# C++ > Data Structures and Algorithm Analysis in C++ Code Examples

## Polynomials

``` Polynomials /* * This code doesn't really do much, and abstraction is not built in. * Thus, I haven't bothered testing it exhaustively. */ #include <iostream.h> #include "vector.h" class Polynomial { enum { MAX_DEGREE = 100 }; friend int main( ); // So I can do a quick test. public: Polynomial( ); void zeroPolynomial( ); Polynomial operator+( const Polynomial & rhs ) const; Polynomial operator*( const Polynomial & rhs ) const; void print( ostream & out ) const; private: vector<int> coeffArray; int highPower; }; int max( int a, int b ) { return a > b ? a : b; } Polynomial::Polynomial( ) : coeffArray( MAX_DEGREE + 1 ) { zeroPolynomial( ); } void Polynomial::zeroPolynomial( ) { for( int i = 0; i <= MAX_DEGREE; i++ ) coeffArray[ i ] = 0; highPower = 0; } Polynomial Polynomial::operator+( const Polynomial & rhs ) const { Polynomial sum; sum.highPower = max( highPower, rhs.highPower ); for( int i = sum.highPower; i >= 0; i-- ) sum.coeffArray[ i ] = coeffArray[ i ] + rhs.coeffArray[ i ]; return sum; } Polynomial Polynomial::operator*( const Polynomial & rhs ) const { Polynomial product; product.highPower = highPower + rhs.highPower; if( product.highPower > MAX_DEGREE ) cerr << "operator* exceeded MAX_DEGREE" << endl; for( int i = 0; i <= highPower; i++ ) for( int j = 0; j <= rhs.highPower; j++ ) product.coeffArray[ i + j ] += coeffArray[ i ] * rhs.coeffArray[ j ]; return product; } void Polynomial::print( ostream & out ) const { for( int i = highPower; i > 0; i-- ) out << coeffArray[ i ] << "x^" << i << " + "; out << coeffArray[ 0 ] << endl; } ostream & operator<<( ostream & out, const Polynomial & rhs ) { rhs.print( out ); return out; } int main( ) { Polynomial p; Polynomial q; p.highPower = 1; p.coeffArray[ 0 ] = 1; p.coeffArray[ 1 ] = 1; q = p + p; p = q * q; q = p + p; cout << q << endl; return 0; } ```