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title	id	challengeType
Fibonacci word	5992e222d397f00d21122931	5

Description

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 :

The Fibonacci Word may be created in a manner analogous to the Fibonacci Sequence as described here:

Define F_Word₁ as 1

Define F_Word₂ as 0

Form F_Word₃ as F_Word₂ concatenated with F_Word₁ i.e.: 01

Form F_Word_n as F_Word_n-1 concatenated with F_word_n-2

Instructions

Tests

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>.');

Challenge Seed

function fibWord (n) {
  // Good luck!
}

After Test

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' }];

Solution

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;
}

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