# Chronal Coordinates

2018-12-06

# Day 06: Chronal Coordinates

**Description:**

--- 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?

--- 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?

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?

--- 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?

**Input:**

264, 340

308, 156

252, 127

65, 75

102, 291

47, 67

83, 44

313, 307

159, 48

84, 59

263, 248

188, 258

312, 240

59, 173

191, 130

155, 266

252, 119

108, 299

50, 84

172, 227

226, 159

262, 177

233, 137

140, 211

108, 175

278, 255

259, 209

233, 62

44, 341

58, 175

252, 74

232, 63

176, 119

209, 334

103, 112

155, 94

253, 255

169, 87

135, 342

55, 187

313, 338

210, 63

237, 321

171, 143

63, 238

79, 132

135, 113

310, 294

289, 184

56, 259

308, 156

252, 127

65, 75

102, 291

47, 67

83, 44

313, 307

159, 48

84, 59

263, 248

188, 258

312, 240

59, 173

191, 130

155, 266

252, 119

108, 299

50, 84

172, 227

226, 159

262, 177

233, 137

140, 211

108, 175

278, 255

259, 209

233, 62

44, 341

58, 175

252, 74

232, 63

176, 119

209, 334

103, 112

155, 94

253, 255

169, 87

135, 342

55, 187

313, 338

210, 63

237, 321

171, 143

63, 238

79, 132

135, 113

310, 294

289, 184

56, 259

**Part 1:**

```
var coords = File
.ReadAllLines(Path.Combine(Path.GetDirectoryName(Util.CurrentQueryPath), @"06_input.txt"))
.Where(p => !string.IsNullOrWhiteSpace(p))
.Select(l => (int.Parse(l.Split(',')[0].Trim()), int.Parse(l.Split(',')[1].Trim())) )
.ToList();
int[][] d = new int[2][];
for (int i = 0; i < 2; i++)
{
var minX = coords.Min(p => p.Item1)-i;
var maxX = coords.Max(p => p.Item1)+i;
var minY = coords.Min(p => p.Item2)-i;
var maxY = coords.Max(p => p.Item2)+i;
int[,] map = new int[1+maxX-minX, 1+maxY-minY];
d[i] = new int[coords.Count];
for (int x = minX; x <= maxX; x++)
for (int y = minX; y <= maxY; y++)
{
var s = coords.Select((c, idx) => new { I = idx, D = Math.Abs(c.Item1 - x) + Math.Abs(c.Item2 - y), V = c }).OrderBy(c => c.D).ToList();
if (s[0].D == s[1].D) { map[x-minX, y-minY]=-1; continue; }
d[i][s[0].I]++;
map[x-minX, y-minY]=s[0].I;
}
//map.Dump();
}
//d[0].Zip(d[1], (a, b) => (a, b)).Dump();
d[0].Zip(d[1], (a, b) => (a, b)).Where(p => p.a == p.b).Max().a.Dump();
```

**Result:**2917

**Part 2:**

```
var coords = File
.ReadAllLines(Path.Combine(Path.GetDirectoryName(Util.CurrentQueryPath), @"06_input.txt"))
.Where(p => !string.IsNullOrWhiteSpace(p))
.Select(l => (int.Parse(l.Split(',')[0].Trim()), int.Parse(l.Split(',')[1].Trim())))
.ToList();
var minX = coords.Min(p => p.Item1) - 5_000;
var maxX = coords.Max(p => p.Item1) + 5_000;
var minY = coords.Min(p => p.Item2) - 5_000;
var maxY = coords.Max(p => p.Item2) + 5_000;
int r = 0;
for (int x = minX; x <= maxX; x++)
for (int y = minX; y <= maxY; y++)
{
var s1 = coords.Sum(c => Math.Abs(c.Item1 - x) + Math.Abs(c.Item2 - y));
if (s1 < 10_000) r++;
Util.Progress=((x-minX)*100)/(maxX-minX);
}
r.Dump();
```

**Result:**44202