NPTEL WEEK 4 ASSIGNMENT FOR MULTIPLYING POLYNOMIALS

Multiply Polynomials

A polynomial of degree n is of the form P(x) = a_nxⁿ + a_n-1x^n-1 + … + a₀. Given two polynomials f(x) and g(x) of degrees n and m respectively, write a program to find the polynomial h(x) given by,

h(x) = f(x) * g(x)

INPUT: Line 1 contains n and m separated by space.

             Line 2 contains the coefficients a_n, a_n-1…, a₀ of f(x) separated by space.

             Line 3 contains the coefficients b_m, b_m-1…, b₀ of g(x) separated by space.

OUTPUT: The degree of h(x) followed by the coefficients c_k, c_k-1…, c₀ of h(x) in next line separated by space.

Sample Input:

2 2

1 2 3

3 2 1

Sample Output:

4

3 8 14 8 3

Constraints:

1 <= n <= 10

1 <= a_i <= 100

PROGRAM:

#include<stdio.h>  

  int main()  

  {  

  int n,m,i,j,k,a[10],b[10],sum=0;  

  scanf("%d%d",&n,&m);  

  for(i=n;i>=0;i--)  

  {  

  scanf("%d",&a[i]);  

  }  

  for(i=m;i>=0;i--)  

  {  

  scanf("%d",&b[i]);  

  }  

  printf("%d\n",n+m);  

  for(i=n+m;i>0;i--) 

  {  

  for(j=n;j>=0;j--)  

  {  

  for(k=m;k>=0;k--)  

  {  

  if(j+k==i)  

  {  

  sum=sum+a[j]*b[k];  

  }  

  }  

  }  

  if(i==0)  

  {  

  printf("%d ",sum);  

  }  

  else  

  {  

  printf("%d ",sum);  

  }  

  sum=0;  

  }  

 printf("%d",a[0]*b[0]);  

  return 0;  

  }