95 lines
3.8 KiB
Markdown
95 lines
3.8 KiB
Markdown
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# Day 8
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You're still riding a camel across Desert Island when you spot a sandstorm quickly approaching.
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When you turn to warn the Elf, she disappears before your eyes! To be fair, she had just finished warning you about ghosts a few minutes ago.
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One of the camel's pouches is labeled "maps" - sure enough, it's full of documents (your puzzle input) about how to navigate the desert.
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At least, you're pretty sure that's what they are; one of the documents contains a list of left/right instructions,
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and the rest of the documents seem to describe some kind of network of labeled nodes.
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It seems like you're meant to use the left/right instructions to navigate the network.
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Perhaps if you have the camel follow the same instructions, you can escape the haunted wasteland!
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After examining the maps for a bit, two nodes stick out: AAA and ZZZ.
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You feel like AAA is where you are now, and you have to follow the left/right instructions until you reach ZZZ.
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This format defines each node of the network individually. For example:
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```
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RL
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AAA = (BBB, CCC)
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BBB = (DDD, EEE)
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CCC = (ZZZ, GGG)
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DDD = (DDD, DDD)
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EEE = (EEE, EEE)
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GGG = (GGG, GGG)
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ZZZ = (ZZZ, ZZZ)
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```
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Starting with AAA, you need to look up the next element based on the next left/right instruction in your input.
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In this example, start with AAA and go right (R) by choosing the right element of AAA, CCC.
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Then, L means to choose the left element of CCC, ZZZ. By following the left/right instructions, you reach ZZZ in 2 steps.
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Of course, you might not find ZZZ right away. If you run out of left/right instructions,
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repeat the whole sequence of instructions as necessary: RL really means RLRLRLRLRLRLRLRL... and so on.
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For example, here is a situation that takes 6 steps to reach ZZZ:
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```
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LLR
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AAA = (BBB, BBB)
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BBB = (AAA, ZZZ)
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ZZZ = (ZZZ, ZZZ)
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```
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Starting at AAA, follow the left/right instructions. How many steps are required to reach ZZZ?
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## Part Two
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The sandstorm is upon you and you aren't any closer to escaping the wasteland.
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You had the camel follow the instructions, but you've barely left your starting position.
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It's going to take significantly more steps to escape!
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What if the map isn't for people - what if the map is for ghosts? Are ghosts even bound by the laws of spacetime? Only one way to find out.
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After examining the maps a bit longer, your attention is drawn to a curious fact:
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the number of nodes with names ending in A is equal to the number ending in Z!
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If you were a ghost, you'd probably just start at every node that ends with A
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and follow all of the paths at the same time until they all simultaneously end up at nodes that end with Z.
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For example:
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```
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LR
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11A = (11B, XXX)
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11B = (XXX, 11Z)
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11Z = (11B, XXX)
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22A = (22B, XXX)
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22B = (22C, 22C)
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22C = (22Z, 22Z)
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22Z = (22B, 22B)
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XXX = (XXX, XXX)
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```
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Here, there are two starting nodes, 11A and 22A (because they both end with A).
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As you follow each left/right instruction, use that instruction to simultaneously navigate away from both nodes you're currently on.
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Repeat this process until all of the nodes you're currently on end with Z.
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(If only some of the nodes you're on end with Z, they act like any other node and you continue as normal.)
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In this example, you would proceed as follows:
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```
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Step 0: You are at 11A and 22A.
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Step 1: You choose all of the left paths, leading you to 11B and 22B.
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Step 2: You choose all of the right paths, leading you to 11Z and 22C.
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Step 3: You choose all of the left paths, leading you to 11B and 22Z.
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Step 4: You choose all of the right paths, leading you to 11Z and 22B.
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Step 5: You choose all of the left paths, leading you to 11B and 22C.
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Step 6: You choose all of the right paths, leading you to 11Z and 22Z.
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```
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So, in this example, you end up entirely on nodes that end in Z after 6 steps.
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Simultaneously start on every node that ends with A. How many steps does it take before you're only on nodes that end with Z?
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