Thursday, November 29

Factorial Of a Number Using Recursion


      
      Write a C program to find factorial of the given number using recursion.

Recursion: A function is called 'recursive' if a statement within the body of a function calls the same function. It is also called 'circular definition'. Recursion is thus a process of defining something in terms of itself.

Program: 

#include <stdio.h>
int fact(int n);
int main() 
{
int x, i;
printf("Enter a value for x: \n");
scanf("%d", &x);
i = fact(x);
printf("\nFactorial of %d is %d", x, i);
return 0;
}
 int fact(int n) 
{

if (n <= 0)                                            // n=0 indicates a terminating condition 
     {
           return (1);
      } 
else
     {
        /* function calling itself */
         return (n * fact(n - 1));            // n*fact(n-1) is a recursive expression 
            
     }
}


Output:

Enter a value for x:
4
Factorial of 4 is 24


Explanation:

fact(n) = n * fact(n-1)
If n=4
fact(4) = 4 * fact(3) there is a call to fact(3)
fact(3) = 3 * fact(2)
fact(2) = 2 * fact(1)
fact(1) = 1 * fact(0)
fact(0) = 1
fact(1) = 1 * 1 = 1
fact(2) = 2 * 1 = 2
fact(3) = 3 * 2 = 6
Thus fact(4) = 4 * 6 = 24
Terminating condition(n <= 0 here;) is a must for a recursive program. Otherwise the program enters into an infinite loop.