51 lines
1.9 KiB
Markdown
51 lines
1.9 KiB
Markdown
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---
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id: 5900f49a1000cf542c50ffac
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title: 'Problem 300: Protein folding'
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challengeType: 5
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forumTopicId: 301954
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dashedName: problem-300-protein-folding
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---
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# --description--
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In a very simplified form, we can consider proteins as strings consisting of hydrophobic (H) and polar (P) elements, e.g. HHPPHHHPHHPH.
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For this problem, the orientation of a protein is important; e.g. HPP is considered distinct from PPH. Thus, there are 2n distinct proteins consisting of n elements.
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When one encounters these strings in nature, they are always folded in such a way that the number of H-H contact points is as large as possible, since this is energetically advantageous. As a result, the H-elements tend to accumulate in the inner part, with the P-elements on the outside. Natural proteins are folded in three dimensions of course, but we will only consider protein folding in two dimensions.
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The figure below shows two possible ways that our example protein could be folded (H-H contact points are shown with red dots).
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The folding on the left has only six H-H contact points, thus it would never occur naturally. On the other hand, the folding on the right has nine H-H contact points, which is optimal for this string.
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Assuming that H and P elements are equally likely to occur in any position along the string, the average number of H-H contact points in an optimal folding of a random protein string of length 8 turns out to be 850 / 28=3.3203125.
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What is the average number of H-H contact points in an optimal folding of a random protein string of length 15? Give your answer using as many decimal places as necessary for an exact result.
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# --hints--
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`euler300()` should return 8.0540771484375.
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```js
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assert.strictEqual(euler300(), 8.0540771484375);
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```
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# --seed--
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## --seed-contents--
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```js
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function euler300() {
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return true;
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}
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euler300();
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```
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# --solutions--
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```js
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// solution required
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```
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