Question 1

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

Method A is indirectly recursive because it calls method B, which calls method C, which calls method D, which calls method A.

Question 2

Consider the following definition of a recursive method.public static int mystery(int[] list, int first, int last)
{
If (first == last)
Return list[first];
Else
Return list[first] + mystery(list, first + 1, last);
}Given the declarationint[] alpha = {1, 4, 5, 8, 9};What is the output of the following statement?System.out.println(mystery(alpha, 0, 4));

Accepted Answer

The method mystery uses recursive addition to find the sum of all the elements in the list between the indices first and last. In this case, since first is 0 and last is 4, the method will recursively call itself with arguments (alpha, 1, 4), (alpha, 2, 4), (alpha, 3, 4), and (alpha, 4, 4). When first == last, the method returns the element at that index. So, the method will return 9, 8, 5, 4, and finally 1. These values will be added together and the final output will be 27.

Question 3

In the recursive algorithm for the nth Fibonacci number, there are ____ base case(s).

Accepted Answer

The recursive algorithm for the nth Fibonacci number has two base cases: when n = 0, it returns 0, and when n = 1, it returns 1. These base cases prevent infinite recursion.

Question 4

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(10));

Accepted Answer

The method returns 10 when the input number is greater than or equal to 10. Since the input here is 10, it directly returns 10 without any recursion.

Question 5

Consider the following definition of a recursive method.public static int strange(int[] list, int first, int last)
{
If (first == last)
Return list[first];
Else
Return list[first] + strange(list, first + 1, last);
}Given the declarationint[] beta = {2, 5, 8, 9, 13, 15, 18, 20, 23, 25};What is the output of the following statement?System.out.println(strange(beta, 4, 7));

Accepted Answer

The answer of Consider the following definition of a recursive...

Question 6

____ is NOT an iterative control structure.

Accepted Answer

Recursion is a type of control structure in which a function calls itself until a base case is reached. It is not considered iterative because it does not involve a loop or repetition of a set of instructions.

Question 7

If you are building a mission control system, ____.

Accepted Answer

In mission control systems, efficiency and reliability are crucial factors. Therefore, it is best to use the most efficient solution possible. Iteration and recursion may not always be the most efficient solutions and may add unnecessary complexity to the system. Intuitive sense is subjective and may not always lead to the most effective solution.

Question 8

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

Accepted Answer

The first step in the Tower of Hanoi recursive algorithm is to move the top n - 1 disks from needle 1 to needle 2, using needle 3 as the intermediate needle. This is because in order to move the largest disk from needle 1 to needle 3, we need to first clear all smaller disks from the top of needle 1, which we can do by moving them to needle 2.

Question 9

Using a recursive algorithm to solve the Tower of Hanoi problem, a computer that can generate one billion moves per second would take ____ years to solve the problem.

Accepted Answer

The Tower of Hanoi problem with n disks can be solved in 2^n - 1 moves. For a large number of disks, this number becomes very large. For example, with 64 disks, it would take 2^64 - 1 moves. At a rate of one billion moves per second (10^9 moves/second), it would take approximately 500 years to solve, as the calculation shows: (2^64 - 1) / (10^9 * 60 * 60 * 24 * 365) ≈ 500 years.

Question 10

The third Fibonacci number is ____.

Accepted Answer

The third Fibonacci number is the sum of the first two Fibonacci numbers. The sequence starts with 0 and 1, so the third number is 0 + 1 = 1. The Fibonacci sequence is created by adding the two previous numbers to get the next number in the sequence, so the third number will always be the sum of the first two.

Quiz 13: Recursion