Suppose we are tracking the execution of some arbitrary minimax tree with the arbitrary utilities and minimax values displayed within each node below. Suppose also that the depth$-$first search is conducted in left$-$to$-$right order in the partial game tree displayed below.

Now, suppose that during minimax search with $-$ pruning, we encounter some State $S($e$.$g$.,$ think about some configuration of a chess state where a piece is moved back and forth to replicate an earlier state$)$ at multiple locations in the game tree.

$3\mathrm{.}3.$ If we were NOT using $-$ pruning, what would be the returned minimax score of $S?$

$3\mathrm{.}4.$ If we WERE to use $-$ pruning, what would be the returned minimax score of $S$ in each of the different subtrees in which it appears? NOTE: State $S$ has different starting values for $,$ based on the unshown subtrees above them.

S

$3\mathrm{.}5.$ Using your answers above, if we were using $-$ pruning, would it be wise to cache $/$ store $/$ memoize the minimax score for state $S$ the first time it was encountered to save on computation whenever we see it later during the search $($like the gravevard in search$)?$ Whv or why not?