Advent-of-Code/2019/10/README.md

# 2019 Day 10: Monitoring Station
Copyright (c) Eric Wastl
#### [Direct Link](https://adventofcode.com/2019/day/10)

## Part 1

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.

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).

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`).

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.

For example, consider the following map:

```
.#..#
.....
#####
....#
...##
```

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:

```
.7..7
.....
67775
....7
...87
```

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:

```
#.........
...A......
...B..a...
.EDCG....a
..F.c.b...
.....c....
..efd.c.gb
.......c..
....f...c.
...e..d..c
```

Here are some larger examples:

- Best is `5,8` with `33` other asteroids detected:
    ```
    ......#.#.
    #..#.#....
    ..#######.
    .#.#.###..
    .#..#.....
    ..#....#.#
    #..#....#.
    .##.#..###
    ##...#..#.
    .#....####
    ```

- Best is `1,2` with `35` other asteroids detected:
    ```
    #.#...#.#.
    .###....#.
    .#....#...
    ##.#.#.#.#
    ....#.#.#.
    .##..###.#
    ..#...##..
    ..##....##
    ......#...
    .####.###.
    ```

- Best is `6,3` with `41` other asteroids detected:
    ```
    .#..#..###
    ####.###.#
    ....###.#.
    ..###.##.#
    ##.##.#.#.
    ....###..#
    ..#.#..#.#
    #..#.#.###
    .##...##.#
    .....#.#..
    ```

- Best is `11,13` with `210` other asteroids detected:
    ```
    .#..##.###...#######
    ##.############..##.
    .#.######.########.#
    .###.#######.####.#.
    #####.##.#.##.###.##
    ..#####..#.#########
    ####################
    #.####....###.#.#.##
    ##.#################
    #####.##.###..####..
    ..######..##.#######
    ####.##.####...##..#
    .#####..#.######.###
    ##...#.##########...
    #.##########.#######
    .####.#.###.###.#.##
    ....##.##.###..#####
    .#.#.###########.###
    #.#.#.#####.####.###
    ###.##.####.##.#..##
    ```

Find the best location for a new monitoring station. **How many other asteroids can be detected from that location**?

## Part 2

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.

The only solution is **complete vaporization by giant laser**.

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.

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.

For example, consider the following map, where the asteroid with the new monitoring station (and laser) is marked `X`:

```
.#....#####...#..
##...##.#####..##
##...#...#.#####.
..#.....X...###..
..#.#.....#....##
```

The first nine asteroids to get vaporized, in order, would be:

```
.#....###24...#..
##...##.13#67..9#
##...#...5.8####.
..#.....X...###..
..#.#.....#....##
```

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:

```
.#....###.....#..
##...##...#.....#
##...#......1234.
..#.....X...5##..
..#.9.....8....76
```

The next nine to be vaporized are then:

```
.8....###.....#..
56...9#...#.....#
34...7...........
..2.....X....##..
..1..............
```

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:

```
......234.....6..
......1...5.....7
.................
........X....89..
.................
```

In the large example above (the one with the best monitoring station location at `11,13`):

- The 1st asteroid to be vaporized is at `11,12`.
- The 2nd asteroid to be vaporized is at `12,1`.
- The 3rd asteroid to be vaporized is at `12,2`.
- The 10th asteroid to be vaporized is at `12,8`.
- The 20th asteroid to be vaporized is at `16,0`.
- The 50th asteroid to be vaporized is at `16,9`.
- The 100th asteroid to be vaporized is at `10,16`.
- The 199th asteroid to be vaporized is at `9,6`.
- **The 200th asteroid to be vaporized is at `8,2`**.
- The 201st asteroid to be vaporized is at `10,9`.
- The 299th and final asteroid to be vaporized is at `11,1`.

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`**.)