Step by Step solution about How to resolve the algorithm Forward difference step by step in the Java programming language

The provided Java code defines a class named FD that contains a method called dif to calculate the n-th order differences of an array of double values. The main method in this code tests the dif method for various values of n. Here's a breakdown of the code:

1. dif Method:

• The dif method takes two parameters:

  • a: An array of double values for which the differences will be calculated.
  • n: An integer representing the order of differences to calculate.

• The method calculates the n-th order differences of the input array a by repeatedly applying the following steps:

  • It creates a new array b with a length one less than the length of a.

  • Iterates through the elements of a except the last element and calculates the difference between adjacent elements, storing these differences in the new array b.

  • Updates the a array to point to the b array.

  • Repeats these steps n times.

  • If the input parameter n is negative, the method returns null.

2. main Method:

• The main method is the entry point of the program.
• It creates an array of double values named a, containing values: {90, 47, 58, 29, 22, 32, 55, 5, 55, 73}.
• It calls the dif method on the array a for different values of n (1, 2, 9, 10, 11, -1, 0) and prints the results.

Example Outputs:

• When n is 1, dif calculates the first-order differences of a: {43, 11, -29, -7, 10, 23, -50, -50, 18}.
• When n is 9, dif calculates the ninth-order differences of a: {67} (since there's only one value left after applying 9th order differences).
• When n is -1, the method returns null because n is negative.
• When n is 10, the method returns an empty array because there are no elements left in the array after applying 10th order differences.
• When n is 11, the method returns null because the array is empty, and you cannot calculate differences on an empty array.
• When n is 0, the method returns the original array a unchanged.

import java.util.Arrays;
public class FD {
    public static void main(String args[]) {
        double[] a = {90, 47, 58, 29, 22, 32, 55, 5, 55, 73};
        System.out.println(Arrays.toString(dif(a, 1)));
        System.out.println(Arrays.toString(dif(a, 2)));
        System.out.println(Arrays.toString(dif(a, 9)));
        System.out.println(Arrays.toString(dif(a, 10)));      //let's test
        System.out.println(Arrays.toString(dif(a, 11)));
        System.out.println(Arrays.toString(dif(a, -1)));
        System.out.println(Arrays.toString(dif(a, 0)));
    }

    public static double[] dif(double[] a, int n) {
        if (n < 0)
            return null; // if the programmer was dumb

        for (int i = 0; i < n && a.length > 0; i++) {
            double[] b = new double[a.length - 1];
            for (int j = 0; j < b.length; j++){
                b[j] = a[j+1] - a[j];
            }
            a = b; //"recurse"
        }
        return a;
    }
}