133 lines
3.3 KiB
Markdown
133 lines
3.3 KiB
Markdown
---
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title: Fibonacci word
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id: 5992e222d397f00d21122931
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challengeType: 5
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forumTopicId: 302269
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---
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## Description
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<section id='description'>
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The Fibonacci Word may be created in a manner analogous to the Fibonacci Sequence <a href="https://hal.archives-ouvertes.fr/docs/00/36/79/72/PDF/The_Fibonacci_word_fractal.pdf" target="_blank">as described here</a>:
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<pre>
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Define F_Word<sub>1</sub> as <strong>1</strong>
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Define F_Word<sub>2</sub> as <strong>0</strong>
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Form F_Word<sub>3</sub> as F_Word<sub>2</sub> concatenated with F_Word<sub>1</sub> i.e.: <strong>01</strong>
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Form F_Word<sub>n</sub> as F_Word<sub>n-1</sub> concatenated with F_word<sub>n-2</sub>
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</pre>
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</section>
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## Instructions
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<section id='instructions'>
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Write a function to return the Fibonacci Words up to <code>n</code>. <code>n</code> will be provided as a parameter to the function. The function should return an array of objects. The objects should be of the form: <code>{ N: 1, Length: 1, Entropy: 0, Word: '1' }</code>.
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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>fibWord</code> is a function.
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testString: assert(typeof fibWord === 'function');
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- text: <code>fibWord(5)</code> should return an array.
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testString: assert(Array.isArray(fibWord(5)));
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- text: <code>fibWord(5)</code> should return <code>[{ N:1, Length:1, Entropy:0, Word:"1" },{ N:2, Length:1, Entropy:0, Word:"0" },{ N:3, Length:2, Entropy:1, Word:"01" },{ N:4, Length:3, Entropy:0.9182958340544896, Word:"010" },{ N:5, Length:5, Entropy:0.9709505944546688, Word:"01001" }]</code>.
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testString: assert.deepEqual(fibWord(5),ans);
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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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function fibWord(n) {
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// Good luck!
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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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let ans=[ { N: 1, Length: 1, Entropy: 0, Word: '1' },
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{ N: 2, Length: 1, Entropy: 0, Word: '0' },
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{ N: 3, Length: 2, Entropy: 1, Word: '01' },
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{ N: 4, Length: 3, Entropy: 0.9182958340544896, Word: '010' },
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{ N: 5, Length: 5, Entropy: 0.9709505944546688, Word: '01001' }];
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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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function fibWord(n) {
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function entropy(s) {
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//create an object containing each individual char
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//and the amount of iterations per char
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function prob(s) {
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var h = Object.create(null);
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s.split('').forEach(function(c) {
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h[c] && h[c]++ || (h[c] = 1);
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});
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return h;
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}
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s = s.toString(); //just in case
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var e = 0, l = s.length, h = prob(s);
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for (var i in h ) {
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var p = h[i]/l;
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e -= p * Math.log(p) / Math.log(2);
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}
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return e;
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}
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var wOne = "1", wTwo = "0", wNth = [wOne, wTwo], w = "", o = [];
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for (var i = 0; i < n; i++) {
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if (i === 0 || i === 1) {
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w = wNth[i];
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} else {
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w = wNth[i - 1] + wNth[i - 2];
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wNth.push(w);
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}
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var l = w.length;
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var e = entropy(w);
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if (l <= 21) {
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o.push({
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N: i + 1,
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Length: l,
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Entropy: e,
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Word: w
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});
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} else {
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o.push({
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N: i + 1,
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Length: l,
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Entropy: e,
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Word: "..."
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});
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}
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}
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return o;
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}
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```
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</section>
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