Consider the following minimax tree: [-inf, +inf] [-inf, +inf] [-inf, +inf] [-inf, +inf] (MY 8 2 1 7 6 12 2 4 5 a. What is the minimax value for the root? (5 points) b. To solve the following alpha-beta pruning problem: the triangles pointed up represent maximizing nodes. The triangles pointing down represent minimizing nodes. The [-, +0] are place holders for the alpha-beta bookkeeping for pruning. Alpha is initialized to negative infinity (-). Beta is initialized to positive infinity (+). Please update alpha-beta values for each node and show your answer step by step. Please note that you may not need to show [-00, +o] for each node. Just use whatever you feel comfortable. However, it should have a number associated with each node except those will be pruned. (10 points) c. Is there another ordering for the children of the node C for which more pruning would result? If so, state the order. (5 points) d. Propose a general, practical method for ordering children of nodes which will tend to Activat increase the opportunities for pruning. You should be concise, but clearly state both what to do about min nodes and max nodes. (5 points) Go to Se