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- Solve day 11 puzzle
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# [Day 11: Cosmic Expansion](https://adventofcode.com/2023/day/11) | ||
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## Part One | ||
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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. | ||
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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. | ||
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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 single giant **image** (your puzzle input). The image includes **empty space** (`.`) and **galaxies** (`#`). For example: | ||
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``` | ||
...#...... | ||
.......#.. | ||
#......... | ||
.......... | ||
......#... | ||
.#........ | ||
.........# | ||
.......... | ||
.......#.. | ||
#...#..... | ||
``` | ||
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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. | ||
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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. | ||
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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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These rows and columns need to be **twice as big**; the result of cosmic expansion therefore looks like this: | ||
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``` | ||
....#........ | ||
.........#... | ||
#............ | ||
............. | ||
............. | ||
........#.... | ||
.#........... | ||
............# | ||
............. | ||
............. | ||
.........#... | ||
#....#....... | ||
``` | ||
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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: | ||
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``` | ||
....1........ | ||
.........2... | ||
3............ | ||
............. | ||
............. | ||
........4.... | ||
.5........... | ||
............6 | ||
............. | ||
............. | ||
.........7... | ||
8....9....... | ||
``` | ||
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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.) | ||
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For example, here is one of the shortest paths between galaxies `5` and `9`: | ||
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``` | ||
....1........ | ||
.........2... | ||
3............ | ||
............. | ||
............. | ||
........4.... | ||
.5........... | ||
.##.........6 | ||
..##......... | ||
...##........ | ||
....##...7... | ||
8....9....... | ||
``` | ||
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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: | ||
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- Between galaxy `1` and galaxy `7`: 15 | ||
- Between galaxy `3` and galaxy `6`: 17 | ||
- Between galaxy `8` and galaxy `9`: 5 | ||
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In this example, after expanding the universe, the sum of the shortest 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 every pair of galaxies. **What is the sum of these lengths?** | ||
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Your puzzle answer was `10313550`. | ||
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**The first half of this puzzle is complete! It provides one gold star:** π | ||
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## Part Two | ||
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The galaxies are much **older** (and thus much **farther apart**) than the researcher initially estimated. | ||
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Now, instead of the expansion you did before, make each empty row or column **one million times** larger. That is, each empty row should be replaced with `1000000` empty rows, and each empty column should be replaced with `1000000` empty columns. | ||
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(In the example above, if each empty row or column were merely `10` times larger, the sum of the shortest paths between every pair of galaxies would be **`1030`**. If each empty row or column were merely `100` times larger, the sum of the shortest paths between every pair of galaxies would be **`8410`**. 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 these new rules, then find the length of the shortest path between every pair of galaxies. **What is the sum of these lengths?** | ||
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Your puzzle answer was `611998089572`. | ||
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**Both parts of this puzzle are complete! They provide two gold stars:** ππ |
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# frozen_string_literal: true | ||
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require_relative "part1" | ||
require_relative "part2" | ||
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module AdventOfCode | ||
module Puzzles2023 | ||
## | ||
# {include:file:lib/puzzles/2023/day11/README.md} | ||
module Day11 | ||
end | ||
end | ||
end |
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