Horner's Rule

Hi! Friends, Whatzz up? I haven't got something special for you today. But it is a problem that you must have encountered in your High School, then why not write code for it? So lets get started!

Horner's rule for evaluating a polynomial:

P(x)=∑k=0nakxk==a0+x(a1+x(a2+⋯+x(an−1+xan)⋯))

given the coefficients a0,a1,…,an and a value for x:

Horner’s method can be used to evaluate polynomial in O(n) time. To understand the method, let us consider 

3x^3 - 5x^2 + 4x - 8. The polynomial can be evaluated as ((3x – 5)x + 4)x – 8. The idea is to initialize result as coefficient of x^n which is 3 in this case, repeatedly multiply result with x and add next coefficient to result. Finally return result.

Following is the C++ implementation of Horner''s Rule:

#include <iostream>

using namespace std;

int horner(int a[], int n, int x)

{

int y = a[0];

for (int i=1; i<n; i++)

y = y*x + a[i];

    return y;

}

int main()

{

//  Evaluating value of 3x3 - 5x2 + 4x - 8 for x = 3

int a[] = {3, -5, 4, -8};

int x = 3;

int n = sizeof(a)/sizeof(a[0]);

cout << "Value of polynomial is eual to " << horner(a, n, x);

return 0;

}