SESSION NOVEL ALGORIHMS AND APPLICATIONS + ...

36 Int'l Conf. Foundations of Computer Science | FCS'11 |
Figure 3: A moderately challenging puzzle that can be solved with the
Test Cell algorithm.
2.3 Extension to the Test Cell Algorithm
For a guaranteed solution to more difficult Sudoku
puzzles, the Test Cell algorithm adopts an easy extension
with the use of “BackPuzzle” puzzle configurations. In this
arrangement, Test Cells are further classified as immediate
or non-immediate (NI) Test Cells. Immediate Test Cells are
the commonest in puzzles falling in the typical Easy,
Medium, and Hard categories while non-immediate Test
Cells begin to occur in the more difficult puzzle categories.
An immediate Test Cell is one for which insertion of the
alpha or beta number leads to a Dead End upon performing
the Easy Cell method for the first chosen insertion, and a
normal progress (i.e. NOT Dead End) for the other. This is
illustrated in Figure 4 and Figure 5 where A and B
represent alpha and beta numbers respectively. It is
instructive to note that the Test Cell algorithm without the
extension assumes only immediate Test Cells for a puzzle.
Figure 4: An immediate Test Cell with the alpha number correct and the
beta number wrong, after performing the Easy Cell method
Figure 5: An immediate Test Cell with the alpha number wrong and the
beta number correct, after performing the Easy Cell method
A non-immediate (NI) Test Cell on the other hand is one
for which either insertion of the alpha or beta number leads
to a normal progress upon performing the Easy Cell
method, such that either insertion appears to be correct.
According to the Test Cell theory however, one of these
insertions will eventually produce a Dead End at a later
stage if you proceed solving the puzzle with it while the
other will not, thereby remaining consistent with the Test
Cell definition. This is illustrated in Figure 6 and Figure 7.
The BackPuzzle configuration mentioned earlier is the
puzzle configuration at the point when a non-immediate
Test Cell is found to exist in the puzzle being solved.
BackPuzzle configurations are useful because if both alpha
and beta insertions of a Test Cell lead to a Dead End (as is
the case when the Test Cell algorithm terminates with no
solution to a puzzle), then the current puzzle configuration
is reset to the most recent BackPuzzle configuration, and a
beta insertion is made in the corresponding non-immediate
Test Cell. This is illustrated in the flow chart for the
extended Test Cell algorithm shown in Figure 8.
Figure 6: A non-immediate (NI) Test Cell where the alpha number is
correct while the beta number is ultimately wrong.
Figure 7: A non-immediate Test Cell where the alpha number is ultimately
wrong while the beta number is correct.