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70 lines
2.0 KiB
Markdown
70 lines
2.0 KiB
Markdown
3 years ago
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https://adventofcode.com/2021/day/5
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## \--- Day 5: Hydrothermal Venture ---
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You come across a field of [hydrothermal
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vents](https://en.wikipedia.org/wiki/Hydrothermal_vent) on the ocean floor!
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These vents constantly produce large, opaque clouds, so it would be best to
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avoid them if possible.
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They tend to form in _lines_ ; the submarine helpfully produces a list of
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nearby lines of vents (your puzzle input) for you to review. For example:
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[code]
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0,9 -> 5,9
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8,0 -> 0,8
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9,4 -> 3,4
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2,2 -> 2,1
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7,0 -> 7,4
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6,4 -> 2,0
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0,9 -> 2,9
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3,4 -> 1,4
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0,0 -> 8,8
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5,5 -> 8,2
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[/code]
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Each line of vents is given as a line segment in the format `x1,y1 -> x2,y2`
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where `x1`,`y1` are the coordinates of one end the line segment and `x2`,`y2`
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are the coordinates of the other end. These line segments include the points
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at both ends. In other words:
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* An entry like `1,1 -> 1,3` covers points `1,1`, `1,2`, and `1,3`.
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* An entry like `9,7 -> 7,7` covers points `9,7`, `8,7`, and `7,7`.
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For now, _only consider horizontal and vertical lines_ : lines where either
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`x1 = x2` or `y1 = y2`.
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So, the horizontal and vertical lines from the above list would produce the
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following diagram:
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[code]
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.......1..
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..1....1..
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..1....1..
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.......1..
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.112111211
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..........
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..........
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..........
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..........
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222111....
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[/code]
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In this diagram, the top left corner is `0,0` and the bottom right corner is
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`9,9`. Each position is shown as _the number of lines which cover that point_
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or `.` if no line covers that point. The top-left pair of `1`s, for example,
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comes from `2,2 -> 2,1`; the very bottom row is formed by the overlapping
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lines `0,9 -> 5,9` and `0,9 -> 2,9`.
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To avoid the most dangerous areas, you need to determine _the number of points
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where at least two lines overlap_. In the above example, this is anywhere in
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the diagram with a `2` or larger - a total of `_5_` points.
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Consider only horizontal and vertical lines. _At how many points do at least
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two lines overlap?_
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