factorial with recursion code example

Example 1: find factoril in C using recursion

#include<stdio.h>
fact(int i, int k){
    k=k*i;
    i--;
    if(i==0){
        return k;
    }
    else{
        fact(i, k);
    }
}
int main()
{
    int k = 1, i, factorial;
    scanf("%d",&i);
    factorial = fact(i, k);
    printf("%d\n",factorial);
    return 0;
}

Example 2: complexity analysis of factorial using recursion

T(n) = T(n-1) + 3   (3 is for As we have to do three constant operations like 
                 multiplication,subtraction and checking the value of n in each recursive 
                 call)

     = T(n-2) + 6  (Second recursive call)
     = T(n-3) + 9  (Third recursive call)
     .
     .
     .
     .
     = T(n-k) + 3k
     till, k = n

     Then,

     = T(n-n) + 3n
     = T(0) + 3n
     = 1 + 3n

Example 3: recursion factorial algorithm

FUNCTION FACTORIAL (N: INTEGER): INTEGER
(* RECURSIVE COMPUTATION OF N FACTORIAL *)

BEGIN
  (* TEST FOR STOPPING STATE *)
  IF N <= 0 THEN
    FACTORIAL := 1
  ELSE
    FACTORIAL := N * FACTORIAL(N - 1)
END; (* FACTORIAL *)