Computes a polynomial by caching intermediate powers of x.

Polynomial2.java

public class Polynomial2 {
    
    public static int totalAdditions = 0;
    public static int totalMultiplications = 0;

    /**
     * Computes the value of the polynomial with the given coefficients
     * at the point x.
     *
     * @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;

        /* This time, we'll assign the x^0 coefficient to result right away. */
        double result = coefficients[0];

        double powerOfX = 1.0;
        for (int i = 1; i <= n; i++) {
            powerOfX *= x;
            result += coefficients[i] * powerOfX;
            totalAdditions += 1;
            totalMultiplications += 2;
        }

        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(Polynomial2.computePolynomial(examplePoly, 3));

        System.out.print("Total additions: ");
        System.out.println(Polynomial2.totalAdditions);
        System.out.print("Total multiplications: ");
        System.out.println(Polynomial2.totalMultiplications);
    }

}