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<title>Day 14 - Advent of Code 2021</title>
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</head><div id="readability-page-1" class="page"><article><h2>--- Day 14: Extended Polymerization ---</h2><p>The incredible pressures at this depth are starting to put a strain on your submarine. The submarine has <a href="https://en.wikipedia.org/wiki/Polymerization" target="_blank">polymerization</a> equipment that would produce suitable materials to reinforce the submarine, and the nearby volcanically-active caves should even have the necessary input elements in sufficient quantities.</p>
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<p>The submarine manual contains <span title="HO
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HO -> OH">instructions</span> for finding the optimal polymer formula; specifically, it offers a <em>polymer template</em> and a list of <em>pair insertion</em> rules (your puzzle input). You just need to work out what polymer would result after repeating the pair insertion process a few times.</p>
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<p>For example:</p>
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<pre><code>NNCB
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CH -> B
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HH -> N
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CB -> H
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NH -> C
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HB -> C
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HC -> B
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HN -> C
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NN -> C
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BH -> H
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NC -> B
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NB -> B
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BN -> B
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BB -> N
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BC -> B
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CC -> N
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CN -> C
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</code></pre>
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<p>The first line is the <em>polymer template</em> - this is the starting point of the process.</p>
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<p>The following section defines the <em>pair insertion</em> rules. A rule like <code>AB -> C</code> means that when elements <code>A</code> and <code>B</code> are immediately adjacent, element <code>C</code> should be inserted between them. These insertions all happen simultaneously.</p>
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<p>So, starting with the polymer template <code>NNCB</code>, the first step simultaneously considers all three pairs:</p>
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<ul>
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<li>The first pair (<code>NN</code>) matches the rule <code>NN -> C</code>, so element <code><em>C</em></code> is inserted between the first <code>N</code> and the second <code>N</code>.</li>
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<li>The second pair (<code>NC</code>) matches the rule <code>NC -> B</code>, so element <code><em>B</em></code> is inserted between the <code>N</code> and the <code>C</code>.</li>
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<li>The third pair (<code>CB</code>) matches the rule <code>CB -> H</code>, so element <code><em>H</em></code> is inserted between the <code>C</code> and the <code>B</code>.</li>
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</ul>
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<p>Note that these pairs overlap: the second element of one pair is the first element of the next pair. Also, because all pairs are considered simultaneously, inserted elements are not considered to be part of a pair until the next step.</p>
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<p>After the first step of this process, the polymer becomes <code>N<em>C</em>N<em>B</em>C<em>H</em>B</code>.</p>
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<p>Here are the results of a few steps using the above rules:</p>
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<pre><code>Template: NNCB
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After step 1: NCNBCHB
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After step 2: NBCCNBBBCBHCB
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After step 3: NBBBCNCCNBBNBNBBCHBHHBCHB
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After step 4: NBBNBNBBCCNBCNCCNBBNBBNBBBNBBNBBCBHCBHHNHCBBCBHCB
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</code></pre>
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<p>This polymer grows quickly. After step 5, it has length 97; After step 10, it has length 3073. After step 10, <code>B</code> occurs 1749 times, <code>C</code> occurs 298 times, <code>H</code> occurs 161 times, and <code>N</code> occurs 865 times; taking the quantity of the most common element (<code>B</code>, 1749) and subtracting the quantity of the least common element (<code>H</code>, 161) produces <code>1749 - 161 = <em>1588</em></code>.</p>
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<p>Apply 10 steps of pair insertion to the polymer template and find the most and least common elements in the result. <em>What do you get if you take the quantity of the most common element and subtract the quantity of the least common element?</em></p>
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</article><p>Your puzzle answer was <code>2360</code>.</p><article><h2 id="part2">--- Part Two ---</h2><p>The resulting polymer isn't nearly strong enough to reinforce the submarine. You'll need to run more steps of the pair insertion process; a total of <em>40 steps</em> should do it.</p>
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<p>In the above example, the most common element is <code>B</code> (occurring <code>2192039569602</code> times) and the least common element is <code>H</code> (occurring <code>3849876073</code> times); subtracting these produces <code><em>2188189693529</em></code>.</p>
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<p>Apply <em>40</em> steps of pair insertion to the polymer template and find the most and least common elements in the result. <em>What do you get if you take the quantity of the most common element and subtract the quantity of the least common element?</em></p>
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</article><p>Your puzzle answer was <code>2967977072188</code>.</p></div> |