Best way to evaluate a matrix-based polynomial in C++ - c++

Question

all. I'm trying to set up a program that evaluates a polynomial depending on the user input of X. Another part of the program I want is to then add these polynomials together. I'm using a 2D array to do this. What do you think would be the best way to write the evaluation function. Been working at this for hours and I'm still not quite sure how to do it. Thanks in advance.
polynomial.h
#ifndef POLYNOMIAL_H
#define POLYNOMIAL_H
#include <iostream>
using namespace std;
#define MAX 100
class Polynomial {
friend ostream &operator<< (ostream &, const Polynomial &);
public :
Polynomial ();
void enterTerms();
int evaluate(Polynomial p, int x);
Polynomial operator +(const Polynomial & );
private :
int terms[MAX][2]; //either static size(MAX rows) or use "new" for dynamic allocation
int n; //number of terms
};
#endif
polynomial.cpp
#include "polynomial.h"
using namespace std;
ostream &operator<< (ostream & out, const Polynomial & p){
for ( int i = 0 ; i < p.n ; i++ ){
if ( i == p.n - 1 )//last term does not have + appended
out << p.terms[i][0] <<"x^"<<p.terms[i][1]<<endl;
else
out << p.terms[i][0]<<"x^"<<p.terms[i][1]<<" + ";
}
return out;
}
Polynomial :: Polynomial(){
for ( int i = 0; i < MAX; i++ ){
terms[i][0] = 0;
terms[i][1] = 0;
}
}
void Polynomial :: enterTerms(){//enterTerms() not in constructor so that no prompt for entering
//terms while doing + - etc., they also produce Poylnomial instance (i.e. invoke constructor)
int num;
cout<<"enter number of terms in polynomial\n";
cin >> num;
n = num >= 0 ? num : 1;
cout << "enter coefficient followed by exponent for each term in polynomial\n";
for ( int i = 0; i < n ; i++)
cin >> terms[i][0] >> terms[i][1] ;
}
Polynomial Polynomial :: operator + ( const Polynomial & p ){
Polynomial temp, sum;
temp.n = n + p.n;
int common = 0;
// first write sum as concatenation of p1 and p2
for ( int i = 0 ; i < n ; i++ ){
temp.terms[i][0] = terms[i][0];
temp.terms[i][1] = terms[i][1];
}
//notice j and k for traversing second half of sum, and whole p2 resp
for ( int j = n, k = 0; j < n + p.n, k < p.n ; j++, k++ ){
temp.terms[j][0] = p.terms[k][0];
temp.terms[j][1] = p.terms[k][1];
}
for ( int l = 0; l < temp.n - 1 ; l++ ){ // 0 to 1 less than length
for ( int m = l + 1 ; m < temp.n ; m++ ){ // 1 more than l to length,so that compared pairs are non redundant
if( temp.terms[l][1] == temp.terms[m][1] ){
common++; //common terms reduce no. of terms in sum (see sum.n decl)
temp.terms[l][0] += temp.terms[m][0]; //coefficients added if exponents same
temp.terms[m][0] = 0;
}
}
}
sum.n = temp.n - common; //if you place it above, common taken as 0 and sum.n is same as temp.n (logical error)
//just to debug, print temporary array
cout << endl << temp;
for ( int q = 0, r = 0; q < temp.n; q++ ){
if ( temp.terms[q][0] == 0 )
continue;
else{
sum.terms[r][0] = temp.terms[q][0];
sum.terms[r][1] = temp.terms[q][1];
r++;
}
}
cout << endl << sum;
return sum;
}
int Polynomial :: evaluate(Polynomial p, int x)
{
Polynomial terms;
return 0;
}
int main()
{
Polynomial p1 , p2;
p1.enterTerms();
p2.enterTerms();
cout << "Please enter the value of x:" << endl;
cin >> x;
//evaluate(p1);
//evaluate(p2);
p1 + p2;
system("PAUSE");
//cin.get();
return 1;
}

Answer 1

Please consider a simpler data structure. A common approach is to use a single array, where the index is the power of x. Just use zeros where no such term exists. Then x^3 + 2*x + 1 is written {1, 2, 0, 1}, since there's no x^2. Also note the reverse order, since p[0] represents x^0. This drastically simplifies operations like addition.
As far as evaluation, just think about the equation. If your polynomial is x^2 + 3*x + 5, and you want to evaluate for x=7, what do you do? Start with power 0, and accumulate each term into a single variable.

Answer 2

You can follow and complete my functions here:
float polyval_point(Eigen::VectorXf v,float x)
{
float s = 0;
for (int i=0;i<v.size();i++)
{
s += v[i] * pow(x,i);
}
return s;
}
Eigen::VectorXf polyval_vector(Eigen::VectorXf v,Eigen::VectorXf X)
{
Eigen::VectorXf S(X.size());
for (int i=0;i<X.size();i++)
{
S[i] = polyval_point(v,X[i]);
}
return S;
}