# C Recursion

In this tutorial, you will learn about the recursive function. Recursive functions are the functions which will call themselves inside it. While using recursion programmers need to be careful in defining an exit condition from the function. If the programmer forgets to mention the exit condition then the program will go into infinite recursion. Recursive functions are very useful in solving many mathematical problems. For example, while calculating the factorial of a number, generating Fibonacci series etc.

## How does recursion works?

Following is the syntax of the recursive function.

{

….

recursive_fun();

…

}

int main()

[

…

recursive_fun();

….

}

### C program to calculate factorial of a given number using recursion:

Here, you will see how we will calculate the factorial of a given number by using recursion. In general, the factorial of a number ‘x’ can be written as x! which can be written as:

n! = x(x-1)(x-2)…..2.1

In maths, a **factorial** is written as *n!* and is written as follows:

The factorial formula for n:

`n! = n(n - 1)(n - 2) ... 2..1`

After all, you can see that first we take an integer and keep multiplying the same integer by a number less than the previous number each time. For example, 4!= 4*3*2*1, which is equal to 24. It is simple and easy to calculate the factorial of a small number. But in the context of large numbers, it is very difficult. For this reason, we will write code for it.

**Code:**

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 | #include<stdio.h> int factorial(int);//Fucntion protoype int main() { int n,fact; printf("Enter a number: "); scanf("%d",&n); fact=factorial(n);//Function call printf("The factorial of the given number is: %d", fact); } int factorial(int x)//Fucntion definition { if(x<=1) return 1; else return (x*factorial(x-1));//Recursive Fucntion } |

**Output:**

The factorial of the given number is: 120

**Analysis:**

### C Program to print the Fibonacci series up to n terms by using recursion:

In this section, you will learn how to calculate the Fibonacci series up to n terms by using recursion. Firstly, Fibonacci series is the series generated by adding previous two numbers in sequence. The numbers are in the following sequence.

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ……..

Therefore, you can see that every number generated later will depend on the previous numbers to generate a sequence. So we can appply the recursion easily here which makes our codes more readable. Now see the code below to see how it works.

**Code:**

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 | #include<stdio.h> int fibonacci(int); int main() { int x,i,f; printf("Enter how many numbers you want to generate. "); scanf("%d", &x); f=fibonacci(x); printf("%d\t", f); } int fibonacci(int n) { if(n==0){ return 0; } if(n==1) { return 1; } else{ return (fibonacci(n-1)+fibonacci(n-2));//Recursion Function } } |

Output:

34

**Analysis:**

In the program above, we have generated a Fibonacci series by using recursion. The use of recursion has enabled the understanding and readability of the program. Recursive functions are powerful but it is important to realize that we must not forget to put the stopping condition. Otherwise, the program won’t stop which may also lead to the crashing of the system.

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