Discussion
Where do admissible heuristics usually come from?
Answer: C
Dropping a constraint gives a relaxed problem whose optimal solution can never cost more than the original's, so its exact cost is an admissible heuristic for the real problem. Straight line distance and the misplaced tile count both arise this way. Empirical measurements may give useful but not provably admissible estimates. Deriving a guarantee from the structure of a relaxation, rather than hoping for one, is what makes the technique so widely applicable.
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