Your job is to implement the root static method for NaturalNumber using the interval halving root algorithm.

Use the following skeleton (Java language) and complete the root method to achieve the proper output:

import components.naturalnumber.NaturalNumber; import components.naturalnumber.NaturalNumber2; import components.simplewriter.SimpleWriter; import components.simplewriter.SimpleWriter1L; /** * Program with implementation of {@code NaturalNumber} secondary operation * {@code root} implemented as static method. * * @author Put your name here * */ public final class NaturalNumberRoot { /** * Private constructor so this utility class cannot be instantiated. */ private NaturalNumberRoot() { } /** * Updates {@code n} to the {@code r}-th root of its incoming value. * * @param n * the number whose root to compute * @param r * root * @updates n * @requires r >= 2 * @ensures n ^ (r) <= #n < (n + 1) ^ (r) */ public static void root(NaturalNumber n, int r) { assert n != null : "Violation of: n is not null"; assert r >= 2 : "Violation of: r >= 2"; // TODO - fill in body } /** * Main method. * * @param args * the command line arguments */ public static void main(String[] args) { SimpleWriter out = new SimpleWriter1L(); final String[] numbers = { "0", "1", "13", "1024", "189943527", "0", "1", "13", "4096", "189943527", "0", "1", "13", "1024", "189943527", "82", "82", "82", "82", "82", "9", "27", "81", "243", "143489073", "2147483647", "2147483648", "9223372036854775807", "9223372036854775808", "618970019642690137449562111", "162259276829213363391578010288127", "170141183460469231731687303715884105727" }; final int[] roots = { 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 15, 15, 15, 15, 15, 2, 3, 4, 5, 15, 2, 3, 4, 5, 15, 2, 2, 3, 3, 4, 5, 6 }; final String[] results = { "0", "1", "3", "32", "13782", "0", "1", "2", "16", "574", "0", "1", "1", "1", "3", "9", "4", "3", "2", "1", "3", "3", "3", "3", "3", "46340", "46340", "2097151", "2097152", "4987896", "2767208", "2353973" }; for (int i = 0; i < numbers.length; i++) { NaturalNumber n = new NaturalNumber2(numbers[i]); NaturalNumber r = new NaturalNumber2(results[i]); root(n, roots[i]); if (n.equals(r)) { out.println("Test " + (i + 1) + " passed: root(" + numbers[i] + ", " + roots[i] + ") = " + results[i]); } else { out.println("*** Test " + (i + 1) + " failed: root(" + numbers[i] + ", " + roots[i] + ") expected <" + results[i] + "> but was <" + n + ">"); } } out.close(); } }