#include<iostream>
#include<vector>
#ifndef Poly
#define Poly

using namespace std;

class poly {
	private:
		vector <double> tab;
	public:
		friend ostream& operator<<(ostream&, poly);
		friend poly operator+(poly p1, poly p2);
		friend poly operator*(poly p1, poly p2);
		double operator()(double x);
		double& operator[](int x);
		poly(double x = 0) {
			tab.push_back(x);
		}

};

#endif




#include <iostream>
#include<cmath>
#include "poly.h"

using namespace std;

double poly::operator()(double x) {
	double res=0;
	unsigned int power=0;
	int i;
	for(i=0;i<tab.size();i++){
		res+=tab[i]*pow(x,power);
		power++;
	}
	return res;
}

double& poly::operator[](int x) {
	if (tab.size() < x) tab.resize(x+1	,0);

	return tab[x];
}


poly operator+(poly p1,poly p2){
	poly tmp;
	(p1.tab.size() > p2.tab.size()) ? tmp.tab.resize(p1.tab.size(), 0) : tmp.tab.resize(p2.tab.size(),0);
	int i;

	for (i = 0;i < tmp.tab.size();i++) {
		if (p1.tab.size() > i&&p2.tab.size() > i)tmp[i] = p1[i] + p2[i];
		else if (p1.tab.size() > i&&p2.tab.size() <= i)tmp[i] = p1[i];
		else tmp[i] = p2[i];
	}
	return tmp;
}

poly operator*(poly p1, poly p2){
	poly tmp;
	tmp.tab.resize(p1.tab.size() + p2.tab.size(), 0);
	int i,j;
	for (i = 0;i < p1.tab.size();i++) {
		if (p1[i] != 0) {
			for (j = 0;j < p2.tab.size();j++) {
				tmp[i + j] += p1[i] * p2[j];
			}
		}
	}
	return tmp;
}

ostream& operator<<(ostream &Out, poly p2) {
	int i;
	for (i = p2.tab.size()-1;i >=0;i--) {

		if(p2[i]!=0){
			if(p2[i]!=1)Out << p2[i];
			if(i>0)Out<<"x";
			if(i>1)Out<<"^"<<i;
			if (i - 1 !=-1 && p2[i - 1] >= 0) Out << " + ";
			}
		}
	return Out;
}


//rule of 3 c++

int main(void)
{
  poly P1;              //Declare object representing polynomial P1

  P1[3] = 2; P1[1] = 3.6; P1[0] = 7;    //Specify coefficients of P1 = 2x^3 + 3.6x + 7

  poly P2=5;                //Declare object representing polynomial P2 = 5
  P2[1] = 3; P2[2] = 6; P2[4] = 1;  //Specify additional coefficients of P2 = x^4 + 6x^2 + 3x + 5

  cout << "Polynomial P1: " << P1 << endl;  //Print P1
  cout << "Polynomial P2: " << P2 << endl;  //Print P2

  poly P3 = P1 + P2;                        //Add P1 and P2
  cout << "Sum of polynomials P1 and P2: " << P3 << endl;   //Print sum of P1 and P2

  P3 = P1 * P2;                         //Multiply P1 by P2
  cout << "Product of polynomials P1 and P2: " << P3 << endl;   //Print product of P1 and P2

  P3 = 2 * P1;                          //Multiply P1 by 2
  cout << "Polynomial P1 multiplied by 2: " << P3 << endl;  //Print product of P1 and 2

  double val = P1(3.14);                        //Calculate the value of P1 at point 3.14
  cout << "Value of polynomial P1 at point 3.14: " << val << endl;  //Print the value of P1 at point 3.14

};