79 lines
2.4 KiB
Org Mode
79 lines
2.4 KiB
Org Mode
** --- Day 6: Universal Orbit Map ---
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You've landed at the Universal Orbit Map facility on Mercury. Because
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navigation in space often involves transferring between orbits, the
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orbit maps here are useful for finding efficient routes between, for
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example, you and Santa. You download a map of the local orbits (your
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puzzle input).
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Except for the universal Center of Mass (=COM=), every object in space
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is in orbit around exactly one other object. An
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[[https://en.wikipedia.org/wiki/Orbit][orbit]] looks roughly like this:
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#+BEGIN_EXAMPLE
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\
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\
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AAA--> o o <--BBB
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/
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/
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#+END_EXAMPLE
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In this diagram, the object =BBB= is in orbit around =AAA=. The path
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that =BBB= takes around =AAA= (drawn with lines) is only partly shown.
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In the map data, this orbital relationship is written =AAA)BBB=, which
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means "=BBB= is in orbit around =AAA=".
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Before you use your map data to plot a course, you need to make sure it
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wasn't corrupted during the download. To verify maps, the Universal
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Orbit Map facility uses /orbit count checksums/ - the total number of
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/direct orbits/ (like the one shown above) and /indirect orbits/.
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Whenever =A= orbits =B= and =B= orbits =C=, then =A= /indirectly orbits/
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=C=. This chain can be any number of objects long: if =A= orbits =B=,
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=B= orbits =C=, and =C= orbits =D=, then =A= indirectly orbits =D=.
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For example, suppose you have the following map:
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#+BEGIN_EXAMPLE
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COM)B
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B)C
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C)D
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D)E
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E)F
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B)G
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G)H
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D)I
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E)J
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J)K
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K)L
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#+END_EXAMPLE
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Visually, the above map of orbits looks like this:
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#+BEGIN_EXAMPLE
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G - H J - K - L
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/ /
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COM - B - C - D - E - F
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\
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I
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#+END_EXAMPLE
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In this visual representation, when two objects are connected by a line,
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the one on the right directly orbits the one on the left.
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Here, we can count the total number of orbits as follows:
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- =D= directly orbits =C= and indirectly orbits =B= and =COM=, a total
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of =3= orbits.
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- =L= directly orbits =K= and indirectly orbits =J=, =E=, =D=, =C=, =B=,
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and =COM=, a total of =7= orbits.
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- =COM= orbits nothing.
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The total number of direct and indirect orbits in this example is =42=.
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/What is the total number of direct and indirect orbits/ in your map
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data?
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