199 lines
6.2 KiB
Plaintext
199 lines
6.2 KiB
Plaintext
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[1]Advent of Code
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• [2][About]
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• [3][Events]
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• [4][Shop]
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• [5][Settings]
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• [6][Log Out]
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br0xen [7](AoC++) 36*
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$year=[8]2023;
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• [9][Calendar]
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• [10][AoC++]
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• [11][Sponsors]
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• [12][Leaderboard]
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• [13][Stats]
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Our [14]sponsors help make Advent of Code possible:
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[15]McGraw Hill - Transforming education, one line of code at a time.
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--- Day 11: Cosmic Expansion ---
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You continue following signs for "Hot Springs" and eventually come across
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an [16]observatory. The Elf within turns out to be a researcher studying
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cosmic expansion using the giant telescope here.
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He doesn't know anything about the missing machine parts; he's only
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visiting for this research project. However, he confirms that the hot
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springs are the next-closest area likely to have people; he'll even take
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you straight there once he's done with today's observation analysis.
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Maybe you can help him with the analysis to speed things up?
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The researcher has collected a bunch of data and compiled the data into a
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single giant image (your puzzle input). The image includes empty space (.)
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and galaxies (#). For example:
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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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..........
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.......#..
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#...#.....
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The researcher is trying to figure out the sum of the lengths of the
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shortest path between every pair of galaxies. However, there's a catch:
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the universe expanded in the time it took the light from those galaxies to
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reach the observatory.
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Due to something involving gravitational effects, only some space expands.
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In fact, the result is that any rows or columns that contain no galaxies
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should all actually be twice as big.
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In the above example, three columns and two rows contain no galaxies:
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v v v
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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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>..........<
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.......#..
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#...#.....
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^ ^ ^
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These rows and columns need to be twice as big; the result of cosmic
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expansion therefore looks like this:
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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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............#
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.............
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.............
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.........#...
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#....#.......
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Equipped with this expanded universe, the shortest path between every pair
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of galaxies can be found. It can help to assign every galaxy a unique
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number:
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....1........
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.........2...
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3............
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.............
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.............
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........4....
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.5...........
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............6
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.............
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.............
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.........7...
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8....9.......
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In these 9 galaxies, there are 36 pairs. Only count each pair once; order
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within the pair doesn't matter. For each pair, find any shortest path
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between the two galaxies using only steps that move up, down, left, or
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right exactly one . or # at a time. (The shortest path between two
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galaxies is allowed to pass through another galaxy.)
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For example, here is one of the shortest paths between galaxies 5 and 9:
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....1........
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.........2...
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3............
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.............
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.............
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........4....
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.5...........
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.##.........6
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..##.........
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...##........
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....##...7...
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8....9.......
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This path has length 9 because it takes a minimum of nine steps to get
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from galaxy 5 to galaxy 9 (the eight locations marked # plus the step onto
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galaxy 9 itself). Here are some other example shortest path lengths:
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• Between galaxy 1 and galaxy 7: 15
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• Between galaxy 3 and galaxy 6: 17
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• Between galaxy 8 and galaxy 9: 5
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In this example, after expanding the universe, the sum of the shortest
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path between all 36 pairs of galaxies is 374.
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Expand the universe, then find the length of the shortest path between
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every pair of galaxies. What is the sum of these lengths?
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Your puzzle answer was 9957702.
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--- Part Two ---
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The galaxies are much older (and thus much farther apart) than the
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researcher initially estimated.
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Now, instead of the expansion you did before, make each empty row or
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column one million times larger. That is, each empty row should be
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replaced with 1000000 empty rows, and each empty column should be replaced
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with 1000000 empty columns.
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(In the example above, if each empty row or column were merely 10 times
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larger, the sum of the shortest paths between every pair of galaxies would
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be 1030. If each empty row or column were merely 100 times larger, the sum
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of the shortest paths between every pair of galaxies would be 8410.
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However, your universe will need to expand far beyond these values.)
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Starting with the same initial image, expand the universe according to
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these new rules, then find the length of the shortest path between every
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pair of galaxies. What is the sum of these lengths?
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Your puzzle answer was 512240933238.
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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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You can also [Shareon [19]Twitter [20]Mastodon] this puzzle.
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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/2023/about
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3. https://adventofcode.com/2023/events
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4. https://teespring.com/stores/advent-of-code
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5. https://adventofcode.com/2023/settings
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6. https://adventofcode.com/2023/auth/logout
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7. Advent of Code Supporter
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https://adventofcode.com/2023/support
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8. https://adventofcode.com/2023
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9. https://adventofcode.com/2023
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10. https://adventofcode.com/2023/support
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11. https://adventofcode.com/2023/sponsors
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12. https://adventofcode.com/2023/leaderboard
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13. https://adventofcode.com/2023/stats
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14. https://adventofcode.com/2023/sponsors
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15. https://mheducation.com/
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16. https://en.wikipedia.org/wiki/Observatory
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17. https://adventofcode.com/2023
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18. https://adventofcode.com/2023/day/11/input
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19. https://twitter.com/intent/tweet?text=I%27ve+completed+%22Cosmic+Expansion%22+%2D+Day+11+%2D+Advent+of+Code+2023&url=https%3A%2F%2Fadventofcode%2Ecom%2F2023%2Fday%2F11&related=ericwastl&hashtags=AdventOfCode
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20. javascript:void(0);
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