a) Consider the following recursive methods. 01. public class Recursion { /* Assume that n is...

  

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a) Consider the following recursive methods. 01. public class Recursion { /* Assume that n is no less than 0 and no greater than the length of the array a */ 02. 03. 04. 05. 06. 07. 08. 09. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. public static boolean ml (int[] a, int n) { if (n <= 0) return true; - if (!m2 (a[n 1])) return false; n - 1); else return ml (a, } /Assume that num is public static boolean m2 (int num) { return m3 (num, 2); } private static boolean m3 (int num, int divisor) { if (num < 2 (num > 2 && num & divisor == 0)) return false; 21. 22. 23. } 24. } if (divisor <= Math.sqrt (num)) return m3 (num, divisor + 1); return true; } public static void main(String[] args) { int[] array(6, 2, 5); ml (array, 3); (i) (10 points) Show the sequence of recursive calls to m2, including arguments, and the return value for each of the following calls to the method m2: Call Sequence of recursive calls to m2 m2 (25) never less than 2 */ m2 (2) m2 (14) m2 (7) m2 (13) Return value (ii) (4 points) Describe what is returned by the method call m2 for any n such that n>=2. (iii) (10 points) Show the sequence of recursive calls to m1, including arguments, and the return value for each of the following calls to the method m1. A call m1 ({2, 6, 5}, 3) means that the first parameter integer array a has the values 2, 6, 5 and the second parameter has value 3. Call ml ({2, 6, 5}, 3) m1 ({23, 3, 7, 33}, 3) m1({23, 3, 7, 33}, 4) m1 ({6, 3, 17, 21, 33}, 5) m1({5}, 1) Sequence of recursive Return value calls to m1 (iv) (6 points) Describe what is returned by the method call m1 (arr, n) for any integer array arr and integer n such that 0 <= n <= arr.length. (v) (30 points) Draw the call stack, or the call tree for the entire execution of the program when you execute the command java Recursion. In each stack frame, include the name and value of all arguments and local variables (you can omit the command-line args). If you choose to draw the call tree, for each method call, you are required to give the method name, and the value for each parameter. b) (15 points) Suppose that a piece of Java code is stored using a String array (e.g, String[] code). Each line is one element of this array. Assume there is a method boolean contains MethodCall (String line) that can check whether a line of code specified by the parameter line contains a method call or not. If the parameter line contains a method call, the method containsMethodCall returns true, otherwise returns false. /** * @precondition arr is non-null * @precondition max is non-negative. * @precondition count is non-negative */ public static boolean noMore ThanNMethod (String[] code, int index, int max, int count) Given the method header shown above, write a recursive method to check whether the parameter array code contains more than max methods. Specifically, if the number of method calls in the piece of code specified by the parameter code is more than the number specified by the parameter max, return false, otherwise return true. Use index to keep track of which array index is being inspected in each recursive call and, count as a counter of the number of method calls. Assume that the parameter arr is not null, the parameter max is non-negative and the parameter count is non-negative. Call the method containsMethodCall (String line) to check whether a line of code contains a method call or not. Assume that contains MethodCall works as intended. Assume that there is at most one method call in a line of code. Example: public static boolean ml (int[] a, int n) { if (n <= 0) return true; } if (!m2 (a[n 1])) return false; else return ml (a, n - 1); Considering the code given above. We will use the String array (whose name is codeArray) shown in the table given below to store the code. Then we want to check whether the code has more than 3 method calls by calling the method: noMoreThanNMethod (codeArray, 0, 3, 0). Since the piece of code only has two method calls, namely codeArray[2] and codeArray [3], the noMoreThanNMethod will return true. The String array codeArray Array index 0 1 2 3 4 String public static boolean m1(int[] a, if (n <= 0) return true; if (!m2 (a[n 1])) return false; else return m1(a, n - 1); } int n) { a) Consider the following recursive methods. 01. public class Recursion { /* Assume that n is no less than 0 and no greater than the length of the array a */ 02. 03. 04. 05. 06. 07. 08. 09. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. public static boolean ml (int[] a, int n) { if (n <= 0) return true; - if (!m2 (a[n 1])) return false; n - 1); else return ml (a, } /Assume that num is public static boolean m2 (int num) { return m3 (num, 2); } private static boolean m3 (int num, int divisor) { if (num < 2 (num > 2 && num & divisor == 0)) return false; 21. 22. 23. } 24. } if (divisor <= Math.sqrt (num)) return m3 (num, divisor + 1); return true; } public static void main(String[] args) { int[] array(6, 2, 5); ml (array, 3); (i) (10 points) Show the sequence of recursive calls to m2, including arguments, and the return value for each of the following calls to the method m2: Call Sequence of recursive calls to m2 m2 (25) never less than 2 */ m2 (2) m2 (14) m2 (7) m2 (13) Return value (ii) (4 points) Describe what is returned by the method call m2 for any n such that n>=2. (iii) (10 points) Show the sequence of recursive calls to m1, including arguments, and the return value for each of the following calls to the method m1. A call m1 ({2, 6, 5}, 3) means that the first parameter integer array a has the values 2, 6, 5 and the second parameter has value 3. Call ml ({2, 6, 5}, 3) m1 ({23, 3, 7, 33}, 3) m1({23, 3, 7, 33}, 4) m1 ({6, 3, 17, 21, 33}, 5) m1({5}, 1) Sequence of recursive Return value calls to m1 (iv) (6 points) Describe what is returned by the method call m1 (arr, n) for any integer array arr and integer n such that 0 <= n <= arr.length. (v) (30 points) Draw the call stack, or the call tree for the entire execution of the program when you execute the command java Recursion. In each stack frame, include the name and value of all arguments and local variables (you can omit the command-line args). If you choose to draw the call tree, for each method call, you are required to give the method name, and the value for each parameter. b) (15 points) Suppose that a piece of Java code is stored using a String array (e.g, String[] code). Each line is one element of this array. Assume there is a method boolean contains MethodCall (String line) that can check whether a line of code specified by the parameter line contains a method call or not. If the parameter line contains a method call, the method containsMethodCall returns true, otherwise returns false. /** * @precondition arr is non-null * @precondition max is non-negative. * @precondition count is non-negative */ public static boolean noMore ThanNMethod (String[] code, int index, int max, int count) Given the method header shown above, write a recursive method to check whether the parameter array code contains more than max methods. Specifically, if the number of method calls in the piece of code specified by the parameter code is more than the number specified by the parameter max, return false, otherwise return true. Use index to keep track of which array index is being inspected in each recursive call and, count as a counter of the number of method calls. Assume that the parameter arr is not null, the parameter max is non-negative and the parameter count is non-negative. Call the method containsMethodCall (String line) to check whether a line of code contains a method call or not. Assume that contains MethodCall works as intended. Assume that there is at most one method call in a line of code. Example: public static boolean ml (int[] a, int n) { if (n <= 0) return true; } if (!m2 (a[n 1])) return false; else return ml (a, n - 1); Considering the code given above. We will use the String array (whose name is codeArray) shown in the table given below to store the code. Then we want to check whether the code has more than 3 method calls by calling the method: noMoreThanNMethod (codeArray, 0, 3, 0). Since the piece of code only has two method calls, namely codeArray[2] and codeArray [3], the noMoreThanNMethod will return true. The String array codeArray Array index 0 1 2 3 4 String public static boolean m1(int[] a, if (n <= 0) return true; if (!m2 (a[n 1])) return false; else return m1(a, n - 1); } int n) {

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