//Poly.h

#ifndef _POLY_H
#define _POLY_H

#include <iostream>
using namespace std;

const int CAPACITY = 100;

class Poly {
     private:
          int degree;  // degree
          int coefs[CAPACITY];  //coefficient array
     public:
          Poly();   //constructor
          ~Poly();    //destructor
          void display(ostream& out) const;
          void input(istream& in);
          int evaluate(int x);
          Poly operator+(const Poly& p);
          Poly operator*(const Poly& p);
};

ostream& operator<<(ostream& out, const Poly& p);
istream& operator>>(istream& in, Poly& p);

#endif


/////////////////////////

//Poly.cpp

#include "Poly.h"

//constructor
Poly::Poly() : degree(0) {
  for (int i = 0; i < CAPACITY; i++) //very important later
    coefs[i] = 0;
}

//destructor
Poly::~Poly() {

}


void Poly::input(istream& in) {
  cout << "Input the polynomial degree (< " << CAPACITY/2 << "): ";
  in >> degree;
  for (int i = 0; i <= degree; i++) {
    cout << "Input coefficient for degree of " << i << ": ";
    in >> coefs[i];
  }
}

void Poly::display(ostream& out) const {
  for (int i = degree; i >= 0; i--) {
    if (i > 0)
       out << coefs[i] << "*" << "x^" << i << " + ";
    else
       out << coefs[i];
  }
  out << endl;
}

//overloading operator+
Poly Poly::operator+(const Poly& p) {
  Poly temp;
  temp.degree = (degree > p.degree) ? degree : p.degree;  //take higher degree
  int i;
  for (i = 0; i <= degree && i <= p.degree; i++)
     temp.coefs[i] = coefs[i] + p.coefs[i];

  for ( ; i <= degree; i++)
     temp.coefs[i] = coefs[i];

  for ( ; i <= p.degree; i++)
     temp.coefs[i] = p.coefs[i];
  return temp;
}


//overloading operator*
Poly Poly::operator*(const Poly& p) {
  Poly temp;
  temp.degree = degree + p.degree; //get the highest degree
  for (int i = 0; i <= degree; i++)
    for (int k = 0; k <= p.degree; k++)
       temp.coefs[i+k] += coefs[i] * p.coefs[k];
  return temp;

}


int Poly::evaluate(int x) {
  int ret = 0;
  for (int i = degree; i >= 0; i--)
	ret = ret * x + coefs[i];
  return ret;
}


ostream& operator<<(ostream& out, const Poly& p) {
  p.display(out);
  return out;
}

istream& operator>>(istream& in, Poly& p) {
  p.input(in);
  return in;
}


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