nCS 226
Homework 4
Programming : Due Monday Febrary 26.

For this assignment, you will implement the towers of Hanoi problem
using a stack structure implemented with a singly linked list.  The
towers of Hanoi is described in problem C-3.11 of the book.

You will implement the solution in the following stages.

1.  You will implement the LinkedStack data structure as described
in the book.

2. With this stack, you will implement a Tower datatype that
   implements the basic operations of the tower of Hanoi problem.  In
   particular, each pole operates like a stack, so it is a natural
   extension of the stack structure. Note it is specialized to
   Integers, and also that it has a "toString" method so that you can
   print the contents of the Stack.  The latter will may require a
   little creative thinking on your part as to how to run through the
   stack so that you can print the elements without disturbing the
   ordering.

   A good definition for a tower class (minus methods) would be:

   abstract class Tower extends LinkedStack<Integer> {
      
    // create a tower of size n

    public Tower(int n);

    // Take the top element from a tower

    public Integer remove();

    // Put an element on a tower.  Throw and exception if
    // the element is out of order

    public void place(Integer o)  throws OutOfOrderException;

    // Query the top element.

    Integer top();

    // Create a printable representation of a tower
    
    public String toString();

}

3. Write a main program that solves the tower problem of size 4.  The
program should create three Towers, one of which is populated with 4
disks numbered 1-4.  It should then move the entire stack from Tower
one Tower to another while guaranteeing that there is never a disk
larger disk on top of a smaller one.  Each move should be printed out
as it is performed.  The stacks should also be printed at the
beginning and end of the program.   Here is the output of my program:

java towers

Starting Configuration


 1
 2
 3
 4
---
Tower 0 

 |
 |
 |
 |
---
Tower 1

 |
 |
 |
 |
---
Tower 2

Moving 1 from 0 to 2
Moving 2 from 0 to 1
Moving 1 from 2 to 1
Moving 3 from 0 to 2
Moving 1 from 1 to 0
Moving 2 from 1 to 2
Moving 1 from 0 to 2
Moving 4 from 0 to 1
Moving 1 from 2 to 1
Moving 2 from 2 to 0
Moving 1 from 1 to 0
Moving 3 from 2 to 1
Moving 1 from 0 to 2
Moving 2 from 0 to 1
Moving 1 from 2 to 1


Ending Configuration

 |
 |
 |
 |
---
Tower 0 

 1
 2
 3
 4
---
Tower 1

 |
 |
 |
 |
---
Tower 2

4. Extra credit (10 pts): Make the towers graphical objects and
   display the solution graphically.


TO SUBMIT:

   Please submit a zipped or tarred folder that contains your source code.
The main program should be in a file called 'towers.java'.