nptel assignment week 4 for horner's rule

Horner's Rule

PROGRAM:You are given a polynomial of degree n. The polynomial is of the form P(x) = a_nxⁿ + a_n-1x^n-1 + … + a₀. For given values k and m, You are required to find P(k) at the end of the m^th iteration of Horner’s rule. The steps involved in the Horner’s rule are given below,

P_n (x) = a_n

P_n-1 (x) = a_n-1 + x * P_n (x)                          1^st iteration.

P_n-2 (x) = a_n-2 + x * P_n-1 (x)                        2^nd iteration.

.

.

P₀ (x) = a₀ + x * P₁ (x)                             n^th iteration.

In general, P_i (x) = a_i + x * P_{i + 1} (x) and P₀(x) is the final result. The input to your program is as follows,

Line 1 contains the integers n, m and k separated by space.

Line 2 contains the coefficients a_n, a_n-1…, a₀ separated by space.

INPUT: Integers n, m, k and the coefficients as described above.

OUTPUT: P(k) value at the end of the m^th iteration.

Sample Input:

2 2 5

3 2 1

Sample Output:

86

Constraints:

1 <= n, k, m <= 10

0 <= a_i <=10

PROGRAM:

#include<stdio.h>  

 int horner(int[],int,int);  

 int main()  

 {  

 int n,m,k,i;  

 int a[10];  

 scanf("%d%d%d",&n,&m,&k);  

 for(i=0;i<=n;++i) 

 

 {  

 scanf("%d",&a[i]);  

 }  

 printf("%d",horner(a,m,k));  

 return 0;  

 }  

 int horner(int a[],int m,int k)  

 {  

 if(m==0){  

 return a[m];  

 }  

 else{  

 return a[m]+k*horner(a,m-1,k);  

 }}