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id	title	challengeType	forumTopicId	dashedName
5a23c84252665b21eecc7ec2	Jaro distance	1	302292	jaro-distance

--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 0 equates to no similarity and 1 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& & \text{if }m=0 \\\\{\frac {1}{3}}\left({\frac {m}{|s_{1}|}}+{\frac {m}{|s_{2}|}}+{\frac {m-t}{m}}\right)& & \text{otherwise}\end{cases}\end{align}

Where:

\(m\) is the number of matching characters;
\(t\) is half the number of transpositions.

Two characters from \(s_1\) and \(s_2\) respectively, are considered matching 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 transpositions.

Example

Given the strings \(s_1\) DWAYNE and \(s_2\) DUANE we find:

\(m = 4\)
\(|s_1| = 6\)
\(|s_2| = 5\)
\(t = 0\)

We find a Jaro score of: \(d_j = \frac{1}{3}\left(\frac{4}{6} + \frac{4}{5} + \frac{4-0}{4}\right) = 0.822\).

--instructions--

Write a function a that takes two strings as parameters and returns the associated Jaro distance.

--hints--

jaro should be a function.

assert(typeof jaro == 'function');

jaro("MARTHA", "MARHTA") should return a number.

assert(typeof jaro('MARTHA', 'MARHTA') == 'number');

jaro("MARTHA", "MARHTA") should return 0.9444444444444445.

assert.equal(jaro('MARTHA', 'MARHTA'), 0.9444444444444445);

jaro("DIXON", "DICKSONX") should return 0.7666666666666666.

assert.equal(jaro('DIXON', 'DICKSONX'), 0.7666666666666666);

jaro("JELLYFISH", "SMELLYFISH") should return 0.8962962962962964.

assert.equal(jaro('JELLYFISH', 'SMELLYFISH'), 0.8962962962962964);

jaro("HELLOS", "CHELLO") should return 0.888888888888889.

assert.equal(jaro('HELLOS', 'CHELLO'), 0.888888888888889);

jaro("ABCD", "BCDA") should return 0.8333333333333334.

assert.equal(jaro('ABCD', 'BCDA'), 0.8333333333333334);

--seed--

--seed-contents--

function jaro(s, t) {

}

--solutions--

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;
}

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