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curriculum/challenges/english/10-coding-interview-prep/rosetta-code/entropy.md

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+---
+title: Entropy
+id: 599d15309e88c813a40baf58
+challengeType: 5
+forumTopicId: 302254
+---
+
+## Description
+<section id='description'>
+Calculate the Shannon entropy H of a given input string.
+Given the discreet random variable $X$ that is a string of $N$ "symbols" (total characters) consisting of $n$ different characters (n=2 for binary), the Shannon entropy of X in bits/symbol is:
+$H_2(X) = -\sum_{i=1}^n \frac{count_i}{N} \log_2 \left(\frac{count_i}{N}\right)$
+where $count_i$ is the count of character $n_i$.
+</section>
+
+## Instructions
+<section id='instructions'>
+
+</section>
+
+## Tests
+<section id='tests'>
+
+```yml
+tests:
+  - text: <code>entropy</code> should be a function.
+    testString: assert(typeof entropy === 'function');
+  - text: <code>entropy("0")</code> should return <code>0</code>
+    testString: assert.equal(entropy('0'), 0);
+  - text: <code>entropy("01")</code> should return <code>1</code>
+    testString: assert.equal(entropy('01'), 1);
+  - text: <code>entropy("0123")</code> should return <code>2</code>
+    testString: assert.equal(entropy('0123'), 2);
+  - text: <code>entropy("01234567")</code> should return <code>3</code>
+    testString: assert.equal(entropy('01234567'), 3);
+  - text: <code>entropy("0123456789abcdef")</code> should return <code>4</code>
+    testString: assert.equal(entropy('0123456789abcdef'), 4);
+  - text: <code>entropy("1223334444")</code> should return <code>1.8464393446710154</code>
+    testString: assert.equal(entropy('1223334444'), 1.8464393446710154);
+
+```
+
+</section>
+
+## Challenge Seed
+<section id='challengeSeed'>
+
+<div id='js-seed'>
+
+```js
+function entropy(s) {
+
+}
+```
+
+</div>
+
+
+
+</section>
+
+## Solution
+<section id='solution'>
+
+
+```js
+function entropy(s) {
+	// Create a dictionary of character frequencies and iterate over it.
+  function process(s, evaluator) {
+    let h = Object.create(null),
+      k;
+    s.split('').forEach(c => {
+      h[c] && h[c]++ || (h[c] = 1); });
+    if (evaluator) for (k in h) evaluator(k, h[k]);
+    return h;
+  }
+	// Measure the entropy of a string in bits per symbol.
+
+  let sum = 0,
+    len = s.length;
+  process(s, (k, f) => {
+    const p = f / len;
+    sum -= p * Math.log(p) / Math.log(2);
+  });
+  return sum;
+}
+
+```
+
+</section>