43 lines
1.0 KiB
Markdown
43 lines
1.0 KiB
Markdown
---
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id: 5900f4fa1000cf542c51000d
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title: 'Problem 398: Cutting rope'
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challengeType: 5
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forumTopicId: 302063
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dashedName: problem-398-cutting-rope
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---
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# --description--
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Inside a rope of length $n$, $n - 1$ points are placed with distance 1 from each other and from the endpoints. Among these points, we choose $m - 1$ points at random and cut the rope at these points to create $m$ segments.
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Let $E(n, m)$ be the expected length of the second-shortest segment. For example, $E(3, 2) = 2$ and $E(8, 3) = \frac{16}{7}$. Note that if multiple segments have the same shortest length the length of the second-shortest segment is defined as the same as the shortest length.
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Find $E({10}^7, 100)$. Give your answer rounded to 5 decimal places behind the decimal point.
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# --hints--
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`cuttingRope()` should return `2010.59096`.
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```js
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assert.strictEqual(cuttingRope(), 2010.59096);
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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 cuttingRope() {
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return true;
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}
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cuttingRope();
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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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