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A loopless algorithm for generating multiple binary tree sequences simultaneously

THEORETICAL COMPUTER SCIENCE 2014年第0期556卷 25-33页

作者： Wu, Ro-Yu Chang, Jou-Ming Chan, Hung-Chang Pai, Kung-Jui Lunghwa Univ Sci & Technol Dept Ind Management Taoyuan Taiwan Natl Taipei Univ Business Inst Informat & Decis Sci Taipei Taiwan Yuanpei Univ Dept Comp Sci & Informat Engn Hsinchu Taiwan Ming Chi Univ Technol Dept Ind Engn & Management New Taipei City Taiwan

Pallo and Wu et al. respectively introduced the left-weight sequences (LW-sequences) and right-weight sequences (RW-sequences) for representing binary trees. In this paper, we introduce two new types of binary tree sequences called the left-child sequences (LC-sequences) and right-child sequences (RC-sequences). Next, we propose a loopless algorithm associated with rotations of binary trees for generating LW-, RW-, LC-, and RC-sequences simultaneously. Moreover, we show that LW- and RW-sequences are generated in Gray-code order, and LC- and RC-sequences are generated so that each sequence can be obtained from its predecessor by changing at most two digits. Our algorithm is shown to be more efficient in both space and time than the existing known algorithms. (C) 2014 Published by Elsevier B.V.

关键词： Binary trees loopless generating algorithms Gray-code order Constant amortized time

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A loopless algorithm for generating the permutations of a multiset

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THEORETICAL COMPUTER SCIENCE 2003年第2期307卷 415-431页

作者： Vajnovszki, V Univ Bourgogne CNRS FRE 2309 LE2I F-21078 Dijon France

Many combinatorial structures can be constructed from simpler components. For example, a permutation can be constructed from cycles, or a Motzkin word from a Dyck word and a combination. In this paper we present a constructor for combinatorial structures, called shuffle oil trajectories (defined previously in a non-combinatorial context), and we show how this constructor enables us to obtain a new loopless generating algorithm for multiset permutations from similar results for simpler objects. (C) 2003 Elsevier B.V. All rights reserved.

关键词： gray codes loopless generating algorithms multiset permutations shuffle combinatorial objects

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A loopless algorithm for generating the permutations of a multiset

A loopless algorithm for generating the permutations of a mu...

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Conference on Random Generation of Combinatorial Objects and Bijective Combinatorics

作者： Vajnovszki, V Univ Bourgogne CNRS FRE 2309 LE2I F-21078 Dijon France

关键词： gray codes loopless generating algorithms multiset permutations shuffle combinatorial objects

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generating a Gray Code for P-Sequences

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Journal of Mathematical Modelling and algorithms 2002年第1期1卷 31-41页

作者： Vajnovszki, Vincent LE2I - CNRS FRE 2309 Université de Bourgogne 21011 Dijon Cedex BP 400 France

P-sequences are used for coding binary trees and they are also an alternative representation for well-formed parentheses strings. We present here the first Gray code and loopless generating algorithm for P-sequences, and extend them in a Gray code and a new loopless generating algorithm for well-formed parentheses strings. Ranking and unranking algorithms are also discussed. © 2002 Kluwer Academic Publishers.

关键词： Gray codes loopless generating algorithms P-sequences parentheses strings

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On the loopless generation of binary tree sequences

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INFORMATION PROCESSING LETTERS 1998年第3期68卷 113-117页

作者： Vajnovszki, V Univ Bourgogne LE2I F-21011 Dijon France

Weight sequences were introduced by Pallo in 1986 for coding binary trees and he presented a constant amortized time algorithm for their generation in lexicographic order. A year later, Roelants van Baronaigien and Ruskey developed a recursive constant amortized time algorithm for generating Gray code for binary trees in Pallo's representation. It is common practice to find a loopless generating algorithm for a combinatorial object when enunciating a Gray code for this object. In this paper we regard weight sequences as variations and apply a Williamson algorithm in order to obtain a loopless generating algorithm for the Roelants van Baronaigien and Ruskey's Gray code for weight sequences. (C) 1998 Elsevier Science B.V. All rights reserved.

关键词： loopless generating algorithms binary tree sequences combinatorial problems design of algorithms

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