Which of the following python functions could be modeled by the following recursive diagram?

Question

A rectangle is labeled ‘mystery left parenthesis n right parenthesis.’ An arrow originates from the rectangle connects to a rhombus. The rhombus is labeled ‘n equals equals 0.’ Two arrows originate from the rhombus. An arrow labeled ‘Yes’ connects to a rectangle labeled ‘Return.’ Another arrow labeled ‘No’ connects to a rectangle labeled ‘left parenthesis n right parenthesis equals left parenthesis n minus 1 right parenthesis.’ An arrow originates from this rectangle and connects to the first rectangle labeled ‘mystery left parenthesis n right parenthesis.’

(1 point)
Responses

def reverse(n):
if len(n) == 0:
return

temp = n[0]
reverse(n[1:])
print(temp)
def reverse(n): if len(n) == 0: return temp = n[0] reverse(n[1:]) print(temp)

def power(b, n):
if n == 0:
return 1
else:
return (b * power(b, n - 1))
def power(b, n): if n == 0: return 1 else: return (b * power(b, n - 1))

def factorial(n):
if n == 0:
return 1
else:
return n * factorial(n - 1)
def factorial(n): if n == 0: return 1 else: return n * factorial(n - 1)

def fib(n):
if n <= 1:
return n
if n > 0:
return fib(n - 1) + fib(n - 2)

Answer 1

The recursive diagram described can be interpreted as follows:

1. The function in the rectangle is named mystery(n).
2. It checks if n is equal to 0. If yes, it returns a value (that's indicated by "Return" in the diagram), and if not, it computes a value involving a recursive call to mystery(n-1).

From the descriptions of the answers provided:

1. The reverse function checks the length of a string or list and acts recursively to print its elements in reverse order. This does not match our diagram.

2. The power function calculates b raised to the power of n recursively and checks if n is 0. This matches the description in the diagram of evaluating the base case when n equals 0 and can be summarized as:

   • If n == 0, return 1
   • Else, return b * power(b, n - 1)

3. The factorial function evaluates n! and checks if n is 0, returning 1 as the base case. This is also a match for the diagram since it follows a similar structure:

   • If n == 0, return 1
   • Else, return n * factorial(n - 1)

4. The fib function calculates Fibonacci numbers and also has a conditional check involving the value of n. It returns the Fibonacci number at position n.

Given the recursive structure described in the diagram, the functions akin to it would be functions that return a result based on comparing n to zero and utilizing recursion with a base case. Both the power function and the factorial function can be modeled by the diagram as they both involve checking n == 0 and making a recursive call with n-1.

However, since the inquiry seems to focus on a single function that most closely matches the description given (where there is a recursive call involving n without other operations), the factorial function (factorial(n)) closely aligns with the structure:

def factorial(n): 
   if n == 0:
       return 1 
   else: 
       return n * factorial(n - 1)

Thus, both power and factorial can fit, but factorial is the more straightforward fit based on the described behavior in the diagram.