adventofcode/2024/day08/problem

Advent of Code

--- Day 8: Resonant Collinearity ---

   You find yourselves on the [16]roof of a top-secret Easter Bunny
   installation.

   While The Historians do their thing, you take a look at the familiar huge
   antenna. Much to your surprise, it seems to have been reconfigured to emit
   a signal that makes people 0.1% more likely to buy Easter Bunny brand
   Imitation Mediocre Chocolate as a Christmas gift! Unthinkable!

   Scanning across the city, you find that there are actually many such
   antennas. Each antenna is tuned to a specific frequency indicated by a
   single lowercase letter, uppercase letter, or digit. You create a map
   (your puzzle input) of these antennas. For example:

 ............
 ........0...
 .....0......
 .......0....
 ....0.......
 ......A.....
 ............
 ............
 ........A...
 .........A..
 ............
 ............

   The signal only applies its nefarious effect at specific antinodes based
   on the resonant frequencies of the antennas. In particular, an antinode
   occurs at any point that is perfectly in line with two antennas of the
   same frequency - but only when one of the antennas is twice as far away as
   the other. This means that for any pair of antennas with the same
   frequency, there are two antinodes, one on either side of them.

   So, for these two antennas with frequency a, they create the two antinodes
   marked with #:

 ..........
 ...#......
 ..........
 ....a.....
 ..........
 .....a....
 ..........
 ......#...
 ..........
 ..........

   Adding a third antenna with the same frequency creates several more
   antinodes. It would ideally add four antinodes, but two are off the right
   side of the map, so instead it adds only two:

 ..........
 ...#......
 #.........
 ....a.....
 ........a.
 .....a....
 ..#.......
 ......#...
 ..........
 ..........

   Antennas with different frequencies don't create antinodes; A and a count
   as different frequencies. However, antinodes can occur at locations that
   contain antennas. In this diagram, the lone antenna with frequency capital
   A creates no antinodes but has a lowercase-a-frequency antinode at its
   location:

 ..........
 ...#......
 #.........
 ....a.....
 ........a.
 .....a....
 ..#.......
 ......A...
 ..........
 ..........

   The first example has antennas with two different frequencies, so the
   antinodes they create look like this, plus an antinode overlapping the
   topmost A-frequency antenna:

 ......#....#
 ...#....0...
 ....#0....#.
 ..#....0....
 ....0....#..
 .#....A.....
 ...#........
 #......#....
 ........A...
 .........A..
 ..........#.
 ..........#.

   Because the topmost A-frequency antenna overlaps with a 0-frequency
   antinode, there are 14 total unique locations that contain an antinode
   within the bounds of the map.

   Calculate the impact of the signal. How many unique locations within the
   bounds of the map contain an antinode?

   Your puzzle answer was 311.

--- Part Two ---

   Watching over your shoulder as you work, one of The Historians asks if you
   took the effects of resonant harmonics into your calculations.

   Whoops!

   After updating your model, it turns out that an antinode occurs at any
   grid position exactly in line with at least two antennas of the same
   frequency, regardless of distance. This means that some of the new
   antinodes will occur at the position of each antenna (unless that antenna
   is the only one of its frequency).

   So, these three T-frequency antennas now create many antinodes:

 T....#....
 ...T......
 .T....#...
 .........#
 ..#.......
 ..........
 ...#......
 ..........
 ....#.....
 ..........

   In fact, the three T-frequency antennas are all exactly in line with two
   antennas, so they are all also antinodes! This brings the total number of
   antinodes in the above example to 9.

   The original example now has 34 antinodes, including the antinodes that
   appear on every antenna:

 ##....#....#
 .#.#....0...
 ..#.#0....#.
 ..##...0....
 ....0....#..
 .#...#A....#
 ...#..#.....
 #....#.#....
 ..#.....A...
 ....#....A..
 .#........#.
 ...#......##

   Calculate the impact of the signal using this updated model. How many
   unique locations within the bounds of the map contain an antinode?

   Your puzzle answer was 1115.

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

   At this point, you should [17]return to your Advent calendar and try
   another puzzle.

   If you still want to see it, you can [18]get your puzzle input.

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