Question $2$

Marks: $8$

a$.$ Assuming the upward$-$facing triangles stand for the maximizing player and downward$-$facing triangles represent the minimizing player, run min$-$max algorithm on the following tree and find the values for each node from A to F$.[3]$

b$.$ State the path from the root node A that will be returned by the min$-$max algorithm. $[1]$

c$.$ What will be the alpha$-$ and beta$-$ values of each node in this tree if alpha$-$beta pruning is run on this tree? Also, illustrate the crossed$-$out branches that would be pruned by alpha$-$beta pruning. $[2+2]$