sudoku_single(I)

function simplifier = sudoku_single(I)

% Function: sudoku_single
%           used for initially solving 9x9 sudoku puzzle         
%
% Input: I = 9x9 sudoku puzzle
%        for example: 
%          I = [0 0 0 3 0 1 7 0 0 ; 
%               1 0 0 0 4 0 0 2 0 ;
%               0 6 0 0 0 0 0 5 0 ;
%               9 0 0 4 0 5 0 0 0 ;
%               0 0 6 0 0 0 1 0 0 ;
%               0 0 0 2 0 6 0 8 9 ;
%               0 7 0 0 0 0 4 9 0 ;
%               0 8 0 0 5 0 0 0 2 ;
%               0 0 9 0 0 7 0 0 0 ;]
% Output: simplifier = 9x9 initial solution leaving unsolved grids zeros
%         for example:   
%           simplifier = [0 0 0 3 0 1 7 0 0 ;
%                         1 0 0 5 4 0 0 2 0 ;
%                         0 6 0 0 0 0 0 5 1 ;
%                         9 0 0 4 0 5 2 0 0 ;
%                         0 0 6 0 0 0 1 0 0 ;
%                         0 0 0 2 0 6 0 8 9 ;
%                         0 7 0 0 0 0 4 9 0 ;
%                         0 8 0 0 5 4 0 7 2 ;
%                         0 0 9 0 0 7 0 0 0 ;]
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% This is a sub-function of the sub-function sudoku_init
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% All copyrights reserved
% By Yue Wu
% 10/05/2009
% ECE Dept, Tufts Univ.
% MA, Medford 02155
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%% 1. Initial settings
simplifier = I;

%% 2. Retrieve existent information
for i = 1:9
    ori_row{i} = setdiff(unique(I(i,:)),0); % existent information of each row
    ori_col{i} = setdiff(unique(I(:,i)),0); % existent information of each column
end

% existent information of each block
list = [1 4 7]; % row/col number list for each block
for x = 1:3 % block number(horizontal)
    for y = 1:3 % block number (vertical)
        i = list(x);
        j = list(y);
        ori_boc{x,y} = setdiff(unique(I(i:i+2,j:j+2)),0); % existent information of each block
    end
end

%% 3. Find possible fill-in number for each grid in sudoku
possi = sudoku_grid_candidates(I); 

%% 4. Logical analysis
% get the numbers might be used for each row, column or block
[row,col,boc] = uniquelize_sudoku(possi);
% find the numbers only appears once for each row, col and boc
uni_row = sudoku_lowmode(row);
uni_col = sudoku_lowmode(col);
uni_boc = sudoku_lowmode(boc);

% calcuate the numbers could be filled for each row, col and boc
for i = 1:9
    sel_row{i} = setdiff(uni_row{i},ori_row{i});
    sel_col{i} = setdiff(uni_col{i},ori_col{i});
    sel_boc{i} = setdiff(uni_boc{i},ori_boc{i});
end

%% 5. fill the numbers that appear once
% fill the numbers that appear once for each row
out_row = fill_unique(sel_row,possi,'row');
ind_row = find(out_row~=0);
simplifier(ind_row) = out_row(ind_row);
% fill the numbers that appear once for each col
out_col = fill_unique(sel_col,possi,'col');
ind_col = setdiff(find(out_col~=0),ind_row);
simplifier(ind_col) = out_col(ind_col);
% fill the numbers that appear once for each boc
out_boc = fill_unique(sel_boc,possi,'boc');
ind_boc = setdiff(find(out_boc~=0),union(ind_row,ind_col));
simplifier(ind_boc) = out_boc(ind_boc);