Abstract
In this paper, we present two new ranking and unranking algorithms for k-ary trees represented by x-sequences in Gray code order. These algorithms are based on a gray code generation algorithm developed by Ahrabian et al.. In mentioned paper, a recursive backtracking generation algorithm for x-sequences corresponding to k-ary trees in Gray code was presented. This generation algorithm is based on Vajnovszki’s algorithm for generating binary trees in Gray code ordering. Up to our knowledge no ranking and unranking algorithms were given for x-sequences in this ordering. we present ranking and unranking algorithms with O(kn) time complexity for x-sequences in this Gray code ordering . Keywords—k-ary Tree Generation, Ranking, Unranking, Gray Code.
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