Homework 11: Sudoku Solver

Milestone 1 Due: Mon. 18 April 2011 at 9:59:59 am

Milestone 2 Due: Friday 22 April 2011 Friday 16 April 2010 at 9:59:59 am

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am 

Tip: Out of Memory Error 

    Try the following:  Go to Edit/Preferences/Micellaneous/JVMs and add the -Xss64M option to the "JVM Args for Interactions JVM" line to increase th amount of memory used.

The Sudoku Game

Sudoku is a 9*9 9x9 grid-based puzzle in which the goal is to place numbers from 1 to 9 in the grid squares taking into account specific constraints. The 9 * 9 x 9 puzzle grid can be seen as divided into 9 sub-grids of size 3*33x3. The 3 main conditions in the classic version of Sudoku state are that each square in the grid contains a number from 1 to 9 and a number cannot be repeated:

• In any line
• In any column
• In any on the 3*3 3x3 sub-puzzles

 Sudoku Sudoku is not limited to 9x9 boards.  An "order" for a Sudoku puzzle can be defined, and thus a Sudoku puzzle is an order^2 order2 x order^2order2 matrix.    A regular Sudoku puzzle is this order = 3.   The above rules can be generalized to any order.   This is Rice, so our system should be able to handle any order of Sudoku puzzle.

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A Sudoku puzzle as needed for this assignment may not be well formed and in general may have no solutions or multiple solutions.   Your solution must be able to handle these situations!   (You only have to find one solution, if one exists however, not all solutions.)

Supporting Code Download

The support code provided contains a DrJava project and , some sample puzzle boards and a few simple Junit teststest.     The code download is coming "Real Soon Now" ...

Download the code here:  HW11.zip  

Full Javadocs are available in the supplied code in the docs folder.   Simply open the index.html file in your browser. 

The assignment

The purpose of this assignment is to build a Java solver that finds all one of the different any possible solutions of the game using a constraint-based approach.

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• An empty board is fully determined by a single value, it's "order", which for a 9x9 board is 3.
• The board is viewable in terms of rows, columns and blocks.
  • Each row, column and block has exactly order*order2 cells, e.g. for order = 3, each row, column and block has 9 cells.
  • Each board has exactly order*order rows² rows, columns and blocks.
• Each cell is a member of exactly one row, one column and one block.
  • No rows share the same cell.   Likewise, no columns or blocks share cells.  This forces the square matrix layout  of rows, columns, and orderxorder order^2 sub-matrix of blocks if one were to display the rows, columns and blocks where each cell is only shown once.
• The rules of Sudoku stipluate that the value in any given cell has very specific constraints:
  unmigrated-wiki-markup
  • The valid values are {{11...order*order}} ² (inclusive), e.g. for order=2, the allowed values are \ [1, 2, 3, 4\]
  •  Any valid value in a cell cannot appear in another cell in the row, column or block to which that cell belongs.   Conversely, each row, column or block must contain every valid value exactly once.

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A "board" is therefore a set of three {{Vector<ICellSet>}}s three Vector<ICellSet>s representing the rows, columns and blocks of the board.   Note that any given cell will appear once in the rows, once in the columns and once in the blocks.   The data structures that we have created enable us to access the cells in multiple methods that clearly represent the cell relationships in the manner that best models the problem at hand, namely the Sudoku board.   We can easily and consistently see the cells in terms of rows or columns or blocks in a manner that is abstractly equivalent, enabling us to easily reuse the same code to process the cells in any direction we choose.   Compare this to a standard NxN matrix representation (a collection of rows) which represents only a single cell relationship feature, namely that they are in rows.   Luckily, accessing the cells in terms of columns is not too difficult, but accessing them in terms of blocks is a bear!

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See the code details wiki page for explanations of the return types of the reduction and solving methods of GameModel.

Supporting Code Details  (click to go to next wiki page)

Running the Application

Starting the program:

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 When your reduceBoard() method is working, clicking the Reduce button will perform a single pass reduction on every cell on the board.  You should thus be able to progress towards a solution by repeatedly clicking the Reduce button, though you might end up with either an unsolvable or irreducible board.    Attempting to reduce an unsolvable or irreducible board will have no effect on the board.

Finding Find a Minimum Choice Cell

Solving the Board

Generating Solvable Puzzles

Programming Tips

Mutating a value outside of an anonymous inner class:

The quandry is that a variable that is declared outside of an anoymous inner class, e.g. visitor implementation, that is accessed by the anonymous inner class must be defined as final (Thanks Sun! Argh...).   There a classic "hack" to get around this:

Define your variable as a one-element array.

