
  double get_coefficient( int exponent ) const;
  int max_degree() const;

  //  Modification
  void assign_coefficient(  double coefficient, int exponent );

  //  A few of the many operators we would want to provide.  These are
  //  ok as friend functions because compiler issues don't generally
  //  arise when the class is not templated.
  friend Polynomial operator+ (const Polynomial& f, const Polynomial& g);
  friend Polynomial operator- (const Polynomial& f, const Polynomial& g);
  friend Polynomial operator* (const Polynomial& f, const Polynomial& g );
  friend Polynomial operator* (double a, const Polynomial& f);
  friend Polynomial operator* (const Polynomial& f, double a);

  // Output operator as a friend function.
  friend ostream& operator<< ( ostream& ostr, const Polynomial& f );

private:
  vector<double> coefficients_;
};


#endif