Algorithms and Data Structures

N.Wirth. Algorithms and Data Structures. Oberon version 107
PROCEDURE B (k: INTEGER);
BEGIN
IF k > 0 THEN
B(k-1); Draw.line(5, h); C(k-1); Draw.line(6, 2*h);
A(k-1); Draw.line(7, h); B(k-1)
END
END B;
PROCEDURE C (k: INTEGER);
BEGIN
IF k > 0 THEN
C(k-1); Draw.line(3, h); D(k-1); Draw.line(4, 2*h);
B(k-1); Draw.line(5, h); C(k-1)
END
END C;
PROCEDURE D (k: INTEGER);
BEGIN
IF k > 0 THEN
D(k-1); Draw.line(1, h); A(k-1); Draw.line(2, 2*h);
C(k-1); Draw.line(3, h); D(k-1)
END
END D;
PROCEDURE Sierpinski* (n: INTEGER);
CONST SquareSize = 512;
VAR i, x0, y0: INTEGER;
BEGIN
Draw.Clear;
h := SquareSize DIV 4;
x0 := Draw.width DIV 2; y0 := Draw.height DIV 2 + h;
i := 0;
REPEAT
INC(i); x0 := x0-h;
h := h DIV 2; y0 := y0+h; Draw.Set(x0, y0);
A(i); Draw.line(7,h); B(i); Draw.line(5,h);
C(i); Draw.line(3,h); D(i); Draw.line(1,h)
UNTIL i = n
END Sierpinski.
The elegance of the use of recursion in these exampes is obvious and convincing. The correctness of the
programs can readily be deduced from their structure and composition patterns. Moreover, the use of an
explicit (decreasing) level parameter guarantees termination since the depth of recursion cannot become
greater than n. In contrast to this recursive formulation, equivalent programs that avoid the explicit use of
recursion are extremely cumbersome and obscure. Trying to understand the programs shown in [3-3]
should easily convince the reader of this.