Discussion
What does it mean for a heuristic to be admissible?
Answer: A
Admissibility means the estimate is optimistic, never exceeding the true remaining cost, and that alone guarantees A star returns an optimal solution in a tree search. Overestimation can cause the algorithm to overlook the best path. Returning zero at the goal is implied but is not the definition, and computational cost is a separate practical concern. A condition stated as a one sided inequality, and buying a strong guarantee, is worth memorising exactly.
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