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# M28 Past Exam Problems

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# Question 13


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# Question 14


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# Question 15


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# Question 16


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# Question 17


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# Question 18


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# Question 19


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# Question 20


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# Question 21


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# Question 22


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# Question 23


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# Question 24


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# Question 25


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📗 [3 points] Which nodes are pruned by alpha-beta pruning? The player moves first.
📗 Select the nodes:



📗 Note: please do not select any edges.
📗 [3 points] Which nodes are pruned by alpha-beta pruning? The player moves first.
📗 Select the nodes:



📗 Note: please do not select any edges.
📗 [4 points] Highlight the nodes that will be alpha-beta pruned in the following game.



📗 [4 points] Enter the smallest integer value of \(A\) such that \(B\) will be alpha-beta pruned? Max player moves first. In the case alpha = beta, prune the node. Enter -100 if you think the answer is negative infinity.

📗 Answer: .
📗 [4 points] Enter the largest integer value of \(A\) such that \(B\) will be alpha-beta pruned? Min player moves first. In the case alpha = beta, prune the node. Enter 100 if you think the answer is infinity.

📗 Answer: .
📗 [3 points] Select the values of \(A\) such that \(B\) will be alpha-beta pruned? The player moves first. In the case alpha = beta, prune the node.

📗 Choices:





None of the above
📗 [3 points] Which nodes are pruned by alpha-beta pruning? The player moves first.
📗 Select the nodes:



📗 [4 points] Consider the following zero-sum game tree. MAX player moves first. Draw a new game tree by re-ordering the children of each internal node (including the root), such that the new game is equivalent to the tree above, but alpha-beta pruning will prune as many nodes as possible. (You do not have to submit the drawing.) Enter the number of nodes pruned.

📗 Answer: .
📗 [4 points] Consider the following zero-sum game tree. MIN player moves first. Draw a new game tree by re-ordering the children of each internal node (including the root), such that the new game is equivalent to the tree above, but alpha-beta pruning will prune as many nodes as possible. (You do not have to submit the drawing.) Enter the number of nodes pruned.

📗 Answer: .
📗 [4 points] Consider the following zero-sum game tree. player moves first. Draw a new game tree by re-ordering the children of each internal node (including the root), such that the new game is equivalent to the tree above, but alpha-beta pruning will prune as many nodes as possible. (You do not have to submit the drawing.) Enter the number of nodes pruned.

📗 Note: in case the diagram is not clear, the values on the leafs (each sub-branch is a row): .
📗 Answer: .
📗 [4 points] For a zero-sum game in which moves first and the value to the MAX player is given in the diagram below, consider the static board evaluation (heuristic function) at the internal states provided in the table below. What are the smallest and largest possible values of \(x\) above and below which IDS (iterative deepening search) with depth limit \(1\) will find the correct solution for the game? You can assume all values are between \(-100\) and \(100\). Enter two numbers between \(-100\) and \(100\) (possibly including \(-100\), \(100\)).
📗 Note: for example, if you think \(10 < x < 20\), enter \(10, 20\); if you think any \(x > 10\) works, enter \(10, 100\); if you think any \(x < 20\) works, enter \(-100, 20\); if you think every \(x\) is okay, enter \(-100, 100\); if you think no such \(x\) exist, enter \(-100, -100\) or \(100, 100\).

State (Action) Left Middle Right
Static Board Evaluation \(x\)

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# Grade


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Last Updated: November 18, 2024 at 11:43 PM