---
title: Jaro distance
id: 5a23c84252665b21eecc7ec2
challengeType: 5
---

## 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  <b>0</b>  equates to no similarity and  <b>1</b>  is an exact match. Definition 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>.
<b>Example</b>
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: \(d_j = \frac{1}{3}\left(\frac{4}{6} + \frac{4}{5} + \frac{4-0}{4}\right) = 0.822\).
Write a function a that takes two strings as parameters and returns the associated Jaro distance.
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: '''<code>jaro</code> should be a function.'''
    testString: 'assert(typeof jaro==''function'',''<code>jaro</code> should be a function.'');'
  - text: '''<code>jaro("''+tests[0][0]+''","''+tests[0][1]+''")</code> should return a number.'''
    testString: 'assert(typeof jaro(tests[0][0],tests[0][1])==''number'',''<code>jaro()</code> should return a number.'');'
  - text: '''<code>jaro("''+tests[0][0]+''","''+tests[0][1]+''")</code> should return <code>''+results[0]+''</code>.'''
    testString: 'assert.equal(jaro(tests[0][0],tests[0][1]),results[0],''<code>jaro("''+tests[0][0]+''","''+tests[0][1]+''")</code> should return <code>''+results[0]+''</code>.'');'
  - text: '''<code>jaro("''+tests[1][0]+''","''+tests[1][1]+''")</code> should return <code>''+results[1]+''</code>.'''
    testString: 'assert.equal(jaro(tests[1][0],tests[1][1]),results[1],''<code>jaro("''+tests[1][0]+''","''+tests[1][1]+''")</code> should return <code>''+results[1]+''</code>.'');'
  - text: '''<code>jaro("''+tests[2][0]+''","''+tests[2][1]+''")</code> should return <code>''+results[2]+''</code>.'''
    testString: 'assert.equal(jaro(tests[2][0],tests[2][1]),results[2],''<code>jaro("''+tests[2][0]+''","''+tests[2][1]+''")</code> should return <code>''+results[2]+''</code>.'');'
  - text: '''<code>jaro("''+tests[3][0]+''","''+tests[3][1]+''")</code> should return <code>''+results[3]+''</code>.'''
    testString: 'assert.equal(jaro(tests[3][0],tests[3][1]),results[3],''<code>jaro("''+tests[3][0]+''","''+tests[3][1]+''")</code> should return <code>''+results[3]+''</code>.'');'
  - text: '''<code>jaro("''+tests[4][0]+''","''+tests[4][1]+''")</code> should return <code>''+results[4]+''</code>.'''
    testString: 'assert.equal(jaro(tests[4][0],tests[4][1]),results[4],''<code>jaro("''+tests[4][0]+''","''+tests[4][1]+''")</code> should return <code>''+results[4]+''</code>.'');'

```

</section>

## Challenge Seed
<section id='challengeSeed'>

<div id='js-seed'>

```js
function jaro (s, t) {
  // Good luck!
}
```

</div>


### After Test
<div id='js-teardown'>

```js
console.info('after the test');
```

</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>