Recursion Factorial

Recursive Functions is Inception, where function can be assumed of dream,where the function can call itself until the base result is obtained.


                                        is the process of repeating items in a self-similar way. In programming languages, if a program allows you to call a function inside the same function, then it is called a recursive call of the function.

Recursion occurs when a thing is defined in terms of itself or of its type. Recursion is used in a variety of disciplines ranging from linguistics to logic. The most common application of recursion is in mathematics and computer science, where a function being defined is applied within its own definition. While this apparently defines an infinite number of instances (function values), it is often done in such a way that no infinite loop or infinite chain of references can occur.


Python allows functions to call itself. 

A Recursive Solution comprises of:
  • Base Part
                        It is the solution to the smallest version of the problem.
  • Inductive part
                        It is the Recursive part of the problem That reduces the complexity of the problem. the solution is expressed in terms of a smaller version of itself. 


            The product of all positive integers less than or equal to n is the factorial of a non-negative integer n, indicated by n!.
                                       $$ n! = n * (n-1) * (n-2) * (n-3) * ... * 3 * 2 * 1 $$  

The above function is the Iterative approach to compute the factorial of a positive integer n.
Since we are using for loop and the loop iterates from 1 to n+1 to calculate the factorial of n.

 $$factorial(n) =\begin{cases}1&\quad\text{if } n\text{ == 0 or 1}\\n * factorial(n-1)&\quad\text{if }n\text{ > 1}\end{cases}$$

The above example shows us the recursive approach of implementing factorial of any positive integer n.
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