CS 1063 -- ThreeHalves class

CS 1063, Fall 2005
`ThreeHalves` class

3/2 calculation, using the ThreeHalves.java class:

The 3/2 Problem starts with an integer >n and repeatedly does one of two things:
- replaces n with n/2 in case n is even, or
- replaces n with (3n+1)/2 in case n is odd.
Continue indefinitely. Note that if the game reaches 1, then 1 is replaced by 2 and then by 1, so the sequence would just continue ..., 2, 1, 2, 1, .... For this reason, we stop the sequence if it ever reaches 1.

Here are several sample calculations:


 7:     7, 11, 17, 26, 13, 20, 10, 5, 8, 4, 2, 1    
     
15:     15, 23, 35, 53, 80, 40, 20, 10, 5, 8, 4, 2, 1

16:     16, 8, 4, 1

Here is a program to do the calculation:

// ThreeHalves.java: do 3/2 calculation
public class ThreeHalves {
   private int n; // starting value

   public ThreeHalves (int nInput) {
      n = nInput;
   }

   public void calculateThreeHalves() {
      // do the ThreeHalves calculation
      System.out.print(n + ":\t");
      while (n != 1) {
         System.out.print(n + ", ");
         if ((n%2) == 0)
            n = n/2;
         else
            n = (3*n + 1)/2;

      }
      System.out.println(n); // final 1
   }
}

// ThreeHalvesTest.java: 3/2 calculation
import java.util.Scanner;

public class ThreeHalvesTest {
   public static void main (String[] args) {
      Scanner in = new Scanner(System.in);
      System.out.print("Type an integer: ");
      int n = in.nextInt(); // starting value
      
      ThreeHalves th = new ThreeHalves(n);
      th.calculateThreeHalves();
      
   }
}

The following produces better looking output:

// ThreeHalves.java: carry out the 3/2 calculation on a positive int.
public class ThreeHalves {
   private int n; // starting value

   public ThreeHalves (int nInput) {
      n = nInput;
   }

   public void calculateThreeHalves() {
      // Carry out the ThreeHalves calculation
      int countItems = 0;  // used to print on several lines
      System.out.print(n + ":\t");
      while (n != 1) {
         System.out.print(n + ", ");
         if ((n%2) == 0)
            n = n/2;
         else
            n = (3*n + 1)/2;
         // skip to next line every 10 items
         countItems++;
         if (countItems%10 == 0) {
            System.out.println();
            System.out.print("    \t");
         }
      }
      System.out.println(n); // final 1
   }
}

Here is a calculation using the second version:


Type an integer for n: 27
27:     27, 41, 62, 31, 47, 71, 107, 161, 242, 121, 
        182, 91, 137, 206, 103, 155, 233, 350, 175, 263, 
        395, 593, 890, 445, 668, 334, 167, 251, 377, 566, 
        283, 425, 638, 319, 479, 719, 1079, 1619, 2429, 3644, 
        1822, 911, 1367, 2051, 3077, 4616, 2308, 1154, 577, 866, 
        433, 650, 325, 488, 244, 122, 61, 92, 46, 23, 
        35, 53, 80, 40, 20, 10, 5, 8, 4, 2, 
        1

Try to find the longest run of any number <= 1000000.
[Answer: 837799 has run length of 330.]
Try to find the longest run of any number <= 10000000.
[Answer: 8400511 has run length of 430.]

Revision date: 2001-02-01. (Please use ISO 8601, the International Standard.)

CS 1063, Fall 2005 ThreeHalves class

CS 1063, Fall 2005
`ThreeHalves` class