Recounting the Rationals: Twice!Recounting the Rationals: Twice!Backhouse, Roland Carl and Ferreira, João F.2008

Paper summaryacawikiThis paper shows the derivation of an algorithm that enables the positive rationals to be enumerated in two different ways. One way is known, and is called Calkin-Wilf-Newman enumeration; the second is new and corresponds to a flattening 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 Calkin-Wilf-Newman enumeration.

This paper shows the derivation of an algorithm that enables the positive rationals to be enumerated in two different ways. One way is known, and is called Calkin-Wilf-Newman enumeration; the second is new and corresponds to a flattening 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 Calkin-Wilf-Newman enumeration.

Your comment:

You must log in before you can post this comment!

You must log in before you can submit this summary! Your draft will not be saved!

Preview:

0

Short Science allows researchers to publish paper summaries that are voted on and ranked! About