Math 121: Introduction to Computing Handout #7 Assignment #2—Simple Java Programs Write programs to solve each of these problems. 1. Write a GraphicsProgram subclass that draws a pyramid consisting of bricks arranged in horizontal rows, so that the number of bricks in each row decreases by one as you move up the pyramid, as shown in the following sample run: The pyramid should be centered at the bottom of the window and should use constants for the following parameters: BRICK_WIDTH The width of each brick (30 pixels) BRICK_HEIGHT The height of each brick (12 pixels) BRICKS_IN_BASE The number of bricks in the base (12) The numbers in parentheses show the values for this diagram, but you must be able to change those values in your program. 2. Given that the weather at this time of year tends to be a mixture of sun and rain, it seems appropriate to draw a rainbow. The rainbow might look like this: The colors of the stripes are clear in the web version of the picture, but are hard to see on a black-and-white printout. Starting at the top, the six arcs are red, orange, yellow, green, blue, and magenta, respectively; cyan makes a lovely color for the sky.– 2 – At first glance, it might seem as if you need to draw arcs on the screen, even though you won’t actually learn about the GArc class until Chapter 8. As it turns out, that class doesn’t really help much. The program that produced the diagram shown at the bottom of the previous page uses only circles, although seeing how this is possible forces you to think outside the box—in a literal rather than a figurative sense. The common center for each circle is some distance below the bottom of the window, and the diameters of the circles are wider than the screen. The GraphicsProgram shows only the part of the figure that actually appears in the window. This process of reducing a picture to the visible area is called clipping. Rather than specify the exact dimensions of each circle, play around with the sizes and positioning of the circles until you get something that matches your aesthetic sensibilities. The only things we’ll be concerned about are: • The top of the arc should not be off the screen. • Each of the arcs in the rainbow should get clipped along the sides of the window, and not along the bottom. 3. Write a GraphicsProgram subclass that draws a partial diagram of the acm.graphics class hierarchy, as follows: The only classes you need to create this picture are GRect, GLabel, and GLine. The major part of the problem is specifying the coordinates so that the different elements of the picture are aligned properly. The aspects of the alignment for which you are responsible are: • The width and height of the class boxes should be specified as named constants so that they are easy to change. • The labels should be centered in their boxes. You can find the width of a label by calling label.getWidth() and the height it extends above the baseline by calling label.getAscent(). If you want to center a label, you need to shift its origin by half of these distances in each direction. • The connecting lines should start and end at the center of the appropriate edge of the box. • The entire figure should be centered in the window.– 3 – For the purposes of this assignment, it is not necessary to break it down into methods, since we won’t cover that topic until next week. If you do read ahead—or if you foolishly don’t start this problem until after Wednesday—feel free to create a method that draws a class box with a particular label at a specified location on the screen. 4. In high-school algebra, you learned that the standard quadratic equation ax2 + bx + c = 0 has two solutions given by the formula x = –b ± b2 – 4ac2a The first solution is obtained by using + in place of ±; the second is obtained by using – in place of ±. Most of this expression contains simple operators covered in Chapter 3. The one piece that’s missing is taking square roots, which you can do by calling the standard function Math.sqrt. For example, the statement double y = Math.sqrt(x); sets y to the square root of x. Write a ConsoleProgram that accepts values for a, b, and c, and then calculates the two solutions. If the quantity under the square root sign is negative, the equation has no real solutions, and your program should display a message to that effect. You may assume that the value for a is nonzero. Your program should be able to duplicate the following sample run: 5. Write a ConsoleProgram that reads in a list of integers, one per line, until a sentinel value of 0 (which you should be able to change easily to some other value). When the sentinel is read, your program should display the smallest and largest values in the list, as illustrated in this sample run:– 4 – Your program should handle the following special cases: • If the user enters only one value before the sentinel, the program should report that value as both the largest and smallest. • If the user enters the sentinel on the very first input line, then no values have been entered, and your program should display a message to that effect. 6. Douglas Hofstadter’s Pulitzer-prize-winning book Gödel, Escher, Bach contains many interesting mathematical puzzles, many of which can be expressed in the form of computer programs. Of these, most require programming skills well beyond the second week of Math 121. In Chapter XII, Hofstadter mentions a wonderful problem that is well within the scope of the control statements that we have covered. The problem can be expressed as follows: Pick some positive integer and call it n. If n is even, divide it by two. If n is odd, multiply it by three and add one. Continue this process until n is equal to one. On page 401 of the Vintage edition, Hofstadter illustrates this process with the following example, starting with the number 15: 15 is odd, so I make 3n + 1: 46 46 is even, so I take half: 23 23 is odd, so I make 3n + 1: 70 70 is even, so I take half: 35 35 is odd, so I make 3n + 1: 106 106 is even, so I take half: 53 53 is odd, so I make 3n + 1: 160 160 is even, so I