Chapter 18 CSC 216

Show the output of the following code public class Test1 { public static void main(String[] args) { System.out.println(f2(2, 0)); } public static int f2(int n, int result) { if (n == 0) return 0; else return f2(n - 1, n + result); } }

0

What is the return value for xMethod(4) after calling the following method? static int xMethod(int n) { if (n == 1) return 1; else return n + xMethod(n - 1); }

10

How many times is the fib method in Listing 18.2 invoked for fib(5)?

15

How many times is the recursive moveDisks method invoked for 4 disks?

15

Which of the following statements are true?

B. Recursive methods usually take more memory space than non-recursive methods. C. A recursive method can always be replaced by a non-recursive method. D. In some cases, however, using recursion enables you to give a natural, straightforward, simple solution to a program that would otherwise be difficult to solve.

Fill in the code to complete the following method for computing a Fibonacci number. public static long fib(long index) { if (index == 0) // Base case return 0; else if (index == 1) // Base case return 1; else // Reduction and recursive calls return __________________; }

C. fib(index - 1) + fib(index - 2) D. fib(index - 2) + fib(index - 1)

Fill in the code to complete the following method for computing factorial. /** Return the factorial for a specified index */ public static long factorial(int n) { if (n == 0) // Base case return 1; else return _____________; // Recursive call }

C. n * factorial(n - 1) D. factorial(n - 1) * n

Analyze the following two programs: A: public class Test { public static void main(String[] args) { xMethod(5); } public static void xMethod(int length) { if (length > 1) { System.out.print((length - 1) + " "); xMethod(length - 1); } } } B: public class Test { public static void main(String[] args) { xMethod(5); } public static void xMethod(int length) { while (length > 1) { System.out.print((length - 1) + " "); xMethod(length - 1); } } }

Program A produces the output 4 3 2 1 and Program B prints 4 3 2 1 1 1 .... 1 infinitely.

Which of the following statements are true?

The Fibonacci series begins with 0 and 1, and each subsequent number is the sum of the preceding two numbers in the series.

Analyze the following functions; public class Test1 { public static void main(String[] args) { System.out.println(f1(3)); System.out.println(f2(3, 0)); } public static int f1(int n) { if (n == 0) return 0; else { return n + f1(n - 1); } } public static int f2(int n, int result) { if (n == 0) return result; else return f2(n - 1, n + result); } }

f2 is tail recursion, but f1 is not

The following program draws squares recursively. Fill in the missing code. import javax.swing.*; import java.awt.*; public class Test extends JApplet { public Test() { add(new SquarePanel()); } static class SquarePanel extends JPanel { public void paintComponent(Graphics g) { super.paintComponent(g); int width = (int)(Math.min(getWidth(), getHeight()) * 0.4); int centerx = getWidth() / 2; int centery = getHeight() / 2; displaySquares(g, width, centerx, centery); } private static void displaySquares(Graphics g, int width, int centerx, int centery) { if (width >= 20) { g.drawRect(centerx - width, centery - width, 2* width, 2 * width); displaySquares(_________, width - 20, centerx, centery); } } } }

g

Fill in the code to complete the following method for checking whether a string is a palindrome. public static boolean isPalindrome(String s) { return isPalindrome(s, 0, s.length() - 1); } public static boolean isPalindrome(String s, int low, int high) { if (high <= low) // Base case return true; else if (s.charAt(low) != s.charAt(high)) // Base case return false; else return _______________________________; }

isPalindrome(s, low + 1, high - 1)

What are the base cases in the following recursive method? public static void xMethod(int n) { if (n > 0) { System.out.print(n % 10); xMethod(n / 10); } }

n <= 0

In the following method, what is the base case? static int xMethod(int n) { if (n == 1) return 1; else return n + xMethod(n - 1); }

n is 1.

Fill in the code to complete the following method for binary search. public static int recursiveBinarySearch(int[] list, int key) { int low = 0; int high = list.length - 1; return __________________________; } public static int recursiveBinarySearch(int[] list, int key, int low, int high) { if (low > high) // The list has been exhausted without a match return -low - 1; // Return -insertion point - 1 int mid = (low + high) / 2; if (key < list[mid]) return recursiveBinarySearch(list, key, low, mid - 1); else if (key == list[mid]) return mid; else return recursiveBinarySearch(list, key, mid + 1, high); }

recursiveBinarySearch(list, key, low, high)

Fill in the code to complete the following method for sorting a list. public static void sort(double[] list) { ___________________________; } public static void sort(double[] list, int high) { if (high > 1) { // Find the largest number and its index int indexOfMax = 0; double max = list[0]; for (int i = 1; i <= high; i++) { if (list[i] > max) { max = list[i]; indexOfMax = i; } } // Swap the largest with the last number in the list list[indexOfMax] = list[high]; list[high] = max; // Sort the remaining list sort(list, high - 1); } }

sort(list, list.length - 1)

Fill in the code to complete the following method for checking whether a string is a palindrome. public static boolean isPalindrome(String s) { if (s.length() <= 1) // Base case return true; else if _____________________________ return false; else return isPalindrome(s.substring(1, s.length() - 1)); }

(s.charAt(0) != s.charAt(s.length() - 1)) // Base case

How many times is the factorial method in Listing 18.1 invoked for factorial(5)?

6

How many times is the recursive moveDisks method invoked for 3 disks?

7

Which of the following statements are true?

A. Every recursive method must have a base case or a stopping condition. B. Every recursive call reduces the original problem, bringing it increasingly closer to a base case until it becomes that case. C. Infinite recursion can occur if recursion does not reduce the problem in a manner that allows it to eventually converge into the base case.

Analyze the following recursive method. public static long factorial(int n) { return n * factorial(n - 1); }

The method runs infinitely and causes a StackOverflowError.

Analyze the following code: public class Test { public static void main(String[] args) { int[] x = {1, 2, 3, 4, 5}; xMethod(x, 5); } public static void xMethod(int[] x, int length) { System.out.print(" " + x[length - 1]); xMethod(x, length - 1); } }

The program displays 5 4 3 2 1 and then raises an ArrayIndexOutOfBoundsException