. For the data structure introduced in Section 11.5.1, devise an algorithm that computes the number of leaves below each internal node of a rooted binary tree. Can you modify your algorithm to return...

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For the data structure introduced in Section 11.5.1, devise an

algorithm that computes the number of leaves below each internal node of a

rooted binary tree. Can you modify your algorithm to return the number of

nodes and leaves below each internal node?

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Devise an R function that takes a tree described by the data

structure in Section 11.5.1 as input, and produces a plot such as the one

shown in as output, using the standard R function plclust (see

Computational Example 10.1).