91 lines
3.2 KiB
Markdown
91 lines
3.2 KiB
Markdown
---
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id: 5a23c84252665b21eecc7ee0
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title: Left factorials
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challengeType: 5
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forumTopicId: 302302
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---
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## Description
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<section id='description'>
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<b>Left factorials</b>, $ !n $, may refer to either <i>subfactorials</i> or to <i>factorial sums</i>. The same notation can be confusingly seen used for the two different definitions. Sometimes, <i>subfactorials</i> (also known as <i>derangements</i>) may use any of the notations:
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<ul>
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<li>$!n`$</li>
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<li>$!n$</li>
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<li>$n¡$</li>
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</ul>
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(It may not be visually obvious, but the last example uses an upside-down exclamation mark.) This task will be using this formula for <b>left factorial</b>:
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$ !n = \sum_{k=0}^{n-1} k! $
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where $!0 = 0$
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</section>
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## Instructions
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<section id='instructions'>
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Write a function to calculate the left factorial of a given number.
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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>leftFactorial</code> should be a function.
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testString: assert(typeof leftFactorial == 'function', '<code>leftFactorial</code> should be a function.');
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- text: <code>leftFactorial(0)</code> should return a number.
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testString: assert(typeof leftFactorial(0) == 'number', '<code>leftFactorial(0)</code> should return a number.');
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- text: <code>leftFactorial(0)</code> should return <code>0</code>.
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testString: assert.equal(leftFactorial(0), 0, '<code>leftFactorial(0)</code> should return <code>0</code>.');
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- text: <code>leftFactorial(1)</code> should return <code>1</code>.
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testString: assert.equal(leftFactorial(1), 1, '<code>leftFactorial(1)</code> should return <code>1</code>.');
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- text: <code>leftFactorial(2)</code> should return <code>2</code>.
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testString: assert.equal(leftFactorial(2), 2, '<code>leftFactorial(2)</code> should return <code>2</code>.');
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- text: <code>leftFactorial(3)</code> should return <code>4</code>.
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testString: assert.equal(leftFactorial(3), 4, '<code>leftFactorial(3)</code> should return <code>4</code>.');
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- text: <code>leftFactorial(10)</code> should return <code>409114</code>.
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testString: assert.equal(leftFactorial(10), 409114, '<code>leftFactorial(10)</code> should return <code>409114</code>.');
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- text: <code>leftFactorial(17)</code> should return <code>22324392524314</code>.
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testString: assert.equal(leftFactorial(17), 22324392524314, '<code>leftFactorial(17)</code> should return <code>22324392524314</code>.');
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- text: <code>leftFactorial(19)</code> should return <code>6780385526348314</code>.
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testString: assert.equal(leftFactorial(19), 6780385526348314, '<code>leftFactorial(19)</code> should return <code>6780385526348314</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 leftFactorial(n) {
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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 leftFactorial(n) {
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if (n == 0)
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return 0
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if (n == 1)
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return 1;
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// Note: for n>=20, the result may not be correct.
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// This is because JavaScript uses 53 bit integers and
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// for n>=20 result becomes too large.
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let res = 2, fact = 2;
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for (var i = 2; i < n; i++) {
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res += fact;
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fact *= (i + 1);
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}
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return res;
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}
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```
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</section>
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