Read at least half of Chapter 2 carefully. Note that the next quiz will cover all of Chapter 2 (and then some!).
Finish all the examples from lab 4. Include the solutions in your submission, all in one file named Lab4.java. Note: the lab collaboration policy continues to apply to the lab problems. So you can collaborate at will to solve these problems. This only applies to the lab problems -- all other problems in this assignment are subject to the usual homework collaboration policy.
Do the following Exercises from Chapter 2 (pp 106-108):
Exercises 2.3, 2.10, 2.11
Write the following method:
public static int maxOf3(int i0, int i1, int i2)
This method takes 3 integers and returns the value of the largest integer. Here is a test method for you:
public static void testMaxOf3() {
System.out.print("Testing maxOf3... ");
assert(maxOf3(1, 2, 3) == 3); // 3rd is max
assert(maxOf3(1, 3, 2) == 3); // 2nd is max
assert(maxOf3(3, 1, 2) == 3); // 1st is max
assert(maxOf3(1, 2, -3) == 2); // one negative
assert(maxOf3(-1, -2, -3) == -1); // all negative
assert(maxOf3(1, 1, 0) == 1); // duplicate values
System.out.println("Passed all tests!");
}
Hint #1: test methods not only help you test your code, they can also help you understand the problem in the first place even before you write any code. Thus, before writing your solution, study each assertion in the test method and be sure you understand why it must be true.
Hint #2: you should use Math.max here, though you cannot simply
call Math.max(i0,i1,i2), as Math.max only works with two parameters.
Write the following method:
public static int medianOf3(int i0, int i1, int i2)
This method takes 3 integers and returns the value of the middle value of the 3. Here is a test method for you:
public static void testMedianOf3() {
System.out.print("Testing medianOf3... ");
assert(medianOf3(2, 1, 3) == 2); // 1st is median
assert(medianOf3(1, 2, 3) == 2); // 2nd is median
assert(medianOf3(1, 3, 2) == 2); // 3rd is median
assert(medianOf3(1, 2, -3) == 1); // one negative
assert(medianOf3(-1, -2, -3) == -2); // all negative
assert(medianOf3(1, 1, 0) == 1); // duplicate values
System.out.println("Passed all tests!");
}
Hint: Think about how your previous solution might inform this
problem...
Write the following method:
public static int hundredsDigit(int i)
This method takes one integer and returns the value of that number's hundreds digit. Here is a test method for you:
public static void testHundredsDigit() {
System.out.print("Testing hundredsDigit... ");
assert(hundredsDigit(100) == 1);
assert(hundredsDigit(123) == 1);
assert(hundredsDigit(1234) == 2);
assert(hundredsDigit(-1234) == 2);
assert(hundredsDigit(0) == 0);
assert(hundredsDigit(12) == 0);
assert(hundredsDigit(-12) == 0);
System.out.println("Passed all tests!");
}
Hint: The test method is very valuable here. It shows that
numbers less than 100 have a 0 as their hundreds digit. It further shows
how you should handle negative numbers. Again, for this and all problems,
carefully scrutinize the test methods that we provide (if and when we do so)
to gain as deep an understanding of the problem as you can prior to
writing any code.
Write the following method:
public static boolean almostEqual(double d1, double d2)
This method takes two doubles and returns true if the two doubles are "almost equal" (within 0.0001 of each other for our purposes) and false otherwise. Here is a test method for you:
public static void testAlmostEqual() {
System.out.print("Testing almostEqual... ");
assert(almostEqual(0, 0.0001/2)); // 0 and epsilon/2
double epsilon = 0.0001;
assert(almostEqual(0, epsilon/2)); // a small positive that is nearly 0!
assert(!almostEqual(0, epsilon)); // this should "just" be false
// use the example from the class notes
double d1 = (29.0 / 7.0) * 7.0;
double d2 = 29.0;
assert(d1 != d2);
assert(almostEqual(d1, d2)); // two very-nearly-equal values
assert(almostEqual(-d1, -d2)); // and their negations
System.out.println("Passed all tests!");
}
Hint #1: Once again, the oh-so-helpful test method shows us that
doubles that are exactly 0.0001 apart are not almost equal. They
must be strictly within that epsilon.
Hint #2: We basically solved this in the class notes, but here we are
placing that code in a method. Why would we do that?
Write the following method:
public static double distance(double x0, double y0, double x1, double y1)
This method takes four doubles, x0, y0, x1, and y1, and returns a double representing the distance from the point (x0,y0) to the point (x1,y1). Here is a test method for you:
public static void testDistance() {
System.out.print("Testing distance... ");
assert(almostEqual(distance(0,0,0,0), 0));
assert(almostEqual(distance(0,0,1,0), 1));
assert(almostEqual(distance(1,0,0,0), 1));
assert(almostEqual(distance(0,0,1,1), Math.sqrt(2)));
assert(almostEqual(distance(0,0,-1,1), Math.sqrt(2)));
assert(almostEqual(distance(4,3,1,7), 5));
System.out.println("Passed all tests!");
}
Hint #1: Here is the distance formula:
Hint #2: You may wish to use both Math.pow and Math.sqrt here.
Hint #3: This is not so much a hint as a thought question: why do
the test assertions use "almostEqual" rather than "=="?
Write the following method:
public static boolean isRightTriangle(double x0, double y0,
double x1, double y1,
double x2, double y2)
This method takes six doubles describing three points (x0, y0), (x1, y1), and (x2, y2), and returns true if the triangle connecting those points is a right triangle and false otherwise. How do you do that? First, find the distances of each side. If we call those distances a, b, and c, where c is the largest side, then the triangle is a right triangle if and only if a2 + b2 = c2 (by the converse of the Pythagorean Theorem).
Here is a test method for you:
public static void testIsRightTriangle() {
System.out.print("Testing isRightTriangle... ");
assert(isRightTriangle(0,0,3,0,0,4)); // 3,4,5 triangle
assert(isRightTriangle(0,0,-3,0,0,-4)); // another 3,4,5 triangle
assert(!isRightTriangle(0,0,1,10,2,0)); // tall isosceles triangle
assert(!isRightTriangle(0,0,0,0,0,0)); // all same points, not a triangle!
double epsilon = 0.0001;
assert(!isRightTriangle(epsilon/10,0,0,0,-epsilon/10,0)); // all nearly same points!
assert(isRightTriangle(0, 0, epsilon, 0, 0, epsilon)); // "barely" a triangle!
System.out.println("Passed all tests!");
}
Hint #1: All the values are doubles, so be sure to use the
appropriate test for equality.
Hint #2: You may want to use some of the methods that you wrote above.
In general, reusing your own code is a Very Good Idea!
Hint #3: Again, scrutinize the test method. It shows several
subtle cases. For example, if two (or more) of the three points are the
same, or even just very nearly the same (or, more specifically, if the
distance between them is "almostEqual" to zero), then you do not have a
triangle, let alone a right triangle, so you should return false.
[This is re-assigned for bonus. If you received full bonus for this in hw3, you may not do this again for bonus, but you may do the next problem instead.] Draw the flag of Panama using Polygons for the stars, and using trigonometry to draw the stars properly. To get you started, here is some sample code using a Polygon:
Polygon p = new Polygon();
p.addPoint(100, 50);
p.addPoint(200, 125);
p.addPoint(300, 50);
page.setColor(Color.black);
page.fillPolygon(p);
This is really all you need for this task, but if you need more information, check out the Java API link from the course web site.
Draw the flag of Venezuela, complete with a semi-circle of stars, but skipping the coat-of-arms in the top-left corner:
You will want to use a "helper method" to draw those stars. Good luck!