67 lines
2.0 KiB
Org Mode
67 lines
2.0 KiB
Org Mode
** --- Day 3: Crossed Wires ---
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The gravity assist was successful, and you're well on your way to the
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Venus refuelling station. During the rush back on Earth, the fuel
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management system wasn't completely installed, so that's next on the
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priority list.
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Opening the front panel reveals a jumble of wires. Specifically, /two
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wires/ are connected to a central port and extend outward on a grid. You
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trace the path each wire takes as it leaves the central port, one wire
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per line of text (your puzzle input).
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The wires twist and turn, but the two wires occasionally cross paths. To
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fix the circuit, you need to /find the intersection point closest to the
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central port/. Because the wires are on a grid, use the
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[[https://en.wikipedia.org/wiki/Taxicab_geometry][Manhattan distance]]
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for this measurement. While the wires do technically cross right at the
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central port where they both start, this point does not count, nor does
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a wire count as crossing with itself.
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For example, if the first wire's path is =R8,U5,L5,D3=, then starting
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from the central port (=o=), it goes right =8=, up =5=, left =5=, and
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finally down =3=:
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#+BEGIN_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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.o-------+.
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...........
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#+END_EXAMPLE
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Then, if the second wire's path is =U7,R6,D4,L4=, it goes up =7=, right
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=6=, down =4=, and left =4=:
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#+BEGIN_EXAMPLE
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...........
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.+-----+...
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.|.....|...
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.|..+--X-+.
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.|..|..|.|.
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.|.-X--+.|.
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.|..|....|.
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.|.......|.
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.o-------+.
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...........
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#+END_EXAMPLE
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These wires cross at two locations (marked =X=), but the lower-left one
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is closer to the central port: its distance is =3 + 3 = 6=.
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Here are a few more examples:
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- =R75,D30,R83,U83,L12,D49,R71,U7,L72=
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=U62,R66,U55,R34,D71,R55,D58,R83= =distance =159=
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- =R98,U47,R26,D63,R33,U87,L62,D20,R33,U53,R51=
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=U98,R91,D20,R16,D67,R40,U7,R15,U6,R7= =distance =135=
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/What is the Manhattan distance/ from the central port to the closest
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intersection?
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To begin, [[file:3/input][get your puzzle input]].
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