CSCI 1103 Lab07: Collatz Methods

Material from Eck Ch 1-4 is needed for these problems as they include methods, while() loops, for() loops, if/else, arrays, and input/output.

Unlike previous labs, you will create only one file for this lab, Collatz.java. It will contain methods that solve each of problems.

Do not modify any of the files provided. You goal is to write create a Collatz.java file that is compatible with the provided files like Steps.java and Generate.java.

There are a series of testing files named as Problem1Tests.java which have tests for methods required in each problem. This will allow you to work on each problem separately.

Recall Lab04 introduced the Collatz Conjecture: starting from any number

• If the number is even, divide it by two.
• If the number is odd, triple it and add one.

This process always seems to converge to the number 1.

We will call a Collatz Sequence a sequence of numbers that obeys this progression. for example

6 3 10 5 16 8 4 2 1

is a Collatz sequence as starting at 6, it follows the rules of halving when even and tripling+1 when odd until 1 is reached.

In contrast the sequence

6 3 10 5 4 2 1
       ^^^

is NOT a Collatz sequence as it does not triple+1 on reaching 5 and

6 3 10 5 16

is NOT a Collatz sequence as it does not end with 1.

This lab develops a series of methods to operate on Collatz sequences.

Below is the structure the Collatz.java file which you should create. Each problem corresponds to one method in the file though later problems make use of earlier methods.

public class Collatz {

  public static int steps(int start);
  // PROBLEM 1
  // Given the starting number start, compute how many steps in the
  // Collatz sequence it takes to reach 1 from start.  A step
  // comprises changing the current value n based on whether it is odd
  // or even:
  //
  //   if n is odd,  multiply it by 3 and add 1
  //   if n is even, divide it by 2
  //
  // If steps(1) is called, it should return 0. If start is less than
  // 1, return -1. Otherwise, use a loop to repeatedly change the
  // value according to it being odd/even counting each step until it
  // becomes 1. Return the number of steps.

  public static void printArray(String idxLabel, String valLabel, int arr[]);
  // PROBLEM 2
  // Print the array arr in two columns with labels at the top. The
  // output of a call like:
  //   Collatz.printArray("INDEX","VALUE",new int[]{10, 22, 31, 15, 128, 3});
  // should appear like the following
  //
  // | INDEX  VALUE|
  // |     0     10|
  // |     1     22|
  // |     2     31|
  // |     3     15|
  // |     4    128|
  // |     5      3|
  // 
  // Use the format specifier
  //   "%6s %6s\n"
  // to prin the initial labels at the top and the format specifier
  //   "%6d %6d\n"
  // to print each element

  public static int [] collatzArray(int start);
  // PROBLEM 3
  // Produce an array which is filled with elements in the Collatz
  // sequence beginning at value start. Use the method steps() to
  // determine how many steps it will take to reach 1. If steps()
  // returns -1, the start value is invalid and null should be
  // returned.  Allocate an array of size [steps+1] so that the start
  // value can be included. Use a loop to fill this array with values
  // in the Collatz sequence. The start value should be at array index
  // [0] and the final value at index [steps] should always be 1.

  public static boolean verify(int [] testSeq );
  // PROBLEM 4
  // Verify that the given testSeq is a valid Collatz sequence.  If
  // the array is empty (length of 0) it is not a valid sequence so
  // return false.  Otherwise use the method collatzArray() to
  // generate the real Collatz sequence form the starting point of
  // testSeq which is at index [0].  If the testSeq array has a
  // different length than the real sequence, it must be incorrect so
  // return false. Otherwise use a loop to walk through testSeq and
  // compare its values to those in real sequence. If any difference
  // is detected, return false.  If all elements in the sequenc are
  // equal, return true.

}

You should feel free at any time to get help from lab staff as you get stuck on the exercises.

By the end of the lab, make sure to demonstrate your code to a staff member. This will ensure that you receive full credit on the lab. Staff might ask you to

• Change what is printed
• Compile and run on the command line
• Run tests in DrJava or on the command line
• Show how to zip the folder with your programs in it

Be ready to do any or all of these.

Ensure that file PARTNERS.txt has your name and the name of your partner in it. This fill is located with the other Java files for the lab and can be edited with DrJava.

Once your are confident your code is working, you are ready to submit. Ensure your folder has all of the required files. Create a zip archive of your lab folder and submit it to blackboard.

On Canvas:

• Click on the Assignments section
• Click on the appropriate link for this lab
• Scroll down to "Attach a File"
• Click "Browse My Computer"
• Select you Zip file and press OK