C - Pyramid

  • image
  • 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.
    • image
    • 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.

This page is auto-translated from /nishio/ABC112C using DeepL. If you looks something interesting but the auto-translated English is not good enough to understand it, feel free to let me know at @nishio_en. I’m very happy to spread my thought to non-Japanese readers.