CS 1073 -- Random Walk in the Plane

CS 1073 Introductory Programming
for Scientific Applications
The Three-halves Problem

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

The 3/2 Problem starts with an integer n and repeatedly replaces n with n/2 in case n is even, and 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 is a sample calculation:

15:     15, 23, 35, 53, 80, 40, 20, 10, 5, 8, 4, 2, 1

Here's a longer calculation:

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

Two really long 3/2 calculations: Long 3/2 calculations.

Use the following Java program as a framework for writing a program that will carry out the 3/2 calculation. The program just starts with a fixed int.

Three-halves Calculation
// ThreeHalves.java: carry out the 3/2 calculation on a positive int. public class ThreeHalves { public static void main (String[] args) { // n: initial value for three-halves sequence int n = 15; System.out.println(n); //============================================================== // Carry out the ThreeHalves calculation // ... fill in code here to repeatedly replacing n // by either (3n+1)/2, if n is odd, or by // n/2, if n is even. // (n is even in case n%2 == 0.) // (n is odd in case n%2 == 1.) // Continue until n gets to 1, if it does. } // end of main }

Three-halves Calculation


// ThreeHalves.java: carry out the 3/2 calculation on a positive int.
public class ThreeHalves {

   public static void main (String[] args) {

      // n: initial value for three-halves sequence
      int n = 15;
      System.out.println(n);

      //==============================================================
      // Carry out the ThreeHalves calculation
      // ... fill in code here to repeatedly replacing n
      //     by either (3n+1)/2, if n is odd, or by
      //                n/2, if n is even.
      //        (n is even in case n%2 == 0.)
      //        (n is odd  in case n%2 == 1.)
      // Continue until n gets to 1, if it does.

   } // end of main
}

A Java program that does the basic task in this section: ThreeHalves.java.
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: 2004-11-24. (Please use ISO 8601, the International Standard.)

CS 1073 Introductory Programming for Scientific Applications The Three-halves Problem

CS 1073 Introductory Programming
for Scientific Applications
The Three-halves Problem