function L = candidate_list(A, r, c)
% generates the candidates for the cell A[r,c]
r1 = A(r,:); c1 = A(:,c);
s1 = r1(r1 ~= 0); s2 = c1(c1 ~= 0);
L = setdiff(1:size(A,1), union(s1,s2));
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function out = DFS_search(Board)
 [r,c] = first_zero_row(Board);
 if (r ~= 0)
     L = candidate_list(Board, r, c);
     while size(L)~= 0
      Board(r,c) = L(1); 
      L = L(2:end);
      out = DFS_search(Board);
      [r1,c1] = first_zero_row(out);
      if r1 == 0 
          return; 
       else Board(r,c) = 0;
      end;
     end;
 end;
 out= Board;
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 function [r,c] = first_zero_row(A)
 % outputs the first row that contains a zero entry
 % returns 0 if there is no such row
  r = 1;
  while r <= size(A,1) 
      if sum(A(r,:)==0) > 0 
          temp = find(A(r,:)==0);
          c = temp(1);
          return;
      else r = r + 1;
      end;
  end;
 r = 0; c = 0;
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 case 1:
  ___________________________________________________________
  
      1     0     0     2     3     0
      0     4     2     0     0     0
      0     0     0     0     0     0
      0     3     0     0     0     0
      0     0     1     3     0     5
      0     1     0     0     0     0
 
    
 Solution:
 
      1     5     4     2     3     6
      5     4     2     1     6     3
      2     6     3     5     1     4
      4     3     5     6     2     1
      6     2     1     3     4     5
      3     1     6     4     5     2
 ____________________________________________________________
 
 case 2:
 
      0     1     0     0     0     2     3     4     0     5
      0     0     6     7     8     0     0     0     0     9
      0     0     0     4     0     0     5     0     0     0
      0     4     1     0     0     0     0    10     2     0
      0     0     0     0     1     0     0     2     0     0
      0    10     0     0     0     0     0     0     0     2
     10     0     7     3     9     0     0     6     1     4
      4     2     0     9     0     5     0     0     0     6
      0     8     0    10     0     0     7     1     0     0
 
 Solution:
 
      6     1     9     8     7     2     3     4    10     5
      2     3     6     7     8     1    10     5     4     9
      1     6     2     4     3     7     5     8     9    10
      7     4     1     6     5     3     9    10     2     8
      3     9    10     5     1     6     4     2     8     7
      8    10     3     1     4     9     6     7     5     2
     10     5     7     3     9     8     2     6     1     4
      4     2     8     9    10     5     1     3     7     6
      9     8     5    10     2     4     7     1     6     3
      5     7     4     2     6    10     8     9     3     1
      
_____________________________________________________________