For instance:

{{final int\[\] x = new int\[\]\{0\}; }}

{{final ICell\[\] aCell = new ICell\[\]\{ new Cell()\}; }}

 An anonymous inner class can thus access these variables by using the array syntax:   {{x\[0\]}} and {{aCell\[0\]}}

You may find that in order to keep track of several properties as you loop through cells and cell sets, that you may need to create multiple one-element array values.

Controlling a loop from inside of an anonymous inner class

 Unfortunately, you cannot break or continue a loop while inside of an anonymous inner class that the loop completely encloses (i.e. the anonymous inner class is defined in the body of the loop).    There are two ways to accomplish this though:

1. Return a boolean or other primitive value from the anonymous inner class (which is probably a visitor being accepted).   Based on the returned value, break or continue with the loop.   Note that returning a value to which you delegate to, e.g. IUtilHostAB/C/D, will not work because you will just find yourself inside another anonymous inner class.
2. Use the one-element array trick described above.   Set its value from inside the anonymous inner class.  After the anonymous inner class returns, break or continue the loop based on that value. 

How to make copies of a board when you don't know which cell is the one you want to guess from

The problem is that if you lose the reference to the cell that you chose to test its values, you can never find that cell again without doing the whole search over again.   This is because a cell doesn't know where it is in the board (it never needs to know!).

The trick is to keep references to everything you need and to make copies at just the right time.  So here's what to do:

1. Keep references to BOTH the original board and the cell you found.
2. Get an array copy of the values in the cell.  Cell.getValueArray() makes a copy.  You can use this array to loop over.
3. In your loop:
   1. Clear the contents of the cell.  This will mutate your original board!
   2. Set the value of the cell to the desired test value.
   3. Make a copy of the orignal board.  
   4. Solve the copy of the board -- you will need to set the current board to the copy.   Don't mess up the original board!
   5. Repeat with the next test value or quit if you find a solution.

 Requirements

Your assignment is to implement:

Testing!

Extra credit

When your findMinChoiceCell() method is working, clicking the Find Min Choice Cell button will pop up a message dialog box displaying the contents of the chosen cell.   It does not show the location of the cell because that information is not available.    Which cell is chosen depends on the heuristic used.  One can manually attempt to solve an irreducible board by getting the values of the cell to be replaced and removing all values except one from the selected cell and then trying to further reduce the cell.

Solve the Board

 Once your solve() method is working, clicking the Solve button will attempt to solve the board from its current configuration.  The result will be a pop-up saying that the board is either solved or unsolvable.  

During the middle of your implementation, after you have implemented the reduceBoard but before you have implemented the solveIrreducibleBoard method, you should do a partial implementation of solve that can solve an easy-level puzzle that never encounters an irreducible board.   At that point, the Solve button may return a message saying that the board is irreducible.

Generating Solvable Puzzles

 A separate, stand-alone, fully-functional utility has been provided that can generate 9x9 Sudoku puzzles from a store of over 50,000 puzzles.    The utility consists of a singleton utility class GeneratePuzzle and a companion GUI application to run it, GeneratePuzzleApp}.   The utilities utilize the files in the {{HW11\data\puzzle_src folder.

1. .In DrJava, right-click the GeneratePuzzleApp class and select "Run File" to start the utility.
2. Select a file from the drop-list (yes, 4,txt is missing--broken link on the download page).   The higher the number, the harder the puzzles.
3. Each file contains about 10,000 puzzles.   Use the number spinner to choose or type a puzzle number from 1-10,000 (approx.).    Specifying "0" as the index will cause the utility to randomly select a puzzle.
4. Click the Generate button and the puzzle will appear in the main display area of the utility.  
5. Click the Save button to save the generated puzzle in a format that the Sudoku solver application can now read. 

This should keep you busy for a while, though your Sudoku solver should be able to easily solve any puzzle in the collection.

Note:  Your Sudoku solver should be able to solve a completely blank puzzle (all dashes, not empty)!

Programming Tips

Updating the View

At the end of the reduceBoard and solve methods, be sure to add the line

view.setCellViews(currentBoard.blks);

This will update the view with the mutated board.   (Note that the IViewAdapter.setCellViews() wants the cells in the format of the blocks, not the rows, because that's how the screen is laid out.)

Your board on the screen will NOT reflect the changes of your algorithms unless you add this line!!

Mutating a value outside of an anonymous inner class:

The quandry is that a variable that is declared outside of an anoymous inner class, e.g. visitor implementation, that is accessed by the anonymous inner class must be defined as final (Thanks Sun! Argh...).   There a classic "hack" to get around this:

Define your variable as a one-element array.

For instance:

 final int[] x = new int[]{0};

final ICell[] aCell = new ICell[]{ new Cell() }; 

 An anonymous inner class can thus access these variables by using the array syntax:   x[0] and aCell[0]

You may find that in order to keep track of several properties as you loop through cells and cell sets, that you may need to create multiple one-element array values.

