Find Nth Factorial
Difficulty: Easy
Understanding The Problem
Problem Description
Write a program to find the
factorial
of a given number
n
.
Problem Note

n
is a nonnegative integer. 
Factorial of a nonnegative integer
n
is the multiplication of all integers smaller than or equal ton
Example
Input: n = 6
Output: 720
Explanation: Factorial of 6 is 6*5*4*3*2*1 which is 720.
Solution

Recursive Solution
: For f(x),
return 1
when x is0
, otherwisereturn x*f(x1)

Iterative Solution
: Iterate from 1 to x and maintain a
factorial
variable.
You can try the problem here.
1. Recursive Solution
We have to find the factorial of a number. Mathematically, the factorial of a number is the product from 1 to that number.
i.e.
factorial(Z) = 1 x 2 x 3 x 4 . . . x (Z2) x (Z1) x Z
Looking over the above equation, we can conclude that the
factorial(Z) = factorial(Z1) x Z
Now, the equation seems like a recursive structure, where
factorial
is a function and we have to find the factorial of
Z
. Now, We know that the factorial of
0
is
1
and factorial doesn’t exist for ve numbers. We can use this as a base case of the recursive function.
Base Case
Now think about the base case, where the function will directly give you results without breaking it again into subproblem.
fact(5)
= 5 * fact(4)
= 5 * 4 * fact(3)
= 5 * 4 * 3 * fact(2)
= 5 * 4 * 3 * 2 * fact(1)
= 5 * 4 * 3 * 2 * 1 * fact(0)
The factorial of a negative number is not defined, so fact(0) is the smallest version of the factorial problem where our solution will terminate. Here n = 0 is the base case which will return 1. Since 0! = 1.
To understand more about recursion, refer here .
Solution Steps

Create a recursive function
factorial(Z)

Return 1 when
Z
is 0. 
Otherwise, return
Z * factorial(Z1)
Pseudo Code
int findFactorial(int n) {
if(n is 0)
return 1
return n * (findFactorial(n1))
}
Complexity Analysis
Time Complexity: O(n)
Space Complexity: O(n)
Critical Ideas To Think
 How did we define the recursive structure?
 Why we returned 1 when n is 1?
 Why is the space complexity is of O(n)? Answer : The recursive function uses stack space and in this case, we are recursively calling the function until n reaches to 0 and that will create n stack frames in the memory.
 Can you draw the recursion tree for this case?
2. Iterative Solution
Instead of going recursive, we can use the logic of factorial in the way we do it in our notebooks and that is multiplying numbers from 1 to n.
So, the straight forward way is to use a for loop and iterate till n while maintaining a variable that will store the factorial.
Solution Steps

Create a
factorial
variable and initialize it with1

Create a for loop and iterate from 1 to
n

In each iteration, multiply
factorial
withi

Return
factorial
Pseudo Code
int findFactorial(int n) {
int factorial = 1
for(int i = 1 to i <= n){
factorial = factorial * i
}
return factorial
}
Complexity Analysis
Time Complexity: O(n)
Space Complexity: O(1)
Critical Ideas To Think

Why we started the iteration from 1 while the base case in recursive function was
n is 0
?  According to you, what should be the maximum number for which you can find the factorial if you are using a single processor system and using some data structure like Big integer?
Comparison Of Different Solutions
Suggested Problems To Solve

Print numbers
n
to1
using a recursive function  Find a minimum element in sorted and rotated array
 Recursive Insertion Sort
 Median of two sorted array of same size
 Inversion count in an array
If you have any more approaches or you find an error/bug in the above solutions, please comment down below.
Happy Coding!
Enjoy Algorithms!