167 lines
3.0 KiB
Markdown
167 lines
3.0 KiB
Markdown
---
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id: 59622f89e4e137560018a40e
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title: Hofstadter Figure-Figure sequences
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challengeType: 5
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forumTopicId: 302286
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dashedName: hofstadter-figure-figure-sequences
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---
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# --description--
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These two sequences of positive integers are defined as:
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$R(1)=1\\ ;\\ S(1)=2 \\\\R(n)=R(n-1)+S(n-1), \\quad n>1.$
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The sequence $S(n)$ is further defined as the sequence of positive integers not present in $R(n)$.
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Sequence $R$ starts:
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<pre>1, 3, 7, 12, 18, ...</pre>
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Sequence $S$ starts:
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<pre>2, 4, 5, 6, 8, ...</pre>
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# --instructions--
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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).
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No maximum value for `n` should be assumed.
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**References**
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<ul>
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<li>
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Sloane's <a href='https://oeis.org/A005228' target='_blank'>A005228</a> and <a href='https://oeis.org/A030124' target='_blank'>A030124</a>.
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</li>
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<li>
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Wikipedia: <a href='https://en.wikipedia.org/wiki/Hofstadter_sequence#Hofstadter_Figure-Figure_sequences' title='wp: Hofstadter_sequence#Hofstadter_Figure-Figure_sequences' target='_blank'>Hofstadter Figure-Figure sequences</a>.
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</li>
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</ul>
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# --hints--
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`ffr` should be a function.
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```js
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assert(typeof ffr === 'function');
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```
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`ffs` should be a function.
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```js
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assert(typeof ffs === 'function');
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```
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`ffr` should return integer.
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```js
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assert(Number.isInteger(ffr(1)));
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```
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`ffs` should return integer.
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```js
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assert(Number.isInteger(ffs(1)));
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```
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`ffr(10)` should return `69`
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```js
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assert.equal(ffr(ffrParamRes[0][0]), ffrParamRes[0][1]);
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```
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`ffr(50)` should return `1509`
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```js
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assert.equal(ffr(ffrParamRes[1][0]), ffrParamRes[1][1]);
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```
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`ffr(100)` should return `5764`
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```js
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assert.equal(ffr(ffrParamRes[2][0]), ffrParamRes[2][1]);
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```
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`ffr(1000)` should return `526334`
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```js
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assert.equal(ffr(ffrParamRes[3][0]), ffrParamRes[3][1]);
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```
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`ffs(10)` should return `14`
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```js
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assert.equal(ffs(ffsParamRes[0][0]), ffsParamRes[0][1]);
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```
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`ffs(50)` should return `59`
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```js
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assert.equal(ffs(ffsParamRes[1][0]), ffsParamRes[1][1]);
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```
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`ffs(100)` should return `112`
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```js
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assert.equal(ffs(ffsParamRes[2][0]), ffsParamRes[2][1]);
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```
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`ffs(1000)` should return `1041`
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```js
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assert.equal(ffs(ffsParamRes[3][0]), ffsParamRes[3][1]);
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```
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# --seed--
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## --after-user-code--
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```js
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const ffrParamRes = [[10, 69], [50, 1509], [100, 5764], [1000, 526334]];
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const ffsParamRes = [[10, 14], [50, 59], [100, 112], [1000, 1041]];
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```
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## --seed-contents--
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```js
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function ffr(n) {
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return n;
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}
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function ffs(n) {
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return n;
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}
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```
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# --solutions--
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```js
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const R = [null, 1];
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const S = [null, 2];
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function extendSequences (n) {
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let current = Math.max(R[R.length - 1], S[S.length - 1]);
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let i;
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while (R.length <= n || S.length <= n) {
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i = Math.min(R.length, S.length) - 1;
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current += 1;
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if (current === R[i] + S[i]) {
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R.push(current);
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} else {
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S.push(current);
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}
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}
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}
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function ffr (n) {
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extendSequences(n);
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return R[n];
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}
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function ffs (n) {
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extendSequences(n);
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return S[n];
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}
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```
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