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

id	title	challengeType	forumTopicId	dashedName
5a23c84252665b21eecc8028	Stern-Brocot sequence	5	302324	stern-brocot-sequence

--description--

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).

1. The first and second members of the sequence are both 1:
• 1, 1
2. Start by considering the second member of the sequence
3. Sum the considered member of the sequence and its precedent, (1 + 1) = 2, and append it to the end of the sequence:
• 1, 1, 2
4. Append the considered member of the sequence to the end of the sequence:
• 1, 1, 2, 1
5. Consider the next member of the series, (the third member i.e. 2)
6. GOTO 3
• ─── Expanding another loop we get: ───
7. Sum the considered member of the sequence and its precedent, (2 + 1) = 3, and append it to the end of the sequence:
• 1, 1, 2, 1, 3
8. Append the considered member of the sequence to the end of the sequence:
• 1, 1, 2, 1, 3, 2
9. Consider the next member of the series, (the fourth member i.e. 1)

--instructions--

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.

--hints--

sternBrocot should be a function.

assert(typeof sternBrocot == 'function');

sternBrocot(2) should return a number.

assert(typeof sternBrocot(2) == 'number');

sternBrocot(2) should return 3.

assert.equal(sternBrocot(2), 3);

sternBrocot(3) should return 5.

assert.equal(sternBrocot(3), 5);

sternBrocot(5) should return 11.

assert.equal(sternBrocot(5), 11);

sternBrocot(7) should return 19.

assert.equal(sternBrocot(7), 19);

sternBrocot(10) should return 39.

assert.equal(sternBrocot(10), 39);

--seed--

--seed-contents--

function sternBrocot(num) {

}

--solutions--

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;
}