d0f66141ef
* Defined Recursion Added an English definition for recursion with examples and external sources. * md-ize and format
68 lines
2.3 KiB
Markdown
68 lines
2.3 KiB
Markdown
---
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title: Recursively Defined Functions
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---
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## Recursively Defined Functions
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This is a stub. <a href='https://github.com/freecodecamp/guides/tree/master/src/pages/mathematics/functions/recursively-defined-functions/index.md' target='_blank' rel='nofollow'>Help our community expand it</a>.
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<a href='https://github.com/freecodecamp/guides/blob/master/README.md' target='_blank' rel='nofollow'>This quick style guide will help ensure your pull request gets accepted</a>.
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<!-- The article goes here, in GitHub-flavored Markdown. Feel free to add YouTube videos, images, and CodePen/JSBin embeds -->
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### A Quick Intro
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Put simply, recursion if a form of defining something using itself within the definition
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This is a common example used to teach recursion, a function to generate the fibonacci numbers:
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```
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f(0) := 0 Base case 0
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f(1) := 1 Base case 1
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f(x) := f(x - 1) + f(x - 2) | x > 1
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```
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Now, defining a function with itself will leave you with a few problems. The biggest is that if you define a function with itself, how are you supposed to know/determine when the function stops?
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Here's a simple example:
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```js
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function foo(x){
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y = x + 1;
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console.log(y);
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foo(y);
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}
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```
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This function takes some number, and adds 1 to it infinitely.
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In order to determine a stopping point, you need to add a base case.
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A base case is a point at which the function does not call the recursive step.
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```js
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function foo(x){
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if(x > 5){
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return x
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}
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y = x + 1;
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console.log(y);
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foo(y);
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}
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```
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This is now equivalent to:
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```js
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function foo(x){
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while(y < 5){
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y = x + 1;
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console.log(y);
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}
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}
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```
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Almost everything that can be defined recursively can also be created with a loop. In fact, most compilers turn your code into a loop anyway, at some point, prior to it being executed.
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It should also be noted that recursion may look cool and allow you to shrink a long loop down into just a few lines of code but there are a few drawbacks. Mainly, performance of a recursive definition is generally slower than that of an iterative one, not to mention, it can be harder to read for people unfamiliar or new to the concept.
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#### More Information:
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<!-- Please add any articles you think might be helpful to read before writing the article -->
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- https://en.wikipedia.org/wiki/Recursion
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- https://introcs.cs.princeton.edu/java/23recursion/
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