Use Algorithm $1$ to build a binary search tree, using alphabetical

order, for the words: oenology, phrenology, campanology,

ornithology, ichthyology, limnology$,$ alchemy, and astrology.

Beginning at this tic$-$tac$-$toe position:

a$)$ Draw the minmax subtree of the game tree $($Hint: $x$ goes next$).$

b$)$ Determine the value of the subtree.