sudoku
I "replied all" to the original message, but since that was to
"r-packages at stat.math.ethz.ch" it might not have gone out there, did it?
If not, below is my reply again. [You have restrict the
randomization so that you permute within and between block rows/columns.]
/Henrik
-------- Original Message --------
Subject: Re: [R] [R-pkgs] sudoku
Date: Sat, 07 Jan 2006 09:36:54 +1100
From: Henrik Bengtsson <hb at maths.lth.se>
To: Brahm, David <David.Brahm at geodecapital.com>
CC: r-packages at stat.math.ethz.ch
References:
<4DD6F8B8782D584FABF50BF3A32B03D801A2BCDB at MSGBOSCLF2WIN.DMN1.FMR.COM>
Brahm, David wrote:
> Any doubts about R's big-league status should be put to rest, now that
> we have a
> Sudoku Puzzle Solver. Take that, SAS! See package "sudoku" on CRAN.
>
> The package could really use a puzzle generator -- contributors are
> welcome!
Last summer I put a quick generator together after discussing with some
friends how these games a generate (and enumerated). I don't know if it
is a correct/complete generator, but consider an empty game with 3x3
grids each with 3x3 cells. Create the initial board by adding 1:9 in
the first row, the c(2:9,1), in the second and so on, to make sure you
have one correct board. From this you can now generate all(?) other
possible boards by permuting rows and columns. You can for instance use
a random seed enumerate all such boards. Finally, you want to remove
some of cells, which you also can by sampling using known random seeds.
See attached code. Example:
> source("Sudoku.R")
> Sudoku$generate()
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9]
[1,] 1 NA 3 4 NA NA NA 8 NA
[2,] 4 NA NA NA 8 NA NA NA NA
[3,] NA 8 NA 1 NA 3 4 5 6
[4,] 2 NA NA NA NA NA NA NA 1
[5,] NA 6 7 NA NA NA 2 NA 4
[6,] 8 NA NA NA NA NA NA 6 NA
[7,] NA NA 5 NA NA 8 9 NA NA
[8,] 6 NA 8 9 1 NA 3 NA NA
[9,] NA 1 NA 3 NA NA NA 7 8
> Sudoku$generate(1)
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9]
[1,] 3 NA 2 5 NA NA NA 9 NA
[2,] 9 NA NA NA 3 NA NA NA NA
[3,] NA 4 NA 8 NA 7 2 3 1
[4,] 2 NA NA NA NA NA NA NA 6
[5,] NA 3 4 NA NA NA 1 NA 9
[6,] 8 NA NA NA NA NA NA 5 NA
[7,] NA NA 9 NA NA 2 6 NA NA
[8,] 7 NA 6 9 1 NA 3 NA NA
[9,] NA 2 NA 6 NA NA NA 1 8
> Sudoku$generate(2)
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9]
[1,] 7 NA 6 1 NA NA NA 2 NA
[2,] 1 NA NA NA 3 NA NA NA NA
[3,] NA 2 NA 7 NA 5 9 8 1
[4,] 8 NA NA NA NA NA NA NA 5
[5,] NA 9 1 NA NA NA 7 NA 8
[6,] 5 NA NA NA NA NA NA 9 NA
[7,] NA NA 5 NA NA 7 2 NA NA
[8,] 9 NA 8 3 2 NA 5 NA NA
[9,] NA 1 NA 6 NA NA NA 7 9
/Henrik
> -- David Brahm (brahm at alum.mit.edu)
>
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roger bos wrote:
As far as generating a sudoku, it can't be too hard because I have a program on my cell phone that does it with a size less than 325K. I don't know the best way to generate these, but one way I was thinking of was starting with a filled up one then randomize the columns and rows. Then make some of them blank. The cell-phone version often generates puzzles that have non-unique solutions. Though I admit this is sometimes annoying, it also can make the puzzle harder. Thanks, Roger On 1/9/06, Martin Maechler <maechler at stat.math.ethz.ch> wrote:
First, "thanks a lot!" to David Brahms for finally tackling this
important problem, and keeping the R language "major league" !
;-) :-) {but the "thanks!" is meant seriously!}
"Detlef" == Detlef Steuer <detlef.steuer at hsu-hamburg.de> on Sun, 8 Jan 2006 12:21:52 +0100 writes:
Detlef> Hey, you spoiled my course! :-) Detlef> I planned using this as an excersise. Alternative Detlef> ideas anyone ... Well, you could *add* to it: 1) When I have been thinking about doing this myself (occasionally in the past weeks), I had always thought that finding *ALL* solutions was a very important property of the algorithm I would want to design. (since this is slightly more general and useful than proofing uniqueness which the current algorithm does not yet do anyway). 2) The current sudoku() prints the result itself and returns a matrix; improved, it should return an object of class "sudoku", with a print() and a plot() method; 3) The plot() method should of course also work for unfinished "sudoku" objects, and in fact, the *input* to sudoku() should also be allowed to be a (typically unfinished) "sudoku" object. 4) Then you could have your students use "grid" and grid.locator() for GUI *input* of a sudoku; i.e. you'd have another function which returns a (typically unfinished) "sudoku" object. 5) You could start looking at *solving* the more general sudokus where the blocks are not 3x3 squares anymore, but more general rectangular polygons of 9 squares each. 6) Now you need to refine the GUI from "4)" because your users need to be able to *draw* the block shapes for the generalized sudokus. 7) Given "1)" is solved, the problem of *generating* sudokus, that David already mentioned in his announcement, becomes more relevant: You want to be sure that the sudokus you generate have exactly one solution. And your generating algorithm could start with a very full sudoku (that has exactly 1 solution) and "erases" squares as much as possible, always checking that no other solution becomes possible. You see, there's lot of interesting exercises left for your course. (;-) Martin Detlef> On Fri, 6 Jan 2006 11:43:44 -0500 "Brahm, David" Detlef> <David.Brahm at geodecapital.com> wrote:
>> Any doubts about R's big-league status should be put to >> rest, now that we have a Sudoku Puzzle Solver. Take >> that, SAS! See package "sudoku" on CRAN. >> >> The package could really use a puzzle generator -- >> contributors are welcome! >> >> -- David Brahm (brahm at alum.mit.edu)
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