187 lines
5.1 KiB
Plaintext
187 lines
5.1 KiB
Plaintext
Advent of Code
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--- Day 8: Resonant Collinearity ---
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You find yourselves on the [16]roof of a top-secret Easter Bunny
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installation.
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While The Historians do their thing, you take a look at the familiar huge
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antenna. Much to your surprise, it seems to have been reconfigured to emit
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a signal that makes people 0.1% more likely to buy Easter Bunny brand
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Imitation Mediocre Chocolate as a Christmas gift! Unthinkable!
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Scanning across the city, you find that there are actually many such
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antennas. Each antenna is tuned to a specific frequency indicated by a
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single lowercase letter, uppercase letter, or digit. You create a map
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(your puzzle input) of these antennas. For example:
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............
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........0...
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.....0......
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.......0....
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....0.......
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......A.....
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............
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............
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........A...
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.........A..
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............
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............
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The signal only applies its nefarious effect at specific antinodes based
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on the resonant frequencies of the antennas. In particular, an antinode
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occurs at any point that is perfectly in line with two antennas of the
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same frequency - but only when one of the antennas is twice as far away as
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the other. This means that for any pair of antennas with the same
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frequency, there are two antinodes, one on either side of them.
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So, for these two antennas with frequency a, they create the two antinodes
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marked with #:
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..........
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...#......
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..........
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....a.....
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..........
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.....a....
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..........
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......#...
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..........
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..........
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Adding a third antenna with the same frequency creates several more
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antinodes. It would ideally add four antinodes, but two are off the right
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side of the map, so instead it adds only two:
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..........
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...#......
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#.........
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....a.....
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........a.
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.....a....
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..#.......
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......#...
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..........
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..........
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Antennas with different frequencies don't create antinodes; A and a count
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as different frequencies. However, antinodes can occur at locations that
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contain antennas. In this diagram, the lone antenna with frequency capital
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A creates no antinodes but has a lowercase-a-frequency antinode at its
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location:
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..........
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...#......
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#.........
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....a.....
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........a.
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.....a....
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..#.......
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......A...
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..........
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..........
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The first example has antennas with two different frequencies, so the
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antinodes they create look like this, plus an antinode overlapping the
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topmost A-frequency antenna:
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......#....#
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...#....0...
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....#0....#.
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..#....0....
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....0....#..
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.#....A.....
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...#........
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#......#....
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........A...
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.........A..
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..........#.
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..........#.
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Because the topmost A-frequency antenna overlaps with a 0-frequency
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antinode, there are 14 total unique locations that contain an antinode
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within the bounds of the map.
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Calculate the impact of the signal. How many unique locations within the
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bounds of the map contain an antinode?
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Your puzzle answer was 311.
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--- Part Two ---
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Watching over your shoulder as you work, one of The Historians asks if you
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took the effects of resonant harmonics into your calculations.
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Whoops!
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After updating your model, it turns out that an antinode occurs at any
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grid position exactly in line with at least two antennas of the same
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frequency, regardless of distance. This means that some of the new
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antinodes will occur at the position of each antenna (unless that antenna
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is the only one of its frequency).
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So, these three T-frequency antennas now create many antinodes:
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T....#....
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...T......
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.T....#...
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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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In fact, the three T-frequency antennas are all exactly in line with two
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antennas, so they are all also antinodes! This brings the total number of
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antinodes in the above example to 9.
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The original example now has 34 antinodes, including the antinodes that
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appear on every antenna:
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##....#....#
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.#.#....0...
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..#.#0....#.
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..##...0....
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....0....#..
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.#...#A....#
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...#..#.....
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#....#.#....
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..#.....A...
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....#....A..
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.#........#.
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...#......##
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Calculate the impact of the signal using this updated model. How many
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unique locations within the bounds of the map contain an antinode?
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Your puzzle answer was 1115.
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Both parts of this puzzle are complete! They provide two gold stars: **
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At this point, you should [17]return to your Advent calendar and try
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another puzzle.
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If you still want to see it, you can [18]get your puzzle input.
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References
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Visible links
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1. https://adventofcode.com/
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2. https://adventofcode.com/2024/about
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3. https://adventofcode.com/2024/events
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4. https://cottonbureau.com/people/advent-of-code
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5. https://adventofcode.com/2024/settings
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6. https://adventofcode.com/2024/auth/logout
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7. Advent of Code Supporter
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https://adventofcode.com/2024/support
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8. https://adventofcode.com/2024
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9. https://adventofcode.com/2024
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10. https://adventofcode.com/2024/support
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12. https://adventofcode.com/2024/leaderboard
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13. https://adventofcode.com/2024/stats
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16. https://adventofcode.com/2016/day/25
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17. https://adventofcode.com/2024
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18. https://adventofcode.com/2024/day/8/input
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