Consider game trees Tree-1 and Tree-2 as shown. The first level is a MAX agent and the second level is a MIN agent. The value in the square node is the output of the utility function.
For what ranges of \( x \) and \( y \), the right child of node B and the right child of node E will be pruned by the alpha-beta pruning algorithm?
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When using alpha-beta pruning, prune branches that cannot affect the decision-making process based on the already explored values of the parent nodes. MIN nodes prune values greater than or equal to their beta values, and MAX nodes prune values less than or equal to their alpha values.
\( x \in [1, \infty) \) and \( y \in (-\infty, 2] \)
\( x \in (-\infty, 2] \) and \( y \in (-\infty, 5] \)
\( x \in (-\infty, 2] \) and \( y \in [2, \infty) \)
\( x \in [1, \infty) \) and \( y \in (-\infty, 5] \)
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The Correct Option isC
Solution and Explanation
To apply the alpha-beta pruning algorithm, we first analyze Tree-1 and Tree-2:
In Tree-1, the right child of node \( B \) (MIN) will be pruned if \( x \in (-\infty, 2] \), since the MIN node will prefer the smaller values.
In Tree-2, the right child of node \( E \) (MIN) will be pruned if \( y \in [2, \infty) \), since the MIN node will prune when \( y \) exceeds the value of \( 5 \).
Thus, the ranges of \( x \) and \( y \) that will cause pruning are \( x \in (-\infty, 2] \) and \( y \in [2, \infty) \), which corresponds to Option C.
