$(20$ points$)($Graph Search and Adversarial Search$)$ Given the following weighted graph where S is the start state and G$1,$ G$2$ are goal states:

$($d$)(4$ points$)$ If this were a two$-$player game where MAX starts at S and MIN controls the

next move:

Draw the minimax game tree $($assuming edge weights are scores$)$

What would be MAX's best first move?

$($e$)(4$ points$)$ For the game tree from part $($d$),$ show how alpha$-$beta pruning would work.

Which nodes would be pruned?