Question 1

Write a recursive definition for K(n), which represents the product of all of the even integers less than or equal to n.

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Question 2

Describe a recursive solution to the Towers of Hanoi puzzle with N disks.

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The answer of Describe a recursive solution to the Towers...

Question 3

Describe a recursive solution to determine whether a String object is a palindrome. You may assume that the string only contains lower case characters (i.e. no numbers, spaces, punctuation, etc). Hint: It may be easiest to describe your solution using pseudocode.

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The answer of Describe a recursive solution to determine whether...

Question 4

Describe the Towers of Hanoi puzzle.

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The answer of Describe the Towers of Hanoi puzzle....

Question 5

The Towers of Hanoi puzzle cannot be solved iteratively.

Accepted Answer

Since it is possible to simulate recursion using an iterative program, any problem that can be solved recursively can also be solved iteratively. Therefore the Tower of Hanoi puzzle must have an iterative solution.

Question 6

A program with infinite recursion will act similarly to a program with an infinite loop.

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A program with infinite recursion will run out of memory. This will cause the program to crash. A program with an infinite loop will appear to "hang."

Question 7

What is recursion?

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The answer of What is recursion?...

Question 8

Write a recursive method that computes the sum of the first n integers.

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The answer of Write a recursive method that computes the...

Question 9

Write a recursive method that computes the product of all of the even integers less than or equal to n.

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The answer of Write a recursive method that computes the...

Question 10

Recursion is necessary.

Accepted Answer

Recursion is not necessary, since it is always possible to program a recursive solution iteratively.

Question 11

What is wrong with the following recursive method that computes the sum of all of the odd positive integers less than or equal to n?
public int sumOfOdds(int n) {
if(n%2 == 0)
return sumOfOdds(n-1);
else
return n + sumOfOdds(n-2);
}

Accepted Answer

The answer of What is wrong with the following recursive...

Question 12

Write a recursive Java method that takes in a String as a parameter and returns true if the String is a palindrome. You may assume that the string only contains lower case characters (i.e. no numbers, spaces, punctuation, etc).

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The answer of Write a recursive Java method that takes...

Question 13

The Fibonacci sequence is defined as the sum of the two previous elements of the sequence, with the first and second numbers in the sequence being 0 and 1 respectively. Write a recursive method that computes the nth Fibonacci number.

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The answer of The Fibonacci sequence is defined as the...

Question 14

In the Towers of Hanoi puzzle, it is legal to move a larger disk to a peg that already contains a smaller disk.

Accepted Answer

In the Towers of Hanoi puzzle, the only valid moves move a disk to a peg that only contains smaller disks.

Question 15

Write the recursive definition of the factorial of a number.

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The answer of Write the recursive definition of the factorial...

Question 16

Give a recursive definition of the sum of the first n integers, S(n).

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The answer of Give a recursive definition of the sum...

Question 17

What are the "base" cases when searching for a path through a maze?

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The answer of What are the "base" cases when searching...

Question 18

Determining whether or not there is a path through a maze has a recursive solution.

Accepted Answer

It is possible to traverse a maze recursively, and therefore there is a recursive solution to determining whether or not there is a path through a maze.

Question 19

The Fibonacci sequence is defined as the sum of the two previous elements of the sequence, with the first and second numbers in the sequence being 0 and 1 respectively. Write a recursive mathematical definition of the Fibonacci numbers.

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