I "replied all" to the original message, but since that was to
"[EMAIL PROTECTED]" 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 <[EMAIL PROTECTED]>
To: Brahm, David <[EMAIL PROTECTED]>
CC: [EMAIL PROTECTED]
References:
<[EMAIL PROTECTED]>
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 ([EMAIL PROTECTED])
>
>
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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 <[EMAIL PROTECTED]> 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 <[EMAIL PROTECTED]>
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> <[EMAIL PROTECTED]> 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 ([EMAIL PROTECTED])
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library(R.oo)
setMethodS3("rotate", "default", function(x, steps, ...) {
n <- length(x);
steps <- steps %% n;
if (steps == 0)
return(x);
partA <- 1:steps;
partB <- (steps+1):n;
x[c(partB,partA)];
})
setMethodS3("rotateColumns", "matrix", function(x, steps, ...) {
idx <- rotate(1:ncol(x), steps=steps);
x[,idx];
})
setMethodS3("rotateRows", "matrix", function(x, steps, ...) {
idx <- rotate(1:nrow(x), steps=steps);
x[idx,];
})
setConstructorS3("Sudoku", function(...) {
extend(Object(), "Sudoku");
})
setMethodS3("generate", "Sudoku", function(static, squareId=0, hideId=0, ...) {
# Generate the root square
X <- matrix(c(
rotate(1:9,0),
rotate(1:9,3),
rotate(1:9,6)
), ncol=9, byrow=TRUE)
X <- rbind(X, rotateColumns(X, 1), rotateColumns(X, 2))
if (squareId != 0) {
set.seed(squareId, kind="Mersenne-Twister");
# Permute rows and columns
rows <- sapply(1:3, FUN=function(x) sample(3)) + 3*rep(sample(0:2),each=3)
cols <- sapply(1:3, FUN=function(x) sample(3)) + 3*rep(sample(0:2),each=3)
X <- X[rows,cols];
}
# Assert that everything is correct
for (kk in 1:9) {
if (any(duplicated(X[kk,])))
throw("Duplicated elements in row #", kk);
if (any(duplicated(X[,kk])))
throw("Duplicated elements in column #", kk);
if (any(rowSums(X) != 45))
throw("Some rows does not sum to 45.");
if (any(colSums(X) != 45))
throw("Some columns does not sum to 45.");
}
Xtrue <- X;
# Empty middle block
X[4:6,4:6] <- NA;
set.seed(hideId, kind="Mersenne-Twister");
# For the rest of the blocks, keep 3 or 4 elements
for (bb in 1:9) {
rows <- 1:3 + 3*(bb-1) %/% 3;
cols <- 1:3 + 3*(bb-1) %% 3;
Xb <- X[rows,cols];
Xb[sample(1:9,5)] <- NA;
X[rows,cols] <- Xb;
}
X;
}, static=TRUE)
###########################################################################
# HISTORY:
# 2005-07-10
# o Created.
###########################################################################
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