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

Wu, Ro-Yu

 
9783639176346: Binary Tree Sequence Rotations and t-ary Tree Enumerations: Binary Trees Rotations, Ranking, Unranking, and Loopless
Couverture souple
ISBN 10 : 3639176340 ISBN 13 : 9783639176346
Editeur : VDM Verlag, 2009

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.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Présentation de l'éditeur

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.

Biographie de l'auteur

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.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
VDM Verlag
Date d'édition
2009
Langue
anglais
ISBN 10 
3639176340
ISBN 13 
9783639176346
Reliure
Broché
Nombre de pages
96
Coordonnées du fabricant
non disponible
Personne responsable
non disponible