79d9012432
* fix(curriculum): tests quotes * fix(curriculum): fill seed-teardown * fix(curriculum): fix tests and remove unneeded seed-teardown
129 lines
3.3 KiB
Markdown
129 lines
3.3 KiB
Markdown
---
|
|
title: Fibonacci word
|
|
id: 5992e222d397f00d21122931
|
|
challengeType: 5
|
|
---
|
|
|
|
## Description
|
|
<section id='description'>
|
|
<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>
|
|
<p>Define F_Word<sub>2</sub> as 0</p>
|
|
<p>Form F_Word<sub>3</sub> as F_Word<sub>2</sub> concatenated with F_Word<sub>1</sub> i.e.: 01</p>
|
|
<p>Form F_Word<sub>n</sub> as F_Word<sub>n-1</sub> concatenated with F_word<sub>n-2</sub></p>
|
|
</section>
|
|
|
|
## Instructions
|
|
<section id='instructions'>
|
|
|
|
</section>
|
|
|
|
## Tests
|
|
<section id='tests'>
|
|
|
|
```yml
|
|
tests:
|
|
- text: <code>fibWord</code> is a function.
|
|
testString: assert(typeof fibWord === 'function', '<code>fibWord</code> is a function.');
|
|
- text: <code>fibWord(5)</code> should return an array.
|
|
testString: assert(Array.isArray(fibWord(5)),'<code>fibWord(5)</code> should return an array.');
|
|
- text: <code>fibWord(5)</code> should return <code>'+JSON.stringify(ans)+'</code>.
|
|
testString: assert.deepEqual(fibWord(5),ans,'<code>fibWord(5)</code> should return <code>'+JSON.stringify(ans)+'</code>.');
|
|
|
|
```
|
|
|
|
</section>
|
|
|
|
## Challenge Seed
|
|
<section id='challengeSeed'>
|
|
|
|
<div id='js-seed'>
|
|
|
|
```js
|
|
function fibWord (n) {
|
|
// Good luck!
|
|
}
|
|
```
|
|
|
|
</div>
|
|
|
|
|
|
### After Test
|
|
<div id='js-teardown'>
|
|
|
|
```js
|
|
let ans=[ { 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' }];
|
|
```
|
|
|
|
</div>
|
|
|
|
</section>
|
|
|
|
## Solution
|
|
<section id='solution'>
|
|
|
|
|
|
```js
|
|
function fibWord(n) {
|
|
function entropy(s) {
|
|
//create an object containing each individual char
|
|
//and the amount of iterations per char
|
|
function prob(s) {
|
|
var h = Object.create(null);
|
|
s.split('').forEach(function(c) {
|
|
h[c] && h[c]++ || (h[c] = 1);
|
|
});
|
|
return h;
|
|
}
|
|
|
|
s = s.toString(); //just in case
|
|
var e = 0, l = s.length, h = prob(s);
|
|
|
|
for (var i in h ) {
|
|
var p = h[i]/l;
|
|
e -= p * Math.log(p) / Math.log(2);
|
|
}
|
|
return e;
|
|
}
|
|
var wOne = "1", wTwo = "0", wNth = [wOne, wTwo], w = "", o = [];
|
|
|
|
for (var i = 0; i < n; i++) {
|
|
if (i === 0 || i === 1) {
|
|
w = wNth[i];
|
|
} else {
|
|
w = wNth[i - 1] + wNth[i - 2];
|
|
wNth.push(w);
|
|
}
|
|
var l = w.length;
|
|
var e = entropy(w);
|
|
|
|
if (l <= 21) {
|
|
o.push({
|
|
N: i + 1,
|
|
Length: l,
|
|
Entropy: e,
|
|
Word: w
|
|
});
|
|
} else {
|
|
o.push({
|
|
N: i + 1,
|
|
Length: l,
|
|
Entropy: e,
|
|
Word: "..."
|
|
});
|
|
}
|
|
}
|
|
return o;
|
|
}
|
|
|
|
```
|
|
|
|
</section>
|