Question 1

The number of calls to recursively calculate the Fibonacci value of 7 is:&#10;A) 7&#10;B) 13&#10;C) 41&#10;D) 39

Accepted Answer

To calculate the Fibonacci value of 7 recursively, the function will be called for each value down to 1. The calls form a binary tree, where each node calls two more nodes (except for the base cases). The total number of calls is 41, as it includes the initial call for 7, and then splits into calls for Fibonacci(6) and Fibonacci(5), and so on, creating a large number of redundant calls due to the overlap in the recursive calls.

Question 2

The operands of an operator are evaluated ________.&#10;A) from right to left.&#10;B) from left to right.&#10;C) at the same time.&#10;D) in an order that is specific to each operator.

Accepted Answer

Operands of an operator are evaluated from left to right. This is known as the left-associativity of operators. However, there are some operators like the exponentiation operator (** in Python) that are evaluated from right to left.

Question 3

The recursion step should:&#10;A) check for the base case.&#10;B) call a fresh copy of the recursive method to work on a smaller problem.&#10;C) make two calls to the recursive method.&#10;D) iterate until it reaches a termination condition.

Accepted Answer

The recursion step should make a call to a fresh copy of the recursive method, but with a smaller problem, until it reaches a base case that can be solved directly without further recursion. This allows the problem to be broken down into smaller sub-problems until a base case is reached. Therefore, option B is the correct choice.

Question 4

After a fractal's pattern is applied several times, the shape of the fractal will generally become ________.&#10;A) disjointed and less detailed.&#10;B) stabilized and more detailed.&#10;C) identical to the original fractal.&#10;D) None of the above.

Accepted Answer

As a fractal pattern is applied repeatedly, it will continue to become more detailed and complex, but it will also stabilize into a recognizable shape. Therefore, choice B is the most accurate answer. Choice A is incorrect because the pattern will not become disjointed but rather more detailed. Choice C is incorrect because the fractal will not remain identical as it becomes more complex with each repetition. Choice D is incorrect because there is a clear answer.

Question 5

When the recursion step executes:&#10;A) this is known as indirect recursion.&#10;B) all of the computer's processes halt until the recursion step has completed executing.&#10;C) the original call to the method is still active.&#10;D) All of the above.

Accepted Answer

During the recursion step, the original call to the method is still active. The other options provided are incorrect. A is incorrect as indirect recursion involves multiple methods calling each other in a circular fashion, while the question only mentions a single method. B is incorrect as the recursion step executes within the method itself and does not halt all computer processes.

Question 6

Fractals that yield an exact copy of the original when a portion of the original image is magnified are called___________________ fractals.&#10;A) strictly self-similar.&#10;B) Koch Curve.&#10;C) similar.&#10;D) mirror.

Accepted Answer

Strictly self-similar fractals are the ones that yield an exact copy of the original when a portion of the original image is magnified. The Koch curve is an example of a self-similar fractal, but not strictly self-similar, as it differs from the original shape at different magnification levels. Fractals can also be similar, meaning they have similar patterns at different scales, or mirror, meaning they have mirror symmetry.

Question 7

Recursion often is preferable to iteration because ________.&#10;A) it is faster.&#10;B) it requires less memory.&#10;C) it models the problem more logically.&#10;D) All of the above.

Accepted Answer

Recursion often models the problem more logically, making the code clearer and easier to understand. However, it may not always be faster or require less memory than iteration.

Question 8

Recursion is often less efficient than iteration because ________.&#10;A) it can cause an explosion of method calls.&#10;B) it is not as intuitive.&#10;C) recursive methods are harder to debug.&#10;D) recursive methods take longer to program.

Accepted Answer

Recursion can cause an explosion of method calls, which can lead to stack overflow errors and slower performance compared to iterative solutions.

Question 9

When a recursive method is called to solve a problem, the method actually is capable of solving only the simplest case(s), or_______ .&#10;A) base case(s).&#10;B) base step(s).&#10;C) recursive call(s).&#10;D) recursion step(s).

Accepted Answer

The base case(s) are the simplest cases that can be solved by the recursive method. The method then calls itself with modified inputs until the base case(s) are reached.

Question 10

All of the following are true for both recursion and iteration except ________.&#10;A) they have a base case.&#10;B) they can cause infinite loops or infinite recursion.&#10;C) they are based on a control statement.&#10;D) both gradually approach termination.

Accepted Answer

Recursion requires a base case to terminate the recursive calls, whereas iteration does not necessarily have a "base case" but rather uses a condition for termination.

Question 11

A recursive method .&#10;A) is a method that calls itself.&#10;B) can be called directly.&#10;C) can be called indirectly through another method.&#10;D) All of the above.

Accepted Answer

The answer of A recursive method .&#10;A) is a method...

Question 12

The current method executing is always the method whose activation record is ________.&#10;A) at the bottom of the stack.&#10;B) at the top of the stack.&#10;C) never placed on the stack.&#10;D) second from the top of the stack, just below the previous method call.

Accepted Answer

The answer of The current method executing is always the...

Question 13

Which of the following is false?&#10;A) Since BigInteger is not a primitive type, we can't use the arithmetic, relational and equality operators with BigIntegers.&#10;B) BigInteger method compareTo compares the BigInteger number that calls the method to the method's BigInteger argument, and returns -1 if the BigInteger that calls the method is less than the argument, 0 if they're equal or 1 if the BigInteger that calls the method is greater than the argument.&#10;C) The value 1 can be implicitly converted to a BigInteger.&#10;D) BigInteger can represent integer values larger than what primitive type long can represent.

Accepted Answer

The answer of Which of the following is false?&#10;A) Since...

Question 14

In recursive backtracking, if one set of recursive calls does not result in a solution to the problem, what happens?&#10;A) The program returns to a previous decision point and makes a different decision.&#10;B) The program backs up to the previous decision point and throws an exception.&#10;C) The program continues, with unexpected results.&#10;D) The program backs up to the original method call.

Accepted Answer

The answer of In recursive backtracking, if one set of...

Question 15

Each time a fractal's pattern is applied to it, the fractal is said to be at a new ________.&#10;A) level.&#10;B) depth.&#10;C) order.&#10;D) All of the above.

Accepted Answer

The answer of Each time a fractal's pattern is applied...

Deck 18: Recursion