Merge pull request #156 from romellem/2019/day-18

2019 - Day 18

2019/18/README.md

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+# Answers
+
+| Part 1 | Part 2 |
+|--------|--------|
+| `2946` | `1222` |
+
+## --- Day 18: Many-Worlds Interpretation ---
+
+As you approach Neptune, a planetary security system detects you and activates a giant [tractor beam](https://en.wikipedia.org/wiki/Tractor_beam) on [Triton](https://en.wikipedia.org/wiki/Triton_(moon))! You have no choice but to land.
+
+A scan of the local area reveals only one interesting feature: a massive underground vault. You generate a map of the tunnels (your puzzle input). The tunnels are too narrow to move diagonally.
+
+Only one _entrance_ (marked `@`) is present among the _open passages_ (marked `.`) and _stone walls_ (`#`), but you also detect an assortment of _keys_ (shown as lowercase letters) and _doors_ (shown as uppercase letters). Keys of a given letter open the door of the same letter: `a` opens `A`, `b` opens `B`, and so on. You aren't sure which key you need to disable the tractor beam, so you'll need to _collect all of them_.
+
+For example, suppose you have the following map:
+
+    #########
+    #b.A.@.a#
+    #########
+
+
+Starting from the entrance (`@`), you can only access a large door (`A`) and a key (`a`). Moving toward the door doesn't help you, but you can move `2` steps to collect the key, unlocking `A` in the process:
+
+    #########
+    #b.....@#
+    #########
+
+
+Then, you can move `6` steps to collect the only other key, `b`:
+
+    #########
+    #@......#
+    #########
+
+
+So, collecting every key took a total of _`8`_ steps.
+
+Here is a larger example:
+
+    ########################
+    #f.D.E.e.C.b.A.@.a.B.c.#
+    ######################.#
+    #d.....................#
+    ########################
+
+
+The only reasonable move is to take key `a` and unlock door `A`:
+
+    ########################
+    #f.D.E.e.C.b.....@.B.c.#
+    ######################.#
+    #d.....................#
+    ########################
+
+
+Then, do the same with key `b`:
+
+    ########################
+    #f.D.E.e.C.@.........c.#
+    ######################.#
+    #d.....................#
+    ########################
+
+
+...and the same with key `c`:
+
+    ########################
+    #f.D.E.e.............@.#
+    ######################.#
+    #d.....................#
+    ########################
+
+
+Now, you have a choice between keys `d` and `e`. While key `e` is closer, collecting it now would be slower in the long run than collecting key `d` first, so that's the best choice:
+
+    ########################
+    #f...E.e...............#
+    ######################.#
+    #@.....................#
+    ########################
+
+
+Finally, collect key `e` to unlock door `E`, then collect key `f`, taking a grand total of _`86`_ steps.
+
+Here are a few more examples:
+
+*       ########################
+        #...............b.C.D.f#
+        #.######################
+        #.....@.a.B.c.d.A.e.F.g#
+        ########################
+        
+
+    Shortest path is `132` steps: `b`, `a`, `c`, `d`, `f`, `e`, `g`
+
+*       #################
+        #i.G..c...e..H.p#
+        ########.########
+        #j.A..b...f..D.o#
+        ########@########
+        #k.E..a...g..B.n#
+        ########.########
+        #l.F..d...h..C.m#
+        #################
+        
+
+    Shortest paths are `136` steps;  
+    one is: `a`, `f`, `b`, `j`, `g`, `n`, `h`, `d`, `l`, `o`, `e`, `p`, `c`, `i`, `k`, `m`
+
+*       ########################
+        #@..............ac.GI.b#
+        ###d#e#f################
+        ###A#B#C################
+        ###g#h#i################
+        ########################
+        
+
+    Shortest paths are `81` steps; one is: `a`, `c`, `f`, `i`, `d`, `g`, `b`, `e`, `h`
+
+
+_How many steps is the shortest path that collects all of the keys?_
+
+-----------------
+
+## --- Part Two ---
+
+You arrive at the vault only to discover that there is not one vault, but _four_ - each with its own entrance.
+
