Question $3$: Adversarial search

$[14]$

The game tree for a two$-$player game is shown below. MIN and MAX layers are labelled to indicate the two players, with MAX playing first.

$4$

$2$

$($a$)$ Perform a minimax search on this game tree. The utility values are shown in RED next to the leaf nodes. Write down the backed$-$up utility values for nodes $E,F,$ and $G.$ What is the minimax value for the root node A$?$

$($b$)$ Perform an alpha$-$beta search on the same game tree using the same utility values given. Write down the alpha and beta values for nodes E$,$ F$,$ and G after the search is complete. Indicate where any cutoffs happen in the tree, and whether it is an alpha or beta cut.