116 lines
3.8 KiB
Markdown
116 lines
3.8 KiB
Markdown
---
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id: 5992e222d397f00d21122931
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title: Fibonacci word
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challengeType: 1
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forumTopicId: 302269
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dashedName: fibonacci-word
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---
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# --description--
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The Fibonacci Word Sequence may be created in a manner analogous to the Fibonacci Sequence, but it focuses on iterating concatenation.
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<pre>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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Entropy calculation is required in this challenge, <a href="https://www.freecodecamp.org/learn/coding-interview-prep/rosetta-code/entropy" target="_blank" rel="noopener noreferrer nofollow">as shown in this Rosetta Code challenge</a>
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# --instructions--
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Write a function to return the first `n` Fibonacci Words. The number of `n` is 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' }`. `Entropy` is computed for the string `Word` and rounded to 8 decimal digits of accuracy. Note that the indices of this sequence start at `1`.
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# --hints--
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`fibWord` should be a function.
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```js
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assert(typeof fibWord === 'function');
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```
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`fibWord(5)` should return an array.
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```js
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assert(Array.isArray(fibWord(5)));
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```
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`fibWord(5)` should return `[{ 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:0.91829583, Word:"010" },{ N:5, Length:5, Entropy:0.97095059, Word:"01001" }]`.
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```js
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assert.deepEqual(fibWord(5), words5);
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```
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`fibWord(7)` should return `[{ 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:0.91829583, Word:"010" },{ N:5, Length:5, Entropy:0.97095059, Word:"01001" }, { N:6, Length:8, Entropy:0.954434, Word:'01001010' }, { N:7, Length:13, Entropy:0.9612366, Word:'0100101001001' }]`.
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```js
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assert.deepEqual(fibWord(7), words7);
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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 words5 = [
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{ 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: 0.91829583, Word: '010' },
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{ N: 5, Length: 5, Entropy: 0.97095059, Word: '01001' }
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];
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const words7 = [
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{ 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: 0.91829583, Word: '010' },
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{ N: 5, Length: 5, Entropy: 0.97095059, Word: '01001' },
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{ N: 6, Length: 8, Entropy: 0.954434, Word: '01001010' },
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{ N: 7, Length: 13, Entropy: 0.9612366, Word: '0100101001001' }
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];
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```
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## --seed-contents--
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```js
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function fibWord(n) {
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}
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```
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# --solutions--
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```js
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// Round to digits
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function roundFloat(num, digits) {
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return Math.round(num * 10.0**digits) / (10.0**digits);
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}
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// Entropy calculation for string with only 0 and 1
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function entropy(word) {
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function digitEntropy(count) {
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return count < 1 ? 0
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: - count / word.length * Math.log2(count / word.length);
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}
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const numZeros = word.split('').filter(e => e === '0').length;
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const numOnes = word.length - numZeros;
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return roundFloat(digitEntropy(numZeros) + digitEntropy(numOnes), 8);
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}
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// Compute array of Fibonacci words
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function fibWord(n) {
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return [...Array(n).keys()]
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.reduce((words, i) => {
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const word = i === 0 ? "1"
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: i === 1 ? "0"
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: words[i - 1].Word + words[i - 2].Word;
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words.push(
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{ N: i + 1, Length: word.length, Entropy: entropy(word), Word: word }
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);
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return words;
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}, []);
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}
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```
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