Find the Last Element

Get the last element of a list, recursively — no loops, no indexing tricks like xs[-1]. Just a function that calls itself.

Quick recap of the tool, so this stands alone. Recursion means solving a problem by calling a function on a smaller piece of itself. Every recursive function needs a base case (the smallest input, answered outright, which stops the recursion) and a recursive case (call yourself on something smaller, then use the result). We’ll treat a list as a first element xs[0] followed by the rest xs[1:].

For summing a list, the base case was the empty list. But “the last element” is different — an empty list has no last element at all. So the natural smallest answerable case isn’t []; it’s a list of exactly one element, whose last element is obviously itself.

def last(xs):
    if len(xs) == 1:
        return ???          # base case: one element — what's the last?
    else:
        return ???          # recursive case: where does the answer live?

Your task: fill in both blanks.

Things to settle before revealing:

• In the base case, the list is [x]. What’s its last element?
• In the recursive case, the last element of [3, 1, 2] is the same as the last element of what shorter list? Write that as a call to last.
• Bonus: what should last([]) do? (There’s no good value to return — note what you’d want to happen.)