Jake Pullen
53 lines
5.1 KiB
Markdown
53 lines
5.1 KiB
Markdown
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<article class="day-desc"><h2>--- Day 8: Haunted Wasteland ---</h2><p>You're still riding a camel across Desert Island when you spot a sandstorm quickly approaching. When you turn to warn the Elf, she disappears before your eyes! To be fair, she had just finished warning you about <em>ghosts</em> a few minutes ago.</p>
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<p>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. At least, you're pretty sure that's what they are; one of the documents contains a list of left/right instructions, and the rest of the documents seem to describe some kind of <em>network</em> of labeled nodes.</p>
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<p>It seems like you're meant to use the <em>left/right</em> instructions to <em>navigate the network</em>. Perhaps if you have the camel follow the same instructions, you can escape the haunted wasteland!</p>
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<p>After examining the maps for a bit, two nodes stick out: <code>AAA</code> and <code>ZZZ</code>. You feel like <code>AAA</code> is where you are now, and you have to follow the left/right instructions until you reach <code>ZZZ</code>.</p>
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<p>This format defines each <em>node</em> of the network individually. For example:</p>
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<pre><code>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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</code></pre>
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<p>Starting with <code>AAA</code>, you need to <em>look up the next element</em> based on the next left/right instruction in your input. In this example, start with <code>AAA</code> and go <em>right</em> (<code>R</code>) by choosing the right element of <code>AAA</code>, <code><em>CCC</em></code>. Then, <code>L</code> means to choose the <em>left</em> element of <code>CCC</code>, <code><em>ZZZ</em></code>. By following the left/right instructions, you reach <code>ZZZ</code> in <code><em>2</em></code> steps.</p>
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<p>Of course, you might not find <code>ZZZ</code> right away. If you run out of left/right instructions, repeat the whole sequence of instructions as necessary: <code>RL</code> really means <code>RLRLRLRLRLRLRLRL...</code> and so on. For example, here is a situation that takes <code><em>6</em></code> steps to reach <code>ZZZ</code>:</p>
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<pre><code>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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</code></pre>
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<p>Starting at <code>AAA</code>, follow the left/right instructions. <em>How many steps are required to reach <code>ZZZ</code>?</em></p>
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<article class="day-desc"><h2 id="part2">--- Part Two ---</h2><p>The <span title="Duhduhduhduhduh! Dah, duhduhduhduhduh!">sandstorm</span> is upon you and you aren't any closer to escaping the wasteland. You had the camel follow the instructions, but you've barely left your starting position. It's going to take <em>significantly more steps</em> to escape!</p>
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<p>What if the map isn't for people - what if the map is for <em>ghosts</em>? Are ghosts even bound by the laws of spacetime? Only one way to find out.</p>
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<p>After examining the maps a bit longer, your attention is drawn to a curious fact: the number of nodes with names ending in <code>A</code> is equal to the number ending in <code>Z</code>! If you were a ghost, you'd probably just <em>start at every node that ends with <code>A</code></em> and follow all of the paths at the same time until they all simultaneously end up at nodes that end with <code>Z</code>.</p>
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<p>For example:</p>
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<pre><code>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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</code></pre>
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<p>Here, there are two starting nodes, <code>11A</code> and <code>22A</code> (because they both end with <code>A</code>). As you follow each left/right instruction, use that instruction to <em>simultaneously</em> navigate away from both nodes you're currently on. Repeat this process until <em>all</em> of the nodes you're currently on end with <code>Z</code>. (If only some of the nodes you're on end with <code>Z</code>, they act like any other node and you continue as normal.) In this example, you would proceed as follows:</p>
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<ul>
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<li>Step 0: You are at <code>11A</code> and <code>22A</code>.</li>
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<li>Step 1: You choose all of the <em>left</em> paths, leading you to <code>11B</code> and <code>22B</code>.</li>
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<li>Step 2: You choose all of the <em>right</em> paths, leading you to <code><em>11Z</em></code> and <code>22C</code>.</li>
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<li>Step 3: You choose all of the <em>left</em> paths, leading you to <code>11B</code> and <code><em>22Z</em></code>.</li>
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<li>Step 4: You choose all of the <em>right</em> paths, leading you to <code><em>11Z</em></code> and <code>22B</code>.</li>
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<li>Step 5: You choose all of the <em>left</em> paths, leading you to <code>11B</code> and <code>22C</code>.</li>
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<li>Step 6: You choose all of the <em>right</em> paths, leading you to <code><em>11Z</em></code> and <code><em>22Z</em></code>.</li>
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</ul>
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<p>So, in this example, you end up entirely on nodes that end in <code>Z</code> after <code><em>6</em></code> steps.</p>
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<p>Simultaneously start on every node that ends with <code>A</code>. <em>How many steps does it take before you're only on nodes that end with <code>Z</code>?</em></p> |