// polymult.cpp
//
//
// This program reads an input n from the user.
// Then, it either reads or randomly generates 2 polynomials,
// 	each with n coefficients
// It multiplies these 2 polynomials.
// Finally, it prints out the result of the multiplication.
//  
//
// A polynomial with n coefficient is represented as
// an array of n integers.
//
//
// The program contains the following subroutines:
//
// void polyread( int *p, int n)
//    This function reads in n coefficients from the user for
//    polynomial p
//
// void polyrand( int *p, int n)
//    This function creates random coefficients for polynomial p,
//    which has n coefficients.
//
// void polyprint( int *p, int n)
//    This function prints the coefficients of the polynomial on the screen
//    starting with the coefficient of the monomial of degree 0.
//
// void polymult( int *p, int *q, int *r, int n)
//    This function multiplies polynomials p and q, each has n coefficients
//    and stores the result in r.
//


#include <iostream.h>
#include <stdlib.h>

void polyread( int *p, int n);
void polyrand( int *p, int n);
void polyprint( int *p, int n);
void polymult( int *p, int *q, int *r, int n);


void main()
{
   int *a,*b,*c,n;
 

   cout << "Enter N: ";
   cin >> n;

   a=new int[n];
   b=new int[n];
   if (n <= 10)
   {
   	polyread(a,n); // read the first polynomial
      polyread(b,n); // read the second polynomial
   }
   else
   {
   	polyrand(a,n); // random first polynomial
   	polyrand(b,n); // random second polynomial
   }

   c=new int[2*n-1];
   polymult(a,b,c,n); // multiplying the polynomials

   // printing out the result 
   cout<< " The coefficients of the first polynomial are" << endl;
   polyprint(a,n);
   cout<< " The coefficients of the second polynomial are" << endl;
   polyprint(b,n);
   cout<< " The coefficients of the resulting polynomial are" << endl;
   polyprint(c,2*n-1);

   // freeing up space at the end
   delete [] c;
   delete [] b;
   delete [] a;
}

void polyread( int *p, int n)
{
	cout << "Please enter the " << n << " coefficients, sep. by spaces\n";
   for (int i = 0; i < n; i++)
   {
   	cin >> p[i];
   }
}

void polyrand( int *p, int n)
{
   for( int i=0; i<n; i++) {
      p[i] = (rand() % 41)-20;
   }  
}
 
void polyprint( int *p, int n)
{
   for( int i=0; i<n; i++) {
      cout << p[i] << " ";
   } 
   cout << endl;
}

void polymult( int *p, int *q, int *r, int n)
{
  
   for( int k=0; k<2*n-1; k++) {
      r[k]=0;
   }
   for( int i=0; i<n; i++) {
      for( int j=0; j<n; j++) {
         r[i+j] += p[i]*q[j];
      }
   }
}