161 lines
2.9 KiB
Markdown
161 lines
2.9 KiB
Markdown
---
|
|
id: 59622f89e4e137560018a40e
|
|
title: Hofstadter Figure-Figure sequences
|
|
challengeType: 5
|
|
forumTopicId: 302286
|
|
dashedName: 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
|
|
|
|
<pre>1, 3, 7, 12, 18, ...</pre>
|
|
|
|
and the sequence $S_n$ contains the values
|
|
|
|
<pre>2, 4, 5, 6, 8, ...</pre>
|
|
|
|
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>.
|
|
|
|
|
|
# --hints--
|
|
|
|
`ffr` should be a function.
|
|
|
|
```js
|
|
assert(typeof ffr === 'function');
|
|
```
|
|
|
|
`ffs` should be a function.
|
|
|
|
```js
|
|
assert(typeof ffs === 'function');
|
|
```
|
|
|
|
`ffr` should return integer.
|
|
|
|
```js
|
|
assert(Number.isInteger(ffr(1)));
|
|
```
|
|
|
|
`ffs` should return integer.
|
|
|
|
```js
|
|
assert(Number.isInteger(ffs(1)));
|
|
```
|
|
|
|
`ffr(10)` should return `69`
|
|
|
|
```js
|
|
assert.equal(ffr(ffrParamRes[0][0]), ffrParamRes[0][1]);
|
|
```
|
|
|
|
`ffr(50)` should return `1509`
|
|
|
|
```js
|
|
assert.equal(ffr(ffrParamRes[1][0]), ffrParamRes[1][1]);
|
|
```
|
|
|
|
`ffr(100)` should return `5764`
|
|
|
|
```js
|
|
assert.equal(ffr(ffrParamRes[2][0]), ffrParamRes[2][1]);
|
|
```
|
|
|
|
`ffr(1000)` should return `526334`
|
|
|
|
```js
|
|
assert.equal(ffr(ffrParamRes[3][0]), ffrParamRes[3][1]);
|
|
```
|
|
|
|
`ffs(10)` should return `14`
|
|
|
|
```js
|
|
assert.equal(ffs(ffsParamRes[0][0]), ffsParamRes[0][1]);
|
|
```
|
|
|
|
`ffs(50)` should return `59`
|
|
|
|
```js
|
|
assert.equal(ffs(ffsParamRes[1][0]), ffsParamRes[1][1]);
|
|
```
|
|
|
|
`ffs(100)` should return `112`
|
|
|
|
```js
|
|
assert.equal(ffs(ffsParamRes[2][0]), ffsParamRes[2][1]);
|
|
```
|
|
|
|
`ffs(1000)` should return `1041`
|
|
|
|
```js
|
|
assert.equal(ffs(ffsParamRes[3][0]), ffsParamRes[3][1]);
|
|
```
|
|
|
|
# --seed--
|
|
|
|
## --after-user-code--
|
|
|
|
```js
|
|
const ffrParamRes = [[10, 69], [50, 1509], [100, 5764], [1000, 526334]];
|
|
const ffsParamRes = [[10, 14], [50, 59], [100, 112], [1000, 1041]];
|
|
```
|
|
|
|
## --seed-contents--
|
|
|
|
```js
|
|
function ffr(n) {
|
|
return n;
|
|
}
|
|
|
|
function ffs(n) {
|
|
return n;
|
|
}
|
|
```
|
|
|
|
# --solutions--
|
|
|
|
```js
|
|
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];
|
|
}
|
|
```
|