Algorithms and Data Structures

N.Wirth. Algorithms and Data Structures. Oberon version 152
key: INTEGER; left, right: Node
END;
VAR R: Texts.Reader; W: Texts.Writer; root: Node;
PROCEDURE tree (n: INTEGER): Node;
VAR new: Node;
x, nl, nr: INTEGER;
BEGIN (*construct perfectly balanced tree with n nodes*)
IF n = 0 THEN new := NIL
ELSE nl := n DIV 2; nr := n-nl-1;
NEW(new); Texts.ReadInt(R, new.key);
new.key := x; new.left := tree(nl); new.right := tree(nr)
END;
RETURN new
END tree;
PROCEDURE PrintTree (t: Node; h: INTEGER);
VAR i: INTEGER;
BEGIN (*print tree t with indentation h*)
IF t # NIL THEN
PrintTree(t.left, h+1);
FOR i := 1 TO h DO Texts.Write(W, TAB) END;
Texts.WriteInt(W, t.key, 6); Texts.WriteLn(W);
PrintTree(t.right, h+1)
END
END PrintTree;
Assume, for example, the following input data for a tree with 21 nodes:
8 9 11 15 19 20 21 7 3 2 1 5 6 4 13 14 10 12 17 16 18
The call root := tree(21) reads the input dara while constructing the perfectly balanced tree shown in Fig.
4.23.
8
9 5
11 7
6 12
15 20
3 1
4 14
17 18
19
21
2
13
10
16
Fig. 4.23. Tree generated by preceding program
Note the simplicity and transparency of this program that is obtained through the use of recursive
procedures. It is obvious that recursive algorithms are particularly suitable when a program is to manipulate
information whose structure is itself defined recursively. This is again manifested in the procedure which