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116 lines
2.1 KiB
Markdown
116 lines
2.1 KiB
Markdown
---
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id: 5a23c84252665b21eecc7ee0
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title: Left factorials
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challengeType: 1
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forumTopicId: 302302
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dashedName: left-factorials
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---
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# --description--
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**Left factorials**, $ !n $, may refer to either *subfactorials* or to *factorial sums*. The same notation can be confusingly seen used for the two different definitions. Sometimes, *subfactorials* (also known as *derangements*) may use any of the notations:
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<ul>
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<li>$!n`$</li>
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<li>$!n$</li>
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<li>$n¡$</li>
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</ul>
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(It may not be visually obvious, but the last example uses an upside-down exclamation mark.) This task will be using this formula for **left factorial**:
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$ !n = \\sum\_{k=0}^{n-1} k! $
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where $!0 = 0$
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# --instructions--
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Write a function to calculate the left factorial of a given number.
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# --hints--
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`leftFactorial` sollte eine Funktion sein.
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```js
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assert(typeof leftFactorial == 'function');
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```
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`leftFactorial(0)` sollte eine Zahl zurückgeben.
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```js
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assert(typeof leftFactorial(0) == 'number');
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```
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`leftFactorial(0)` sollte `0` zurückgeben.
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```js
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assert.equal(leftFactorial(0), 0);
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```
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`leftFactorial(1)` sollte `1` zurückgeben.
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```js
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assert.equal(leftFactorial(1), 1);
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```
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`leftFactorial(2)` sollte `2` zurückgeben.
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```js
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assert.equal(leftFactorial(2), 2);
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```
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`leftFactorial(3)` sollte `4` zurückgeben.
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```js
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assert.equal(leftFactorial(3), 4);
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```
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`leftFactorial(10)` sollte `409114` zurückgeben.
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```js
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assert.equal(leftFactorial(10), 409114);
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```
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`leftFactorial(17)` sollte `22324392524314` zurückgeben.
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```js
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assert.equal(leftFactorial(17), 22324392524314);
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```
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`leftFactorial(19)` sollte `6780385526348314` zurückgeben.
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```js
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assert.equal(leftFactorial(19), 6780385526348314);
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```
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# --seed--
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## --seed-contents--
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```js
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function leftFactorial(n) {
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}
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```
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# --solutions--
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```js
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function leftFactorial(n) {
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if (n == 0) return 0;
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if (n == 1) 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,
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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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