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<b>Data Structures and Algorithms 
with Object-Oriented Design Patterns in C++</b><br>
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<H3><A NAME="SECTION0010401000000000000000">Preorder Traversal</A></H3>
<P>
The first depth-first traversal method
we consider is called
<em>preorder traversal</em><A NAME=15866>&#160;</A><A NAME=15867>&#160;</A>.
Preorder traversal is defined recursively as follows.
To do a preorder traversal of a general tree:
<OL><LI> Visit the root first; and then<LI> do a preorder traversal each of the subtrees of the root
	one-by-one in the order given.
</OL>
Preorder traversal gets its name from the fact that it visits the root first.
In the case of a binary tree,
the algorithm becomes:
<OL><LI> Visit the root first; and then<LI> traverse the left subtree; and then<LI> traverse the right subtree.
</OL>
For example, a preorder traversal of the tree shown in Figure&nbsp;<A HREF="page257.html#figtree5" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page257.html#figtree5"><IMG  ALIGN=BOTTOM ALT="gif" SRC="cross_ref_motif.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/icons/cross_ref_motif.gif"></A>
visits the nodes in the following order:
<P> <IMG WIDTH=334 HEIGHT=14 ALIGN=BOTTOM ALT="displaymath63846" SRC="img1145.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/img1145.gif"  ><P>
Notice that the preorder traversal visits the nodes of the tree
in precisely the same order in which they are written
in Equation&nbsp;<A HREF="page257.html#eqntreest" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page257.html#eqntreest"><IMG  ALIGN=BOTTOM ALT="gif" SRC="cross_ref_motif.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/icons/cross_ref_motif.gif"></A>.
A preorder traversal is often done when it is necessary
to print a textual representation of a tree.
<P>
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