3.5 KiB
id | title | challengeType | forumTopicId | dashedName |
---|---|---|---|---|
5a23c84252665b21eecc7ec2 | Jaro distance | 5 | 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;
}