147 lines
3.5 KiB
Markdown
147 lines
3.5 KiB
Markdown
---
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id: 5a23c84252665b21eecc7ec2
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title: Jaro distance
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challengeType: 5
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forumTopicId: 302292
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dashedName: jaro-distance
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---
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# --description--
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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.
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**Definition**
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The Jaro distance \\( d_j \\) of two given strings \\(s_1\\) and \\(s_2\\) is
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\\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}
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Where:
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<ul>
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<li>\(m\) is the number of <i>matching characters</i>;</li>
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<li> \(t\) is half the number of <i>transpositions</i>.</li>
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</ul>
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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\\).
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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*.
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**Example**
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Given the strings \\(s_1\\) *DWAYNE* and \\(s_2\\) *DUANE* we find:
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<ul>
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<li>\(m = 4\)</li>
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<li>\(|s_1| = 6\)</li>
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<li>\(|s_2| = 5\)</li>
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<li>\(t = 0\)</li>
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</ul>
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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\\).
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# --instructions--
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Write a function a that takes two strings as parameters and returns the associated Jaro distance.
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# --hints--
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`jaro` should be a function.
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```js
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assert(typeof jaro == 'function');
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```
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`jaro("MARTHA", "MARHTA")` should return a number.
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```js
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assert(typeof jaro('MARTHA', 'MARHTA') == 'number');
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```
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`jaro("MARTHA", "MARHTA")` should return `0.9444444444444445`.
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```js
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assert.equal(jaro('MARTHA', 'MARHTA'), 0.9444444444444445);
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```
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`jaro("DIXON", "DICKSONX")` should return `0.7666666666666666`.
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```js
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assert.equal(jaro('DIXON', 'DICKSONX'), 0.7666666666666666);
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```
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`jaro("JELLYFISH", "SMELLYFISH")` should return `0.8962962962962964`.
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```js
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assert.equal(jaro('JELLYFISH', 'SMELLYFISH'), 0.8962962962962964);
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```
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`jaro("HELLOS", "CHELLO")` should return `0.888888888888889`.
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```js
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assert.equal(jaro('HELLOS', 'CHELLO'), 0.888888888888889);
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```
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`jaro("ABCD", "BCDA")` should return `0.8333333333333334`.
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```js
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assert.equal(jaro('ABCD', 'BCDA'), 0.8333333333333334);
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```
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# --seed--
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## --seed-contents--
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```js
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function jaro(s, t) {
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}
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```
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# --solutions--
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```js
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function jaro(s, t) {
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var s_len = s.length;
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var t_len = t.length;
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if (s_len == 0 && t_len == 0) return 1;
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var match_distance = Math.max(s_len, t_len) / 2 - 1;
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var s_matches = new Array(s_len);
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var t_matches = new Array(t_len);
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var matches = 0;
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var transpositions = 0;
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for (var i = 0; i < s_len; i++) {
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var start = Math.max(0, i - match_distance);
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var end = Math.min(i + match_distance + 1, t_len);
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for (var j = start; j < end; j++) {
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if (t_matches[j]) continue;
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if (s.charAt(i) != t.charAt(j)) continue;
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s_matches[i] = true;
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t_matches[j] = true;
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matches++;
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break;
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}
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}
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if (matches == 0) return 0;
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var k = 0;
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for (var i = 0; i < s_len; i++) {
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if (!s_matches[i]) continue;
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while (!t_matches[k]) k++;
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if (s.charAt(i) != t.charAt(k)) transpositions++;
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k++;
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}
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return ((matches / s_len) +
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(matches / t_len) +
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((matches - transpositions / 2.0) / matches)) / 3.0;
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}
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```
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