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

 
9783639176346: Binary Tree Sequence Rotations and t-ary Tree Enumerations: Binary Trees Rotations, Ranking, Unranking, and Loopless

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.

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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.

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Ro-Yu Wu
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Book Description Book Condition: New. Publisher/Verlag: VDM Verlag Dr. Müller | Binary Trees Rotations, Ranking, Unranking, and Loopless | In this book, we consider a transformation on binarytrees using new types of rotations. Each of the newlyproposed rotations is permitted only at nodes on theleft-arm or the right-arm of a tree. Consequently, wedevelop a linear time algorithm with at most n 1rotations for converting weight sequences between anytwo binary trees.we use right distance sequences (or RD-sequences forshort), to describe all t-ary trees with n internalnodes. Using a t-ary recursion tree and itsconcomitant tables, a systematical way can help us toinvestigate the structural representation of t-arytrees. Consequently, we develop efficient algorithmsfor determining the rank of a given t-ary tree inlexicographic order (i.e., the ranking algorithm),and for converting a positive integer to itscorresponding RD-sequence (i.e., the unrankingalgorithm). Both the ranking and unranking algorithmscan be run in O(tn) time and without really buildingany auxiliary table. In addition, we also present aloopless algorithm to enumerate Gray-codes of t-arytrees using RD-sequences. | Format: Paperback | Language/Sprache: english | 140 gr | 96 pp. Bookseller Inventory # K9783639176346

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Book Description VDM Verlag Aug 2009, 2009. Taschenbuch. Book Condition: Neu. 220x150x6 mm. Neuware - 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. 96 pp. Englisch. Bookseller Inventory # 9783639176346

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Book Description VDM Verlag Aug 2009, 2009. Taschenbuch. Book Condition: Neu. 220x150x6 mm. Neuware - 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. 96 pp. Englisch. Bookseller Inventory # 9783639176346

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Book Description VDM Verlag Dr. Muller Aktiengesellschaft Co. KG, Germany, 2012. Paperback. Book Condition: New. 152 x 229 mm. Language: English . Brand New Book. 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. Bookseller Inventory # KNV9783639176346

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