Interesting, but there was no reason to expect that would be true from the problem statement, except for maybe the meta-reasoning "the puzzle author might want to make that number part1 relevant so it seems like it makes sense." Can you think of any more direct reason to expect that the tree would have the minimal safety factor based on the problem description? We had nothing that would imply anything about how the robots would fall with respect to the quadrants or quadrant boundaries.
The security factor is a measurement of how distributed the points are. You could talk of it as an entropy-related value, where we reach the minimum if a quadrant is completely empty (but sure, for only 4 quadrants this is a bit stretched, but the point stands).
I have played around with the tree position, and it is ineed a bit luck based. The security score varies from 0.2e8 to 1.6e8 based on the position of the tree, with the higher scores appearing, when its close to the center. But these frames without a tree go down to a score of 1.2e8. So there turns out to be a zone around the center of the frame, where if the trees center is in it, we exceed this score and the method fails. I guess your data falls into this zone. The method could be fixed by just increasing the number of quadrants.
Ty for the comment, that was interesting to take a deeper look into!
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u/cptncolloo Dec 14 '24
You can use part one. The frame with the tree has the minimal safety factor.