2008 | OriginalPaper | Chapter
Recounting the Rationals: Twice!
Authors : Roland Backhouse, João F. Ferreira
Published in: Mathematics of Program Construction
Publisher: Springer Berlin Heidelberg
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We derive an algorithm that enables the rationals to be efficiently enumerated in two different ways. One way is known and is credited to Moshe Newman; it corresponds to a deforestation of the so-called Calkin-Wilf tree of rationals. The second is new and corresponds to a deforestation of the Stern-Brocot tree of rationals. We show that both enumerations stem from the same simple algorithm. In this way, we construct a Stern-Brocot enumeration algorithm with the same time and space complexity as Newman’s algorithm.