fill_unique(sel_cell,candi,keyword)

function output = fill_unique(sel_cell,candi,keyword)
% Function: fill_unique
%           used for filling number in sudoku_stage1
%           
% Input: sel_cell = the number could be filled in
%        candi = 9x9 cell (candidats cell)
%                whose elements are possible numbers for its corresponding grid
%        For example:
%        candi = {[2,4,5,8],[2,4,5,9],[2,4,5,8],3,[2,6,8,9],1,7,[4,6],[4,6,8];
%                 1,[3,5,9],[3,5,7,8],[5,6,7,8,9],4,[8,9],[3,6,8,9],2,[3,6,8];
%                 [2,3,4,7,8],6,[2,3,4,7,8],[7,8,9],[2,7,8,9],[2,8,9],[3,8,9],5,[1,3,4,8];
%                 9,[1,2,3],[1,2,3,7,8],4,[1,3,7,8],5,[2,3,6],[3,6,7],[3,6,7];
%                 [2,3,4,5,7,8],[2,3,4,5],6,[7,8,9],[3,7,8,9],[3,8,9],1,[3,4,7],[3,4,5,7];
%                 [3,4,5,7],[1,3,4,5],[1,3,4,5,7],2,[1,3,7],6,[3,5],8,9;
%                 [2,3,5,6],7,[1,2,3,5],[1,6,8],[1,2,3,6,8],[2,3,8],4,9,[1,3,5,6,8];
%                 [3,4,6],8,[1,3,4],[1,6,9],5,[3,4,9],[3,6],[1,3,6,7],2;
%                 [2,3,4,5,6],[1,2,3,4,5],9,[1,6,8],[1,2,3,6,8],7,[3,5,6,8],[1,3,6],[1,3,5,6,8];}
%         keyword = 'row', 'col', or 'boc'
% Output: output = 9x9 matrix with only filled numbers nonzeros 
% 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% This is a sub-function of the sub-function sudoku_stage1
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% All copyrights reserved
% By Yue Wu
% 10/05/2009
% ECE Dept, Tufts Univ.
% MA, Medford 02155
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% initialization
output = zeros(9); 
[lookx,looky] = meshgrid(1:3);

for i = 1:9
    if ~isempty(sel_cell{i}) % possible number exists
        for j = 1:9
            % according to different keyword get the information from candi
            switch keyword 
                case 'row'
                    tmp = candi{i,j}; 
                case 'col'
                    tmp = candi{j,i};
                case 'boc'
                    [x,y] = ind2sub([3,3],i);
                    cx = (x-1)*3+lookx(j);
                    cy = (y-1)*3+looky(j);
                    tmp = candi{cx,cy};
            end
            
            inter = intersect(sel_cell{i},tmp); 
            if ~isempty(inter) % if current grid contains the number just appears once
                % according to its keyword, filled in the number in output matrix
                switch keyword
                    case 'row'
                        output(i,j) = inter;
                    case 'col'
                        output(j,i) = inter;
                    case 'boc'
                        output(cx,cy) = inter;
                end
            end
        end
    end
end