Shidoku solver matlab code - matlab

Question

I'm trying to write a Shidoku ( smaller and easier 4x4 variant of Sudoku) solver code in MATLAB.
I have found some soduko solver (9x9) but i could't revise them to be suitable for my problem. For example:
% Solving Sudoku Using Recursive Backtracking
function X = sudoku(X)
% SUDOKU Solve Sudoku using recursive backtracking.
% sudoku(X), expects a 9-by-9 array X.
% Fill in all “singletons”.
% C is a cell array of candidate vectors for each cell.
% s is the first cell, if any, with one candidate.
% e is the first cell, if any, with no candidates.
[C,s,e] = candidates(X);
while ~isempty(s) && isempty(e)
X(s) = C{s};
[C,s,e] = candidates(X);
end
% Return for impossible puzzles.
if ~isempty(e)
return
end
% Recursive backtracking.
if any(X(:) == 0)
Y = X;
z = find(X(:) == 0,1); % The first unfilled cell.
for r = [C{z}] % Iterate over candidates.
X = Y;
X(z) = r; % Insert a tentative value.
X = sudoku(X); % Recursive call.
if all(X(:) > 0) % Found a solution.
return
end
end
end
% ------------------------------
function [C,s,e] = candidates(X)
C = cell(9,9);
tri = #(k) 3*ceil(k/3-1) + (1:3);
for j = 1:9
for i = 1:9
if X(i,j)==0
z = 1:9;
z(nonzeros(X(i,:))) = 0;
z(nonzeros(X(:,j))) = 0;
z(nonzeros(X(tri(i),tri(j)))) = 0;
C{i,j} = nonzeros(z)';
end
end
end
L = cellfun(#length,C); % Number of candidates.
s = find(X==0 & L==1,1);
e = find(X==0 & L==0,1);
end % candidates
end % sudoku
Any help will be helpful.

Answer 1

Just reduce the problem dimensionality from 3 to 2 (I know now that it is said "9x9" instead of "3x3", but the important dimensional number for the puzzle is N=3):
% SHIDOKU Solve Shidoku using recursive backtracking.
% shidoku(X), expects a 4-by-4 array X.
function X = shidoku(X)
[C,s,e] = candidates(X);
while ~isempty(s) && isempty(e)
X(s) = C{s};
[C,s,e] = candidates(X);
end;
if ~isempty(e)
return
end;
if any(X(:) == 0)
Y = X;
z = find(X(:) == 0,1);
for r = [C{z}]
X = Y;
X(z) = r;
X = shidoku(X);
if all(X(:) > 0)
return;
end;
end;
end;
% ------------------------------
function [C,s,e] = candidates(X)
C = cell(4,4);
bi = #(k) 2*ceil(k/2-1) + (1:2);
for j = 1:4
for i = 1:4
if X(i,j)==0
z = 1:4;
z(nonzeros(X(i,:))) = 0;
z(nonzeros(X(:,j))) = 0;
z(nonzeros(X(bi(i),bi(j)))) = 0;
C{i,j} = transpose(nonzeros(z));
end;
end;
end;
L = cellfun(#length,C); % Number of candidates.
s = find(X==0 & L==1,1);
e = find(X==0 & L==0,1);
end % candidates
end % shidoku