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Fun with Clojure: Turning Cats into Dogs in Hanoi
- leif 16y agoNever noticed before that Hanoi states are homomorphic to Sierpinski triangles. That's gorgeous. :-)
- phob 16y agoisomorphic?
- leif 16y agoAn isomorphism requires a metric, which metric do you mean? I'm talking group homomorphic, though they're also topologically isomorphic, a.k.a. homeomorphic.
- phob 16y agoSaying that two groups are homomorphic doesn't tell me much more than there exists a group homomorphism... As far as I know, isomorphism implies one can be transformed into the other through renaming. I don't know anything about topology, so I'll take your word for it.
- merraksh 16y agoThis can be cast as a shortest path problem. Implementations on huge graphs (several million nodes), i.e. larger than the one defined by a dictionary, are very efficient and usually take advantage of both the source and destination rather than just performing breadth first search from the source. I can think of Andrew Goldberg's work, see e.g. http://research.microsoft.com/en-us/people/goldberg/ http://research.microsoft.com/en-us/people/goldberg/
- jkkramer 16y agoThanks for the Goldberg pointer. I have a rudimentary bidirectional, parallel BFS working which I'll be blogging about once it's ready. It runs very fast even on huge graphs.
- finin 16y agoIn the fall of 1980 I taught my first class (AI) as a professor. The TA, Jeff Shrager, suggested this word problem, which he called dog-cat, as a good homework exercise for implementing the A* search algorithm. The students had to do it for three letter words in Lisp and on a Univac computer that the University of Pennsylvania’s Moore School had at the time. I’ve been using the problem on and off for 30 years now in homework assignments.