2017 Day 07 Complete

2017/day07/problem

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+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.
+
+References
+
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