function [list,nums] = scan_sq(stat_sum,candi)
% Function: scan_sq
% used for a desired sequence for filling unfilled grids in a
% half-done sudoku puzzle
%
% Input: stat_sum = 9x9 matrix caluates the number of pieces of information
% each unfilled grid has
% candi = possible numbers for each grid
% {[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];}
% Output: list = indices of unfilled grid
% nums = possible numbers for each grid
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% This is a sub-function of the main function sudoku_yue
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% By Yue Wu
% 10/05/2009
% ECE Dept, Tufts Univ.
% MA, Medford 02155
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% the basic idea is always to fill in the grid with most number of pieces of
% informations
% when the number of piece of information equals for two grid, then compare
% the number of possible number for each grid
p_num = setdiff(unique(stat_sum),0);
list = [];
nums = [];
for i = 1:numel(p_num)
clear c_num tmp_ind
c_num = p_num(end-i+1);
tmp_ind = find(stat_sum == c_num);
if numel(tmp_ind)>1
clear num_times sq ix
for j = 1:numel(tmp_ind)
[x,y] = ind2sub([9,9],tmp_ind(j));
num_times(j) = numel(candi{x,y});
end
[sq,ix] = sort(num_times);
nums = [nums,sq];
else
ix = 1;
nums = [nums,numel(candi{tmp_ind})];
end
list = [list,tmp_ind(ix)'];
end
