ABC112C

https://gyazo.com/26703e70d37462b7f880bcd2126d9014

Thoughts.

It's tempting to ignore the 0-height vertex, but that's no good because you can create a pattern that can't be determined without hinting at the 0-height vertex.

If there are three points of the same height, that's definite, depending on the placement.

https://gyazo.com/fc11dd9f3a19cd2f8c5de5d6d876d47d

Hmmm, it's possible that there are no dots of the same height at all.

Constraints created by a single observation point

I am the pinnacle, huh?

There is 1 high vertex in 8 squares around you, or...

and for every square, if there is a vertex there, there will be a constraint on how high it can be.

The constraint of the second observation point makes most vertices impossible.

It is not too late to update 100 observation points for 100 x 100 squares.

In fact, the number of possible candidates is drastically reduced after the second one, so we could even put that on the list and just update that part of the list.

Official Explanation

There was proof that "not all observation points are zero."

When 0, the form of the constraint is different.

Inequality Constraints.

The style is to first create position and height pairs at non-zero observation points, and then eliminate inconsistencies.

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