function fillBoard()
%
% Checks to see if there are any places where the board has only
% one valid location, and if so it fills in that location with
% the assigned value. 
%
% Author: Greg Coombe
% Date: Nov 29, 2005

global B;
global Valid;
global RegionTable;

% Let's keep track of how many elements we fill in
count = 0;

% Loop over every cell, and check whether only one valid value exists
% If so, then fill in this value
for i=1:9,
    for j=1:9,
        % if there isn't an assigned value here yet
        if ( B(i,j) == 0 )            
            % Create a T/F vector for valid values
            tf_vec = Valid(i,j,:) == 1;
            % If there is only one true value
            if ( sum( tf_vec  ) == 1 )
                %
                % Possibility #1: There are no other valid
                % choices for this cell
                %
            
                % get the index of the true value
                tmp = 1:9;
                value = tmp(tf_vec);
                % do some paranoia checks; this should be a scalar value
                if ( all( size(value) ~= 1))
                    error('Error in logic; multiple valid values!!')
                end %if
                % looks good, assign the value.
                B(i,j) = value;
                Valid(i,j,:) = zeros(1,9);
                count = count+1;
            else
                %
                % Possibility #2: There are no other valid
                % places in this row, column, or region for 
                % this value
                %
                for v=1:9
                    if ( Valid(i,j,v) )
                        rsum = sum(Valid(i,:,v));
                        csum = sum(Valid(:,j,v));
                        % look up our region neighbors in table
                        region_i = RegionTable(i,:);
                        region_j = RegionTable(j,:);
                        val_reg = Valid(region_i, region_j, v);
                        rgsum = sum(sum(val_reg));
                        
                        %if ( rsum == 1 || csum == 1 || rgsum == 1)
                        if (  rsum == 1 || csum == 1 || rgsum == 1)
                           % Assign the value
                           B(i,j) = v;
                           computeValid;
                           return;
                        end
                    end
                end
            end
        end %if
        computeValid;
    end %for
end %for
    
%disp(['Filled in ' num2str(count) ' values.']);