--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

and the sequence $S_n$ contains the values

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

<p>Rosetta: <a href='https://rosettacode.org/wiki/Hofstadter_Figure-Figure_sequences' target='_blank'>Hofstadter Figure-Figure sequences</a></p>.

--before-each--

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

--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--

--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];
}