[R] [R-pkgs] sudoku

[Martin Maechler]

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)