Recounting the Rationals: Twice!

Authors:
Roland Backhouse;João F. Ferreira
Affiliations:
School of Computer Science, University of Nottingham, Nottingham, England NG8 1BB;School of Computer Science, University of Nottingham, Nottingham, England NG8 1BB
Venue:
MPC '08 Proceedings of the 9th international conference on Mathematics of Program Construction
Year:
2008

Citing 3
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Abstract

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.