Added Solution for 2021 day 14

2021/day14_extended_polymerization/challenge.txt

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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.
+
+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.
+
+For example:
+
+```
+NNCB
+
+CH -> B
+HH -> N
+CB -> H
+NH -> C
+HB -> C
+HC -> B
+HN -> C
+NN -> C
+BH -> H
+NC -> B
+NB -> B
+BN -> B
+BB -> N
+BC -> B
+CC -> N
+CN -> C
+
+```
+
+The first line is the *polymer template* - this is the starting point of the process.
+
+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.
+
+So, starting with the polymer template `NNCB`, the first step simultaneously considers all three pairs:
+
+* The first pair (`NN`) matches the rule `NN -> C`, so element `*C*` is inserted between the first `N` and the second `N`.
+* The second pair (`NC`) matches the rule `NC -> B`, so element `*B*` is inserted between the `N` and the `C`.
+* The third pair (`CB`) matches the rule `CB -> H`, so element `*H*` is inserted between the `C` and the `B`.
+
+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.
+
+After the first step of this process, the polymer becomes `N*C*N*B*C*H*B`.
+
+Here are the results of a few steps using the above rules:
+
+```
+Template:     NNCB
+After step 1: NCNBCHB
+After step 2: NBCCNBBBCBHCB
+After step 3: NBBBCNCCNBBNBNBBCHBHHBCHB
+After step 4: NBBNBNBBCCNBCNCCNBBNBBNBBBNBBNBBCBHCBHHNHCBBCBHCB
+
+```
+
+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*`.
+
+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?*
+
+Your puzzle answer was `2408`.
+
+\--- Part Two ---
+----------
+
+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.
+
+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*`.
+
+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?*
+
+Your puzzle answer was `2651311098752`.
+
+Both parts of this puzzle are complete! They provide two gold stars: \*\*
+
+At this point, you should [return to your Advent calendar](/2021) and try another puzzle.
+
+If you still want to see it, you can [get your puzzle input](14/input).