3.0 KiB
id | title | challengeType | forumTopicId | dashedName |
---|---|---|---|---|
59622f89e4e137560018a40e | Hofstadter Figure-Figure sequences | 5 | 302286 | hofstadter-figure-figure-sequences |
--description--
These two sequences of positive integers are defined as:
R(1)=1\\ ;\\ S(1)=2 \\\\R(n)=R(n-1)+S(n-1), \\quad n>1.
The sequence S(n)
is further defined as the sequence of positive integers not present in R(n)
.
Sequence R
starts:
1, 3, 7, 12, 18, ...
Sequence S
starts:
2, 4, 5, 6, 8, ...
--instructions--
Create two functions named ffr
and ffs
that when given n
return R(n)
or S(n)
respectively. (Note that R(1) = 1 and S(1) = 2 to avoid off-by-one errors).
No maximum value for n
should be assumed.
References
- Sloane's A005228 and A030124.
- Wikipedia: 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];
}