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id	title	challengeType	forumTopicId	dashedName
59622f89e4e137560018a40e	Hofstadter Figure-Figure sequences	1	302286	hofstadter-figure-figure-sequences

--description--

The Hofstadter Figure-Figure sequences R_n and S_n are given by

R_1 = 1\\ ;\\ S_1 = 2 \\\\R_n = R_{n-1} + S_{n-1}, \\quad n>1.

Specifically, the sequence R_n contains the values

1, 3, 7, 12, 18, ...

and the sequence S_n contains the values

2, 4, 5, 6, 8, ...

The sequence R_n is defined by the recurrence relation R_n = R_{n-1} + S_{n-1}, while S_n is defined as sequence of positive integers that are not included in the sequence R_n.

--instructions--

Create two functions named ffr and ffs that return R(n) or S(n), respectively, for any index n. Note that the Hofstadter Figure-Figure sequences are 1-indexed, with R_1 = 1 and S_1 = 2.

No maximum value for n should be assumed.

References

Rosetta: Hofstadter Figure-Figure sequences

--hints--

ffr should be a function.

assert(typeof ffr === 'function');

ffs should be a function.

assert(typeof ffs === 'function');

ffr should return integer.

assert(Number.isInteger(ffr(1)));

ffs should return integer.

assert(Number.isInteger(ffs(1)));

ffr(10) should return 69

assert.equal(ffr(ffrParamRes[0][0]), ffrParamRes[0][1]);

ffr(50) should return 1509

assert.equal(ffr(ffrParamRes[1][0]), ffrParamRes[1][1]);

ffr(100) should return 5764

assert.equal(ffr(ffrParamRes[2][0]), ffrParamRes[2][1]);

ffr(1000) should return 526334

assert.equal(ffr(ffrParamRes[3][0]), ffrParamRes[3][1]);

ffs(10) should return 14

assert.equal(ffs(ffsParamRes[0][0]), ffsParamRes[0][1]);

ffs(50) should return 59

assert.equal(ffs(ffsParamRes[1][0]), ffsParamRes[1][1]);

ffs(100) should return 112

assert.equal(ffs(ffsParamRes[2][0]), ffsParamRes[2][1]);

ffs(1000) should return 1041

assert.equal(ffs(ffsParamRes[3][0]), ffsParamRes[3][1]);

--seed--

--after-user-code--

const ffrParamRes = [[10, 69], [50, 1509], [100, 5764], [1000, 526334]];
const ffsParamRes = [[10, 14], [50, 59], [100, 112], [1000, 1041]];

--seed-contents--

function ffr(n) {
  return n;
}

function ffs(n) {
  return n;
}

--solutions--

const R = [null, 1];
const S = [null, 2];

function extendSequences (n) {
  let current = Math.max(R[R.length - 1], S[S.length - 1]);
  let i;
  while (R.length <= n || S.length <= n) {
    i = Math.min(R.length, S.length) - 1;
    current += 1;
    if (current === R[i] + S[i]) {
      R.push(current);
    } else {
      S.push(current);
    }
  }
}

function ffr (n) {
  extendSequences(n);
  return R[n];
}

function ffs (n) {
  extendSequences(n);
  return S[n];
}

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