4.3 Practice Problems
4.3.1 Console Applications
a. Anagrammer. Prompts the user for a word and produces an anagram using a helper method that splits a string into two parts at a randomly selected index and returns the result of swapping the parts. The helper method is applied three times.
Output 4.3.1a
Enter a word: hippopotamus
popotamuship
shippopotamu
otamushippop
b. Babylonian Square Root. Approximates the square root of a user-selected number n using the
Babylonian method with n/2 as the initial approximation. This method is based on the following
fact: if a positive number k is an approximation to the square root of n, then the average of
k and n/k is a more accurate approximation. Here a helper method takes two arguments, a
floating-point number and its approximate square root, and returns the improved approximation. The
program calls the method five times and displays each result. For the sake of comparison, the actual
rounded square root is displayed using the static sqrt method in the Math class.
Output 4.3.1b
Enter a positive number: 90
45.0
23.5
13.664893617021276
10.125556968105812
9.506978456631614
Approximated square root: 9.506978456631614
True rounded square root: 9.486832980505138
4.3.2 Graphics Applications
a. Line Joins. Displays three centered equilateral triangles, each with a different line join
style (rounded, beveled, and mitered). The Polygon class provides the method setStrokeLineJoin
for specifying how adjacent sides are joined. The argument is a constant declared in the
StrokeLineJoin class.
Output 4.3.2a
Create the center triangle first, then duplicate it twice and translate one copy to the left and the
other to the right. Implement a helper method that sets the fill color, stroke color, and stroke
width of a polygon. Call this method from start for each triangle.
b. Flowers. Displays five symmetrical flower shapes as shown below.
Output 4.3.2b
The start method does not create these shapes directly; instead, the task is delegated to a helper
method with parameters specifying the location of a flower and the horizontal and vertical radii of
its petals. The method creates four ellipses differing only in their angle of rotation. These
ellipses are combined into a single Shape using the static Shape.union method, filled with a
randomly generated color, and returned to the caller. The start method adds the returned shape to
the root node. Provide a helper method that generates a color with random RGB values.
c. Daisy. Displays a daisy in a flower pot as shown below. Each petal is obtained from a helper method that returns an ellipse centered at a specified location with specified dimensions, rotation angle, and fill color. The task of creating the flower pot (a polygon) is delegated to a second helper method.
Output 4.3.2c
