how to best control difficulty?

jazzjunkie · Posted: Sun May 21, 2006 11:20 pm Post subject: how to best control difficulty?

I've been scanning this forum, but I havn't found much in the way of creation, beyond
add one hint -> apply solver, or
subtract one filled square -> apply solver.

I've been tinkering with a modification to the subtraction method, with some success. What I'd like to know is,
is it old hat? just plain wrong?

Here it is, in broad terms:
I'll assign a difficulty to each solving technique for reducing a square's candidates. Based on the puzzle's desired difficulty rating, a difficulty for each square will be preferred by the algorithm.

step 1: choose remove a random remaining square (the difficulty of each square could be calculated, but that would take more time)

step 2: check conditions a, and b, see below (each square will store an array of its candidates, so checking b will be easy).
- if condition a is true, the square should be removed, regardless of desired difficulty

step 3: add the value of the random square as a candidate for ALL of its neighbors (squares in the same row, col, or box).

step 4: using standard solving techniques*, try to eliminate all of the candidates added in step 3.
-apply methods from easiest to hardest, and if successful, keep track of the difficulty required.

*locked candidates, naked/hidden groups, etc.

step 5: test condition c.
-if invalid, remove the rest of the candidates added, and mark the square as a final clue.
-if valid, check the highest difficulty technique needed against the desired level for the square. If too high or too low, store the location of the square as a potential, and try to find a better one.

step 6: once all remaining squares are marked as final, it's done.

Other subtraction methods I have found are slightly different: they remove one square randomly, then apply a full blown solver algorithm to make sure the removal was valid.

Mine may possibly leave room for multiple solutions or an unsolvable puzzle, but I can't see how yet.

Above, I refer to
a square may be removed when one or more of the following apply:

a -it is a member of a filled row or column or box

b -removing it would leave it with only one candidate

c -removing it would make it a candidate for another square in its row AND column AND box.

These are, as far as I can determine, the only way to legally remove a square.

How does it look?