Advent of Code

--- Day 7: Recursive Circus ---

   Wandering further through the circuits of the computer, you come upon a tower
   of programs that have gotten themselves into a bit of trouble. A recursive
   algorithm has gotten out of hand, and now they're balanced precariously in a
   large tower.

   One program at the bottom supports the entire tower. It's holding a large
   disc, and on the disc are balanced several more sub-towers. At the bottom of
   these sub-towers, standing on the bottom disc, are other programs, each
   holding their own disc, and so on. At the very tops of these
   sub-sub-sub-...-towers, many programs stand simply keeping the disc below
   them balanced but with no disc of their own.

   You offer to help, but first you need to understand the structure of these
   towers. You ask each program to yell out their name, their weight, and (if
   they're holding a disc) the names of the programs immediately above them
   balancing on that disc. You write this information down (your puzzle input).
   Unfortunately, in their panic, they don't do this in an orderly fashion; by
   the time you're done, you're not sure which program gave which information.

   For example, if your list is the following:

 pbga (66)
 xhth (57)
 ebii (61)
 havc (66)
 ktlj (57)
 fwft (72) -> ktlj, cntj, xhth
 qoyq (66)
 padx (45) -> pbga, havc, qoyq
 tknk (41) -> ugml, padx, fwft
 jptl (61)
 ugml (68) -> gyxo, ebii, jptl
 gyxo (61)
 cntj (57)

   ...then you would be able to recreate the structure of the towers that looks
   like this:

                 gyxo
               /
          ugml - ebii
        /      \
       |         jptl
       |
       |         pbga
      /        /
 tknk --- padx - havc
      \        \
       |         qoyq
       |
       |         ktlj
        \      /
          fwft - cntj
               \
                 xhth

   In this example, tknk is at the bottom of the tower (the bottom program), and
   is holding up ugml, padx, and fwft. Those programs are, in turn, holding up
   other programs; in this example, none of those programs are holding up any
   other programs, and are all the tops of their own towers. (The actual tower
   balancing in front of you is much larger.)

   Before you're ready to help them, you need to make sure your information is
   correct. What is the name of the bottom program?

   Your puzzle answer was ___________.

--- Part Two ---

   The programs explain the situation: they can't get down. Rather, they could
   get down, if they weren't expending all of their energy trying to keep the
   tower balanced. Apparently, one program has the wrong weight, and until it's
   fixed, they're stuck here.

   For any program holding a disc, each program standing on that disc forms a
   sub-tower. Each of those sub-towers are supposed to be the same weight, or
   the disc itself isn't balanced. The weight of a tower is the sum of the
   weights of the programs in that tower.

   In the example above, this means that for ugml's disc to be balanced, gyxo,
   ebii, and jptl must all have the same weight, and they do: 61.

   However, for tknk to be balanced, each of the programs standing on its disc
   and all programs above it must each match. This means that the following sums
   must all be the same:

     * ugml + (gyxo + ebii + jptl) = 68 + (61 + 61 + 61) = 251
     * padx + (pbga + havc + qoyq) = 45 + (66 + 66 + 66) = 243
     * fwft + (ktlj + cntj + xhth) = 72 + (57 + 57 + 57) = 243

   As you can see, tknk's disc is unbalanced: ugml's stack is heavier than the
   other two. Even though the nodes above ugml are balanced, ugml itself is too
   heavy: it needs to be 8 units lighter for its stack to weigh 243 and keep the
   towers balanced. If this change were made, its weight would be 60.

   Given that exactly one program is the wrong weight, what would its weight
   need to be to balance the entire tower?

   Your puzzle answer was ______.

   Both parts of this puzzle are complete! They provide two gold stars: **

   At this point, you should return to your advent calendar and try another
   puzzle.

   If you still want to see it, you can get your puzzle input.

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