//-----------------------------------------------------------------------------
//
// A Polynomial Class
//
// Author: Iamthwee 2008 (c)
//
// Improvements:
// Could use a dynamic array as opposed to a static one.
// Could improve the print function to tidy up the output.
// Suffers from a space complexity issue but achieves lexicographic sorting 
// very easily. I.e. prints terms in order of powers highest to lowest
// Could use operator overloading for code syntax candy lovers.
//
// Notes:
// Bugs may exist, not thorougly tested.
//
//------------------------------------------------------------------------------

#include <iostream>

using namespace std;

class Polynomial
{
//define private member functions
private:
   int coef[100];  // array of coefficients
   // coef[0] would hold all coefficients of x^0
   // coef[1] would hold all x^1
   // coef[n] = x^n ...

   int deg;        // degree of polynomial (0 for the zero polynomial)

//define public member functions
public:
   Polynomial::Polynomial() //default constructor
   {
      for ( int i = 0; i < 100; i++ )
      {
         coef[i] = 0;
      }
   }
   void set ( int a , int b ) //setter function
   {
      //coef = new Polynomial[b+1];
      coef[b] = a;
      deg = degree();
   }

   int degree()
   {
      int d = 0;
      for ( int i = 0; i < 100; i++ )
         if ( coef[i] != 0 ) d = i;
      return d;
   }

   void print()
   {
      for ( int i = 99; i >= 0; i-- ) {
         if ( coef[i] != 0 ) {
            cout << coef[i] << "x^" << i << " ";
         }
      }
   }

   // use Horner's method to compute and return the polynomial evaluated at x
   int evaluate ( int x )
   {
      int p = 0;
      for ( int i = deg; i >= 0; i-- )
         p = coef[i] + ( x * p );
      return p;
   }

   // differentiate this polynomial and return it
   Polynomial differentiate()
   {
      if ( deg == 0 )  {
         Polynomial t;
         t.set ( 0, 0 );
         return t;
      }
      Polynomial deriv;// = new Polynomial ( 0, deg - 1 );
      deriv.deg = deg - 1;
      for ( int i = 0; i < deg; i++ )
         deriv.coef[i] = ( i + 1 ) * coef[i + 1];
      return deriv;
   }

   Polynomial plus ( Polynomial b )
   {
      Polynomial a = *this; //a is the poly on the L.H.S
      Polynomial c;

      for ( int i = 0; i <= a.deg; i++ ) c.coef[i] += a.coef[i];
      for ( int i = 0; i <= b.deg; i++ ) c.coef[i] += b.coef[i];
      c.deg = c.degree();

      return c;
   }

   Polynomial minus ( Polynomial b )
   {
      Polynomial a = *this; //a is the poly on the L.H.S
      Polynomial c;

      for ( int i = 0; i <= a.deg; i++ ) c.coef[i] += a.coef[i];
      for ( int i = 0; i <= b.deg; i++ ) c.coef[i] -= b.coef[i];
      c.deg = c.degree();

      return c;
   }

   Polynomial times ( Polynomial b )
   {
      Polynomial a = *this; //a is the poly on the L.H.S
      Polynomial c;

      for ( int i = 0; i <= a.deg; i++ )
         for ( int j = 0; j <= b.deg; j++ )
            c.coef[i+j] += ( a.coef[i] * b.coef[j] );
      c.deg = c.degree();
      return c;
   }
};

int main()
{
   Polynomial a, b, c, d;
   a.set ( 7, 4 ); //7x^4
   a.set ( 1, 2 ); //x^2

   b.set ( 6, 3 ); //6x^3
   b.set ( -3, 2 ); //-3x^2

   c = a.minus ( b ); // (7x^4 + x^2) - (6x^3 - 3x^2)

   c.print();

   cout << "\n";

   c = a.times ( b ); // (7x^4 + x^2) * (6x^3 - 3x^2)
   c.print();

   cout << "\n";

   d = c.differentiate().differentiate();
   d.print();
   
   cout << "\n";
   
   cout << c.evaluate ( 2 ); //substitue x with 2

   cin.get();
}