Question 1

public static int exampleRecursion (int n)
{
If (n == 0)
Return 0;
Else
Return exampleRecursion(n - 1) + n * n * n;
}Which of the following is an invalid call to the method in the accompanying figure?

Accepted Answer

A)  exampleRecursion(-1) 
B)  exampleRecursion( 0) 
C)  exampleRecursion(1) 
D)  exampleRecursion(999)

Question 2

public static int func2(int m, int n)
{
If (n == 0)
Return 0;
Else
Return m + func2(m, n - 1);
}What is the limiting condition of the code in the accompanying figure?

Accepted Answer

A)  n >= 0 
B)  m > n 
C)  m >= 0 
D)  n > m

Question 3

If every recursive call results in another recursive call, then the recursive method (algorithm) is said to have infinite recursion.

Accepted Answer

A) True 
 B)False

Question 4

The third Fibonacci number is ____.

Accepted Answer

A)  the sum of the first two Fibonacci numbers 
B)  the sum of the last two Fibonacci numbers 
C)  the product of the first two Fibonacci numbers 
D)  the product of the last two Fibonacci numbers

Question 5

What is the first step in the Tower of Hanoi recursive algorithm?

Accepted Answer

A)  Move the top n disks from needle 1 to needle 2, using needle 3 as the intermediate needle. 
B)  Move disk number n from needle 1 to needle 3. 
C)  Move the top n - 1 disks from needle 2 to needle 3, using needle 1 as the intermediate needle. 
D)  Move the top n - 1 disks from needle 1 to needle 2, using needle 3 as the intermediate needle.

Question 6

In the base case of a recursive solution, the solution is obtained through a call to a smaller version of the original method.

Accepted Answer

A) True 
 B)False

Question 7

public static int func2(int m, int n)
{
If (n == 0)
Return 0;
Else
Return m + func2(m, n - 1);
}Which of the following statements about the code in the accompanying is always true?

Accepted Answer

A)  func2(m, n) = func2(n, m) for m >= 0 
B)  func2(m, n) = m * n for n >= 0 
C)  func2(m, n) = m + n for n >= 0 
D)  func2(m, n) = n * m for m >= 0

Question 8

A method that calls another method and eventually results in the original method call is called indirectly recursive.

Accepted Answer

A) True 
 B)False

Question 9

A program will terminate after completing any particular recursive call.

Accepted Answer

A) True 
 B)False

Question 10

The following is an example of a recursive method.public static int recFunc(int x)
{
 return (nextNum(nextNum(x)));
}where nextNum is method such that nextNum(x) = x + 1.

Accepted Answer

A) True 
 B)False

Question 11

Every recursive call has its own code.

Accepted Answer

A) True 
 B)False

Question 12

Which of the following statements describe the base case of a recursive algorithm?
(i) F(0) = 0;
(ii) F(x) = 2 * F(x - 1);
(iii) if (x == 0)
F(x) = 5 + x;

Accepted Answer

A)  Only (i) 
B)  Only (ii) 
C)  Only (iii) 
D)  Both (i) and (iii)

Question 13

The base case starts the recursion.

Accepted Answer

A) True 
 B)False

Question 14

You can think of a recursive method as having unlimited copies of itself.

Accepted Answer

A) True 
 B)False

Question 15

public static int exampleRecursion (int n)
{
If (n == 0)
Return 0;
Else
Return exampleRecursion(n - 1) + n * n * n;
}What is the output of exampleRecursion(0)?

Accepted Answer

A)  0 
B)  3 
C)  9 
D)  27

Question 16

public static int exampleRecursion (int n)
{
If (n == 0)
Return 0;
Else
Return exampleRecursion(n - 1) + n * n * n;
}What does the code in the accompanying figure do?

Accepted Answer

A)  Returns the cube of the number n 
B)  Returns the sum of the cubes of the numbers, 0 to n 
C)  Returns three times the number n 
D)  Returns the next number in a Fibonacci sequence

Question 17

Assume there are four methods A, B, C, and D. If method A calls method B, method B calls method C, method C calls method D, and method D calls method A, which of the following methods is indirectly recursive?

Accepted Answer

A)  A 
B)  B 
C)  C 
D)  D

Question 18

A recursive solution is always a better alternative to an iterative solution.

Accepted Answer

A) True 
 B)False

Question 19

Consider the following definition of a recursive method.public static int recFunc(int num)
{
If (num >= 10)
Return 10;
Else
Return num * recFunc(num + 1);
}What is the output of the following statement?System.out.println(recFunc(8));

Accepted Answer

A)  8 
B)  72 
C)  720 
D)  None of these

Question 20

public static int exampleRecursion (int n)
{
If (n == 0)
Return 0;
Else
Return exampleRecursion(n - 1) + n * n * n;
}How many base cases are in the code in the accompanying figure?

Accepted Answer

A)  zero 
B)  one 
C)  two 
D)  three

Exam 13: Recursion

public static int exampleRecursion (int n) { If (n == 0) Return 0; Else Return exampleRecursion(n - 1) + n * n * n; }Which of the following is an invalid call to the method in the accompanying figure?

public static int func2(int m, int n) { If (n == 0) Return 0; Else Return m + func2(m, n - 1) ; }What is the limiting condition of the code in the accompanying figure?

If every recursive call results in another recursive call, then the recursive method (algorithm) is said to have infinite recursion.

The third Fibonacci number is ____.

What is the first step in the Tower of Hanoi recursive algorithm?

In the base case of a recursive solution, the solution is obtained through a call to a smaller version of the original method.

public static int func2(int m, int n) { If (n == 0) Return 0; Else Return m + func2(m, n - 1) ; }Which of the following statements about the code in the accompanying is always true?

A method that calls another method and eventually results in the original method call is called indirectly recursive.

A program will terminate after completing any particular recursive call.

The following is an example of a recursive method.public static int recFunc(int x) { return (nextNum(nextNum(x))); }where nextNum is method such that nextNum(x) = x + 1.

Every recursive call has its own code.

Which of the following statements describe the base case of a recursive algorithm? (i) F(0) = 0; (ii) F(x) = 2 * F(x - 1) ; (iii) if (x == 0) F(x) = 5 + x;

The base case starts the recursion.

You can think of a recursive method as having unlimited copies of itself.

public static int exampleRecursion (int n) { If (n == 0) Return 0; Else Return exampleRecursion(n - 1) + n * n * n; }What is the output of exampleRecursion(0) ?

public static int exampleRecursion (int n) { If (n == 0) Return 0; Else Return exampleRecursion(n - 1) + n * n * n; }What does the code in the accompanying figure do?

Assume there are four methods A, B, C, and D. If method A calls method B, method B calls method C, method C calls method D, and method D calls method A, which of the following methods is indirectly recursive?

A recursive solution is always a better alternative to an iterative solution.

Consider the following definition of a recursive method.public static int recFunc(int num) { If (num >= 10) Return 10; Else Return num * recFunc(num + 1) ; }What is the output of the following statement?System.out.println(recFunc(8) ) ;

public static int exampleRecursion (int n) { If (n == 0) Return 0; Else Return exampleRecursion(n - 1) + n * n * n; }How many base cases are in the code in the accompanying figure?