Prentice.Hall.Introduction.to.Java.Programming,.Brief.Version.9th.(2014).[sharethefiles.com]

756 Chapter 20 Recursion
20.20
✓Point✓ How do you obtain the midpoint between two points?
20.21 What is the base case for the displayTriangles method?
48 displayTriangles(g, order, p1, p2, p3);
49 }
50
51
52
53
private static void displayTriangles(Graphics g, int order,
Point p1, Point p2, Point p3) {
if (order == 0) {
54 // Draw a triangle to connect three points
draw a triangle
55 g.drawLine(p1.x, p1.y, p2.x, p2.y);
56 g.drawLine(p1.x, p1.y, p3.x, p3.y);
57 g.drawLine(p2.x, p2.y, p3.x, p3.y);
58 }
59 else {
60 // Get the midpoint on each edge of the triangle
61 Point p12 = midpoint(p1, p2);
62 Point p23 = midpoint(p2, p3);
63 Point p31 = midpoint(p3, p1);
64
65 // Recursively display three triangles
top subtriangle
left subtriangle
right subtriangle
66
67
68
69
displayTriangles(g, order - 1, p1, p12, p31);
displayTriangles(g, order - 1, p12, p2, p23);
displayTriangles(g, order - 1, p31, p23, p3);
}
70 }
71
72 private static Point midpoint(Point p1, Point p2) {
73 return new Point((p1.x + p2.x) / 2, (p1.y + p2.y) / 2);
74 }
75 }
main method omitted 76 }
The initial triangle has three points set in proportion to the panel size (lines 44–46). If
displayTriangle method order == 0, the displayTriangles(g, order, p1, p2, p3) method displays a
triangle that connects the three points p1, p2, and p3 in lines 55–57, as shown in
Figure 20.10a. Otherwise, it performs the following tasks:
1. Obtain the midpoint between p1 and p2 (line 61), the midpoint between p2 and p3 (line
62), and the midpoint between p3 and p1 (line 63), as shown in Figure 20.10b.
2. Recursively invoke displayTriangles with a reduced order to display three smaller
Sierpinski triangles (lines 66–68). Note that each small Sierpinski triangle is structurally
identical to the original big Sierpinski triangle except that the order of a small
triangle is one less, as shown in Figure 20.10b.
A Sierpinski triangle is displayed in a SierpinskiTrianglePanel. The order property in
the inner class SierpinskiTrianglePanel specifies the order for the Sierpinski triangle.
The Point class, introduced in Section 16.8, Mouse Events, represents a point on a component.
The midpoint(Point p1, Point p2) method returns the midpoint between p1 and
p2 (lines 72–74).
20.22 How many times is the displayTriangles method invoked for a Sierpinski triangle
of order 0, order 1, order 2, and order n?