Binary Tree Sequence Rotations and t-ary Tree Enumerations: Binary Trees Rotations, Ranking, Unranking, and Loopless

Ro-Yu Wu, Yue-Li Wang, Jou-Ming Chang

ISBN 10: 3639176340 / ISBN 13: 9783639176346

Published by VDM Verlag, 2009

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Bibliographic Details

• Title: Binary Tree Sequence Rotations and t-ary Tree Enumerations: Binary Trees Rotations, Ranking, Unranking, and Loopless
• Publisher: VDM Verlag
• Publication Date: 2009
• Language: English
• ISBN 10: 3639176340
• ISBN 13: 9783639176346
• Binding: Paperback
• Condition: Like New
• Book Type: book

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Synopsis

In this book, we consider a transformation on binary trees using new types of rotations. Each of the newly proposed rotations is permitted only at nodes on the left-arm or the right-arm of a tree. Consequently, we develop a linear time algorithm with at most n ? 1 rotations for converting weight sequences between any two binary trees. we use right distance sequences (or RD-sequences for short), to describe all t-ary trees with n internal nodes. Using a t-ary recursion tree and its concomitant tables, a systematical way can help us to investigate the structural representation of t-ary trees. Consequently, we develop efficient algorithms for determining the rank of a given t-ary tree in lexicographic order (i.e., the ranking algorithm), and for converting a positive integer to its corresponding RD-sequence (i.e., the unranking algorithm). Both the ranking and unranking algorithms can be run in O(tn) time and without really building any auxiliary table. In addition, we also present a loopless algorithm to enumerate Gray-codes of t-ary trees using RD-sequences.

About the Author

Ro-Yu Wu, PhD: Studied Information Management at the National Taiwan University of Science and Technology. Associate professor at the Department of Industrial Management at Lunghwa University of Science and Technology., Taiwan.