Average depth in a binary search tree with repeated keys

Margaret Archibald 1 Julien Clément 2, 3
2 Equipe AMACC - Laboratoire GREYC - UMR6072
GREYC - Groupe de Recherche en Informatique, Image, Automatique et Instrumentation de Caen
Abstract : Random sequences from alphabet $\{1, \ldots,r\}$ are examined where repeated letters are allowed. Binary search trees are formed from these, and the average left-going depth of the first $1$ is found. Next, the right-going depth of the first $r$ is examined, and finally a merge (or 'shuffle') operator is used to obtain the average depth of an arbitrary node, which can be expressed in terms of the left-going and right-going depths. The variance of each of these parameters is also found.
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Margaret Archibald, Julien Clément. Average depth in a binary search tree with repeated keys. Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities, 2006, Nancy, France. pp.309-320. ⟨hal-01184700⟩

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