ee1e8abd87
* feat(tools): add seed/solution restore script * chore(curriculum): remove empty sections' markers * chore(curriculum): add seed + solution to Chinese * chore: remove old formatter * fix: update getChallenges parse translated challenges separately, without reference to the source * chore(curriculum): add dashedName to English * chore(curriculum): add dashedName to Chinese * refactor: remove unused challenge property 'name' * fix: relax dashedName requirement * fix: stray tag Remove stray `pre` tag from challenge file. Signed-off-by: nhcarrigan <nhcarrigan@gmail.com> Co-authored-by: nhcarrigan <nhcarrigan@gmail.com>
116 lines
2.0 KiB
Markdown
116 lines
2.0 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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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` should be a function.
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```js
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assert(typeof leftFactorial == 'function');
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```
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`leftFactorial(0)` should return a number.
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```js
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assert(typeof leftFactorial(0) == 'number');
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```
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`leftFactorial(0)` should return `0`.
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```js
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assert.equal(leftFactorial(0), 0);
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```
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`leftFactorial(1)` should return `1`.
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```js
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assert.equal(leftFactorial(1), 1);
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```
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`leftFactorial(2)` should return `2`.
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```js
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assert.equal(leftFactorial(2), 2);
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```
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`leftFactorial(3)` should return `4`.
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```js
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assert.equal(leftFactorial(3), 4);
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```
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`leftFactorial(10)` should return `409114`.
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```js
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assert.equal(leftFactorial(10), 409114);
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```
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`leftFactorial(17)` should return `22324392524314`.
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```js
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assert.equal(leftFactorial(17), 22324392524314);
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```
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`leftFactorial(19)` should return `6780385526348314`.
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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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