AdventOfCode/2024/16/16.md

## \-\-- Day 16: Reindeer Maze \-\--

It\'s time again for the [Reindeer Olympics](/2015/day/14)! This year,
the big event is the *Reindeer Maze*, where the Reindeer compete for the
*[lowest
score]{title="I would say it's like Reindeer Golf, but knowing Reindeer, it's almost certainly nothing like Reindeer Golf."}*.

You and The Historians arrive to search for the Chief right as the event
is about to start. It wouldn\'t hurt to watch a little, right?

The Reindeer start on the Start Tile (marked `S`) facing *East* and need
to reach the End Tile (marked `E`). They can move forward one tile at a
time (increasing their score by `1` point), but never into a wall (`#`).
They can also rotate clockwise or counterclockwise 90 degrees at a time
(increasing their score by `1000` points).

To figure out the best place to sit, you start by grabbing a map (your
puzzle input) from a nearby kiosk. For example:

    ###############
    #.......#....E#
    #.#.###.#.###.#
    #.....#.#...#.#
    #.###.#####.#.#
    #.#.#.......#.#
    #.#.#####.###.#
    #...........#.#
    ###.#.#####.#.#
    #...#.....#.#.#
    #.#.#.###.#.#.#
    #.....#...#.#.#
    #.###.#.#.#.#.#
    #S..#.....#...#
    ###############

There are many paths through this maze, but taking any of the best paths
would incur a score of only `7036`. This can be achieved by taking a
total of `36` steps forward and turning 90 degrees a total of `7` times:

    ###############
    #.......#....E#
    #.#.###.#.###^#
    #.....#.#...#^#
    #.###.#####.#^#
    #.#.#.......#^#
    #.#.#####.###^#
    #..>>>>>>>>v#^#
    ###^#.#####v#^#
    #>>^#.....#v#^#
    #^#.#.###.#v#^#
    #^....#...#v#^#
    #^###.#.#.#v#^#
    #S..#.....#>>^#
    ###############

Here\'s a second example:

    #################
    #...#...#...#..E#
    #.#.#.#.#.#.#.#.#
    #.#.#.#...#...#.#
    #.#.#.#.###.#.#.#
    #...#.#.#.....#.#
    #.#.#.#.#.#####.#
    #.#...#.#.#.....#
    #.#.#####.#.###.#
    #.#.#.......#...#
    #.#.###.#####.###
    #.#.#...#.....#.#
    #.#.#.#####.###.#
    #.#.#.........#.#
    #.#.#.#########.#
    #S#.............#
    #################

In this maze, the best paths cost `11048` points; following one such
path would look like this:

    #################
    #...#...#...#..E#
    #.#.#.#.#.#.#.#^#
    #.#.#.#...#...#^#
    #.#.#.#.###.#.#^#
    #>>v#.#.#.....#^#
    #^#v#.#.#.#####^#
    #^#v..#.#.#>>>>^#
    #^#v#####.#^###.#
    #^#v#..>>>>^#...#
    #^#v###^#####.###
    #^#v#>>^#.....#.#
    #^#v#^#####.###.#
    #^#v#^........#.#
    #^#v#^#########.#
    #S#>>^..........#
    #################

Note that the path shown above includes one 90 degree turn as the very
first move, rotating the Reindeer from facing East to facing North.

Analyze your map carefully. *What is the lowest score a Reindeer could
possibly get?*

Your puzzle answer was `108504`.

The first half of this puzzle is complete! It provides one gold star: \*

## \-\-- Part Two \-\-- {#part2}

Now that you know what the best paths look like, you can figure out the
best spot to sit.

Every non-wall tile (`S`, `.`, or `E`) is equipped with places to sit
along the edges of the tile. While determining which of these tiles
would be the best spot to sit depends on a whole bunch of factors (how
comfortable the seats are, how far away the bathrooms are, whether
there\'s a pillar blocking your view, etc.), the most important factor
is *whether the tile is on one of the best paths through the maze*. If
you sit somewhere else, you\'d miss all the action!

So, you\'ll need to determine which tiles are part of *any* best path
through the maze, including the `S` and `E` tiles.

In the first example, there are `45` tiles (marked `O`) that are part of
at least one of the various best paths through the maze:

    ###############
    #.......#....O#
    #.#.###.#.###O#
    #.....#.#...#O#
    #.###.#####.#O#
    #.#.#.......#O#
    #.#.#####.###O#
    #..OOOOOOOOO#O#
    ###O#O#####O#O#
    #OOO#O....#O#O#
    #O#O#O###.#O#O#
    #OOOOO#...#O#O#
    #O###.#.#.#O#O#
    #O..#.....#OOO#
    ###############

In the second example, there are `64` tiles that are part of at least
one of the best paths:

    #################
    #...#...#...#..O#
    #.#.#.#.#.#.#.#O#
    #.#.#.#...#...#O#
    #.#.#.#.###.#.#O#
    #OOO#.#.#.....#O#
    #O#O#.#.#.#####O#
    #O#O..#.#.#OOOOO#
    #O#O#####.#O###O#
    #O#O#..OOOOO#OOO#
    #O#O###O#####O###
    #O#O#OOO#..OOO#.#
    #O#O#O#####O###.#
    #O#O#OOOOOOO..#.#
    #O#O#O#########.#
    #O#OOO..........#
    #################

Analyze your map further. *How many tiles are part of at least one of
the best paths through the maze?*

Answer:

Although it hasn\'t changed, you can still [get your puzzle
input](16/input).