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curriculum/challenges/english/10-coding-interview-prep/rosetta-code/left-factorials.md

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