116 lines
4.4 KiB
Markdown
116 lines
4.4 KiB
Markdown
---
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title: Jaro distance
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id: 5a23c84252665b21eecc7ec2
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challengeType: 5
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---
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## Description
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<section id='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 <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
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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: <ul><li>\(m\) is the number of <i>matching characters</i>;</li><li> \(t\) is half the number of <i>transpositions</i>.</li></uL>
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Two characters from \(s_1\) and \(s_2\) respectively, are considered <i>matching</i> only if they are the same and not farther than \(\left\lfloor\frac{\max(|s_1|,|s_2|)}{2}\right\rfloor-1\).
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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 <i>transpositions</i>.
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<b>Example</b>
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Given the strings \(s_1\) <i>DWAYNE</i> and \(s_2\) <i>DUANE</i> we find:
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<ul><li>\(m = 4\)</li><li>\(|s_1| = 6\) </li><li>\(|s_2| = 5\) </li><li>\(t = 0\) </li></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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Write a function a that takes two strings as parameters and returns the associated Jaro distance.
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</section>
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## Instructions
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<section id='instructions'>
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</section>
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## Tests
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<section id='tests'>
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```yml
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tests:
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- text: <code>jaro</code> should be a function.
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testString: assert(typeof jaro=='function','<code>jaro</code> should be a function.');
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- text: <code>jaro("MARTHA", "MARHTA")</code> should return a number.
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testString: assert(typeof jaro('MARTHA', 'MARHTA')=='number','<code>jaro()</code> should return a number.');
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- text: <code>jaro("MARTHA", "MARHTA")</code> should return <code>0.9444444444444445</code>.
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testString: assert.equal(jaro('MARTHA', 'MARHTA'), 0.9444444444444445,'<code>jaro("MARTHA", "MARHTA")</code> should return <code>0.9444444444444445</code>.');
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- text: <code>jaro("DIXON", "DICKSONX")</code> should return <code>0.7666666666666666</code>.
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testString: assert.equal(jaro('DIXON', 'DICKSONX'), 0.7666666666666666,'<code>jaro("DIXON", "DICKSONX")</code> should return <code>0.7666666666666666</code>.');
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- text: <code>jaro("JELLYFISH", "SMELLYFISH")</code> should return <code>0.8962962962962964</code>.
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testString: assert.equal(jaro('JELLYFISH', 'SMELLYFISH'), 0.8962962962962964,'<code>jaro("JELLYFISH", "SMELLYFISH")</code> should return <code>0.8962962962962964</code>.');
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- text: <code>jaro("HELLOS", "CHELLO")</code> should return <code>0.888888888888889</code>.
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testString: assert.equal(jaro('HELLOS', 'CHELLO'), 0.888888888888889,'<code>jaro("HELLOS", "CHELLO")</code> should return <code>0.888888888888889</code>.');
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- text: <code>jaro("ABCD", "BCDA")</code> should return <code>0.8333333333333334</code>.
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testString: assert.equal(jaro('ABCD', 'BCDA'), 0.8333333333333334,'<code>jaro("ABCD", "BCDA")</code> should return <code>0.8333333333333334</code>.');
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```
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</section>
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## Challenge Seed
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<section id='challengeSeed'>
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<div id='js-seed'>
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```js
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function jaro (s, t) {
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// Good luck!
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}
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```
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</div>
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</section>
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## Solution
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<section id='solution'>
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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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</section>
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