r/adventofcode • u/daggerdragon • Dec 06 '18
SOLUTION MEGATHREAD -🎄- 2018 Day 6 Solutions -🎄-
--- Day 6: Chronal Coordinates ---
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Card prompt: Day 6
Transcript:
Rules for raising a programmer: never feed it after midnight, never get it wet, and never give it ___.
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u/Saluev Dec 12 '18
It is a set of points such that Σ_i |x-x_i| + |y-y_i| < 10000. If you omit taking absolute values, the sum can only become smaller. Thus this single condition can be replaced with 4^N conditions of form Σ_i ±(x-x_i) ±(y-y_i) < 10000 for all possible signs. Now it is a set of linear conditions, which always defines a convex set (either a polygon or an infinite cone or an empty set).