120 lines
3.6 KiB
Org Mode
120 lines
3.6 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=
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=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=
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= 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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Your puzzle answer was =860=.
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** --- Part Two ---
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It turns out that this circuit is very timing-sensitive; you actually
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need to /minimize the signal delay/.
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To do this, calculate the /number of steps/ each wire takes to reach
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each intersection; choose the intersection where the /sum of both wires'
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steps/ is lowest. If a wire visits a position on the grid multiple
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times, use the steps value from the /first/ time it visits that position
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when calculating the total value of a specific intersection.
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The number of steps a wire takes is the total number of grid squares the
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wire has entered to get to that location, including the intersection
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being considered. Again consider the example from above:
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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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In the above example, the intersection closest to the central port is
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reached after =8+5+5+2 = 20= steps by the first wire and =7+6+4+3 = 20=
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steps by the second wire for a total of =20+20 = 40= steps.
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However, the top-right intersection is better: the first wire takes only
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=8+5+2 = 15= and the second wire takes only =7+6+2 = 15=, a total of
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=15+15 = 30= steps.
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Here are the best steps for the extra examples from above:
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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=
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= =610= steps
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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=
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= =410= steps
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/What is the fewest combined steps the wires must take to reach an
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intersection?/
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Your puzzle answer was =9238=.
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Both parts of this puzzle are complete! They provide two gold stars: **
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