The document describes a quiz asking students to apply minimax and alpha-beta pruning algorithms to a game tree. For minimax, students are asked to: 1) compute backed-up node values and 2) indicate the optimal MAXIMIZER move. For alpha-beta pruning, students are asked to: 1) count evaluated nodes/leaves and 2) indicate pruned parts of the tree.

1. Quiz 3
(30 Minutes)
Please refer to Figure 1 and answer the following questions.
MAX
3
6
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5
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9
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Figure 1
1. Apply the minimax algorithm to the game tree in Figure 1, where it is the MAXIMIZER’s
turn to play. The values estimated by the evaluation function are indicated at the leaf nodes.
Assume that the search always visits children in a left-to-right order.
i)
Compute the backed-up values computed by the minimax algorithm. Show your
answer by writing values at the appropriate nodes in the above tree.
ii)
Indicate the proper move for the MAXIMIZER by marking the line with bold
indicator(
) to the root’s outgoing edges.

2. Answer:
6
6
3
5
3
5
4
5
6
3
6
8
5
7
7
6
5
9
5
6
7
4
5
6
9
6
8
8

3. 2. Apply alpha beta pruning to the game tree in Figure 1.
i)
Using the alpha-betapruning procedure (and standard left-to-right evaluation of
nodes), how many of the nodes and leaves will get evaluated?
ii)
Indicate all parts of the tree that are pruned / cut off.
Answer:
i)
21 nodes (nodes with cut-off are not included and 12 nodes (nodes with cut-off are not
included and not including leaf nodes)
ii)
MAX
6
6
3
5
3
5
4
5
6
3
5
7
6
7
6
5
6
9
5
6
7
4
5
6
9
8