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I am currently working on a assignment for my A.I course. I am currently struggling to prove that something is not monotonic rather then the opposite. So far, I can't seem to find a way to prove this without knowing the cost of moving from n -> n', which we are not given. Since it is a "sliding block puzzle game" I could find the minimum cost, but I'm unsure if that is what is expected. If you have any suggestions I would be grateful.

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Gipjoe
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  • Welcome to Stack Overflow. You can improve your question. Please read [How to Ask](http://stackoverflow.com/help/how-to-ask) including the link "How to ask questions the smart way." A question with multiple questions is difficult to answer. – zhon Nov 24 '16 at 02:49

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The question says that "For each node n, h(n) is the estimate of the cost (in moves)" (emphasis mine). The way I interpret that is that you can safely assume that every move has a cost of 1.

Dennis Soemers
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  • Hey thanks! I was thinking the same thing but I wasn't quite sure if there was another was we could show that it is infact not monotonic. – Gipjoe Nov 24 '16 at 14:38
  • @Gipjoe I suppose in this case it could also be proven under the assumption that all costs are nonnegative (>= 0). Some people may take that assumption for granted, but in my opinion that should still be stated explicitly if you're allowed to assume that. Anyway, saying that the h(n) values given to you are measured in moves means you can treat every edge as having a cost of one. – Dennis Soemers Nov 24 '16 at 15:15