freeCodeCamp/guide/english/mathematics/functions/recursively-defined-functions/index.md

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Recursively Defined Functions

Recursively Defined Functions

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A Quick Intro

Put simply, recursion if a form of defining something using itself within the definition

This is a common example used to teach recursion, a function to generate the fibonacci numbers:

f(0) := 0  Base case 0
f(1) := 1  Base case 1
f(x) := f(x - 1) + f(x - 2) | x > 1

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?

Here's a simple example:

function foo(x){
  y = x + 1;
  console.log(y);
  foo(y);
}

This function takes some number, and adds 1 to it infinitely. In order to determine a stopping point, you need to add a base case.

A base case is a point at which the function does not call the recursive step.

function foo(x){
  if(x > 5){
    return x
  }
  y = x + 1;
  console.log(y);
  foo(y);
}

This is now equivalent to:

function foo(x){
  while(y < 5){
    y = x + 1;
    console.log(y);
  }
}

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.

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.

More Information:

• https://en.wikipedia.org/wiki/Recursion
• https://introcs.cs.princeton.edu/java/23recursion/