[2018] [Day 6]: Chronal Coordinates

[victoraugustofd]

Challenge description

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?

Challenge input

292, 73
204, 176
106, 197
155, 265
195, 59
185, 136
54, 82
209, 149
298, 209
274, 157
349, 196
168, 353
193, 129
94, 137
177, 143
196, 357
272, 312
351, 340
253, 115
109, 183
252, 232
193, 258
242, 151
220, 345
336, 348
196, 203
122, 245
265, 189
124, 57
276, 204
309, 125
46, 324
345, 228
251, 134
231, 117
88, 112
256, 229
49, 201
142, 108
150, 337
134, 109
288, 67
297, 231
310, 131
208, 255
246, 132
232, 45
356, 93
356, 207
83, 97

Challenge year

2018

[victoraugustofd]

Challenge link

https://adventofcode.com/2018/day/6