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The Computer Journal 1987 30(6):569-572; doi:10.1093/comjnl/30.6.569
© 1987 by British Computer Society
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Lexicographic Listing and Ranking of t-ary Trees

M. C. Er *

Department of Computer Science, University of Western Australia, Nedlands, WA 6009, Australia

Received 1 December 1985; revised 1 September 1986

This paper presents three simple and efficient algorithms for generating, ranking and unranking t-ary trees in a lexicographic order. The simplest idea of encoding a t-ary tree with n nodes as a bit-string of length t*n is exploited to its full advantages. It is proved that the lexicographic order in the set of t-ary trees with n nodes is preserved in the set of bit-strings of length t*n, using the above encoding scheme. Thus by generating all bit-strings in the lexicographic order, a simple decoding algorithm can convert them to t-ary trees in the same order. Finally, the theoretical basis for ranking a lexicographic listing of bit-strings is discussed, and the ranking and the unranking algorithms are derived.

* Now at: Dept. of Maths, and Computing Sciences, St. Francis Xavier University, Antigonish, Nova Scotia, Canada B2G ICO.


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