PHP - Recursive Function

A function which can call itself is known as recursive function. A recursive function generally ends with one or more boundary conditions which defines exit conditions from the function, otherwise it will go into an infinite loop.

Example: Factorial of a number

The factorial of a positive integer is the multiplication of all positive integer less than or equal to that number.

factorial of number n = n! = n(n-1)(n-2)...1

In the example below, a recursive function called factorial() is used to calculate factorial of a number.

<?php
function factorial($x) {
  if ($x == 0 || $x == 1)
    return 1;
  else 
    return $x*factorial($x-1);    
}

echo "3! =  ".factorial(3)."\n";
echo "5! =  ".factorial(5)."\n";
echo "10! =  ".factorial(10)."\n";
?>

The output of the above code will be:

3! =  6
5! =  120
10! =  3628800

Example: Fibonacci Sequence

Fibonacci terms are generally represented as F_n. A Fibonacci term is the sum of two previous terms and starts with 0 and 1. Mathematically, it can be represented as:

F_n = F_n-1 + F_n-2

With boundary conditions: F₀ = 0 and F₁ = 1

The Fibonacci Sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233...

In the example below, a recursive function called fib() is created to find out the nth term of Fibonacci sequence.

<?php
function fib($n) {
  if ($n == 0)
    {return 0;}
  elseif ($n == 1)
    {return 1;}
  else
    {return fib($n-1) + fib($n-2);}
}

echo "Fibonacci 5th term: ".fib(5)."\n";
echo "Fibonacci 6th term: ".fib(6)."\n";
echo "Fibonacci 7th term: ".fib(7)."\n";
?>

The above code will give the following output:

Fibonacci 5th term: 5
Fibonacci 6th term: 8
Fibonacci 7th term: 13