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It is never enough of these Japanese ‘fill the grid’ puzzles…
One concern: while it is a good practice that the validators are slightly easier then the IDE tests, this puzzle takes it a bit too far: my dumb backtracking solution takes 214 secs (!) to solve IDE TEST #04 (over a billion iterations…), yet it still passes 100% of the validators.
As there is obviously a much better approach with cutting the iteration count by better utilizing the info from the partially filled grid, my code should not have passed. Now I am not motivated enough to improve it…
I should try to submit even if all the tests don’t pass more often, I never do that
If you manage to find the motivation you could improve it by at least a factor of 713, test #4 is taking ~0.3s for me with our slow language. (assuming you went with PHP for that one too)
I am passing IDE test case #4 100% of the time with my Python non-DLX Algorithm X implementation. Really great puzzle! Reducing the grid before starting the backtracking required a lot more thought than I first imagined.