A weblog can be used to celebrate achievements or the write away frustrations. This post belongs to the latter category.

When I completed the ALS technique in SudoCue, I figured that there must be a counterpart, like hidden subsets are the counterpart for naked subsets. An ALS is defined as N cells having N+1 digits as candidates in a single house. Any digit that you can take away from the set will lock the remaining digits in these cells. It can act as a strong link in any chain, but the more basic application is a pairs of ALS’ with a shared digit, which is connected in such a way that it cannot appear in both sets at the same time. From here, we can eliminate any candidate that can see all instances of another digit in both sets. This sounds like a rate occasion, but ALS’ are abundant in any Sudoku.

So what about the counterpart?

Almost Locked Digits is the “hidden” counterpart. It has N digits confined to N+1 cells within a single house. The trigger mechanism is actually more flexible. Any move that would force one of the surplus candidates into any of the N+1 cells will lock the set. Now the easiest application would be a similar XZ rule. Find a conjugate pair with each end in an ALD. Either one of the ALD’s must be locked. Any shared peer for one of the digits can be eliminated. Simple, elegant, easy to implement.

Only, they do not exist. I tested this on numerous puzzles, even with ALS disabled, and although an average sudoku contains hundreds of ALD’s, they just won’t connect with an XZ rule. Pretty frustrating. I’m not even sure whether the code or the ALD logic has failed. The logic looks pretty solid and the code does find the ALD’s with the conjugate pairs that trigger them.

I’m going to run a couple of severe debug runs to check out the code, and if that doesn’t work, I’ll drop it in the trashcan.

I cannot resist posting a few words about ALS (Almost Locked Sets), a very advanced solving technique with a lot of solving power. As I stated earlier, I just missed the deadline for 1.5.1 with these new solving techniques. They are now released in 1.5.1.1

One of them, long overdue, is Empty Rectanges. It does not solve anything new, but it is an easy to use alternative for multi-coloring and sometimes even for Nishio. Many other sudoku programs already supported ER, but having the most powerful techniques already implemented makes you lazy, I guess. The templates catch any single digit elimination, so I was not encouraged to implement lower-level single digit techniques. However, after the overwhelming success of my finned-fish implementation, it seemed the right time to do Empty Rectangles as well. Having restructured the solver in such a way that it is now very easy to add new techniques does also help.

The real thing I wanted to talk about is ALS. It is a bad acronym, but commonly known in the sudoku community. An Almost Locked Set is a situation where N cells have N+1 digits as their candidates. The simplest ALS is a single cell with only 2 candidates. Consider the following grid:

How many Almost Locked Set does this grid contain? 10? 20?

No, there are almost 200 ALS’s in this grid, with only 96 candidates left. Most of them are harmless, but when you can pick the right combinations, they can become incredible solving tools. My list of 50,000 sudokus that require tabling steps is reduced to half its size, now ALS can be used. There is no single technique that had such a tremendous impact.

I will expand my solving guide to tell more about the power of ALS.

I have brought 2 releases of SudoCue to the site in a very short period of time. The visible improvements can be seen on the release notes page of the www.sudocue.net website, but the internal restructuring is not seen by the outside world. Here are a few notes on how the architecture has changed.

First, a virtual class named Trick has been added. This class can save itself to the configuration file, has a name, a base score, a sequence number, an optional administration score, several classification flags, tries and usage counters, and a Performed method which reports a successful application of the trick.

A Tricks class contains a collection of Trick instances which can be enumerated.

The user can enable or disable any of these tricks through the options panel, and also change the order in which they are tried.

Several tricks that are basically different sizes of a single technique have a base class that performs the technique, with the size property of the derived class as a parameter. There are 2 tricks which are kept at the end of the collection, the DLX brute force solver and a Surrender class the does nothing, but declares the puzzle unsolvable. This trick cannot be disabled by the user for obvious reasons.

The only thing that I need to add a new technique is define a new class derived from the Trick class and add it initially to the Tricks collection. In earlier versions, I had to change the Log, the Options class, the Options dialog, the main solving method in the Grid class and the Analyzer dialog, even before I could start coding the nitty gritty stuff. This hassle disencouraged me from quickly adding new tricks.

There is also a strict separation between setup and play mode. The solver does nothing in setup mode, but validates and rates the puzzle when you switch to play mode. Earlier, the program had the habit of kicking in too soon, filling the log with complicated tabling chains when all it had to do it wait for all the clues to arrive. With uniqueness, this could even lead to a solving path going the wrong way.

With these changes, the program is ready to be expanded with all the lovely tricks that have been developed in the last months. Some have already been added to the program. More will follow.