99 lines
2.9 KiB
Markdown
99 lines
2.9 KiB
Markdown
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---
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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(''+tests[0]+'')</code> should return a number.'
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testString: 'assert(typeof gamma(tests[0])==''number'',''<code>gamma(''+tests[0]+'')</code> should return a number.'')'
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- text: '<code>gamma(''+tests[0]+'')</code> should return <code>''+results[0]+''</code>.'
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testString: 'assert.equal(gamma(tests[0]),results[0],''<code>gamma(''+tests[0]+'')</code> should return <code>''+results[0]+''</code>.'')'
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- text: '<code>gamma(''+tests[1]+'')</code> should return <code>''+results[1]+''</code>.'
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testString: 'assert.equal(gamma(tests[1]),results[1],''<code>gamma(''+tests[1]+'')</code> should return <code>''+results[1]+''</code>.'')'
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- text: '<code>gamma(''+tests[2]+'')</code> should return <code>''+results[2]+''</code>.'
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testString: 'assert.equal(gamma(tests[2]),results[2],''<code>gamma(''+tests[2]+'')</code> should return <code>''+results[2]+''</code>.'')'
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- text: '<code>gamma(''+tests[3]+'')</code> should return <code>''+results[3]+''</code>.'
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testString: 'assert.equal(gamma(tests[3]),results[3],''<code>gamma(''+tests[3]+'')</code> should return <code>''+results[3]+''</code>.'')'
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- text: '<code>gamma(''+tests[4]+'')</code> should return <code>''+results[4]+''</code>.'
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testString: 'assert.equal(gamma(tests[4]),results[4],''<code>gamma(''+tests[4]+'')</code> should return <code>''+results[4]+''</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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### After Test
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<div id='js-teardown'>
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```js
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console.info('after the test');
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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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