Controlling a loop from inside of an anonymous inner class

 Unfortunately, you cannot break or continue a loop while inside of an anonymous inner class that the loop completely encloses (i.e. the anonymous inner class is defined in the body of the loop).    There are two ways to accomplish this though:

1. Return a boolean or other primitive value from the anonymous inner class (which is probably a visitor being accepted).   Based on the returned value, break or continue with the loop.   Note that returning a value to which you delegate to, e.g. IUtilHostAB/C/D, will not work because you will just find yourself inside another anonymous inner class.
2. Use the one-element array trick described above.   Set its value from inside the anonymous inner class.  After the anonymous inner class returns, break or continue the loop based on that value. 

How to make copies of a board when you don't know which cell is the one you want to guess from

The problem is that if you lose the reference to the cell that you chose to test its values, you can never find that cell again without doing the whole search over again.   This is because a cell doesn't know where it is in the board (it never needs to know!).

The trick is to keep references to everything you need and to make copies at just the right time.  So here's what to do:

1. Keep references to BOTH the original board and the cell you found.
2. Get an array copy of the values in the cell.  Cell.getValueArray() makes a copy.  You can use this array to loop over.
3. In your loop:
   1. Clear the contents of the cell.  This will mutate your original board!
   2. Set the value of the cell to the desired test value.
   3. Make a copy of the orignal board.  
   4. Solve the copy of the board -- you will need to set the current board to the copy.   Don't mess up the original board!
   5. Repeat with the next test value if no solution or quit if you find a solution.

 Requirements

Your assignment is to implement the following methods of GameModel:

• Milestone 1
  • reduceCellSet (15 pts)
  • reduceBoard  (15 pts)
  • solve -- partical solution for easy puzzles that have no irredicible states. 
• Milestone 2
  • findMinChoiceCell (15 pts)  -- Be sure to describe what your heuristic is trying to do in some comments accompanying your code!   Simply picking the first or a random cell will NOT garner full credit!
  • solveIrreducibleBoard (20 pts)
  • solve - full solution (20 pts)

You are also required to have complete unit tests for the above methods.  (15 pts)

Javadocs are already complete in the supplied code. If you add any fields, methods or classes, complete Javadocs will be expected for them. It is suggested that you do some level of Javadocs for your anonymous inner classes, if only to help keep things straight in your own head.

 Your code must work for ANY order puzzle!   (To within machine limits, of course.) 

Testing Procedures

The supplied code contains a simple test routine that gives you examples on how to instantiate a GameModel, {[Board}} and test them.

It is reasonable to test your code by the following process:

1. Instantiate a GameModel using the supplied dummy IViewAdapter object.
2. Load a test output puzzle into the model and then save a reference to model's current board -- this is your reference output board
3. Load a test input puzzle into the model.
4. Run your desired operation.
5. Get a reference to the model's current board -- this is the test output board.
6. Use assertEquals to compare the output board to the reference board.  

It is highly recommended that you start testing with 2x2 boards.   Carefully construct SIMPLE boards that will test just the feature in question. 

After you are satisfied with your tests on 2x2 boards THEN move on to 3x3 boards.    Note: testing irreducible boards with choices that lead to unsolvable boards may be impossible on a 2x2 board. 

The supplied code does NOT contain a full suite of test boards!  

Extra credit

If you are attempting an extra credit task, put a note to such at the top of your GameModel class. If you don't, the staff might not see it and grade it.

(10 pts) Incorporate the supplied GeneratePuzzle utility capability into the main Sudoku solvesolver, both in the view and the model, to enable the user to generate and solve any of the 50,000 supplied puzzles. 50,000 supplied puzzles.   Remember that the view and the model MUST be kept separate--the only way they can communicate is via IModelAdapter and IViewAdapter, their respective adapters.    Neither GameFrame nor GameModel may contain a reference to the other!      (It is actually possible to add this feature without modifying GameModel at all, though you are not required to do this.)

(10 pts) As any seasoned Sudoku player knows, there are other reduction rubrics that can be applied to more quickly reduce a board.   For instance, if an unsolved cell includes a value choice that no other unsolved cell in its cell contains, then the cell must have that value (this can be extended to a sub-set of values spread across multiple cells in a cell set).    Can you incorporate additional reduction rubrics in a modular, flexible and extensible fashion?

(10 pts) Challenge!  Come up with a Sudoku puzzle (any order) that your solver can solve but the staff's solution cannot!

Submission

Submit via Owlspace a .zip file containing the entire HW11 folder, including all the support code and data.  Don't forget to add as header to the GameModel class, your names and idsIDs.   Be sure to mention if you did any extra credit tasks too.