91Ó°ÊÓ

Draw the expression trees for the following expressions: (a) \(a(b+c)\) (b) \(a b+c\) (c) \(a b+a c\) (d) \(b b-4 a c\) (e) \(\left(\left(a_{3} x+a_{2}\right) x+a_{1}\right) x+a_{0}\)

Suppose that an undirected tree has diameter \(d\) and that you would like to select a vertex of the tree as a root so that the resulting rooted tree has the smallest depth possible. How would such a root be selected and what would be the depth of the tree (in terms of \(d\) )?