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

There is an interesting application of the preorder traversal algorithm that produces
a string representation of an entire tree. Let us assume again that for each element e
stored in tree T, calling e.toString() returns a string associated with e. The
parenthetic string representation P(T) of tree T is recursively defined as follows. If
T consists of a single node v, then
P(T) = v.element().toString().
Otherwise,
P(T) = v.element().toString() + " (" + P(T 1 ) + "," + ··· + ", "+ P(T k ) +")",
where v is the root of T and T 1 , T 2 ,..., T k are the subtrees rooted at the children of v,
which are given in order if T is an ordered tree.
Note that the above definition of P(T) is recursive. Also, we are using "+" here to
denote string concatenation. The parenthetic representation of the tree of Figure 7.2
is shown in Figure 7.7.
Figure 7.7: Parenthetic representation of the tree of
Figure 7.2. Indentation, line breaks and spaces have
been added for clarity.
Note that, technically speaking, there are some computations that occur between
and after the recursive calls at a node's children in the above algorithm. We still
consider this algorithm to be a preorder traversal, however, since the primary action
of printing a node's contents occurs prior to the recursive calls.
The Java method parentheticRepresentation, shown in Code Fragment
7.10, is a variation of method toStringPreorder (Code Fragment 7.9). It
implements the definition given above to output a parenthetic string representation
of a tree T. As with the method toStringPreorder, the method
parentheticRepresentation makes use of the toString method that
is defined for every Java object. In fact, we can view this method as a kind of
toString() method for tree objects.
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