7. Write a recursive algorithm that calculates and returns the length of a list.

To write a recursive algorithm that calculates and returns the length of a list, you can follow these steps:

1. Define a function, let's call it list_length, that takes a list as input.
2. Check if the list is empty. If it is, return 0 as the length of the list.
3. If the list is not empty, remove the first element from the list and recursively call the list_length function on the remaining elements of the list.
4. Add 1 to the result of the recursive call to account for the removed element.
5. Return the final result.

Here is an example implementation in Python:

def list_length(lst):
    if not lst:  # check if the list is empty
        return 0
    else:
        return 1 + list_length(lst[1:])  # recursively call list_length on the remaining elements

# Example usage:
my_list = [1, 2, 3, 4, 5]
print(list_length(my_list))  # Output: 5

In this example, the list_length function takes a list as input. If the list is empty, it returns 0. Otherwise, it removes the first element from the list and recursively calls itself on the remaining elements. The result of the recursive call is then incremented by 1 and returned as the final length of the list.