2.9 KiB
id | title | challengeType | forumTopicId | dashedName |
---|---|---|---|---|
59622f89e4e137560018a40e | Hofstadter Figure-Figure sequences | 5 | 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];
}