 # Recursion in C++ with example

The process in which a function calls itself is known as recursion and the corresponding function is called the recursive function. The popular example to understand the recursion is factorial function.

Factorial function: f(n) = n*f(n-1), base condition: if n<=1 then f(n) = 1. Don’t worry we wil discuss what is base condition and why it is important.

In the following diagram. I have shown that how the factorial function is calling itself until the function reaches to the base condition. Lets solve the problem using C++ program.

## C++ recursion example: Factorial

```#include <iostream>
using namespace std;
//Factorial function
int f(int n){
/* This is called the base condition, it is
* very important to specify the base condition
* in recursion, otherwise your program will throw
* stack overflow error.
*/
if (n <= 1)
return 1;
else
return n*f(n-1);
}
int main(){
int num;
cout<<"Enter a number: ";
cin>>num;
cout<<"Factorial of entered number: "<<f(num);
return 0;
}```

Output:

```Enter a number: 5
Factorial of entered number: 120```

### Base condition

In the above program, you can see that I have provided a base condition in the recursive function. The condition is:

```if (n <= 1)
return 1;```

The purpose of recursion is to divide the problem into smaller problems till the base condition is reached. For example in the above factorial program I am solving the factorial function f(n) by calling a smaller factorial function f(n-1), this happens repeatedly until the n value reaches base condition(f(1)=1). If you do not define the base condition in the recursive function then you will get stack overflow error.

## Direct recursion vs indirect recursion

Direct recursion: When function calls itself, it is called direct recursion, the example we have seen above is a direct recursion example.

Indirect recursion: When function calls another function and that function calls the calling function, then this is called indirect recursion. For example: function A calls function B and Function B calls function A.

### Indirect Recursion Example in C++

```#include <iostream>
using namespace std;
int fa(int);
int fb(int);
int fa(int n){
if(n<=1)
return 1;
else
return n*fb(n-1);
}
int fb(int n){
if(n<=1)
return 1;
else
return n*fa(n-1);
}
int main(){
int num=5;
cout<<fa(num);
return 0;
}```

Output:

`120`