GATE DA 2025 Set 1 — Question 43
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Artificial Intelligence → Adversarial Search → Alpha-Beta Pruning
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Question
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 and , the right child of node and the right child of node will be pruned by alpha-beta pruning algorithm?
Correct answer
(C) x ∈ (-∞, 2] and y ∈ [2, ∞)
Solution
In alpha-beta pruning, a node is pruned if the current search path already has a better option elsewhere. For a MIN node, pruning occurs if its current value becomes less than or equal to the value passed from its parent MAX node.Tree-1:
1.Root node (MAX) visits its left child (leaf 2). It updates its .
2. then visits its right child, node (MIN), passing .
3. visits its first child . It updates its .
4.Pruning of 's right child (value 1) occurs if , which means . Thus, .
Tree-2:1.Root node (MAX) visits its left child (MIN). has children 5 and , so its value is .
2. updates its .
3. then visits its right child (MIN), passing .
4. visits its first child 2. It updates its .
5.Pruning of 's right child (triangle) occurs if , which means .
6.This inequality holds if (always true) and . Thus, .
Combining these results, we find and , which matches option (C).Continue learning with Success Tracker
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