# Recursion in Python

The term Recursion can be defined as the process of defining something in terms of itself. In simple words, it is a process in which a function calls itself directly or indirectly.

Advantages of using recursion

• A complicated function can be split down into smaller sub-problems utilizing recursion.
• Sequence creation is simpler through recursion than utilizing any nested iteration.
• Recursive functions render the code look simple and effective.

Disadvantages of using recursion

• A lot of memory and time is taken through recursive calls which makes it expensive for use.
• Recursive functions are challenging to debug.
• The reasoning behind recursion can sometimes be tough to think through.

Syntax:

def func(): <--
|
| (recursive call)
|
func() ----

Example 1: A Fibonacci sequence is the integer sequence of 0, 1, 1, 2, 3, 5, 8….

## Python3

 # Program to print the fibonacci series upto n_terms # Recursive functiondef recursive_fibonacci(n):  if n <= 1:      return n  else:      return(recursive_fibonacci(n-1) + recursive_fibonacci(n-2)) n_terms = 10 # check if the number of terms is validif n_terms <= 0:  print("Invalid input ! Please input a positive value")else:  print("Fibonacci series:")for i in range(n_terms):    print(recursive_fibonacci(i))

Output
Fibonacci series:
0
1
1
2
3
5
8
13
21
34

Example 2: The factorial of 6 is denoted as 6! = 1*2*3*4*5*6 = 720.

## Python3

 # Program to print factorial of a number# recursively. # Recursive functiondef recursive_factorial(n):  if n == 1:      return n  else:      return n * recursive_factorial(n-1) # user inputnum = 6 # check if the input is valid or notif num < 0:  print("Invalid input ! Please enter a positive number.")elif num == 0:  print("Factorial of number 0 is 1")else:  print("Factorial of number", num, "=", recursive_factorial(num))

Output
Factorial of number 6 = 720

## What is Tail-Recursion?

A unique type of recursion where the last procedure of a function is a recursive call. The recursion may be automated away by performing the request in the current stack frame and returning the output instead of generating a new stack frame. The tail-recursion may be optimized by the compiler which makes it better than non-tail recursive functions.

Is it possible to optimize a program by making use of a tail-recursive function instead of non-tail recursive function?
Considering the function given below in order to calculate the factorial of n, we can observe that the function looks like a tail-recursive at first but it is a non-tail-recursive function. If we observe closely, we can see that the value returned by Recur_facto(n-1) is used in Recur_facto(n), so the call to Recur_facto(n-1) is not the last thing done by Recur_facto(n).

## Python3

 # Program to calculate factorial of a number# using a Non-Tail-Recursive function.  # non-tail recursive functiondef Recur_facto(n):        if (n == 0):         return 1       return n * Recur_facto(n-1)    # print the resultprint(Recur_facto(6))

Output
720

We can write the given function Recur_facto as a tail-recursive function. The idea is to use one more argument and in the second argument, we accommodate the value of the factorial. When n reaches 0, return the final value of the factorial of the desired number.

## Python3

 # Program to calculate factorial of a number# using a Tail-Recursive function. # A tail recursive function def Recur_facto(n, a = 1):        if (n == 0):         return a        return Recur_facto(n - 1, n * a)    # print the resultprint(Recur_facto(6))

Output
720

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