solving sudoku programmatically

[satish bodas]

Hello ,

I was bitten with the sudoku bug and was an avid solver of the daily sudo in the newspaper.

Thought would go about developing a program that would solve the puzzle once you feed it the problem .

I thought of two posible approaches
- apply brute force
- apply logic

Went with the apply logic approach ::

what I did was whenever I could deduce a solution to one of the sqaures manually - I listed down the steps / rules used to deduce the solution

I then converted these steps / rules into programmatic logic

That way whatever puzzles my mind could solve I put them down into code

I was able to solve simple / medium level puzzles

since I myself am not able to solve complex / difficult sudoku puzzles ( my limitation ) - couldnt write the code .

what are your thoughts ?

just curious - is this approach even remotely close to AI ?

Looking forward to your comments !

Thanks ,
~satish

[Ulf Dittmer]

No, that's not AI. Sudoku is a purely logical game - the fact that you can write down rules to solve it that always apply, no matter which state the game is in, is an indication of that. Putting a number down into a field is always either 100% correct or 100% wrong.

That's very different from a game like chess where, in any given position, there are multiple possible moves that lead to victory or defeat, some more likely than others to do so, and where the player needs to evaluate each move (or at least as many as possible).

There was a discussion on brute force solvers a while back: http://www.javaranch.com
[ October 11, 2008: Message edited by: Ulf Dittmer ]

[Geoffrey Falk]

I wrote one that uses a recursive algorithm to solve Sudoku puzzles. If there are multiple solutions (or so solution), it will tell you that as well.
I tried to attach the source but I'm having trouble with attachments.

Geoffrey

[salvin francis]

Here would be my approach:

The "3's" rule:

if box 1 has a number in row/col "x" and box2 has the same number in row/col "y", check the no of empty cells in row/col "z"
for each empty cell in "z", check in corresponding col/row [Note the order here, col/row not row/col] for same number.
if the number of cells that match is exactly 1, then that is the right number.

This is not an exhaustive rule, but this would solve some obvious parts of the puzzle.

I would suggest code:

//sorry for any lexical erros in typing :)
class SmallBox
{
    private int cells[][] = new int [3][3];
    ...
    public boolean hasNumber(int no){...}
    ...
    public int[][] getEmptyCellIndexes(){...}
}

class PuzzleBox
{
    private SmallBox smallBoxes [][];
    ...
}

you could also use special numbers for cells : eg -1 or 0 for an empty cell

[salvin francis]

The "entire row/col" rule

parse and check entire row/col and find out missing numbers.
check every empty cell for possiblity of a number occuring there, if the number of possibility is exactly one, there you go...

[Ulf Dittmer]

This subject has been discussed extensively (including programmatic solutions) in http://www.coderanch.com/t/35387/Programming-Diversions/SoDuko-puzzle