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# //-----------------------------------------------------------------------------
# //
# // A Polynomial Class
# //
# // Author: Iamthwee 2008 (c)
# //
# // Improvements:
# // Could use a dynamic array as opposed to a static one.
# // Could improve the print function to tidy up the output.
# // Suffers from a space complexity issue but achieves lexicographic sorting
# // very easily. I.e. prints terms in order of powers highest to lowest
# // Could use operator overloading for code syntax candy lovers.
# //
# // Notes:
# // Bugs may exist, not thorougly tested.
# //
# //------------------------------------------------------------------------------
#
# #include <iostream>
#
# using namespace std;
#
# class Polynomial
# {
# //define private member functions
# private:
# int coef[100]; // array of coefficients
# // coef[0] would hold all coefficients of x^0
# // coef[1] would hold all x^1
# // coef[n] = x^n ...
#
# int deg; // degree of polynomial (0 for the zero polynomial)
#
# //define public member functions
# public:
# Polynomial::Polynomial() //default constructor
# {
# for ( int i = 0; i < 100; i++ )
# {
# coef[i] = 0;
# }
# }
# void set ( int a , int b ) //setter function
# {
# //coef = new Polynomial[b+1];
# coef[b] = a;
# deg = degree();
# }
#
# int degree()
# {
# int d = 0;
# for ( int i = 0; i < 100; i++ )
# if ( coef[i] != 0 ) d = i;
# return d;
# }
#
# void print()
# {
# for ( int i = 99; i >= 0; i-- ) {
# if ( coef[i] != 0 ) {
# cout << coef[i] << "x^" << i << " ";
# }
# }
# }
#
# // use Horner's method to compute and return the polynomial evaluated at x
# int evaluate ( int x )
# {
# int p = 0;
# for ( int i = deg; i >= 0; i-- )
# p = coef[i] + ( x * p );
# return p;
# }
#
# // differentiate this polynomial and return it
# Polynomial differentiate()
# {
# if ( deg == 0 ) {
# Polynomial t;
# t.set ( 0, 0 );
# return t;
# }
# Polynomial deriv;// = new Polynomial ( 0, deg - 1 );
# deriv.deg = deg - 1;
# for ( int i = 0; i < deg; i++ )
# deriv.coef[i] = ( i + 1 ) * coef[i + 1];
# return deriv;
# }
#
# Polynomial plus ( Polynomial b )
# {
# Polynomial a = *this; //a is the poly on the L.H.S
# Polynomial c;
#
# for ( int i = 0; i <= a.deg; i++ ) c.coef[i] += a.coef[i];
# for ( int i = 0; i <= b.deg; i++ ) c.coef[i] += b.coef[i];
# c.deg = c.degree();
#
# return c;
# }
#
# Polynomial minus ( Polynomial b )
# {
# Polynomial a = *this; //a is the poly on the L.H.S
# Polynomial c;
#
# for ( int i = 0; i <= a.deg; i++ ) c.coef[i] += a.coef[i];
# for ( int i = 0; i <= b.deg; i++ ) c.coef[i] -= b.coef[i];
# c.deg = c.degree();
#
# return c;
# }
#
# Polynomial times ( Polynomial b )
# {
# Polynomial a = *this; //a is the poly on the L.H.S
# Polynomial c;
#
# for ( int i = 0; i <= a.deg; i++ )
# for ( int j = 0; j <= b.deg; j++ )
# c.coef[i+j] += ( a.coef[i] * b.coef[j] );
# c.deg = c.degree();
# return c;
# }
# };
#
# int main()
# {
# Polynomial a, b, c, d;
# a.set ( 7, 4 ); //7x^4
# a.set ( 1, 2 ); //x^2
#
# b.set ( 6, 3 ); //6x^3
# b.set ( -3, 2 ); //-3x^2
#
# c = a.minus ( b ); // (7x^4 + x^2) - (6x^3 - 3x^2)
#
# c.print();
#
# cout << "\n";
#
# c = a.times ( b ); // (7x^4 + x^2) * (6x^3 - 3x^2)
# c.print();
#
# cout << "\n";
#
# d = c.differentiate().differentiate();
# d.print();
#
# cout << "\n";
#
# cout << c.evaluate ( 2 ); //substitue x with 2
#
# cin.get();
# }