CSCI 241 Labs: Lab 6
Going Loopy

There are 5 checkpoints , including the clean-up checkpoint, in this lab. Work together with your partner using just one of your accounts. CHANGE WHO IS CONTROLLING THE COMPUTER AFTER EACH CHECKPOINT! If you need help with any exercise, raise your hand.

Copy the directory /home/student/Classes/Cs241/Labs/Lab06 to your account.

Change directories into Lab06 and start BlueJ by entering bluej&.

This lab is much like last week's lab, in that it emphasizes using loops and ifs to solve interesting problems. The only difference is that the problems this week are probably a bit more difficult, but then you have an additional week of learning under your belts, too.

 Finding Prime Numbers

Recall from high school math that a prime number is one that can only be (evenly) divided by 1 and itself. Open the PrimeNumber class. This file contains listing 5.15 found on page 189 of your text. This program finds and prints the first 50 prime numbers. Examine the code and run the program to see its output. It can be improved in a number of ways - and guess what you get to do now!

Your tasks for this checkpoint:

  1. Modify the code so that the primes print in 10 columns, each 6 characters wide.
  2. The program only finds the first 50 primes. Modify the program so that it finds and prints all prime numbers less than 5,000. It should then print the total number of primes it found.
    Hint: The final prime before 5,000 is 4,999.
    Note: By default, BlueJ's terminal window will limit the lines of output you see, but you can change that setting by choosing Options-Unlimited Buffering.

1 Be prepared to answer the following questions:

  1. Why does the inner for loop start at 2, rather than 1?
  2. Why does the inner for loop stop at number/2 instead of number?
  3. Could we reduce the upper bound on divisor even further? Explain. Hint: The answer is yes. The real question is why.
  4. Explain why we use break to exit the inner for loop. Can you modify the code so you do not use a break?

Perfect Numbers

Since we are working with number sequences, let's try another one: A number is perfect if the sum of all its positive divisors, excluding itself, add to be the original number.

For example, 6 is perfect because 1 + 2 + 3 = 6.

Similarly, 28 is perfect because 1 + 2 + 4 + 7 + 14 = 28. Perfect numbers are really pretty rare. There are only 4 of them less than 10,000.

Open the Perfect class. It contains a for loop that counts from 1 to 10,000. All that's missing is the code to find all the divisors of i and sum them. Add this code.
Hint: Finding the divisors of i is similar to what you did in checking to see if a number was prime. The biggest difference is that we aren't going to stop when we find one divisor. We need to find them all and sum them.

Complete the Perfect number program so that it find all perfect numbers less than 10,000.

2 Show us your revised code and demonstrate how it runs. Be ready to answer the following questions:

  1. We declared int sum = 0; inside the outer for loop. Would it work just as well to place this line before the loop?  Explain why or why not.
  2. There are only 49 known perfect numbers. The last one was discovered in 2016 and is 44,677,235 digits long. That isn't the number! That is how many digits it contains! Do you think there are more?

Computing PI

You all know that Pi is a constant whose value is approximately 3.141592653589793238462643383279502884197169399375105820974944592307816406286...
but that its digits go on forever.
Did you ever wonder how Pi is calculated? There are numerous ways to do so. For this exercise, you will use an algorithm that works and is simple to program (but others exist that converge faster than this one). Here is the mathematical formula:

               1     1     1     1             1           1     
Pi = 4 * (1 - --- + --- - --- + --- - ... - ------- + ----------)
               3     5     7     9           2*i+1     2*(i+1)+1

Open the ComputePi class. Your sum variable should keep the sum of the fractions seen in the parentheses in the above formula. Each time the loop runs, you should add ONE fraction to that sum. (Note: the sign variable is there to help you change whether you are adding or subtracting the fraction. Don't forget to update it at the end of the loop body, if you choose to use it.) As you work, feel free to "tweak" the existing code if you wish.
Change the limit on the for loop so that it runs through the loop 1,000,000 times.
Before you run it again, comment out the printf() statement that is inside the loop for obvious reasons.

3 Show us this program when you are ready.

  1. How many digits were accurately calculated when the loop ran only 100 times?
  2. How many digits were accurately calculated with the loop ran 1,000,000 times?

Print Pattern

Open the PrintPattern class. It contains a complete program to print the pattern:
1
1 2
1 2 3
1 2 3 4
1 2 3 4 5
1 2 3 4 5 6

KEEP THIS CODE!

Add additional loops, so that it follows this pattern with
1 2 3 4 5 6
1 2 3 4 5
1 2 3 4
1 2 3
1 2
1

Now, add yet another loop, so that the entire pattern is
1
1 2
1 2 3
1 2 3 4
1 2 3 4 5
1 2 3 4 5 6 
1 2 3 4 5 6
1 2 3 4 5
1 2 3 4
1 2 3
1 2
1
1
1 2
1 2 3
1 2 3 4
1 2 3 4 5
1 2 3 4 5 6 
1 2 3 4 5 6
1 2 3 4 5
1 2 3 4
1 2 3
1 2
1
1
1 2
1 2 3
1 2 3 4
1 2 3 4 5
1 2 3 4 5 6 
1 2 3 4 5 6
1 2 3 4 5
1 2 3 4
1 2 3
1 2
1

4 Show us your completed program.

After the Lab

Return to Firefox, log onto Canvas and print the next programming assignment, #5, if you haven't already. Be sure to exit Firefox before you log out and leave the lab.

5 Show us that you have logged out, turned off your monitor, cleaned up, and pushed in your chairs for this last checkpoint.