Computing with Catalan Families
نویسنده
چکیده
We study novel arithmetic algorithms on a canonical number representation based on the Catalan family of combinatorial objects. For numbers corresponding to Catalan objects of low structural complexity our algorithms provide super-exponential gains while their average case complexity is within constant factors of their traditional counterparts.
منابع مشابه
Computing with Catalan Families, Generically
We describe arithmetic algorithms on a canonical number representation based on the Catalan family of combinatorial objects specified as a Haskell type class. Our algorithms work on a generic representation that we illustrate on instances members of the Catalan family, like ordered binary and multiway trees. We validate the correctness of our algorithms by defining an instance of the same type ...
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