Do the following Board Game AI problems from Chapter $9$ in the Millington book on pp$.$

$799-800.$

a$.9-1$

$9\mathrm{.}1$ Devise a scoring function for Tic$-$Tac$-$Toe.

b$.9-2$

$9\mathrm{.}2$ Show how minimax values are bubbled up on the tree in Figure $9\mathrm{.}19$:

c$.9-3$

$9\mathrm{.}3$ Show how negamax values are bubbled up on the tree in Exercise $9\mathrm{.}2.$

d$.9-4$

$9\mathrm{.}4$ Show how AB minimax values are bubbled up on the tree in Exercise $9\mathrm{.}2.$Figure $9\mathrm{.}19$: Minimax values in a tree