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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
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