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GATE DA 2025 Q43: Alpha-beta pruning: ranges of x and y

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.

Tree-1: MAX root A with children: a leaf of value 2 and MIN node B, whose children are leaf x and leaf 1 (dotted edge). Tree-2: MAX root C with MIN children D (leaves 5 and y) and E (leaf 2 and a subtree on a dotted edge).
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For what ranges of xx and yy, the right child of node BB and the right child of node EE will be pruned by alpha-beta pruning algorithm?

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Answer: C (official GATE 2025 final answer key)

Concept used: Alpha-beta pruning: a MIN node is cut off once its value falls to or below the MAX player's best so far (alpha).

First step: In Tree-1, MAX already has 2 from the left leaf, so α=2\alpha = 2. Node B can stop as soon as its running minimum, xx, is at most 2.

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Source: official GATE 2025 DA question paper and final answer key, organised by IIT Roorkee. Question paper · Answer key

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