Homework 1

Implementing Search to solve a "Challenge"

Due: Friday, February 13th, 1:00 PM

Introduction

[Note: This problem was originally created by Dr. Shaw as a Math contest activity.]

Suppose that you have a 3x3 pendent of jewels.  Each of the 9 jewels is either a diamond, a ruby, or an emerald.  These jewels can be changed by casting a spell at a particular jewel.  This spell will change a diamond into a ruby, a ruby into an emerald, or an emerald into a diamond. Unfortunately, the spell also modifies the jewels touching the particular jewels both horizontally and vertically! 

Thus, if you started with the following pendant:

DRE
RED
EDR

and cast a spell at the center emerald, you would end up with the following pendant

DEE
EDR
ERR

The "goal" of this puzzle is that given a starting pendent, find the shortest sequence of spells that will turn the pendent into one containing 9 of the same jewel. 

BEAUTIFUL!  A straightforward search problem where at each node in the search you have 9 possible next moves (9 possible spell locations).  The challenge is picking which of the 5 strategies we might use.  We will talk about this in class, but I think there are two which make the most sense. 

Requirements

For this homework you should write a program that fits the following requirements:

• Your code must provide an easy way for me to indicate the "starting state" of the puzzle as a SINGLE, string of all capital letters such as "DREREDEDR" which would be the pendent described above. .  You have three choices for this. 
  • You may design your code to ask the user for this input during run-time,
  • you may require it as command line input at startup,
  • or you can provide an instance variable at the top of your code which is set before compile time...

public class JewelGame {

public static void main(String[] args) {

String start = "DREREDEDR";

....

}

}

• You must use one of the five uninformed search techniques we studied in session 7 or session 8 to find an optimal solution.
• When a solution is found you need to print out the sequence of moves that will get you from the initial state to the goal state.
• Your code must also print the total number of nodes expanded so far (gives us an idea of time) and the number of nodes still stored in memory (gives us an idea of memory usage).
• You must also produce a short "read me" file (readme.txt) which explains to me, the tester, how to use your program.  How do I change the input and how do I switch between strategies if you implemented more than one.  how would I launch your code if I were sitting at a computer in the lab?  Do NOT assume I  know anything about running code in the language you choose.
• You should devise a solution which uses the concept of a search tree.  That is, you should develop a data structure which represents a node (knows its state, its parent, its cost/depth, etc...)  You also need to maintain the queue of unexpanded nodes remaining.  I think that an OO solution is much cleaner in the long run and will reward good OO design.  However, some students will struggle with this, so the majority of the points will be awarded for code that simply works.
• For a few bonus points, you may implement more than one search strategy (again, I think that only two of these REALLY make sense).

Hints from past experience with this assignment...

Remember what happens when you "copy" a referential data type in Java... you only get a copy of the reference, not a copy of the object.  This means that if you have a node that you want to copy several times and modify to create the children nodes, you need to be careful what you do to copy the node.  Students have a habit of saying something like:

    //Assume that Node parent was created elsewhere
    Node child1 = parent;
    Node child2 = parent;
    Node child3 = parent;
    child1.modifyOneWay();
    child2.modifyAnotherWay();
    child3.modifyYETAnotherWay();

This just gives you FOUR variables all of which point to the same single instant.  Students end up forgetting this and then being surprised when child1, child2, and child3 are identical and TOTALLY screwed up (in essence, they just cast 3 different spells on the same single object.

You will need to write code which produces a true, second copy of whatever data structure you use in your tree.

2)  When it gets to be time to test your code, start with simple problems.  For example,

DED
EEE
DED

can EASILY be turned into a pendent of all diamonds by casting the spell on the center emerald.  Shortest solution is ONE move.  If your code can't solve this, than you have a significant problem.  Similarly, your code should detect that

EEE
EEE
EEE

is already a solution and requires no moves at all.

Similar "copy by value" vs. "copy by reference" problems exist in other language.  Make sure you pay attention to this issue.

Submitting Your Work

Prior to the deadline, use the homework submission system (http://math-cs.cns.uni.edu/~schafer/submit/which_course.cgi) to upload any files you have produced. 

You should bundle all of your files (including your readme.txt) into a zip file.

In addition to online copies, please submit hard copies of this lab at the start of class on the day this lab is due.