Recursion is a programming technique where a function calls itself. Recursion is also a technique of “Making a loop in a functional way”. Recursive functions have two parts. “Base case” and “The Recursive function”.

Recursion in computer science is a method of solving a problem where the solution depends on solutions to smaller instances of the same problem.

Wikipedia

Skeleton of a Recursive function:

function skeleton() { // Base case // Recursive function }

Before we move forward, we need to know about **Factorial**.

It’s a mathematical term. The factorial of a positive integer *n*, denoted by *n*! and is the product of all positive integers less than or equal to *n*.

n! = n * (n – 1) * (n – 2) * (n – 3) * … .. * 3 * 2 * 1

Example: 5! = 5 * 4 * 3 * 2 * 1 = 120

Here,

5! = n!, n = 5, (n – 1) = 4, (n – 2) = 3, … ..

So, the factorial of 5 is 120. Here are a couple of things about factorial —

- Can’t be a negative number
- Factorial of 0 is equal to 1

Now let’s create a **Recursive Function **of *Factorial* —

function fact($n) { // Base case if ( $n === 0 ) { return 1; } // recursive function return $n * fact( $n - 1 ); } echo fact(4); // 4 * 3 * 2 * 1 = 24

Now, you must be thinking, where is the loop? How it’s iterating and getting data?

The diagram down below will show the entire process of recursion.

When I’ve called `fact(4)`

it went into the function and got `fact(3)`

and then it went into `fact(3)`

and got `fact(2)`

… .. and so on. Finally, it went to `fact(0)`

and got 1 from the * base case*.

Then it started returning the value to

`fact(1)`

, `fact(2)`

… .. and so on, that’s why finally `fact(4)`

got 6 from `fact(3)`

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