Computes a polynomial using Horner's Rule.

HornersRule.java

public class HornersRule {

    public static int totalAdditions = 0;
    public static int totalMultiplications = 0;

    /**
     * Computes the value of the polynomial with the given coefficients
     * at the point x, using Horner's Rule.
     *
     * @param coefficients An array of coefficients: a_i = coefficients[i]
     * @param x The value at which to evaluate the polynomial.
     * @return The value of the polynomial at the point x.
     */
    public static double computePolynomial(double[] coefficients, double x) {
        int n = coefficients.length - 1;
        double result = coefficients[n];

        for (int i = n-1; i >= 0; i--) {
            result = (result * x) + coefficients[i];
            totalAdditions += 1;
            totalMultiplications += 1;
        }

        return result;
    }

    public static void main(String[] args) {
        double[] examplePoly = new double[]{ -7, 1, -3, 2, 5 };

        System.out.println("Polynomial: 5x^4 + 2x^3 - 3x^2 + x - 7");
        System.out.print("x=3: ");
        System.out.println(HornersRule.computePolynomial(examplePoly, 3));

        System.out.print("Total additions: ");
        System.out.println(HornersRule.totalAdditions);
        System.out.print("Total multiplications: ");
        System.out.println(HornersRule.totalMultiplications);
    }

}