# Evaluating a polynomial at a given value of x and n

To solve a polynomial equation I have written following program, is there any way to optimize this program.

Following code is working code:

Program takes input n,x where n is the deg of polynomial and x is the point at which the polynomial is to be evaluated.

   #include<stdio.h>

int power(int x, int y);

int main()
{
// n is the deg of polynomial
// x is the value of polynomial for which it is to be evaluated
int x=0,n=0,A[10],sum=0,i=0,M=0,y=0;

printf("Enter value of n,x \n");
scanf("%d %d",&n,&x);

printf("Enter the coeficients\n");

for(i=0;i<=n;i++)          //Taking coefiecent values
{
scanf("%d",&A[i]);
}

y=n;
for(i=0;i<=n;i++)
{
M=power(x,y);
sum=sum+(A[i]*M);
y--;
}

printf("\nSum of polynomial is %d",sum);

return 0;
}

int power(int x, int y)
{
int result = x;
int i;
if(y == 0) return 1;
if(x < 0 || y < 0) return 0;

for(i = 1; i < y; ++i)
result *= x;

return result;
}


By following Horner's Method only n multiplications are needed.

#include <stdio.h>

int main()
{
// n is the deg of polynomial
// x is the value of polynomial for which it is to be evaluated
int x=0,n=0,A[10],b,i;

printf("Enter value of n,x \n");
scanf("%d %d",&n,&x);

//Taking coefficient values
printf("Enter the coeficients\n");

for(i=0;i<=n;i++) scanf("%d",&A[i]);

for(i = n - 1,b = A[n];i >= 0;i--) b = b*x + A[i];

printf("\nSum of polynomial is %d\n",b);

return 0;
}


If user enters the coefficients in A[n], A[n-1], ... A[1], A[0] order, code gets nice and tight. No need to save all the coefficients and no need to limit them to 10. Calculate the sum as you go.

BTW: Always good to check the results of scanf().

#include<stdio.h>

int main() {
// n is the deg of polynomial
// x is the value of polynomial for which it is to be evaluated
int x, n, A;
long sum = 0;  // or use long long

printf("Enter value of n,x \n");
if (scanf("%d %d", &n, &x) != 2) {
}

printf("Enter the coefficients\n");  // spelling change
while (n-- >= 0) {
if (scanf("%d", &A) != 1) {