Comp 170-201 -- Dordal/Nabicht -- Lab 3, Wed, Sept 11, 2002

1. Write a program to find the sum of the squares 1^2 + 2^2 + ... + 1000^2.
Use a for loop or a while loop. Hint: the answer is 333833500.


2. Write a program to print "Floyd's Triangle":

         1
         2  3
         4  5  6
         7  8  9 10
         11 12 13 14 15
         ...

Print the first 15 rows. Can you figure out how to get the columns
to line up neatly? Or, at least, more neatly than I managed?
(Hint: convert the number to a string, and just handle three cases
for 1-digit, 2-digit, and 3-digit numbers:
        if (str.length() == 1) ...
        else if (str.length() == 2) ...
        else ...
)
(You don't have to *do* the neat alignment; just figure out how.)


3. Both the above can be written as for loops. Consider Kakutani's Problem:
take a number N and:
        if N is even, N = N/2
        if N is odd,  N = 3*N +1
See how long (if ever) it takes to get to 1. For example, if N=30,
the sequence of N's is 
   30, 15, 46, 23, 70, 35, 106, 53, 160, 80, 40, 20, 10, 5, 16, 8, 4, 2, 1
Write a loop to implement Kakutani's problem.

I did all these in a single program.

====================================================

Here are some supplemental questions. You should submit *written*
answers to these, and also the three programs above.
You can, if you want, type the answers into a big comment in your program.

Q1. Make your program 1 above into an infinite loop.
Explain how you did this, and how you were able to halt the
running program.


Q2. Put a println statement into the body of the loop of program 1 above.
Describe how this might help debugging.


Q3. Leave off a loop-closing "}" from the first program. What error
message do you get?


Q4. Why do you need a while loop rather than a for loop for the
Kakutani program?


Q5. What happens if you run the Kakutani program starting with N=27?
How long toes it toake to get to 1?


Q6. Put a semicolon right after the (condition) of a while loop; for example:
        while (N != 1); {...}
Does it compile or run? What happens?