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170 lines
4.0 KiB
Markdown
170 lines
4.0 KiB
Markdown
https://adventofcode.com/2021/day/13
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## \--- Day 13: Transparent Origami ---
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You reach another volcanically active part of the cave. It would be nice if
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you could do some kind of thermal imaging so you could tell ahead of time
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which caves are too hot to safely enter.
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Fortunately, the submarine seems to be equipped with a thermal camera! When
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you activate it, you are greeted with:
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[code]
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Congratulations on your purchase! To activate this infrared thermal imaging
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camera system, please enter the code found on page 1 of the manual.
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[/code]
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Apparently, the Elves have never used this feature. To your surprise, you
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manage to find the manual; as you go to open it, page 1 falls out. It's a
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large sheet of [transparent
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paper](https://en.wikipedia.org/wiki/Transparency_\(projection\))! The
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transparent paper is marked with random dots and includes instructions on how
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to fold it up (your puzzle input). For example:
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[code]
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6,10
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0,14
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9,10
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0,3
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10,4
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4,11
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6,0
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6,12
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4,1
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0,13
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10,12
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3,4
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3,0
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8,4
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1,10
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2,14
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8,10
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9,0
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fold along y=7
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fold along x=5
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[/code]
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The first section is a list of dots on the transparent paper. `0,0` represents
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the top-left coordinate. The first value, `x`, increases to the right. The
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second value, `y`, increases downward. So, the coordinate `3,0` is to the
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right of `0,0`, and the coordinate `0,7` is below `0,0`. The coordinates in
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this example form the following pattern, where `#` is a dot on the paper and
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`.` is an empty, unmarked position:
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[code]
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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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......#...#
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#..........
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#.#........
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[/code]
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Then, there is a list of _fold instructions_. Each instruction indicates a
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line on the transparent paper and wants you to fold the paper _up_ (for
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horizontal `y=...` lines) or _left_ (for vertical `x=...` lines). In this
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example, the first fold instruction is `fold along y=7`, which designates the
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line formed by all of the positions where `y` is `7` (marked here with `-`):
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[code]
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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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......#...#
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#..........
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#.#........
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[/code]
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Because this is a horizontal line, fold the bottom half _up_. Some of the dots
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might end up overlapping after the fold is complete, but dots will never
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appear exactly on a fold line. The result of doing this fold looks like this:
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[code]
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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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[/code]
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Now, only `17` dots are visible.
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Notice, for example, the two dots in the bottom left corner before the
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transparent paper is folded; after the fold is complete, those dots appear in
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the top left corner (at `0,0` and `0,1`). Because the paper is transparent,
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the dot just below them in the result (at `0,3`) remains visible, as it can be
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seen through the transparent paper.
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Also notice that some dots can end up _overlapping_ ; in this case, the dots
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merge together and become a single dot.
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The second fold instruction is `fold along x=5`, which indicates this line:
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[code]
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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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[/code]
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Because this is a vertical line, fold _left_ :
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[code]
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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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[/code]
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The instructions made a square!
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The transparent paper is pretty big, so for now, focus on just completing the
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first fold. After the first fold in the example above, `_17_` dots are visible
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- dots that end up overlapping after the fold is completed count as a single
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dot.
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_How many dots are visible after completing just the first fold instruction on
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your transparent paper?_
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