148 lines
4.8 KiB
Plaintext
148 lines
4.8 KiB
Plaintext
Advent of Code
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--- Day 6: Chronal Coordinates ---
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The device on your wrist beeps several times, and once again you feel like
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you're falling.
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"Situation critical," the device announces. "Destination indeterminate.
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Chronal interference detected. Please specify new target coordinates."
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The device then produces a list of coordinates (your puzzle input). Are they
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places it thinks are safe or dangerous? It recommends you check manual page
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729. The Elves did not give you a manual.
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If they're dangerous, maybe you can minimize the danger by finding the
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coordinate that gives the largest distance from the other points.
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Using only the Manhattan distance, determine the area around each coordinate
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by counting the number of integer X,Y locations that are closest to that
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coordinate (and aren't tied in distance to any other coordinate).
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Your goal is to find the size of the largest area that isn't infinite. For
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example, consider the following list of coordinates:
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1, 1
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1, 6
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8, 3
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3, 4
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5, 5
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8, 9
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If we name these coordinates A through F, we can draw them on a grid,
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putting 0,0 at the top left:
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..........
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.A........
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..........
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........C.
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...D......
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.....E....
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.B........
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..........
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..........
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........F.
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This view is partial - the actual grid extends infinitely in all directions.
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Using the Manhattan distance, each location's closest coordinate can be
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determined, shown here in lowercase:
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aaaaa.cccc
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aAaaa.cccc
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aaaddecccc
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aadddeccCc
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..dDdeeccc
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bb.deEeecc
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bBb.eeee..
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bbb.eeefff
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bbb.eeffff
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bbb.ffffFf
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Locations shown as . are equally far from two or more coordinates, and so
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they don't count as being closest to any.
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In this example, the areas of coordinates A, B, C, and F are infinite -
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while not shown here, their areas extend forever outside the visible grid.
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However, the areas of coordinates D and E are finite: D is closest to 9
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locations, and E is closest to 17 (both including the coordinate's location
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itself). Therefore, in this example, the size of the largest area is 17.
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What is the size of the largest area that isn't infinite?
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Your puzzle answer was 3989.
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--- Part Two ---
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On the other hand, if the coordinates are safe, maybe the best you can do is
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try to find a region near as many coordinates as possible.
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For example, suppose you want the sum of the Manhattan distance to all of
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the coordinates to be less than 32. For each location, add up the distances
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to all of the given coordinates; if the total of those distances is less
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than 32, that location is within the desired region. Using the same
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coordinates as above, the resulting region looks like this:
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..........
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.A........
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..........
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...###..C.
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..#D###...
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..###E#...
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.B.###....
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..........
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..........
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........F.
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In particular, consider the highlighted location 4,3 located at the top
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middle of the region. Its calculation is as follows, where abs() is the
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absolute value function:
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• Distance to coordinate A: abs(4-1) + abs(3-1) = 5
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• Distance to coordinate B: abs(4-1) + abs(3-6) = 6
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• Distance to coordinate C: abs(4-8) + abs(3-3) = 4
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• Distance to coordinate D: abs(4-3) + abs(3-4) = 2
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• Distance to coordinate E: abs(4-5) + abs(3-5) = 3
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• Distance to coordinate F: abs(4-8) + abs(3-9) = 10
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• Total distance: 5 + 6 + 4 + 2 + 3 + 10 = 30
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Because the total distance to all coordinates (30) is less than 32, the
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location is within the region.
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This region, which also includes coordinates D and E, has a total size of
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16.
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Your actual region will need to be much larger than this example, though,
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instead including all locations with a total distance of less than 10000.
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What is the size of the region containing all locations which have a total
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distance to all given coordinates of less than 10000?
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Your puzzle answer was 49715.
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Both parts of this puzzle are complete! They provide two gold stars: **
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References
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Visible links
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. https://adventofcode.com/
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. https://adventofcode.com/2018/about
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. https://adventofcode.com/2018/events
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. https://teespring.com/adventofcode
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. https://adventofcode.com/2018/settings
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. https://adventofcode.com/2018/auth/logout
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. Advent of Code Supporter
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https://adventofcode.com/2018/support
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. https://adventofcode.com/2018
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. https://adventofcode.com/2018
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. https://adventofcode.com/2018/support
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. https://adventofcode.com/2018/sponsors
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. https://adventofcode.com/2018/leaderboard
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. https://adventofcode.com/2018/stats
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. https://adventofcode.com/2018/sponsors
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. https://en.wikipedia.org/wiki/Taxicab_geometry
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. https://en.wikipedia.org/wiki/Integer
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. https://en.wikipedia.org/wiki/Taxicab_geometry
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. https://en.wikipedia.org/wiki/Absolute_value
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. https://adventofcode.com/2018
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. https://adventofcode.com/2018/day/6/input
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