// -------------------------------------------
// lag.txt // Hints for Lagrange polynomials 
// -------------------------------------------

// ------------------------------------------------------------
//   vec.h   vectors    // sketch 
// ------------------------------------------------------------


 class vec
  { protected :
      int n;
	  double *v;
	  
	public:
	 vec (int ni, double xi = 0); // constructor initializes v too
	 vec (const vec &vi); // copy constructor
	 // A whole set of other constructors
     virtual ~vec();      // destructor
   };

     vec::vec(int ni,double xi) // constructor
      {  n = ni;
	     v = new double[ni];
	     for (int i = 0; i < n; i++)  v[i] = xi;  }


 	 vec::vec(const vec &vi) // copy constructor
	 { 
	   n = vi.n;
	   v = new double[n];
	   for (int i = 0; i < n; i++) v[i] = vi.v[i]; }

	   
	vec::~vec() { if (v != NULL) { delete [] v; v = NULL;}}


// -------------------------------------------------------
//  lpoly   // sketch
// -------------------------------------------------------
class lpoly : public fun, public vec
   {
     private:
       vec *pvx, *pvf;
     public:
       lpoly(const vec &vxi, const vec &vfi);
	   ~lpoly();
       vec getvx(); // to fetch the vx array as a vector
       vec getvf();
       double f(double x); };


   lpoly::lpoly(const vec &vxi,  const vec &vfi):
	     vec(vxi.getn()) // make sure vector part has right dim
     {  
	    pvx = new vec(vxi); // internal vector copies of data
	    pvf = new vec(vfi); 
	    // code for building the double array v[]
		// inside the vector part, that is to say,
		// the coefficients by Newton DD
	 }


   lpoly::~lpoly() { delete pvx,pvf; }

     double lpoly::f(double x) // degree = n-1 for n points
     { 
	    double y = 0; // store for result
	    // code for the Lagrange polynomial 
		return y;
	 }