130 lines
4.3 KiB
Markdown
130 lines
4.3 KiB
Markdown
---
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title: Hofstadter Figure-Figure sequences
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id: 59622f89e4e137560018a40e
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challengeType: 5
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---
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## Description
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<section id='description'>
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<p>These two sequences of positive integers are defined as:</p>
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<p><big>$$R(1)=1\ ;\ S(1)=2 \\R(n)=R(n-1)+S(n-1), \quad n>1.$$</big></p>
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<p>The sequence <big>$S(n)$</big> is further defined as the sequence of positive integers not present in <big>$R(n)$</big>.</p><p>Sequence <big>$R$</big> starts:</p>
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<p>1, 3, 7, 12, 18, ...</p>
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<p>Sequence <big>$S$</big> starts:</p>
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<p>2, 4, 5, 6, 8, ...</p>
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Task:
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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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Sloane's <a href="http://oeis.org/A005228" title="link: http://oeis.org/A005228">A005228</a> and <a href="http://oeis.org/A030124" title="link: http://oeis.org/A030124">A030124</a>.
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<a href="http://mathworld.wolfram.com/HofstadterFigure-FigureSequence.html" title="link: http://mathworld.wolfram.com/HofstadterFigure-FigureSequence.html">Wolfram MathWorld</a>
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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">Hofstadter Figure-Figure sequences</a>.
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</section>
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## Instructions
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<section id='instructions'>
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</section>
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## Tests
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<section id='tests'>
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```yml
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tests:
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- text: <code>ffr</code> is a function.
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testString: assert(typeof ffr === 'function', '<code>ffr</code> is a function.');
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- text: <code>ffs</code> is a function.
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testString: assert(typeof ffs === 'function', '<code>ffs</code> is a function.');
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- text: <code>ffr</code> should return integer.
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testString: assert(Number.isInteger(ffr(1)), '<code>ffr</code> should return integer.');
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- text: <code>ffs</code> should return integer.
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testString: assert(Number.isInteger(ffs(1)), '<code>ffs</code> should return integer.');
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- text: <code>ffr()</code> should return <code>69</code>
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testString: assert.equal(ffr(ffrParamRes[0][0]), ffrParamRes[0][1], '<code>ffr()</code> should return <code>69</code>');
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- text: <code>ffr()</code> should return <code>1509</code>
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testString: assert.equal(ffr(ffrParamRes[1][0]), ffrParamRes[1][1], '<code>ffr()</code> should return <code>1509</code>');
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- text: <code>ffr()</code> should return <code>5764</code>
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testString: assert.equal(ffr(ffrParamRes[2][0]), ffrParamRes[2][1], '<code>ffr()</code> should return <code>5764</code>');
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- text: <code>ffr()</code> should return <code>526334</code>
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testString: assert.equal(ffr(ffrParamRes[3][0]), ffrParamRes[3][1], '<code>ffr()</code> should return <code>526334</code>');
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- text: <code>ffs()</code> should return <code>14</code>
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testString: assert.equal(ffs(ffsParamRes[0][0]), ffsParamRes[0][1], '<code>ffs()</code> should return <code>14</code>');
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- text: <code>ffs()</code> should return <code>59</code>
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testString: assert.equal(ffs(ffsParamRes[1][0]), ffsParamRes[1][1], '<code>ffs()</code> should return <code>59</code>');
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- text: <code>ffs()</code> should return <code>112</code>
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testString: assert.equal(ffs(ffsParamRes[2][0]), ffsParamRes[2][1], '<code>ffs()</code> should return <code>112</code>');
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- text: <code>ffs()</code> should return <code>1041</code>
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testString: assert.equal(ffs(ffsParamRes[3][0]), ffsParamRes[3][1], '<code>ffs()</code> should return <code>1041</code>');
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```
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</section>
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## Challenge Seed
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<section id='challengeSeed'>
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<div id='js-seed'>
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```js
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// noprotect
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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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</div>
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### After Test
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<div id='js-teardown'>
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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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</div>
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</section>
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## Solution
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<section id='solution'>
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```js
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// noprotect
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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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</section>
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