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curriculum/challenges/english/10-coding-interview-prep/rosetta-code/stern-brocot-sequence.md

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+---
+id: 5a23c84252665b21eecc8028
+title: Stern-Brocot sequence
+challengeType: 5
+forumTopicId: 302324
+---
+
+## Description
+
+<section id='description'>
+For this task, the Stern-Brocot sequence is to be generated by an algorithm similar to that employed in generating the <a href="https://rosettacode.org/wiki/Fibonacci sequence" target="_blank">Fibonacci sequence</a>.
+<ol>
+  <li>The first and second members of the sequence are both 1:</li>
+    <ul><li>1, 1</li></ul>
+  <li>Start by considering the second member of the sequence</li>
+  <li>Sum the considered member of the sequence and its precedent, (1 + 1) = 2, and append it to the end of the
+    sequence:</li>
+    <ul><li>1, 1, 2</li></ul>
+  <li>Append the considered member of the sequence to the end of the sequence:</li>
+    <ul><li>1, 1, 2, 1</li></ul>
+  <li>Consider the next member of the series, (the third member i.e. 2)</li>
+  <li>GOTO 3 </li>
+    <ul>
+      <li></li>
+      <li> ─── Expanding another loop we get: ───</li>
+      <li></li>
+    </ul>
+  <li>Sum the considered member of the sequence and its precedent, (2 + 1) = 3, and append it to the end of the
+    sequence:</li>
+    <ul><li>1, 1, 2, 1, 3</li></ul>
+  <li>Append the considered member of the sequence to the end of the sequence:</li>
+    <ul><li>1, 1, 2, 1, 3, 2</li></ul>
+  <li>Consider the next member of the series, (the fourth member i.e. 1)</li>
+</ol>
+</section>
+
+## Instructions
+
+<section id='instructions'>
+Create a function that returns the $ n^{th} $ member of the sequence using the method outlined above.
+</section>
+
+## Tests
+
+<section id='tests'>
+
+```yml
+tests:
+  - text: <code>sternBrocot</code> should be a function.
+    testString: assert(typeof sternBrocot == 'function');
+  - text: <code>sternBrocot(2)</code> should return a number.
+    testString: assert(typeof sternBrocot(2) == 'number');
+  - text: <code>sternBrocot(2)</code> should return <code>3</code>.
+    testString: assert.equal(sternBrocot(2), 3);
+  - text: <code>sternBrocot(3)</code> should return <code>5</code>.
+    testString: assert.equal(sternBrocot(3), 5);
+  - text: <code>sternBrocot(5)</code> should return <code>11</code>.
+    testString: assert.equal(sternBrocot(5), 11);
+  - text: <code>sternBrocot(7)</code> should return <code>19</code>.
+    testString: assert.equal(sternBrocot(7), 19);
+  - text: <code>sternBrocot(10)</code> should return <code>39</code>.
+    testString: assert.equal(sternBrocot(10), 39);
+```
+
+</section>
+
+## Challenge Seed
+
+<section id='challengeSeed'>
+<div id='js-seed'>
+
+```js
+function sternBrocot(num) {
+
+}
+```
+
+</div>
+</section>
+
+## Solution
+
+<section id='solution'>
+
+```js
+function sternBrocot(num) {
+  function f(n) {
+    return n < 2
+      ? n
+      : n & 1
+      ? f(Math.floor(n / 2)) + f(Math.floor(n / 2 + 1))
+      : f(Math.floor(n / 2));
+  }
+
+  function gcd(a, b) {
+    return a ? (a < b ? gcd(b % a, a) : gcd(a % b, b)) : b;
+  }
+  var n;
+  for (n = 1; f(n) != num; n++);
+  return n;
+}
+```
+
+</section>