Gray-Code Ranking and Unranking on Left-Weight Sequences of Binary Trees

Ro-Yu WU; Jou-Ming CHANG; Sheng-Lung PENG; Chun-Liang LIU

doi:10.1587/transfun.E99.A.1067

Special Section on Discrete Mathematics and Its Applications

Gray-Code Ranking and Unranking on Left-Weight Sequences of Binary Trees

Ro-Yu WU, Jou-Ming CHANG, Sheng-Lung PENG, Chun-Liang LIU

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Keywords: ranking algorithms, unranking algorithms, Gray-code order, left-weight sequences, left-distance sequence

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2016 Volume E99.A Issue 6 Pages 1067-1074

DOI https://doi.org/10.1587/transfun.E99.A.1067

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Abstract

Left-weight sequences (LW-sequences for short) are in common currency for encoding binary trees. In [16], Wu et al. proposed an algorithm associated with tree rotations for listing all binary trees in diverse representations including LW-sequences. In particular, such a list of LW-sequences is generated in Gray-code order. In this paper, based on this ordering, we present efficient ranking and unranking algorithms. For binary trees with n internal nodes, the time complexity and the space requirement in each of our ranking and unranking algorithms are O(n²) and O(n), respectively.

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