Problem Description

You are given the following game tree with nodes and utility values at the leaves:Utility Values at Leaf Nodes:$-1=3-2=5-3=6-4=9-5=1-6=2-7=0$Minimax AlgorithmMinimax evaluates all leaf nodes to find the optimal move.

Alpha$-$Beta Pruning Algorithm

Alpha$-$Beta Pruning can prune some branches of the tree to avoid unnecessary evaluations.

Tasks

Solve the Problem Using Minimax Algorithm

Apply the Minimax algorithm to find the optimal move for the maximizing player starting at node $A.$

Show all steps, including the evaluation of all leaf nodes and the backtracking to determine the values of the intermediate nodes $($B$,$ C$,$ D$,$ E$,$ F$,$ G$).$

What is the final path and utility value suggested by the Minimax algorithm?

Solve the Problem Using Alpha$-$Beta Pruning Algorithm

Apply the Alpha$-$Beta Pruning algorithm to the same game tree.

Show all steps, including which branches are pruned and the intermediate values of $($alpha$)$ and $($beta$)$ at each node.

What is the final path and utility value suggested by the Alpha$-$Beta Pruning algorithm?

Identify at least three nodes where the $$ and $$ values remain different at the end of the traversal.

Comparison and Analysis

Compare the paths and utility values suggested by Minimax and Alpha$-$Beta Pruning.

Explain why the paths suggested by the two algorithms are different or the same.