Exercise 3.36

Invent a heuristic function for the 8-puzzle that sometimes overestimates, and show how it can lead to a suboptimal solution on a particular problem. (You can use a computer to help if you want.) Prove that if $h$ never overestimates by more than $c$, A using $h$ returns a solution whose cost exceeds that of the optimal solution by no more than $c$.

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