CS 110: Introduction
to Computing with Java
Lab 4
Do the
following exercises before coming to lab.
1. What is printed by the following Java statements:
int i = 2, j = 3, k = 6;
if (i < k / j)
System.out.println(“Good”);
else
System.out.println(“Bad”);
System.out.println(“Done”);
if (i == k % j)
System.out.println(“True”);
else
if (i / k == k % j)
System.out.println(“Almost
true”);
else
System.out.println(“False”);
switch (i * (j + k))
{
case 0:
System.out.println(“Zero”);
break;
case 1:
System.out.println(“One”);
break;
case 2:
System.out.println(“Two”);
break;
default:
System.out.println(“None of
the above”);
break;
}
2. What is wrong with this set of Java statements
and how would you fix it?
import java.util.Scanner;
. . .
Scanner scan = new Scanner(System.in);
if (scan.next() == “Hello”)
System.out.println(“Hello to you”);
else
System.out.println(“Goodbye”);
3. What is wrong with this set of Java
statements and how would you fix it?
if (i < j)
System.out.println(“i is smaller”);
count++;
else
System.out.println(“i is larger or equal”);
count;
4. What is wrong with this set of Java
statements and how would you fix it?
// total all positive numbers entered, stop
on entry of 1
final int SENTINEL_VALUE = 1;
int
total = 0;
while (true)
{
int
value = scan.nextInt();
if (value ==
SENTINEL_VALUE)
break;
else
total +=
value;
}
5. Rewrite the code in problem 4 using a “do . .
. while” statement instead of a “while” statement.
You
will not be allowed to work on the lab if you have not already completed these
tasks.
One of the
things that computers can do well is implement algorithms that would be tedious
for manual calculations. One general
problem in mathematics is solving:
f(x) =
0 for all
When the
function f(x) is a quadratic polynomial,
we learned a formula in algebra that we can use to solve that equation for
zero, one or two roots. We will use that
formula in Project 1. However, when the
function f(x) is not a quadratic polynomial, the problem can be solved using an
iterative method (or algorithm) that would be tedious to do manually, but is
easy for a computer to do. The method is
called
In
Basically,
Newton’s method uses some geometry to improve the guess at a root. (There is also a way to look at this
algorithm from the point of view of Calculus, but we choose to use the geometry
explanation.) See the Diagram Newton Diagram.jpg that goes with the following
explanation of the steps:
1. Make your first guess at a root (x = 0
is a
2. Calculate f(x) at your guess (x = 0)
which we assume is = 1
3. Calculate the slope of f(x) at your
guess (x = 0) which we assume is 1/2
4. Your second guess is 2
5. Calculate f(x) at your guess (x = 2)
which we assume is  1/2
6. Calculate the slope of f(x) at your
guess (x = 2) which we assume is 2
7. Your third guess is 1.75
8. Do your see that the guesses are
geometrically converging on the true root where f(x) crosses the xaxis?
However,
there are some problems with Newton’s Method.
It may fail to converge in a reasonable number of iterations (such as
10) with a given function and a given initial guess. It also may fail due to a possible divide by
zero in the algorithm (when the slope is zero).
While your code is iterating it must check for these conditions. If they
occur your code must stop the iterations and inform the user that the algorithm
has failed to calculate a root and why.
You can
download a set of .java files from Lab4.zip. The Java code provides a Class named Function
that has a method named f that takes a double argument and returns the value of
f(x). It also has a method named fprime that takes a double argument for x and returns the
value of the slope of f(x).
The Java code
provides a Newton class that implements the Newton’s method
algorithm, but does not check for the conditions that can cause the algorithm
to fail. Build your Dr
Java project file using these files, save the two java source files in your
project, and compile the project as in all previous labs.
The code that
you have been provided executes Newton’s Method, but it fails to check for the
two error conditions that are mentioned above.
Run the main method and enter the following

0.5 Root is: 5.292219477318755E10
(essentially == 0.0) after 3 iterations.
+
1.5 Root is: 1.732050807684724
(essentially == the square root of 3) after 4 iterations.
1.0 Root is: Infinity after 1 iterations. NOTE: fprime(1.0) is 0.0 and
Newton’s method fails to converge.
100000000.0 Root is: 1.7320508075692247 (essentially
== the square root of 3) after 43 iterations. NOTE: Made too many iterations.
In the main
method in class Newton, there is a place inside the while loop where a comment
line says
//
you need to add your code here
Since these
checks are for error conditions, it is usually considered acceptable to “break”
out of the loop when they occur rather than check for these conditions in the “while
(condition)”.
You
must add a check for the max number of iterations being exceeded. There is an integer symbolic constant
available for you to use. If your code
finds that the max number of iterations has been exceeded, it must print “Loop
terminated for max iterations.” and break out of the loop.
You
must also add a check for the
Your finished
program should produce the following results for the two error conditions:
1.0 Loop terminated on fprime equals 0. ç Due to your added code
Root is: 1.0 after 0 iterations.
100000000.0 Loop terminated for max iterations. ç Due to your
added code
Root is: 97656.25000341334 after 10
iterations.
Run your program with an appropriate
initial value to get it to produce each of the possible roots. Try values within the range of 2.0 to +2.0.
This lab
gives you some experience writing conditional statements inside a loop, another
skill that you will use again in programs that you write.
Before
you leave, have your TA check off that you completed the lab. Make sure that you save a copy of your
work. You may complete the code on your
own. Turn in your lab report to the TA
during the week following the exam.
Write a
document describing your experiences. Except for the graph, your lab report must be
printed (not handwritten).
Answer the
following questions related to what you did in this week’s lab:
1. Read the code in the class Function
and draw a graph of the functions f(x) and fprime(x).
2. Based on the graph, how many roots are
there and what are their correct values?.
3. Are the
Note: You should work alone on the lab report.