Matlab 求解数独的程序

数独是近年来非常流行的游戏，有很多解法，在mathworks的file exchange里面可以找到很多，但我觉得下面的这个递归解法是比较简洁的。

来自Mathworks

 

function S = sodoku(M,S)
%[S,Mout] = sodoku(M,[S])
%
%A recursive program that solves 'sodoku' puzzles.
%
%Inputs:  M  partially filled 9x9 matrix with zeros in 'blank' cells
%         S  list of solutions (only used during recursive calls)
%
%Outputs: S  list of solutions
%
%Example:
%
%M = [0,0,1,9,0,0,0,0,8;6,0,0,0,8,5,0,3,0;0,0,7,0,6,0,1,0,0;...
%     0,3,4,0,9,0,0,0,0;0,0,0,5,0,4,0,0,0;0,0,0,0,1,0,4,2,0;...
%     0,0,5,0,7,0,9,0,0;0,1,0,8,4,0,0,0,7;7,0,0,0,0,9,2,0,0];
%
%S = sodoku(M)
%
%Written by G.M. Boynton, 6/3/05

%If this is the first call, then zero out the solution matrix
if ~exist('S','var')
    S = zeros([size(M),0]);
end

%find the first blank cell, or zero
firstId = find(M(:)==0, 1 );
if isempty(firstId)  %If there aren't any zeros, then we have a solution!
    S(:,:,size(S,3)+1) = M;  %save it
else %calculate the list of all valid numbers that can go into this cell
    [i,j] = ind2sub([9,9],firstId);
    for k=1:9  %loop through all 9 possibilities
        ii = (ceil(i/3)-1)*3+1;
        jj = (ceil(j/3)-1)*3+1;
        mm = M(ii:ii+2,jj:jj+2); %these are the indices into the 3x3 block containing that cell
        if sum(M(i,:)==k)==0 && sum(M(:,j)==k)==0 && sum(mm(:)==k)==0  %OK for column, row, and 3x3 block
            M(i,j) = k;  %put this number in,
            S = sodoku(M,S); %and call this function recursively!
        end
    end
end