+On your map, find the area in the middle that looks like this:
+
+    ...
+    .@.
+    ...
+
+
+Update your map to instead use the correct data:
+
+    @#@
+    ###
+    @#@
+
+
+This change will split your map into four separate sections, each with its own entrance:
+
+<pre><code>#######       #######
+#a.#Cd#       #a.#Cd#
+##...##       ##<b>@#@</b>##
+##.@.##  --&gt;  ##<b>###</b>##
+##...##       ##<b>@#@</b>##
+#cB#Ab#       #cB#Ab#
+#######       #######
+</code></pre>
+
+Because some of the keys are for doors in other vaults, it would take much too long to collect all of the keys by yourself. Instead, you deploy four remote-controlled robots. Each starts at one of the entrances (`@`).
+
+Your goal is still to _collect all of the keys in the fewest steps_, but now, each robot has its own position and can move independently. You can only remotely control a single robot at a time. Collecting a key instantly unlocks any corresponding doors, regardless of the vault in which the key or door is found.
+
+For example, in the map above, the top-left robot first collects key `a`, unlocking door `A` in the bottom-right vault:
+
+    #######
+    #@.#Cd#
+    ##.#@##
+    #######
+    ##@#@##
+    #cB#.b#
+    #######
+
+
+Then, the bottom-right robot collects key `b`, unlocking door `B` in the bottom-left vault:
+
+    #######
+    #@.#Cd#
+    ##.#@##
+    #######
+    ##@#.##
+    #c.#.@#
+    #######
+
+
+Then, the bottom-left robot collects key `c`:
+
+    #######
+    #@.#.d#
+    ##.#@##
+    #######
+    ##.#.##
+    #@.#.@#
+    #######
+
+
+Finally, the top-right robot collects key `d`:
+
+    #######
+    #@.#.@#
+    ##.#.##
+    #######
+    ##.#.##
+    #@.#.@#
+    #######
+
+
+In this example, it only took _`8`_ steps to collect all of the keys.
+
+Sometimes, multiple robots might have keys available, or a robot might have to wait for multiple keys to be collected:
+
+    ###############
+    #d.ABC.#.....a#
+    ######@#@######
+    ###############
+    ######@#@######
+    #b.....#.....c#
+    ###############
+
+
+First, the top-right, bottom-left, and bottom-right robots take turns collecting keys `a`, `b`, and `c`, a total of `6 + 6 + 6 = 18` steps. Then, the top-left robot can access key `d`, spending another `6` steps; collecting all of the keys here takes a minimum of _`24`_ steps.
+
+Here's a more complex example:
+
+    #############
+    #DcBa.#.GhKl#
+    #.###@#@#I###
+    #e#d#####j#k#
+    ###C#@#@###J#
+    #fEbA.#.FgHi#
+    #############
+
+
+*   Top-left robot collects key `a`.
+*   Bottom-left robot collects key `b`.
+*   Top-left robot collects key `c`.
+*   Bottom-left robot collects key `d`.
+*   Top-left robot collects key `e`.
+*   Bottom-left robot collects key `f`.
+*   Bottom-right robot collects key `g`.
+*   Top-right robot collects key `h`.
+*   Bottom-right robot collects key `i`.
+*   Top-right robot collects key `j`.
+*   Bottom-right robot collects key `k`.
+*   Top-right robot collects key `l`.
+
+In the above example, the fewest steps to collect all of the keys is _`32`_.
+
+Here's an example with more choices:
+
+    #############
+    #g#f.D#..h#l#
+    #F###e#E###.#
+    #dCba@#@BcIJ#
+    #############
+    #nK.L@#@G...#
+    #M###N#H###.#
+    #o#m..#i#jk.#
+    #############
+
+
+One solution with the fewest steps is:
+
+*   Top-left robot collects key `e`.
+*   Top-right robot collects key `h`.
+*   Bottom-right robot collects key `i`.
+*   Top-left robot collects key `a`.
+*   Top-left robot collects key `b`.
+*   Top-right robot collects key `c`.
+*   Top-left robot collects key `d`.
+*   Top-left robot collects key `f`.
+*   Top-left robot collects key `g`.
+*   Bottom-right robot collects key `k`.
+*   Bottom-right robot collects key `j`.
+*   Top-right robot collects key `l`.
+*   Bottom-left robot collects key `n`.
+*   Bottom-left robot collects key `m`.
+*   Bottom-left robot collects key `o`.
+
+This example requires at least _`72`_ steps to collect all keys.
+
+After updating your map and using the remote-controlled robots, _what is the fewest steps necessary to collect all of the keys?_