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 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 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))

Answer 1

The recursive diagram you described indicates a function that checks if \( n \) is equal to 0, and if so, it returns some value. If \( n \) is not 0, it makes a recursive call with \( n \) decreased by 1.

Here’s a breakdown of the two functions in the provided options:

1. Factorial Function:

   • If \( n \) is 0, it returns 1 (base case).
   • If \( n \) is not 0, it returns \( n \) times the factorial of \( n - 1 \).

   This aligns with the description because it first checks if \( n == 0 \) and then reduces \( n \) for the recursive call.

2. Power Function:

   • If \( n \) is 0, it returns 1 (base case).
   • If \( n \) is not 0, it returns \( b \) times the power of \( b \) to \( n - 1 \).

   This function also matches the recursive structure because it checks for \( n == 0 \) and subsequently makes a recursive call with \( n - 1 \).

Both functions fit the recursive model. However, which one is the exact match depends on the context or specifics around how the recursive calls are described in the diagram you mentioned.

Given the specific behavior of the diagram with respect to the variable being decremented, both functions could potentially match. However, based on typical problems presented, the factorial function is frequently associated with describing such diagrams, due to its common use in illustrating simple recursion.

Conclusion

Both factorial(n) and power(b, n) can be modeled by the given recursive diagram; however, without additional context, I would lean towards the factorial function as the most traditional example, focusing on \( n \) decrementing.