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+---
+title: Jaro distance
+id: 5a23c84252665b21eecc7ec2
+challengeType: 5
+forumTopicId: 302292
+---
+
+## Description
+<section id='description'>
+The Jaro distance is a measure of similarity between two strings. The higher the Jaro distance for two strings is, the more similar the strings are. The score is normalized such that <code>0</code> equates to no similarity and <code>1</code> is an exact match. 
+<strong>Definition</strong>
+The Jaro distance  \( d_j \)  of two given strings  \(s_1\)  and  \(s_2\) is
+\begin{align}d_j = \begin{cases}0&amp;  & \text{if }m=0 \\\\{\frac {1}{3}}\left({\frac {m}{|s_{1}|}}+{\frac {m}{|s_{2}|}}+{\frac {m-t}{m}}\right)&amp; & \text{otherwise}\end{cases}\end{align}
+Where:
+<ul>
+  <li>\(m\) is the number of <i>matching characters</i>;</li>
+  <li> \(t\) is half the number of <i>transpositions</i>.</li>
+</uL>
+Two characters from  \(s_1\)   and  \(s_2\)   respectively, are considered <i>matching</i> only if they are the same and not farther than  \(\left\lfloor\frac{\max(|s_1|,|s_2|)}{2}\right\rfloor-1\).
+Each character of  \(s_1\)   is compared with all its matching characters in  \(s_2\) . The number of matching (but different sequence order) characters divided by 2 defines the number of <i>transpositions</i>.
+<strong>Example</strong>
+Given the strings  \(s_1\)   <i>DWAYNE</i>  and  \(s_2\)   <i>DUANE</i>  we find:
+<ul>
+  <li>\(m = 4\)</li>
+  <li>\(|s_1| = 6\)</li>
+  <li>\(|s_2| = 5\)</li>
+  <li>\(t = 0\)</li>
+</ul>
+We find a Jaro score of: \(d_j = \frac{1}{3}\left(\frac{4}{6} + \frac{4}{5} + \frac{4-0}{4}\right) = 0.822\).
+</section>
+
+## Instructions
+<section id='instructions'>
+Write a function a that takes two strings as parameters and returns the associated Jaro distance.
+</section>
+
+## Tests
+<section id='tests'>
+
+```yml
+tests:
+  - text: <code>jaro</code> should be a function.
+    testString: assert(typeof jaro=='function');
+  - text: <code>jaro("MARTHA", "MARHTA")</code> should return a number.
+    testString: assert(typeof jaro('MARTHA', 'MARHTA')=='number');
+  - text: <code>jaro("MARTHA", "MARHTA")</code> should return <code>0.9444444444444445</code>.
+    testString: assert.equal(jaro('MARTHA', 'MARHTA'), 0.9444444444444445);
+  - text: <code>jaro("DIXON", "DICKSONX")</code> should return <code>0.7666666666666666</code>.
+    testString: assert.equal(jaro('DIXON', 'DICKSONX'), 0.7666666666666666);
+  - text: <code>jaro("JELLYFISH", "SMELLYFISH")</code> should return <code>0.8962962962962964</code>.
+    testString: assert.equal(jaro('JELLYFISH', 'SMELLYFISH'), 0.8962962962962964);
+  - text: <code>jaro("HELLOS", "CHELLO")</code> should return <code>0.888888888888889</code>.
+    testString: assert.equal(jaro('HELLOS', 'CHELLO'), 0.888888888888889);
+  - text: <code>jaro("ABCD", "BCDA")</code> should return <code>0.8333333333333334</code>.
+    testString: assert.equal(jaro('ABCD', 'BCDA'), 0.8333333333333334);
+
+```
+
+</section>
+
+## Challenge Seed
+<section id='challengeSeed'>
+
+<div id='js-seed'>
+
+```js
+function jaro(s, t) {
+
+}
+```
+
+</div>
+
+</section>
+
+## Solution
+<section id='solution'>
+
+
+```js
+function jaro(s, t) {
+  var s_len = s.length;
+  var t_len = t.length;
+
+  if (s_len == 0 && t_len == 0) return 1;
+
+  var match_distance = Math.max(s_len, t_len) / 2 - 1;
+
+  var s_matches = new Array(s_len);
+  var t_matches = new Array(t_len);
+
+  var matches = 0;
+  var transpositions = 0;
+
+  for (var i = 0; i < s_len; i++) {
+    var start = Math.max(0, i - match_distance);
+    var end = Math.min(i + match_distance + 1, t_len);
+
+    for (var j = start; j < end; j++) {
+      if (t_matches[j]) continue;
+      if (s.charAt(i) != t.charAt(j)) continue;
+      s_matches[i] = true;
+      t_matches[j] = true;
+      matches++;
+      break;
+    }
+  }
+
+  if (matches == 0) return 0;
+
+  var k = 0;
+  for (var i = 0; i < s_len; i++) {
+    if (!s_matches[i]) continue;
+    while (!t_matches[k]) k++;
+    if (s.charAt(i) != t.charAt(k)) transpositions++;
+    k++;
+  }
+
+  return ((matches / s_len) +
+    (matches / t_len) +
+    ((matches - transpositions / 2.0) / matches)) / 3.0;
+}
+
+```
+
+</section>