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GATE DA 2024 Q23: Combination of two admissible heuristics that stays admissible

Question

Let h1h_1 and h2h_2 be two admissible heuristics used in A∗A^* search.

Which ONE of the following expressions is always an admissible heuristic?

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Answer: D (official GATE 2024 final answer key)

Concept used: A heuristic is admissible if it never overestimates the true cost h∗h^*.

First step: Both h1h_1 and h2h_2 lie in [0,h∗][0, h^*], so their difference is at most max⁡(h1,h2)≤h∗\max(h_1, h_2) \le h^*; sums and products can exceed h∗h^*.

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Source: official GATE 2024 DA question paper and final answer key, organised by IISc Bangalore. Question paper · Answer key

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