Abstract
We consider a general additive weight of random trees which depends on the structure of the subtrees, on weight functions defined on the number of internal and external nodes and on the degrees of the nodes appearing in the tree and its subtrees. Choosing particular weight functions, the corresponding weight is an important parameter appearing in the analysis of sorting and searching algorithms. For a simply generated family of rooted planar trees ?, we shall derive a general approach to the computation of the average weight of a tree T?? with n nodes and m leaves for arbitrary weight functions. This general result implies exact and asymptotic expressions for many types of average weights of a tree T?? with n nodes if the weight functions are arbitrary polynomials in the number of nodes and leaves with coefficients depending on the node degrees.
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