adventofcode/2018/day06/problem

Advent of Code

--- Day 6: Chronal Coordinates ---

   The device on your wrist beeps several times, and once again you feel like
   you're falling.

   "Situation critical," the device announces. "Destination indeterminate.
   Chronal interference detected. Please specify new target coordinates."

   The device then produces a list of coordinates (your puzzle input). Are they
   places it thinks are safe or dangerous? It recommends you check manual page
   729. The Elves did not give you a manual.

   If they're dangerous, maybe you can minimize the danger by finding the
   coordinate that gives the largest distance from the other points.

   Using only the Manhattan distance, determine the area around each coordinate
   by counting the number of integer X,Y locations that are closest to that
   coordinate (and aren't tied in distance to any other coordinate).

   Your goal is to find the size of the largest area that isn't infinite. For
   example, consider the following list of coordinates:

 1, 1
 1, 6
 8, 3
 3, 4
 5, 5
 8, 9

   If we name these coordinates A through F, we can draw them on a grid,
   putting 0,0 at the top left:

 ..........
 .A........
 ..........
 ........C.
 ...D......
 .....E....
 .B........
 ..........
 ..........
 ........F.

   This view is partial - the actual grid extends infinitely in all directions.
   Using the Manhattan distance, each location's closest coordinate can be
   determined, shown here in lowercase:

 aaaaa.cccc
 aAaaa.cccc
 aaaddecccc
 aadddeccCc
 ..dDdeeccc
 bb.deEeecc
 bBb.eeee..
 bbb.eeefff
 bbb.eeffff
 bbb.ffffFf

   Locations shown as . are equally far from two or more coordinates, and so
   they don't count as being closest to any.

   In this example, the areas of coordinates A, B, C, and F are infinite -
   while not shown here, their areas extend forever outside the visible grid.
   However, the areas of coordinates D and E are finite: D is closest to 9
   locations, and E is closest to 17 (both including the coordinate's location
   itself). Therefore, in this example, the size of the largest area is 17.

   What is the size of the largest area that isn't infinite?

   Your puzzle answer was 3989.

--- Part Two ---

   On the other hand, if the coordinates are safe, maybe the best you can do is
   try to find a region near as many coordinates as possible.

   For example, suppose you want the sum of the Manhattan distance to all of
   the coordinates to be less than 32. For each location, add up the distances
   to all of the given coordinates; if the total of those distances is less
   than 32, that location is within the desired region. Using the same
   coordinates as above, the resulting region looks like this:

 ..........
 .A........
 ..........
 ...###..C.
 ..#D###...
 ..###E#...
 .B.###....
 ..........
 ..........
 ........F.

   In particular, consider the highlighted location 4,3 located at the top
   middle of the region. Its calculation is as follows, where abs() is the
   absolute value function:

     • Distance to coordinate A: abs(4-1) + abs(3-1) =  5
     • Distance to coordinate B: abs(4-1) + abs(3-6) =  6
     • Distance to coordinate C: abs(4-8) + abs(3-3) =  4
     • Distance to coordinate D: abs(4-3) + abs(3-4) =  2
     • Distance to coordinate E: abs(4-5) + abs(3-5) =  3
     • Distance to coordinate F: abs(4-8) + abs(3-9) = 10
     • Total distance: 5 + 6 + 4 + 2 + 3 + 10 = 30

   Because the total distance to all coordinates (30) is less than 32, the
   location is within the region.

   This region, which also includes coordinates D and E, has a total size of
   16.

   Your actual region will need to be much larger than this example, though,
   instead including all locations with a total distance of less than 10000.

   What is the size of the region containing all locations which have a total
   distance to all given coordinates of less than 10000?

   Your puzzle answer was 49715.

   Both parts of this puzzle are complete! They provide two gold stars: **

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