Recounting the Rationals: Twice!
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.
KeywordsCalkin-Wilf tree Stern-Brocot tree algorithm derivation enumeration algorithm rational numbers
Unable to display preview. Download preview PDF.
- 1.Aigner, M., Ziegler, G.: Proofs From The Book, 3rd edn. Springer, Heidelberg (2004)Google Scholar