JavaScript - 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.

function factorial(x){
  if (x == 0) {
    return 1;
  } else {
    return x*factorial(x-1);
  }
}

var txt;
txt = "factorial(3): " + factorial(3) + "<br>";
txt = txt + "factorial(5): " + factorial(5) + "<br>";
txt = txt + "factorial(10): " + factorial(10) + "<br>";

The output (value of txt) after running above script will be:

factorial(3): 6
factorial(5): 120
factorial(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.

function fib(n){
  if (n == 0) {
    return 0;
  } else if (n == 1) {
    return 1;
  } else {
    return fib(n-1) + fib(n-2);
  }
}

var txt;
txt = "Fibonacci 5th term: " + fib(5) + "<br>";
txt = txt + "Fibonacci 6th term: " + fib(6) + "<br>";
txt = txt + "Fibonacci 7th term: " + fib(7) + "<br>";

The output (value of txt) after running above script will be:

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