115 lines
2.6 KiB
Markdown
115 lines
2.6 KiB
Markdown
---
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id: 5a23c84252665b21eecc8028
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title: Stern-Brocot sequence
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challengeType: 5
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forumTopicId: 302324
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dashedName: stern-brocot-sequence
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---
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# --description--
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For this task, the Stern-Brocot sequence is to be generated by an algorithm similar to that employed in generating the [Fibonacci sequence](<https://rosettacode.org/wiki/Fibonacci sequence>).
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<ol>
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<li>The first and second members of the sequence are both 1:</li>
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<ul><li>1, 1</li></ul>
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<li>Start by considering the second member of the sequence</li>
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<li>Sum the considered member of the sequence and its precedent, (1 + 1) = 2, and append it to the end of the
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sequence:</li>
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<ul><li>1, 1, 2</li></ul>
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<li>Append the considered member of the sequence to the end of the sequence:</li>
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<ul><li>1, 1, 2, 1</li></ul>
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<li>Consider the next member of the series, (the third member i.e. 2)</li>
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<li>GOTO 3 </li>
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<ul>
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<li></li>
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<li> ─── Expanding another loop we get: ───</li>
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<li></li>
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</ul>
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<li>Sum the considered member of the sequence and its precedent, (2 + 1) = 3, and append it to the end of the
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sequence:</li>
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<ul><li>1, 1, 2, 1, 3</li></ul>
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<li>Append the considered member of the sequence to the end of the sequence:</li>
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<ul><li>1, 1, 2, 1, 3, 2</li></ul>
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<li>Consider the next member of the series, (the fourth member i.e. 1)</li>
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</ol>
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# --instructions--
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Create a function that returns the position in the Stern-Brocot sequence at which $ n $ is first encountered, where the sequence is generated with the method outlined above. Note that this sequence uses 1 based indexing.
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# --hints--
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`sternBrocot` should be a function.
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```js
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assert(typeof sternBrocot == 'function');
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```
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`sternBrocot(2)` should return a number.
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```js
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assert(typeof sternBrocot(2) == 'number');
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```
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`sternBrocot(2)` should return `3`.
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```js
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assert.equal(sternBrocot(2), 3);
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```
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`sternBrocot(3)` should return `5`.
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```js
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assert.equal(sternBrocot(3), 5);
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```
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`sternBrocot(5)` should return `11`.
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```js
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assert.equal(sternBrocot(5), 11);
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```
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`sternBrocot(7)` should return `19`.
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```js
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assert.equal(sternBrocot(7), 19);
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```
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`sternBrocot(10)` should return `39`.
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```js
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assert.equal(sternBrocot(10), 39);
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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 sternBrocot(num) {
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}
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```
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# --solutions--
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```js
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function sternBrocot(num) {
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function f(n) {
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return n < 2
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? n
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: n & 1
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? f(Math.floor(n / 2)) + f(Math.floor(n / 2 + 1))
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: f(Math.floor(n / 2));
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}
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function gcd(a, b) {
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return a ? (a < b ? gcd(b % a, a) : gcd(a % b, b)) : b;
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}
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var n;
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for (n = 1; f(n) != num; n++);
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return n;
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}
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```
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