Data Structures and Algorithms in Java[1].pdf - Fulvio Frisone

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Give the output of printExpression(T, T.root()) (Code Fragment
7.27).
R-7.21
Describe, in pseudo-code, an algorithm for computing the number of
descendents of each node of a binary tree. The algorithm should be based on the
Euler tour traversal.
R-7.22
Let T be a (possibly improper) binary tree with n nodes, and let D be the sum of
the depths of all the external nodes of T. Show that if T has the minimum
number of external nodes possible, then D is O(n) and if T has the maximum
number of external nodes possible, then D is O(n log n).
R-7.23
Let T be a binary tree with n nodes, and let p be the level numbering of the
nodes of T, as given in Section 7.3.5.
a.
Show that, for every node v of T, p(v) ≤ 2 n − 1.
b.
Show an example of a binary tree with seven nodes that attains the above
upper bound on p(v) for some node v.
R-7.24
Show how to use the Euler tour traversal to compute the level number, defined
in Section 7.3.5, of each node in a binary tree T.
R-7.25
Draw the binary tree representation of the following arithmetic expression: "(((5
+ 2) * (2 − 1))/((2 + 9) + ((7 − 2) − 1)) * 8)".
R-7.26
Let T be a binary tree with n nodes that is realized with an array list, S, and let p
be the level numbering of the nodes in T, as given in Section 7.3.5. Give
pseudo-code descriptions of each of the methods root, parent, left,
right, hasLeft, hasRight, isInternal, isExternal, and isRoot.
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