Program and time complexity of factorial using iteration and recursion in C

Program and time complexity of factorial using iteration and recursion in C

Factorial can be calculated using iteration and recursion .In iterative method for loop so time complexity is O(n) and space complexity is O(1).But in recursion time complexity is O(n) and space complexity is O(n).

Factorial is 

5!=5*4*3*2*1=120

#include <stdio.h>

void main() {

    int n;

    int i;

    int f=1;

    printf("enter number");

    scanf("%d",&n);

    for(i=1;i<=n;i++)

    {

        f=f*i;

    }

    printf("factorial of a number is %d",f);

}

Factorial using recursion

#include <stdio.h>

int fact(int n)

{

    int f;

    if(n==1)

      return(1);

    else

    f=n*fact(n-1);

    return(f);

}

void main() {

    int n;

    int i;

    printf("enter number");

    scanf("%d",&n);

    printf("factorial of a number is %d",fact(n));

}

Time complexity using recursion in factorial

T(n)=T(n-1)+c

T(n-1)=T(n-1-1)+c

Put the value of T(n-1)

T(n)=T(n-2)+2c

In general term

T(n)=T(n-k)+kc

n-k=0

n=k

T(n)=T(0)+kc

T(n)=1+nc

T(n)=O(n)

So time complexity of factorial using recursion is O(n) and space complexity is also O(n).