194 lines
6.5 KiB
Markdown
194 lines
6.5 KiB
Markdown
# 2019 Day 10: Monitoring Station
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Copyright (c) Eric Wastl
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#### [Direct Link](https://adventofcode.com/2019/day/10)
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## Part 1
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You fly into the asteroid belt and reach the Ceres monitoring station. The Elves here have an emergency: they're having trouble tracking all of the asteroids and can't be sure they're safe.
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The Elves would like to build a new monitoring station in a nearby area of space; they hand you a map of all of the asteroids in that region (your puzzle input).
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The map indicates whether each position is empty (`.`) or contains an asteroid (`#`). The asteroids are much smaller than they appear on the map, and every asteroid is exactly in the center of its marked position. The asteroids can be described with `X,Y` coordinates where `X` is the distance from the left edge and `Y` is the distance from the top edge (so the top-left corner is `0,0` and the position immediately to its right is `1,0`).
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Your job is to figure out which asteroid would be the best place to build a **new monitoring station**. A monitoring station can **detect** any asteroid to which it has **direct line of sight** - that is, there cannot be another asteroid **exactly** between them. This line of sight can be at any angle, not just lines aligned to the grid or diagonally. The **best** location is the asteroid that can **detect** the largest number of other asteroids.
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For example, consider the following map:
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```
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.#..#
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.....
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#####
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....#
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...##
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```
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The best location for a new monitoring station on this map is the highlighted asteroid at `3,4` because it can detect `8` asteroids, more than any other location. (The only asteroid it cannot detect is the one at `1,0`; its view of this asteroid is blocked by the asteroid at `2,2`.) All other asteroids are worse locations; they can detect `7` or fewer other asteroids. Here is the number of other asteroids a monitoring station on each asteroid could detect:
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```
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.7..7
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.....
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67775
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....7
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...87
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```
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Here is an asteroid (`#`) and some examples of the ways its line of sight might be blocked. If there were another asteroid at the location of a capital letter, the locations marked with the corresponding lowercase letter would be blocked and could not be detected:
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```
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#.........
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...A......
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...B..a...
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.EDCG....a
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..F.c.b...
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.....c....
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..efd.c.gb
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.......c..
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....f...c.
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...e..d..c
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```
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Here are some larger examples:
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- Best is `5,8` with `33` other asteroids detected:
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```
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......#.#.
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#..#.#....
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..#######.
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.#.#.###..
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.#..#.....
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..#....#.#
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#..#....#.
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.##.#..###
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##...#..#.
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.#....####
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```
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- Best is `1,2` with `35` other asteroids detected:
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```
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#.#...#.#.
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.###....#.
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.#....#...
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##.#.#.#.#
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....#.#.#.
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.##..###.#
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..#...##..
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..##....##
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......#...
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.####.###.
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```
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- Best is `6,3` with `41` other asteroids detected:
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```
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.#..#..###
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####.###.#
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....###.#.
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..###.##.#
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##.##.#.#.
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....###..#
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..#.#..#.#
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#..#.#.###
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.##...##.#
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.....#.#..
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```
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- Best is `11,13` with `210` other asteroids detected:
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```
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.#..##.###...#######
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##.############..##.
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.#.######.########.#
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.###.#######.####.#.
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#####.##.#.##.###.##
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..#####..#.#########
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####################
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#.####....###.#.#.##
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##.#################
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#####.##.###..####..
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..######..##.#######
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####.##.####...##..#
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.#####..#.######.###
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##...#.##########...
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#.##########.#######
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.####.#.###.###.#.##
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....##.##.###..#####
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.#.#.###########.###
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#.#.#.#####.####.###
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###.##.####.##.#..##
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```
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Find the best location for a new monitoring station. **How many other asteroids can be detected from that location**?
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## Part 2
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Once you give them the coordinates, the Elves quickly deploy an Instant Monitoring Station to the location and discover the worst: there are simply too many asteroids.
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The only solution is **complete vaporization by giant laser**.
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Fortunately, in addition to an asteroid scanner, the new monitoring station also comes equipped with a giant rotating laser perfect for vaporizing asteroids. The laser starts by pointing **up** and always rotates **clockwise**, vaporizing any asteroid it hits.
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If multiple asteroids are **exactly** in line with the station, the laser only has enough power to vaporize **one** of them before continuing its rotation. In other words, the same asteroids that can be **detected** can be vaporized, but if vaporizing one asteroid makes another one detectable, the newly-detected asteroid won't be vaporized until the laser has returned to the same position by rotating a full 360 degrees.
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For example, consider the following map, where the asteroid with the new monitoring station (and laser) is marked `X`:
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```
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.#....#####...#..
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##...##.#####..##
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##...#...#.#####.
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..#.....X...###..
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..#.#.....#....##
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```
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The first nine asteroids to get vaporized, in order, would be:
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```
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.#....###24...#..
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##...##.13#67..9#
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##...#...5.8####.
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..#.....X...###..
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..#.#.....#....##
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```
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Note that some asteroids (the ones behind the asteroids marked `1`, `5`, and `7`) won't have a chance to be vaporized until the next full rotation. The laser continues rotating; the next nine to be vaporized are:
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```
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.#....###.....#..
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##...##...#.....#
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##...#......1234.
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..#.....X...5##..
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..#.9.....8....76
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```
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The next nine to be vaporized are then:
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```
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.8....###.....#..
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56...9#...#.....#
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34...7...........
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..2.....X....##..
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..1..............
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```
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Finally, the laser completes its first full rotation (`1` through `3`), a second rotation (`4` through `8`), and vaporizes the last asteroid (`9`) partway through its third rotation:
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```
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......234.....6..
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......1...5.....7
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.................
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........X....89..
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.................
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```
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In the large example above (the one with the best monitoring station location at `11,13`):
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- The 1st asteroid to be vaporized is at `11,12`.
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- The 2nd asteroid to be vaporized is at `12,1`.
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- The 3rd asteroid to be vaporized is at `12,2`.
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- The 10th asteroid to be vaporized is at `12,8`.
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- The 20th asteroid to be vaporized is at `16,0`.
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- The 50th asteroid to be vaporized is at `16,9`.
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- The 100th asteroid to be vaporized is at `10,16`.
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- The 199th asteroid to be vaporized is at `9,6`.
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- **The 200th asteroid to be vaporized is at `8,2`**.
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- The 201st asteroid to be vaporized is at `10,9`.
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- The 299th and final asteroid to be vaporized is at `11,1`.
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The Elves are placing bets on which will be the **200th** asteroid to be vaporized. Win the bet by determining which asteroid that will be; **what do you get if you multiply its X coordinate by `100` and then add its Y coordinate**? (For example, `8,2` becomes **`802`**.) |