The average height of planted plane trees with M leaves
نویسندگان
چکیده
منابع مشابه
On the average hyperoscillations of planted plane trees
Assume that the leaves of a planted plane tree are enumerated from left to right by 1, 2, . . . . The j-th s-turn of the tree is defined to be the root of the (unique) subtree of minimal height with leaves j, j + 1, . . ., j + s -1 . If all trees with n nodes are regarded equally likely, the average level number of the j-th s-turn tends to a finite limit a . (j), which is of order j 1/2 . The j...
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An ordered tree with height h is b-balanced if all its leaves have a level l with h − b <= l <= h, where at least one leaf has a level equal to h − b. For large n, we shall compute asymptotic equivalents to the number of all b-balanced ordered trees with n nodes and of all such trees with height h. Furthermore, assuming that all b-balanced ordered trees with n nodes are equally likely, we shall...
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Multi-edge trees as introduced in a recent paper of Dziemiańczuk are plane trees where multiple edges are allowed. We first show that d-ary multi-edge trees where the out-degrees are bounded by d are in bijection with classical d-ary trees. This allows us to analyse parameters such as the height. The main part of this paper is concerned with multi-edge trees counted by their number of edges. Th...
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The average height of a binary tree with n internal nodes is shown to be asymptotic to 2 6. This represents the average stack height of the simplest recursive tree traversal algorithm. The method used in this estimation is also applicable to the analysis of traversal algorithms of unary-binary trees, unbalanced 2-3 trees, t-ary trees for any t, and other families of trees. It yields the two pre...
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Structured documents, like books, articles, and web pages, are composed of chapters, sections, paragraphs, figures, appendices, indices, etc. The occurrences of these components are mutually constrained; for instance, it is understood that a section is part of a chapter and that appendices are located at the end of a document. This hierarchical layout is meant to facilitate reading, and it supp...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 1983
ISSN: 0095-8956
DOI: 10.1016/0095-8956(83)90019-9