Gray-Code Ranking and Unranking on Left-Weight Sequences of Binary Trees

被引：1

作者：

Wu, Ro-Yu ^{[1
]}

Chang, Jou-Ming ^{[2
]}

Peng, Sheng-Lung ^{[3
]}

Liu, Chun-Liang ^{[4
]}

机构：

[1] Lunghwa Univ Sci & Technol, Dept Ind Management, Taoyuan, Taiwan

[2] Natl Taipei Univ Business, Inst Informat & Decis Sci, Taipei 10051, Taiwan

[3] Natl Dong Hwa Univ, Dept Comp Sci & Informat Engn, Hualien, Taiwan

[4] Natl Taiwan Normal Univ, Dept Humanity & Social Sci, Taipei, Taiwan

来源：

IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES | 2016年 / E99A卷 / 06期

关键词：

ranking algorithms; unranking algorithms; Gray-code order; left-weight sequences; left-distance sequence; K-ARY TREES; LOOPLESS GENERATION; NONREGULAR TREES; ROTATIONS; ALGORITHM; ORDER;

D O I：

10.1587/transfun.E99.A.1067

中图分类号：

TP3 [计算技术、计算机技术];

学科分类号：

0812 ;

摘要：

Left-weight sequences (LW-sequences for short) are in common currency for encoding binary trees. In [16], Wu et al. proposed an algorithm associated with tree rotations for listing all binary trees in diverse representations including LW-sequences. In particular, such a list of LW-sequences is generated in Gray-code order. In this paper, based on this ordering, we present efficient ranking and unranking algorithms. For binary trees with n internal nodes, the time complexity and the space requirement in each of our ranking and unranking algorithms are O(n(2)) and O(n), respectively.

引用

页码：1067 / 1074

页数：8

共 13 条

[1] Ranking Left-weight Sequences of Binary Trees in Gray-code Order
Wu, Ro-Yu
Chang, Jou-Ming
Peng, Sheng-Lung
Chang, Shun-Chieh
2015 INTERNATIONAL COMPUTER SCIENCE AND ENGINEERING CONFERENCE (ICSEC), 2015, : 100 - 105
[2] Ranking and Unranking of Non-regular Trees in Gray-Code Order
Wu, Ro-Yu
Chang, Jou-Ming
Chen, An-Hang
Ko, Ming-Tat
IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES, 2013, E96A (06) : 1059 - 1065
[3] Ranking and Unranking t-ary Trees in a Gray-Code Order
Wu, Ro-Yu
Chang, Jou-Ming
Chen, An-Hang
Liu, Chun-Liang
COMPUTER JOURNAL, 2013, 56 (11): : 1388 - 1395
[4] ENUMERATING, RANKING AND UNRANKING BINARY-TREES
PALLO, JM
COMPUTER JOURNAL, 1986, 29 (02): : 171 - 175
[5] Gray-Code/Binary Transformation through Software.
Wehlan, H.
Regelungstechnik RT, 1980, 28 (02): : 61 - 63
[6] Loopless Algorithms for Listing Zaks' Sequences in Gray-Code Order
Wu, Ro-Yu
Hsu, Cheng-Hsien
Chang, Jou-Ming
JOURNAL OF INTERNET TECHNOLOGY, 2014, 15 (04): : 679 - 684
[7] A loopless Gray-code algorithm for listing k-ary trees
van Baronaigien, DR
JOURNAL OF ALGORITHMS, 2000, 35 (01) : 100 - 107
[8] Ranking and Unranking of t-Ary Trees Using RD-Sequences
Wu, Ro-Yu
Chang, Jou-Ming
Wang, Yue-Li
IEICE TRANSACTIONS ON INFORMATION AND SYSTEMS, 2011, E94D (02): : 226 - 232
[9] Quaternary gray-code phase unwrapping for binary fringe projection profilometry
He, Xiaoyu
Zheng, Dongliang
Kemao, Qian
Christopoulos, George
OPTICS AND LASERS IN ENGINEERING, 2019, 121 : 358 - 368
[10] Amortized efficiency of generation, ranking and unranking left-child sequences in lexicographic order
Pai, Kung-Jui
Chang, Jou-Ming
Wu, Ro-Yu
Chang, Shun-Chieh
DISCRETE APPLIED MATHEMATICS, 2019, 268 : 223 - 236

← 1 2 →