The magic of a number system

Authors:
Amr Elmasry;Claus Jensen;Jyrki Katajainen
Affiliations:
Max-Planck Institut für Informatik, Saarbrücken, Germany;The Royal Library, Copenhagen, Denmark;Department of Computer Science, University of Copenhagen, Denmark
Venue:
FUN'10 Proceedings of the 5th international conference on Fun with algorithms
Year:
2010

Citing 10
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Abstract

We introduce a new number system that supports increments with a constant number of digit changes. We also give a simple method that extends any number system supporting increments to support decrements using the same number of digit changes. In the new number system the weight of the ith digit is 2i-1, and hence we can implement a priority queue as a forest of heap-ordered complete binary trees. The resulting data structure guarantees O(1) worst-case cost per insert and O(lg n) worst-case cost per delete, where n is the number of elements stored.