Evaluating a polynomial at a given value of x and n

Question

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;
}

Answer 1

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;
}

Answer 2

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) {
 return 1; // bad input
 }
 printf("Enter the coefficients\n"); // spelling change
 while (n-- >= 0) {
 if (scanf("%d", &A) != 1) {
 return 1; // bad input
 }
 sum *= x;
 sum += A;
 }
 printf("\nSum of polynomial is %ld", sum);
 return 0;
}