Hello, everyone. My current university assignment is to represent Horner's method using recursion. Before this task we had to do it with a loop, which was easy. But I have no idea how to do this using recursion with only 2 parameters which cannot be changed.

public static double evalHornerRec(double[] a, double x)

This is the function i have to use

   private static int horner(int a[], int x, int n){
            int h;
            if(n>0)
                h=horner(a, x, n-1);
            else
                return a[n];
 
            return h*x a[n];
     }

I found something like this but it has 3 parameters and not 2

CodePudding user response：

As I said in the comment, keep chopping the head off the poly array and pass the chopped version down the recursion call, like so (this may help):

public class Main {
    static int horner(int a[], int x) {
        switch (a.length) {
            case 1:  return a[0];
            default: return a[0]   x * horner(Arrays.copyOfRange(a, 1, a.length), x);
        }
    }

    public static void main(String[] args) {
        // 2x^3 - 6x^2   2x - 1 for x = 3 => 5
        int[] poly = {-1, 2, -6, 2};
        System.out.println(horner(poly, 3)); // 5
    }
}

CodePudding user response：

In order to use two-args method, you can call the method containing the actual recursive logic, providing the 0 (the first index of the given array) as the third argument.

Note that the base case of the recursion is when we're hitting the last element a_n, i.e. when index n is equal to a.length - 1.

Otherwise, the call should be handled by the recursive case, containing the logic compliant with the Horner's rule.

public static double evalHornerRec(double[] a, double x) {
    
    return horner(a, x, 0);
}

private static double horner(double a[], double x, int n) {
    if (n == a.length - 1) return a[n];
    
    return a[n]   x * horner(a, x, n   1);
}