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alexchao26
94 lines
2.9 KiB
Plaintext
94 lines
2.9 KiB
Plaintext
--- Day 18: Many-Worlds Interpretation ---
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As you approach Neptune, a planetary security system detects you and activates a giant tractor beam on Triton! You have no choice but to land.
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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.
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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.
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For example, suppose you have the following map:
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#########
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#b.A.@.a#
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#########
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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:
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#########
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#b.....@#
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#########
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Then, you can move 6 steps to collect the only other key, b:
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#########
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#@......#
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#########
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So, collecting every key took a total of 8 steps.
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Here is a larger example:
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########################
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#f.D.E.e.C.b.A.@.a.B.c.#
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######################.#
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#d.....................#
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########################
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The only reasonable move is to take key a and unlock door A:
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########################
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#f.D.E.e.C.b.....@.B.c.#
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######################.#
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#d.....................#
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########################
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Then, do the same with key b:
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########################
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#f.D.E.e.C.@.........c.#
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######################.#
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#d.....................#
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########################
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...and the same with key c:
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########################
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#f.D.E.e.............@.#
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######################.#
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#d.....................#
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########################
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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:
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########################
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#f...E.e...............#
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######################.#
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#@.....................#
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########################
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Finally, collect key e to unlock door E, then collect key f, taking a grand total of 86 steps.
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Here are a few more examples:
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########################
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#...............b.C.D.f#
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#.######################
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#.....@.a.B.c.d.A.e.F.g#
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########################
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Shortest path is 132 steps: b, a, c, d, f, e, g
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#################
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#i.G..c...e..H.p#
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########.########
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#j.A..b...f..D.o#
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########@########
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#k.E..a...g..B.n#
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########.########
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#l.F..d...h..C.m#
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#################
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Shortest paths are 136 steps;
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one is: a, f, b, j, g, n, h, d, l, o, e, p, c, i, k, m
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########################
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#@..............ac.GI.b#
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###d#e#f################
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###A#B#C################
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###g#h#i################
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########################
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Shortest paths are 81 steps; one is: a, c, f, i, d, g, b, e, h
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How many steps is the shortest path that collects all of the keys?
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