The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
Generation of Binary Trees from Ballot Sequences
Journal of the ACM (JACM)
On the Generation of Binary Trees
Journal of the ACM (JACM)
A Note on Enumerating Binary Trees
Journal of the ACM (JACM)
A numbering system for binary trees
Communications of the ACM
A compendium of key search references
ACM SIGIR Forum
The generation of binary trees as a numerical problem
Journal of the ACM (JACM)
Optimal parallel encoding and decoding algorithms for trees
CSC '91 Proceedings of the 19th annual conference on Computer Science
An O(1) Time Algorithm for Generating Multiset Permutations
ISAAC '99 Proceedings of the 10th International Symposium on Algorithms and Computation
An approach to certificate path discovery in mobile Ad Hoc networks
Proceedings of the 1st ACM workshop on Security of ad hoc and sensor networks
Theoretical Computer Science
Generating random binary trees - A survey
Information Sciences: an International Journal
An improved kernel size for rotation distance in binary trees
Information Processing Letters
Ranking and unranking of non-regular trees with a prescribed branching sequence
Mathematical and Computer Modelling: An International Journal
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A new algorithm that, for the first time, exploits the rotational geometry of binary trees is developed in order to allow for the lexicographic generation of computer representations of these trees in average time O(1) per tree. “Rotation” codewords for these trees (in average time O(1) per tree) are also generated. It is shown how these codewords relate to lattice paths, and, using this relationship, that n(n - 1)/(n + 2) is the average number of rotations needed to generate a binary tree on n nodes. Finally, a necessary and sufficient condition that a codeword represent a full binary tree (each node has 0 or 2 sons) on n = 2m + 1 nodes is given and how to contract this codeword to obtain the codeword for the binary tree on m nodes for which this full tree is the extended binary tree is shown.