Questions

Conceptual

1. Which of the following are required in a recursive function that does not infinitely recur?

   1. A base case without a recursive function call

   2. Recursive case that progresses toward the base case

   3. Arguments changing in the recursive case

   4. All of the above

Code Writing

1. Write a recursive function named sum that has an int parameter number and returns an int that is the sum of all nonnegative integers up to and including number (1 + 2 + ... + number). For example, sum(number=4) should evaluate to 1 + 2 + 3 + 4 = 10. If a negative argument for number is given, just return -1 (What case is this?). It may help to come up with your base case and recursive case before beginning to write any code.

1    def sum(number: int) -> int:
2        """Sum of all nonnegative integers up to and including number."""
3        if number < 0: # Edge case
4            return -1
5        elif number > 0: # Recursive case
6            return number + sum(number=number - 1)
7        else: # Base case
8            return 0