Q$4$: Tom and Jerry $[20-$points$]$

Bored at home, Tom and Jerry decided to play a game.

For this question, assume that branches are visited in left to right order.

$($a$)[3$ pts$]$ To analyze the game, Tom drew a game tree. However, Jerry quickly erased all the leaf node values in the tree, as

shown below, and asked Tom to think about running alpha$-$beta pruning on game trees with the same structure.

The maximum possible number of leaf nodes pruned $=$

$($ii$)1pt$

The minimum possible number of leaf nodes pruned $=$

Tom answered the questions correctly, so Jerry filled out the leaf node values.

$($b$)[2$ pts$]$ Using alpha beta pruning, how many leaf nodes can be pruned?

$($c$)[11$ pts$]$ Tom rearranges the leaf node values from the tree above such that alpha beta pruning prunes the maximum

amount of leaf nodes. Each leaf node value could have been moved to any of the other leaf nodes $($or not moved at all$).$