The following recursive function will print the nth power of 2.

Question

def powerOf2(n):
if n == 0:
return 1
else:
return (2 * powerOf2(n - 1))
(1 point)
Responses

A rectangle is labeled ‘power Of 2 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 2 superscript n baseline.’ 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 ‘power Of 2 left parenthesis n right parenthesis.’
Image with alt text: A rectangle is labeled ‘power Of 2 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 2 superscript n baseline.’ 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 ‘power Of 2 left parenthesis n right parenthesis.’

A rectangle is labeled ‘power Of 2 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 ‘left parenthesis n right parenthesis equals left parenthesis n minus 1 right parenthesis.’ Another arrow labeled ‘No’ connects to a rectangle labeled ‘1.’ An arrow originates from this rectangle and connects to the first rectangle labeled ‘power Of 2 left parenthesis n right parenthesis.’

Answer 1

The recursive function you've provided for calculating the nth power of 2 seems to have been described in a flowchart format. Let's clarify how it would depict the structure of your function, specifically showing the logic based on the description you've provided for both flowcharts.

Recursive Function Explanation

The function powerOf2(n) operates as follows:

1. Base Case: If n is 0, it returns 1 because \(2^0 = 1\).
2. Recursive Case: If n is not 0, it recursively calls itself with the argument of \(n - 1\) and multiplies the result by 2. This is grounded in the property that \(2^n = 2 \times 2^{(n-1)}\).

Interpretation of Flowchart Options

1. First Flowchart Option:

   • Start: Rectangle labeled 'powerOf2(n)'
   • Decision: A rhombus labeled 'n == 0'
     • If Yes: Connect to a rectangle labeled 'Return 1'.
     • If No: Connect to a rectangle for 'powerOf2(n - 1)' followed by multiplication by 2 to get 'Return 2 * powerOf2(n - 1)'.

2. Second Flowchart Option:

   • Start: Rectangle labeled 'powerOf2(n)'
   • Decision: A rhombus labeled 'n == 0'
     • If Yes: This would ideally return 1 (should be labeled as 'Return 1').
     • If No: The flow leads to execution of 'powerOf2(n - 1)' followed by the multiplication by 2 to yield 'Return 2 * powerOf2(n - 1)'.

Conclusion

Based on what you've described and the logic of the function, the correct choice would be the first flowchart option. This option accurately represents the recursive flow of the function correctly, maintaining the correct labeling and returning values.

Please ensure that the return for the base case in your flowchart is correctly labeled as 'Return 1' instead of 'Return 2 superscript n baseline', which does not accurately represent the code provided. The second flowchart option would not work properly as it incorrectly breaks the logical flow of the execution of the recursive function.

In summary, in flowchart form based on your description:

• Power of 2(n) → Decision (Is n == 0?) → Yes → Return 1
• No → Power of 2(n-1) → Return 2 * power of 2(n-1)

This logically describes how the recursion works.