sudoku_grid_candidates(I)

function candidates = sudoku_grid_candidates(I)
% Function: sudoku_grid_candidates
%           used for getting all possible reasonable numbers for each grid 
%           in 9x9 sudoku puzzle
%           
% Input: I = 9x9 sudoku puzzle (2D matrix)
%        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: candiates = 9x9 cells for each cell listing possible numbers for
%         its corresponding grid
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% This is a sub-function of the main function sudoku_yue and sub-function
% sudoku_stage1
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% All copyrights reserved
% By Yue Wu
% 10/05/2009
% ECE Dept, Tufts Univ.
% MA, Medford 02155
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%% 1. Initial settings
sizx = 9; 
candidates = {}; % initially assign an empty cell
plist = 1:9; % list of possible numbers for each grid
bocmap = [1 1 1 2 2 2 3 3 3]; % block map list, which means row 3 is on block row 1

%% 2. Calculate Candidats
    for i = 1:sizx
        for j = 1:sizx
            clear row col boc bocn alist alist
            if I(i,j) == 0 % if the grid is empty in the puzzle
                row = unique(I(i,:)); % existent numbers along its row
                col = unique(I(:,j)); % existent numbers along its column
                boc = I((bocmap(i)-1)*3+1:bocmap(i)*3,(bocmap(j)-1)*3+1:bocmap(j)*3); % crop its corresponding block
                bocn = unique(boc); % existent numbers in its block
                alist = union(union(row,col),bocn); % already existent numbers
                clist = setdiff(plist,alist); % numbers could be used in the grid
                candidates{i,j} = clist; % assign these numbers to the candidates cell
            else  % if the grid is already filled
                candidates{i,j} = I(i,j); % assign its number to candidats cell
            end
        end
    end