Minimax and Alpha$-$Beta Pruning $(5$ points$)$

a$.$ Perform the minimax algorithm on the adversarial search tree in Figure $2$ by

annotating the MIN and MAX nodes with their respective values. $(1$ point$)$

max

min

max

min

Figure $2$: Adversarial Search Tree for Minimax

b$.$ Perform the alpha$-$beta pruning algorithm on the adversarial search tree in Figure $3.$

Indicate MAX nodes with their alpha values and MIN nodes with their beta values.

Further, indicate branches that must be pruned. $(4$ points$)$

Figure $3$: Adversarial Search Tree for Alpha Beta Pruning