Backtracking method

Author: aniket0112

BackTrackAlgo.m

@@ -0,0 +1,9 @@
+FilterAndOCR;                                           %ImageProcess and fix bugs maunally
+SettingOutputMatrix;                                    %Set a Matrix to be fed to SudokuSolver
+ANSWER=OUT; %ANSWER is answer matrix while OUT is question matrix
+[minimumarray,all_elements_possible]=MoreAccurateSpace(ANSWER);             %Function finds all coordinates where least no. of elements can exist 
+[x,ANSWER]= SolveSudoku(ANSWER,minimumarray,all_elements_possible);
+while x~=1
+[x,ANSWER]= SolveSudoku(ANSWER,minimumarray,all_elements_possible);
+end
+ANSWER

CheckForSUDOKUconsistency.m

@@ -1,5 +1,7 @@
-function[flag]=CheckForSUDOKUconsistency(ANSWER)
-flag=0;
+%this function checks for row,column,3x3box consistency and the next
+%possible elements must not be zero. i.e. no further solution
+function[flag]=CheckForSUDOKUconsistency(ANSWER,all_possible_elements)
+flag=0;%flag 1 means inconsistent
 for i=1:9
     k=1;
     l=1;
@@ -42,9 +44,18 @@
             clear elements;
             clear element_array;
     end
+    s=size(all_possible_elements);
+    for i=1:s(1)
+        if all_possible_elements(i,3)==0
+            flag=1;
+            return
+        end
+    end
+    
     clear row;
     clear column;
     clear u_row;
     clear u_column;
 end
+clear all_possible_elements;
 end

SolveSudoku.m

@@ -0,0 +1,42 @@
+function [flag,ANSWER]=SolveSudoku(ANSWER,minimumarray,all_possible_elements)%minimumarray contains coordinates with lease possible candidates 
+                                                    %all_possible_elements has all empty coordinates and possible candidates size
+flag2=0;                                            %Flag2 to notify that a swap has been done in this function earlier
+if CheckForEmptyBox(ANSWER)==0                      %if flag is 1 loop ends and answer is displayed
+    flag=1; 
+    return
+end
+s3=size(minimumarray);
+        for i=1:s3(1)
+            if CheckForSUDOKUconsistency(ANSWER,all_possible_elements)==0  %true
+            if flag2==1
+                [minimumarray1,all_possible_elements1]=MoreAccurateSpace(ANSWER);%If it was already swapped from previous assigned value then no need to check for next coordinate
+            else            
+            min_array=FindMinArray(minimumarray(i,1),minimumarray(i,2));    %Finds which smaller 3x3 array where element (x,y) belongs
+            elements=CollectElements(min_array,ANSWER);                     %extract that 3x3array
+            possible_elements=PossibleValues(elements,minimumarray(i,1),minimumarray(i,2),ANSWER);%finds XOR of all elements in row,column and 3x3 array with 1-9 characters
+            ANSWER(minimumarray(i,1),minimumarray(i,2))=possible_elements(1,1);%amend ANSWER array with possible element or supposed possible element
+            swappingtemp=possible_elements(1,1);                            %temporary variable
+            [minimumarray1,all_possible_elements1]=MoreAccurateSpace(ANSWER);%calculate all parameters calculated above for recursion
+            end
+            if(SolveSudoku(ANSWER,minimumarray1,all_possible_elements1)==1)
+                flag=1;                                                    %if recursion ends in flag=1 then return 1
+                return
+            end
+            s2=size(possible_elements);                                     %if recursion does not give 1 return then check if stepped out function had two elements or one
+                if s2(2)==1
+                flag=2;                                                     %if one then no swapping possible, simply back trace further till a two possible element arrives
+                return
+            else
+            possible_elements=setxor(swappingtemp,possible_elements);       %xor of swapppingtemp with possible_elements gives element not put in that box
+            if numel(possible_elements)==0                                  %in case a swap was performed earlier xor output will have no elements
+                flag=2;                                                     %back trace further
+                return
+            end
+            ANSWER(minimumarray(i,1),minimumarray(i,2))=possible_elements;  %change or swap element
+            flag2=1;                                                        %flag a change
+            end
+         end
+        end
+    flag=0;
+    return
+end