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Generation of binary trees from (0-1) codes. (English) Zbl 0742.68024
Summary: A binary tree can be represented by a code reflecting the traversal of the corresponding regular binary tree in a given monotonic order. A different coding scheme based on the branches of a regular binary tree with $$n$$-nodes is proposed. It differs from the coding scheme generally used and makes no distinction between internal nodes and terminal nodes. A code of a regular binary tree with $$n$$-nodes is formed by labeling the left branches by 0’s and the right branches by 1’s and then traversing these branches in pre-order. The root is always assumed to be on a left branch. Different order of traversals yield different codes. An efficient nonrecursive Pascal program of $$O(n \log_ 2 n)$$ time complexity using the backtracking approach is given to generate these codes in colexicographic order.

##### MSC:
 68W10 Parallel algorithms in computer science 68R05 Combinatorics in computer science 68P05 Data structures 68R10 Graph theory (including graph drawing) in computer science
##### Keywords:
binary tree; monotonic order; coding scheme; backtracking
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##### References:
 [1] DOI: 10.1145/322169.322170 [2] DOI: 10.1145/359423.359434 · Zbl 0345.68025 [3] DOI: 10.1145/322077.322082 · Zbl 0379.68029 [4] Knuth D.E., The art of computer programming 1 (1983) [5] Rusky F., SIAM J.Comput 7 pp 745– (1978) [6] DOI: 10.1137/0208006 · Zbl 0406.05026 [7] DOI: 10.1080/00207168508803477 · Zbl 0655.68080 [8] DOI: 10.1016/0304-3975(80)90073-0 · Zbl 0422.05026
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