``` 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 ``` ```package algs11; import stdlib.*; import java.util.Arrays; /* PROBLEM 1: Run the program algs11.XAutoboxingValueOf and answer the following questions. QUESTION: What is the difference between the following two statements: x = "Dog"; x = new String("Dog"); ANSWER: QUESTION: What is the difference between the following two statements: x = Integer.valueOf (3); x = new Integer (3); ANSWER: QUESTION: Aside from the difference in the numbers, what is the difference between the following two statements: x = Integer.valueOf (12); x = Integer.valueOf (132973); ANSWER: PROBLEM 2: Using the formula given in class, write recursive versions of "average", "copy" and "reverse", using the iterative versions below as a starting point. The iterative versions are "averageI", "plusOneI" and "reverseI". HINT: You will need to define helper functions. */ public class MyArrayFunctions { public static double max (double[] a) { return 0.0; // TODO } public static double maxI (double[] a) { int N = a.length; double result = Double.NEGATIVE_INFINITY; for (int i = 0; i < N; i++) if (a[i] > result) result = a[i]; return result; } public static double[] plusOne (double[] a) { return null; //TODO } public static double[] plusOneI (double[] a) { int N = a.length; double[] result = new double[N]; for (int i = 0; i < N; i++) result[i] = a[i] + 1; return result; } public static void reverse (double[] a) { return; //TODO } public static void reverseI (double[] a) { int N = a.length; for (int i = 0; i < N / 2; i++) { double temp = a[i]; a[i] = a[N - 1 - i]; a[N - i - 1] = temp; } } public static void test (double[] a) { StdOut.format ("max: %f\n", maxI (a)); double[] b = plusOne (a); StdOut.format ("plusOne: %s\n", Arrays.toString (b)); reverse (a); StdOut.format ("reverse: %s\n", Arrays.toString (a)); } public static void testI (double[] a) { StdOut.format ("max: %f\n", maxI (a)); double[] b = plusOneI (a); StdOut.format ("plusOne: %s\n", Arrays.toString (b)); reverseI (a); StdOut.format ("reverse: %s\n", Arrays.toString (a)); } public static void main (String[] args) { test(new double[] { 10, 20, 60, 40, 50 }); test(new double[] { 60, 20, 30, 40 }); test(new double[] { 10, 20, 60 }); test(new double[] { 10, 20 }); test(new double[] { 10 }); test(new double[] { }); } } ```