69 lines
3.4 KiB
Markdown
69 lines
3.4 KiB
Markdown
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# 2021 Day 14: Extended Polymerization
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Copyright (c) Eric Wastl
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#### [Direct Link](https://adventofcode.com/2021/day/14)
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## Part 1
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The incredible pressures at this depth are starting to put a strain on your submarine. The submarine has [polymerization](https://en.wikipedia.org/wiki/Polymerization) 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.
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The submarine manual contains instructions for finding the optimal polymer formula; specifically, it offers a **polymer template** and a list of **pair insertion** rules (your puzzle input). You just need to work out what polymer would result after repeating the pair insertion process a few times.
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For example:
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```
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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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```
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The first line is the **polymer template** - this is the starting point of the process.
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The following section defines the **pair insertion** rules. A rule like `AB -> C` means that when elements `A` and `B` are immediately adjacent, element `C` should be inserted between them. These insertions all happen simultaneously.
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So, starting with the polymer template `NNCB`, the first step simultaneously considers all three pairs:
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- The first pair (`NN`) matches the rule `NN` -> `C`, so element `C` is inserted between the first `N` and the second `N`.
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- The second pair (`NC`) matches the rule `NC` -> `B`, so element `B` is inserted between the `N` and the `C`.
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- The third pair (`CB`) matches the rule `CB -> H`, so element `H is inserted between the `C` and the `B`.
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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.
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After the first step of this process, the polymer becomes `NCNBCHB`.
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Here are the results of a few steps using the above rules:
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```
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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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```
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This polymer grows quickly. After step 5, it has length 97; After step 10, it has length 3073. After step 10, `B` occurs 1749 times, `C` occurs 298 times, `H` occurs 161 times, and `N` occurs 865 times; taking the quantity of the most common element (B, 1749) and subtracting the quantity of the least common element (`H`, 161) produces `1749 - 161 = 1588`.
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Apply 10 steps of pair insertion to the polymer template and find the most and least common elements in the result. **What do you get if you take the quantity of the most common element and subtract the quantity of the least common element?**
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## Part 2
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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 **40 steps** should do it.
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In the above example, the most common element is `B` (occurring `2192039569602` times) and the least common element is `H` (occurring `3849876073` times); subtracting these produces **`2188189693529`**.
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Apply **40** steps of pair insertion to the polymer template and find the most and least common elements in the result. **What do you get if you take the quantity of the most common element and subtract the quantity of the least common element?**
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