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86 lines
1.9 KiB
Markdown
86 lines
1.9 KiB
Markdown
---
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id: 594810f028c0303b75339ad5
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title: Y combinator
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challengeType: 1
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forumTopicId: 302345
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dashedName: y-combinator
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---
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# --description--
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In strict <a href="https://www.freecodecamp.org/news/the-principles-of-functional-programming/" target="_blank" rel="noopener noreferrer nofollow">functional programming</a> and the lambda calculus, functions (lambda expressions) don't have state and are only allowed to refer to arguments of enclosing functions. This rules out the usual definition of a recursive function wherein a function is associated with the state of a variable and this variable's state is used in the body of the function.
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The Y combinator is itself a stateless function that, when applied to another stateless function, returns a recursive version of the function. The Y combinator is the simplest of the class of such functions, called fixed-point combinators.
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# --instructions--
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Define the stateless Y combinator function and use it to compute the factorials. The `factorial(N)` function is already given to you.
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# --hints--
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Y sollte eine Funktion zurückgeben.
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```js
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assert.equal(typeof Y((f) => (n) => n), 'function');
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```
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factorial(1) sollte 1 zurückgeben.
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```js
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assert.equal(factorial(1), 1);
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```
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factorial(2) sollte 2 zurückgeben.
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```js
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assert.equal(factorial(2), 2);
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```
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factorial(3) sollte 6 zurückgeben.
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```js
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assert.equal(factorial(3), 6);
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```
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factorial(4) sollte 24 zurückgeben.
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```js
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assert.equal(factorial(4), 24);
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```
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factorial(10) sollte 3628800 zurückgeben.
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```js
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assert.equal(factorial(10), 3628800);
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```
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# --seed--
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## --after-user-code--
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```js
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var factorial = Y(f => n => (n > 1 ? n * f(n - 1) : 1));
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```
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## --seed-contents--
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```js
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function Y(f) {
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return function() {
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};
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}
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var factorial = Y(function(f) {
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return function (n) {
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return n > 1 ? n * f(n - 1) : 1;
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};
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});
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```
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# --solutions--
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```js
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var Y = f => (x => x(x))(y => f(x => y(y)(x)));
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```
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