Question

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

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:

```python
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.