Exercise $6($Adopted from Russel and Norvig$)$: Consider the map below. Two friends

$(P$ and $E)$ want to avoid each other. The problem then becomes a two$-$player

pursuit$-$evasion game. We assume now that the players take turns moving. The

game ends only when the players are on the same node; the terminal payoff to the

pursuer is minus the total time taken. $($The evader "wins" by never losing.$)$

a$)$ Construct the game tree and mark the value of terminal nodes

b$)$ Apply alpha$-$beta pruning on the game tree assuming that the tree is

evaluated from left to right

c$)$ Can you prove anything in general about who wins the game on a map that

is a tree?