<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>5</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Roland Backhouse</style></author><author><style face="normal" font="default" size="100%">João F. Ferreira</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Recounting the Rationals: Twice!</style></title><secondary-title><style face="normal" font="default" size="100%">Mathematics of Program Construction (LNCS 5133)</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2008</style></year></dates><publisher><style face="normal" font="default" size="100%">Springer</style></publisher><abstract><style face="normal" font="default" size="100%">&lt;p&gt;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.&lt;/p&gt;
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