Abstract
Generating binary trees is a well-known problem. In this paper, we add some constraints to leaves of these trees. Such trees are used in the morphing of polygons, where a polygon P is represented by a binary tree T and each angle of P is a weight on a leaf of T. In the following, we give two algorithms to generate all binary trees, without repetitions, having the same weight distribution to their leaves and representing all parallel polygons to P.
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References
T. Beyer, S.M. Hedetniemi: Constant time generation of rooted trees. SIAM Journal on Computing 9(4) (1980) 706–712.
L. Guibas, J. Hershberger and S. Suri: Morphing Simple Polygons. Discrete and Computational Geometry 24 (2000) 1–34.
J.F. Korsh, P. LaFollette: Loopless generation of Gray codes for k-ary trees. Information Processing Letters 70 (1999) 7–11.
A.V. Kozina: Coding and generation of nonisomorphic trees. Cybernetics 15 (1979) 645–651.
Z. Li, S. Nakano: Efficient Generation of Plane Triangulations without Repetitions. International Colloquium on Automata, Languages and Programming 2001, 433–443.
S. Nakano: Efficient generation of plane trees. Information Processing Letters 84 (2002) 167–172.
J. M. Pallo: Enumerating, Ranking and Unranking Binary Trees. The Computer Journal 29(2) (1986) 171–175.
J. M. Pallo: An efficient upper bound of the rotation distance of binary trees. Information Processing Letters 73 (2000) 87–92.
M.V.S. Ramanath, T.R. Walsh: Enumeration and Generation of a Class of Regular Digraphs. Journal of Graph Theory 11(4) (1987) 471–479.
G. Tinhofer, H. Schreck: Linear Time Tree Codes. Computing 33 (1984) 211–225.
V. Vajnovszki: On the loopless generation of binary tree sequences. Information Processing Letters 68 (1998) 113–117.
R. A. Wright, B. Richmond, A. Odlyzko and B. D. McKay: Constant time generation of free trees. SIAM Journal on Computing 15(2) (1986) 540–548.
L. Xiang, K. Ushijima, C. Tang: Efficient loopless generation of Gray codes for k-ary trees. Information Processing Letters 76 (2000) 169–174.
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© 2003 Springer-Verlag Berlin Heidelberg
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Effantin, B. (2003). Generation of Valid Labeled Binary Trees. In: Kumar, V., Gavrilova, M.L., Tan, C.J.K., L’Ecuyer, P. (eds) Computational Science and Its Applications — ICCSA 2003. ICCSA 2003. Lecture Notes in Computer Science, vol 2667. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44839-X_27
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DOI: https://doi.org/10.1007/3-540-44839-X_27
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