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

Creativity
C-7.1
For each node v in a tree T, let pre(v) be the rank of v in a preorder traversal of
T, let post(v) be the rank of v in a postorder traversal of T, let depth (v) be the
depth of v, and let desc(v) be the number of descendents of v, not counting v
itself. Derive a formula defining post(v) in terms of desc(v), depth(v), and
pre(v), for each node v in T.
C-7.2
Let T be a tree whose nodes store strings. Give an efficient algorithm that
computes and prints, for every node v of T, the string stored at v and the height
of the subtree rooted at v.
C-7.3
Design algorithms for the following operations for a binary tree T:
•
preorderNext(v): return the node visited after node v in a preorder
traversal of T
•
inorderNext(v): return the node visited after node v in an inorder
traversal of T
•
postorderNext(v): return the node visited after node v in a postorder
traversal of T.
What are the worst-case running times of your algorithms?
C-7.4
Give an O(n)-time algorithm for computing the depth of all the nodes of a tree
T, where n is the number of nodes of T.
C-7.5
The indented parenthetic representation of a tree T is a variation of the
parenthetic representation of T (see Figure 7.7) that uses indentation and line
breaks as illustrated in Figure 7.21. Give an algorithm that prints this
representation of a tree.
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