The Way Recursion Works

Recursive function is the function that, as part of its execution, it invokes itself.

For example, if we at a function fact(n) that does factorial of number n.

   fact(1) = 1
   fact(2) =2 * 1
   fact(3) =3 * 2 * 1
   fact(4) =4 * 3 * 2 * 1
   fact(5) =5 * 4 * 3 * 2 * 1
   ......

We can define the above lines like this:

   fact(1) = 1
   fact(2) =2 * fact(1)
   fact(3) =3 * fact(2)
   fact(4) =4 * fact(3)
   fact(5) =5 * fact(4)
    ........

 So, we can say that,
  fact(n) = n * fact(n-1)   is the formula to find the factorial of any number.

Every recursive function has two parts:
Base Case: It terminates the recursive process.
Recursive Case: Where the recursion actually occurs. In other words, where it calls the function itself. From this case, the program keeps running, means it keeps calling the function.
To terminate the program from this state, we the base case. When, program faces the base case, it stops calling the function.

In this example for base case , we can assume when n is 1, it will return 1.
Else, it will recall the function and for this, we can plug the factorial calculation formula we found above.

Python code for factorial calculation is given below:

Let's take another example of finding the Fibonacci series:
In this example for base case , we can assume

fibonacci(1)==1 and fibonacci(0) == 0

 

Else, it will recall the function and for this,

fibonacci(5) = fibonacci(4) + fibonacci(3)

fibonacci(3) = fibonacci(2) + fibonacci(1)

fibonacci(4) = fibonacci(3) + fibonacci(2)

fibonacci(2) = fibonacci(1) + fibonacci(0)

So, we can say that,
fibonacci(n) = fibonacci(n-1) + fibonacci(n-2)  is the formula to find Fibonacci series.

Now let's look at the python code for this:

 

GitHub Link for the code is here