120 lines
3.1 KiB
Markdown
120 lines
3.1 KiB
Markdown
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---
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title: Fibonacci word
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id: 5992e222d397f00d21122931
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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>Write a function to return the Fibonacci Words upto N. N will be provided as a parameter to the function. The function should return an array of objects. The objects should be of the form : { N: 1, Length: 1, Entropy: 0, Word: '1' }. More details are given below : </p><p>The Fibonacci Word may be created in a manner analogous to the Fibonacci Sequence <a href="http://hal.archives-ouvertes.fr/docs/00/36/79/72/PDF/The_Fibonacci_word_fractal.pdf" title="link: http://hal.archives-ouvertes.fr/docs/00/36/79/72/PDF/The_Fibonacci_word_fractal.pdf">as described here</a>:</p><p>Define F_Word<sub>1</sub> as 1</p>
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<p>Define F_Word<sub>2</sub> as 0</p>
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<p>Form F_Word<sub>3</sub> as F_Word<sub>2</sub> concatenated with F_Word<sub>1</sub> i.e.: 01</p>
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<p>Form F_Word<sub>n</sub> as F_Word<sub>n-1</sub> concatenated with F_word<sub>n-2</sub></p>
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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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- text: <code>fibWord</code> is a function.
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testString: 'assert(typeof fibWord === "function", "<code>fibWord</code> is a function.");'
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- text: <code>fibWord(5)</code> should return an array.
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testString: 'assert(Array.isArray(fibWord(5)),"<code>fibWord(5)</code> should return an array.");'
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- text: <code>fibWord(5)</code> should return <code>'+JSON.stringify(ans)+'</code>.
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testString: 'assert.deepEqual(fibWord(5),ans,"<code>fibWord(5)</code> should return <code>"+JSON.stringify(ans)+"</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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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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console.info('after the test');
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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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