Re: A Su Doku solver

*To*: mathgroup at smc.vnet.net*Subject*: [mg60558] Re: [mg60534] A Su Doku solver*From*: Zhe Hu <iamhuzhe at gmail.com>*Date*: Tue, 20 Sep 2005 05:19:21 -0400 (EDT)*References*: <200509191007.GAA25694@smc.vnet.net>*Reply-to*: iamhuzhe at gmail.com*Sender*: owner-wri-mathgroup at wolfram.com

It's great to see another one-page solution.(There is one interesting solution in J language at http://www.vector.org.uk/archive/v214/sudoku.htm) I tried one from www.sudoku.com <http://www.sudoku.com> myGrid = {{0, 6, 0, 1, 0, 4, 0, 5, 0}, {0, 0, 8, 3, 0, 5, 6, 0, 0}, {2, 0, 0, 0, 0, 0, 0, 0, 1}, {8, 0, 0, 4, 0, 7, 0, 0, 6}, {0, 0, 6, 0, 0, 0, 3, 0, 0}, {7, 0, 0, 9, 0, 1, 0, 0, 4}, {5, 0, 0, 0, 0, 0, 0, 0, 2}, {0, 0, 7, 2, 0, 6, 9, 0, 0}, {0, 4, 0, 5, 0, 8, 0, 7, 0}} It failed to fill in each cell. On 9/19/05, Valeri Astanoff <astanoff at yahoo.fr> wrote: > > Dear group, > > Here is my little Mathematica "Su Doku" solver : > > In[1]:=sudoku[m_List?MatrixQ /;Length[m] == 9 ]:= > FixedPoint[doku,m]; > > doku[m_List?MatrixQ /; Length[m] == 9]:= > Module[{mi,r,sq,sel}, > mi=MapIndexed[Prepend[#2,#1]&,m,{2}]; > r={0,i_Integer,j_Integer} :> > {sq =(Which[ > 1 <= i <= 3 && 1 <= j <= 3, mi[[{1,2,3}]] [[All,{1,2,3}]], > 1 <= i <= 3 && 4 <= j <= 6, mi[[{1,2,3}]] [[All,{4,5,6}]], > 1 <= i <= 3 && 7 <= j <= 9, mi[[{1,2,3}]] [[All,{7,8,9}]], > 4 <= i <= 6 && 1 <= j <= 3, mi[[{4,5,6}]] [[All,{1,2,3}]], > 4 <= i <= 6 && 4 <= j <= 6, mi[[{4,5,6}]] [[All,{4,5,6}]], > 4 <= i <= 6 && 7 <= j <= 9, mi[[{4,5,6}]] [[All,{7,8,9}]], > 7 <= i <= 9 && 1 <= j <= 3, mi[[{7,8,9}]] [[All,{1,2,3}]], > 7 <= i <= 9 && 4 <= j <= 6, mi[[{7,8,9}]] [[All,{4,5,6}]], > 7 <= i <= 9 && 7 <= j <= 9, mi[[{7,8,9}]] [[All,{7,8,9}]], > True,Print["err"]] // Flatten[#,1]&)[[All,1]] // Union; > > sel := Complement[Range[9], mi[[i,All,1]], mi[[All,j,1]],sq]; > If[Length[sel] == 1, sel[[1]],0],i,j}; > (mi//.r)[[All,All,1]] > ]; > > A grid example : > > In[3]:= > myGrid={{0,8,0,0,0,1,6,0,0}, > {0,7,0,4,0,0,0,2,1}, > {5,0,0,3,9,6,0,0,0}, > {2,0,4,0,5,0,1,3,0}, > {0,0,8,9,0,7,5,0,0}, > {0,5,7,0,3,0,9,0,2}, > {0,0,0,5,6,3,0,0,9}, > {3,1,0,0,0,2,0,5,0}, > {0,0,5,8,0,0,0,4,0}}; > > In[4]:= > sudoku[myGrid]//Timing > > Out[4]= > {0.016 Second, > {{4,8,3,2,7,1,6,9,5}, > {9,7,6,4,8,5,3,2,1}, > {5,2,1,3,9,6,4,7,8}, > {2,9,4,6,5,8,1,3,7}, > {1,3,8,9,2,7,5,6,4}, > {6,5,7,1,3,4,9,8,2}, > {8,4,2,5,6,3,7,1,9}, > {3,1,9,7,4,2,8,5,6}, > {7,6,5,8,1,9,2,4,3}}} > > > It's more fun to compete : does any one have a shorter and/or faster > solution? > > > v.a. > >

**References**:**A Su Doku solver***From:*"Valeri Astanoff" <astanoff@yahoo.fr>