AoC, Day 11, Parts 1 and 2 (Solved)

2023/11/README.md

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+## \-\-\- Day 11: Cosmic Expansion ---
+
+You continue following signs for "Hot Springs" and eventually come across an [observatory](https://en.wikipedia.org/wiki/Observatory). The Elf within turns out to be a researcher studying cosmic expansion using the giant telescope here.
+
+He doesn't know anything about the missing machine parts; he's only visiting for this research project. However, he confirms that the hot springs are the next-closest area likely to have people; he'll even take you straight there once he's done with today's observation analysis.
+
+Maybe you can help him with the analysis to speed things up?
+
+The researcher has collected a bunch of data and compiled the data into a single giant _image_ (your puzzle input). The image includes _empty space_ ( `.`) and _galaxies_ ( `#`). For example:
+
+```
+...#......
+.......#..
+#.........
+..........
+......#...
+.#........
+.........#
+..........
+.......#..
+#...#.....
+
+```
+
+The researcher is trying to figure out the sum of the lengths of the _shortest path between every pair of galaxies_. However, there's a catch: the universe expanded in the time it took the light from those galaxies to reach the observatory.
+
+Due to something involving gravitational effects, _only some space expands_. In fact, the result is that _any rows or columns that contain no galaxies_ should all actually be twice as big.
+
+In the above example, three columns and two rows contain no galaxies:
+
+```
+   v  v  v
+ ...#......
+ .......#..
+ #.........
+>..........<
+ ......#...
+ .#........
+ .........#
+>..........<
+ .......#..
+ #...#.....
+   ^  ^  ^
+
+```
+
+These rows and columns need to be _twice as big_; the result of cosmic expansion therefore looks like this:
+
+```
+....#........
+.........#...
+#............
+.............
+.............
+........#....
+.#...........
+............#
+.............
+.............
+.........#...
+#....#.......
+
+```
+
+Equipped with this expanded universe, the shortest path between every pair of galaxies can be found. It can help to assign every galaxy a unique number:
+
+```
+....1........
+.........2...
+3............
+.............
+.............
+........4....
+.5...........
+............6
+.............
+.............
+.........7...
+8....9.......
+
+```
+
+In these 9 galaxies, there are _36 pairs_. Only count each pair once; order within the pair doesn't matter. For each pair, find any shortest path between the two galaxies using only steps that move up, down, left, or right exactly one `.` or `#` at a time. (The shortest path between two galaxies is allowed to pass through another galaxy.)
+
+For example, here is one of the shortest paths between galaxies `5` and `9`:
+
+```
+....1........
+.........2...
+3............
+.............
+.............
+........4....
+.5...........
+.##.........6
+..##.........
+...##........
+....##...7...
+8....9.......
+
+```
+
+This path has length `9` because it takes a minimum of _nine steps_ to get from galaxy `5` to galaxy `9` (the eight locations marked `#` plus the step onto galaxy `9` itself). Here are some other example shortest path lengths:
+
+- Between galaxy `1` and galaxy `7`: 15
+- Between galaxy `3` and galaxy `6`: 17
+- Between galaxy `8` and galaxy `9`: 5
+
+In this example, after expanding the universe, the sum of the shortest path between all 36 pairs of galaxies is `374`.
+
+Expand the universe, then find the length of the shortest path between every pair of galaxies. _What is the sum of these lengths?_