Python - 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.

def factorial(x):
  if x == 0 or x ==1:
    return 1
  else:
    return x*factorial(x-1)

print("3! = ", factorial(3))
print("5! = ", factorial(5))
print("10! = ", factorial(10))

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.

def fib(n):
  if n == 0:
    return 0
  elif n == 1:
    return 1
  else:
    return fib(n-1) + fib(n-2)

print("Fibonacci 5th term:", fib(5))
print("Fibonacci 6th term:", fib(6))
print("Fibonacci 7th term:", fib(7))

The above code will give the following output:

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