79d9012432
* fix(curriculum): tests quotes * fix(curriculum): fill seed-teardown * fix(curriculum): fix tests and remove unneeded seed-teardown
89 lines
2.6 KiB
Markdown
89 lines
2.6 KiB
Markdown
---
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title: Gamma function
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id: 5a23c84252665b21eecc7e76
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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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Implement one algorithm (or more) to compute the <a href="https://en.wikipedia.org/wiki/Gamma function">Gamma</a> ($\Gamma$) function (in the real field only).
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The Gamma function can be defined as:
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<div style='padding-left: 4em;'><big><big>$\Gamma(x) = \displaystyle\int_0^\infty t^{x-1}e^{-t} dt$</big></big></div>
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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>gamma</code> should be a function.
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testString: assert(typeof gamma=='function','<code>gamma</code> should be a function.')
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- text: <code>gamma(.1)</code> should return a number.
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testString: assert(typeof gamma(.1)=='number','<code>gamma(.1)</code> should return a number.')
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- text: <code>gamma(.1)</code> should return <code>9.513507698668736</code>.
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testString: assert.equal(gamma(.1), 9.513507698668736,'<code>gamma(.1)</code> should return <code>9.513507698668736</code>.')
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- text: <code>gamma(.2)</code> should return <code>4.590843711998803</code>.
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testString: assert.equal(gamma(.2), 4.590843711998803,'<code>gamma(.2)</code> should return <code>4.590843711998803</code>.')
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- text: <code>gamma(.3)</code> should return <code>2.9915689876875904</code>.
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testString: assert.equal(gamma(.3), 2.9915689876875904,'<code>gamma(.3)</code> should return <code>2.9915689876875904</code>.')
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- text: <code>gamma(.4)</code> should return <code>2.218159543757687</code>.
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testString: assert.equal(gamma(.4), 2.218159543757687,'<code>gamma(.4)</code> should return <code>2.218159543757687</code>.')
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- text: <code>gamma(.5)</code> should return <code>1.7724538509055159</code>.
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testString: assert.equal(gamma(.5), 1.7724538509055159,'<code>gamma(.5)</code> should return <code>1.7724538509055159</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 gamma (x) {
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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 gamma(x) {
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var p = [0.99999999999980993, 676.5203681218851, -1259.1392167224028,
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771.32342877765313, -176.61502916214059, 12.507343278686905,
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-0.13857109526572012, 9.9843695780195716e-6, 1.5056327351493116e-7
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];
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var g = 7;
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if (x < 0.5) {
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return Math.PI / (Math.sin(Math.PI * x) * gamma(1 - x));
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}
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x -= 1;
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var a = p[0];
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var t = x + g + 0.5;
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for (var i = 1; i < p.length; i++) {
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a += p[i] / (x + i);
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}
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var result=Math.sqrt(2 * Math.PI) * Math.pow(t, x + 0.5) * Math.exp(-t) * a;
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return result;
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}
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```
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</section>
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