Abstract
A new type of sequences called left-child sequences (LC-sequences for short) was recently introduced by Wu et al. [19] for representing binary trees. In particular, they pointed out that such sequences have a natural interpretation from the view point of data structure and gave a characterization of them. Based on such a characterization, there is an algorithm to generate all LC-sequences of binary trees with n internal nodes in lexicographic order. In this paper, we extend our study to the ranking and unranking problems. By integrating a measure called “left distances” introduced by Mäkinen [8] to represent binary trees, we develop efficient ranking and unranking algorithms for LC-sequences in lexicographic order. With a help of aggregate analysis, we show that both ranking and unranking algorithms can be run in amortized cost of \(\mathcal {O}(n)\) time and space.
This research was partially supported by MOST grants 104-2221-E-131-004 (Kung-Jui Pai), 104-2221-E-262-005 (Ro-Yu Wu) and 104-2221-E-141-002-MY3 (Jou-Ming Chang) from the Ministry of Science and Technology, Taiwan.
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Pai, KJ., Wu, RY., Chang, JM., Chang, SC. (2016). Amortized Efficiency of Ranking and Unranking Left-Child Sequences in Lexicographic Order. In: Chan, TH., Li, M., Wang, L. (eds) Combinatorial Optimization and Applications. COCOA 2016. Lecture Notes in Computer Science(), vol 10043. Springer, Cham. https://doi.org/10.1007/978-3-319-48749-6_37
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