A loopless gray code for minimal signed-binary representations

  • Authors:
  • Gurmeet Singh Manku;Joe Sawada

  • Affiliations:
  • Google Inc.;University of Guelph, Canada

  • Venue:
  • ESA'05 Proceedings of the 13th annual European conference on Algorithms
  • Year:
  • 2005

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Abstract

A string ... a2a1a0 over the alphabet {–1,0,1} is said to be a minimal signed-binary representation of an integer n if n = ∑k≥0ak2k and the number of non-zero digits is minimal. We present a loopless (and hence a Gray code) algorithm for generating all minimal signed binary representations of a given integer n.