Clinic #23: Implement Trie

The last corner of this drawing is the one this clinic needs: words spelled downwards one letter per step, where “cat” and “car” walk the same first two steps and only split at the third.

Before you start. A tree, from Trees (BST, balancing, heaps, tries), is a shape with one starting point at the top, branches going down, and nothing ever looping back up. A hash set, from Hashing, is a box that answers “is this exact thing in here?” in one step, however full the box is; this clinic needs nothing else.