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

Example 7.6: The preorder traversal of the tree associated with a document, as
in Example 7.3, examines an entire document sequentially, from beginning to end.
If the external nodes are removed before the traversal, then the traversal examines
the table of contents of the document. (See Figure 7.6.)
The preorder traversal is also an efficient way to access all the nodes of a tree. To
justify this, let us consider the running time of the preorder traversal of a tree T with
n nodes under the assumption that visiting a node takes O(1) time. The analysis of
the preorder traversal algorithm is actually similar to that of algorithm height2
(Code Fragment 7.7), given in Section 7.2.1. At each node v, the nonrecursive part
of the preorder traversal algorithm requires time O(1 + c v ), where c v is the number
of children of v. Thus, by Proposition 7.5, the overall running time of the preorder
traversal of T is O(n).
Algorithm toStringPreorder(T, v), implemented in Java in Code
Fragment 7.9, performs a preorder printing of the subtree of a node v of T, that is, it
performs the preorder traversal of the subtree rooted at v and prints the element
stored at a node when the node is visited. Recall that, for an ordered tree T, method
T.children(v) returns an iterable collection that accesses the children of v in
order.
Code Fragment 7.9: Method toStringPreorder(T, v)
that performs a preorder printing of the elements in the
subtree of node v of T.
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