adventofcode/2024/day10/problem

Advent of Code

--- Day 10: Hoof It ---

   You all arrive at a [16]Lava Production Facility on a floating island in
   the sky. As the others begin to search the massive industrial complex, you
   feel a small nose boop your leg and look down to discover a reindeer
   wearing a hard hat.

   The reindeer is holding a book titled "Lava Island Hiking Guide". However,
   when you open the book, you discover that most of it seems to have been
   scorched by lava! As you're about to ask how you can help, the reindeer
   brings you a blank [17]topographic map of the surrounding area (your
   puzzle input) and looks up at you excitedly.

   Perhaps you can help fill in the missing hiking trails?

   The topographic map indicates the height at each position using a scale
   from 0 (lowest) to 9 (highest). For example:

 0123
 1234
 8765
 9876

   Based on un-scorched scraps of the book, you determine that a good hiking
   trail is as long as possible and has an even, gradual, uphill slope. For
   all practical purposes, this means that a hiking trail is any path that
   starts at height 0, ends at height 9, and always increases by a height of
   exactly 1 at each step. Hiking trails never include diagonal steps - only
   up, down, left, or right (from the perspective of the map).

   You look up from the map and notice that the reindeer has helpfully begun
   to construct a small pile of pencils, markers, rulers, compasses,
   stickers, and other equipment you might need to update the map with hiking
   trails.

   A trailhead is any position that starts one or more hiking trails - here,
   these positions will always have height 0. Assembling more fragments of
   pages, you establish that a trailhead's score is the number of 9-height
   positions reachable from that trailhead via a hiking trail. In the above
   example, the single trailhead in the top left corner has a score of 1
   because it can reach a single 9 (the one in the bottom left).

   This trailhead has a score of 2:

 ...0...
 ...1...
 ...2...
 6543456
 7.....7
 8.....8
 9.....9

   (The positions marked . are impassable tiles to simplify these examples;
   they do not appear on your actual topographic map.)

   This trailhead has a score of 4 because every 9 is reachable via a hiking
   trail except the one immediately to the left of the trailhead:

 ..90..9
 ...1.98
 ...2..7
 6543456
 765.987
 876....
 987....

   This topographic map contains two trailheads; the trailhead at the top has
   a score of 1, while the trailhead at the bottom has a score of 2:

 10..9..
 2...8..
 3...7..
 4567654
 ...8..3
 ...9..2
 .....01

   Here's a larger example:

 89010123
 78121874
 87430965
 96549874
 45678903
 32019012
 01329801
 10456732

   This larger example has 9 trailheads. Considering the trailheads in
   reading order, they have scores of 5, 6, 5, 3, 1, 3, 5, 3, and 5. Adding
   these scores together, the sum of the scores of all trailheads is 36.

   The reindeer gleefully carries over a protractor and adds it to the pile.
   What is the sum of the scores of all trailheads on your topographic map?

   Your puzzle answer was 744.

--- Part Two ---

   The reindeer spends a few minutes reviewing your hiking trail map before
   realizing something, disappearing for a few minutes, and finally returning
   with yet another slightly-charred piece of paper.

   The paper describes a second way to measure a trailhead called its rating.
   A trailhead's rating is the number of distinct hiking trails which begin
   at that trailhead. For example:

 .....0.
 ..4321.
 ..5..2.
 ..6543.
 ..7..4.
 ..8765.
 ..9....

   The above map has a single trailhead; its rating is 3 because there are
   exactly three distinct hiking trails which begin at that position:

 .....0.   .....0.   .....0.
 ..4321.   .....1.   .....1.
 ..5....   .....2.   .....2.
 ..6....   ..6543.   .....3.
 ..7....   ..7....   .....4.
 ..8....   ..8....   ..8765.
 ..9....   ..9....   ..9....

   Here is a map containing a single trailhead with rating 13:

 ..90..9
 ...1.98
 ...2..7
 6543456
 765.987
 876....
 987....

   This map contains a single trailhead with rating 227 (because there are
   121 distinct hiking trails that lead to the 9 on the right edge and 106
   that lead to the 9 on the bottom edge):

 012345
 123456
 234567
 345678
 4.6789
 56789.

   Here's the larger example from before:

 89010123
 78121874
 87430965
 96549874
 45678903
 32019012
 01329801
 10456732

   Considering its trailheads in reading order, they have ratings of 20, 24,
   10, 4, 1, 4, 5, 8, and 5. The sum of all trailhead ratings in this larger
   example topographic map is 81.

   You're not sure how, but the reindeer seems to have crafted some tiny
   flags out of toothpicks and bits of paper and is using them to mark
   trailheads on your topographic map. What is the sum of the ratings of all
   trailheads?

   Your puzzle answer was 1651.

   Both parts of this puzzle are complete! They provide two gold stars: **

   At this point, you should [18]return to your Advent calendar and try
   another puzzle.

   If you still want to see it, you can [19]get your puzzle input.

References

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  16. https://adventofcode.com/2023/day/15
  17. https://en.wikipedia.org/wiki/Topographic_map
  18. https://adventofcode.com/2024
  19. https://adventofcode.com/2024/day/10/input