On the generation of binary trees from (0-1) codes

An efficient recursive a algorithm for the generating all shapes of binary trees with n-nodes is presented. A binary tree with n-nodes is represented by 2(n−1) zeros and ones in a certain predetermined order. This scheme encodes the non-null links of a binary tree by 1's and the null links by 0...

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Veröffentlicht in:International journal of computer mathematics Jg. 69; H. 3-4; S. 243 - 251
Hauptverfasser: Ahrabian, H., Nowzari-Dalini, A.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Abingdon Gordon and Breach Science Publishers 01.01.1998
Taylor and Francis
Schlagworte:
Binary tree
code
Combinatorics
Combinatorics. Ordered structures
Exact sciences and technology
G.2.1 Combinatorial Algorithm
G.2.2 Graph Theory (Trees)
Graph theory
Mathematics
recursion
Sciences and techniques of general use
traversal
Graph theory
Binary tree
Recursive algorithm
Algorithm
Code
ISSN:0020-7160, 1029-0265
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Zusammenfassung:An efficient recursive a algorithm for the generating all shapes of binary trees with n-nodes is presented. A binary tree with n-nodes is represented by 2(n−1) zeros and ones in a certain predetermined order. This scheme encodes the non-null links of a binary tree by 1's and the null links by 0's in a pre-order traversal. The algorithm generates C n numbers of such codes. The algorithm is based on the idea of shifting '1' bits one space to the right. It is shown that the generation time per tree is constant O(1). The ranking and unranking algorithms are discussed. Also, an alternate way to obtain the Catalan numbers is given.
ISSN:0020-7160
1029-0265
DOI:10.1080/00207169808804721