Algorithms and Data Structures

N.Wirth. Algorithms and Data Structures. Oberon version 155
(Fig. 4.25). The sentinel may be considered as a common, shared representative of all external nodes by
which the original tree was extended (see Fig. 4.19):
PROCEDURE locate (x: INTEGER; t: Node): Node;
BEGIN
s.key := x; (*sentinel*)
WHILE t.key # x DO
IF t.key < x THEN t := t.right ELSE t := t.left END
END;
RETURN t
END locate
Note that in this case locate(x, t) yields the value s instead of NIL, i.e., the pointer to the sentinel, if no
key with value x is found in the tree with root t.
t
4
2
5
1
3
6
s
Fig. 4.25. Search tree with sentinel
4.4.3 Tree Search and Insertion
The full power of the dynamic allocation technique with access through pointers is hardly displayed by
those examples in which a given set of data is built, and thereafter kept unchanged. More suitable examples
are those applications in which the structure of the tree itself varies, i.e., grows and/or shrinks during the
execution of the program. This is also the case in which other data representations, such as the array, fail
and in which the tree with elements linked by pointers emerges as the most appropriate solution.
We shall first consider only the case of a steadily growing but never shrinking tree. A typical example is
the concordance problem which was already investigated in connection with linked lists. It is now to be
revisited. In this problem a sequence of words is given, and the number of occurrences of each word has
to be determined. This means that, starting with an empty tree, each word is searched in the tree. If it is
found, its occurrence count is incremented; otherwise it is inserted as a new word (with a count initialized
to 1). We call the underlying task tree search with insertion. The following data type definitions are
assumed:
TYPE Node = POINTER TO RECORD
key, count: INTEGER;
left, right: Node
END
Finding the search path is again straightforward. However, if it leads to a dead end (i.e., to an empty
subtree designated by a pointer value NIL), then the given word must be inserted in the tree at the place of