14 - Min and Max Irregular Tetrahedral Shadows

Hi Adam!

Double-checking the example testcases, it looks like the max value answers were incorrect for some reason... They've been updated now to reflect what the checker would actually expect for those testcases.

However I've not modified the actual checker code yet, so the discrepency between your answers and the "expected" ones still stands. I have some suspicion that the cause may be the "interval-size" of your solution code... If you are finding that your min values slightly greater the "expected" mins, and that the max values are slightly lesser than the "expected" maxs, then that may be the case. Tradeoff with computation cost may start to become an issue, but maybe not so much if we are working with integer-rounding?

The checker logic here is actually using a bit of "insight" into the problem to only check <20 orientations per testcase (giving the exact number may reveal the logic). While I haven't quite mathematically proved this logic (and am unable to find mention of it online), I have tested it against a great many testcases within the bounds of this problem and it has always held true.

But... without an actual proof I'm not going to claim that there exist no edge cases that I haven't thought of yet! If you increase your "resolution" and find that your answers still do not match up, then I'd be interested in the results that you did get for whatever given testcases you used. I'd be glad for some edge cases to scrutinize my method with :)

However if you find that your answers do line up with the "expected" values as with as resolution increases but the computational cost becomes unreasonable, then I would encourage you to visualize the tetrahedrons themselves when they are producing the min/max values, and try to identify any patterns you see :)