Step by Step solution about How to resolve the algorithm Horner's rule for polynomial evaluation step by step in the C# programming language

==> Notes for the code and the AI responses...

• The first answer managed to get the idea of the code but it missed lots of explanations.
• The second answer is okay and its explanation is good in brief.

Here I will explain the code myself and add extra explanations on the AI answers.

The provided C# code snippet demonstrates the Horner's method for evaluating a polynomial. It takes an array of coefficients and a variable as inputs and returns the result of evaluating the polynomial at that variable.

--> The code has the following structure:

• A Horner method that takes a coefficient array and a variable as inputs and returns the result of evaluating the polynomial at that variable.

• The Horner's method is implemented using the Aggregate method of the Enumerable class. This method takes an initial value and a function as inputs and combines the elements of the array into a single value by applying the function to each element and the previous result.

• In this case, the initial value is 0 and the function is (accumulator, coefficient) => accumulator * variable + coefficient. The function takes the previous result and the current coefficient in the array, multiplies them by the value of variable, and adds them together.

• The Reverse method is used to reverse the order of the coefficients in the array. This is necessary because the Horner's method requires the coefficients to be in reverse order.

• A Main method that creates an array of coefficients and a variable, and then calls the Horner method to evaluate the polynomial at that variable.

--> The example in the Main method: evaluates the polynomial -19x^3 + 7x^2 - 4x + 6 at x = 3.

--> The output of the program: will be -10.

using System;
using System.Linq;

class Program
{
    static double Horner(double[] coefficients, double variable)
    {
        return coefficients.Reverse().Aggregate(
                (accumulator, coefficient) => accumulator * variable + coefficient);
    }

    static void Main()
    {
        Console.WriteLine(Horner(new[] { -19.0, 7.0, -4.0, 6.0 }, 3.0));
    }
}