Factorial of a Number

Given a non-negative integers n, compute the factorial of the given number.

Note: Factorial of n is defined as n * (n -1) * (n - 2) * ... * 1. For n = 0, the factorial is defined as 1.

Examples:

Input: n = 5
Output: 120
Explanation: 5! = 5 * 4 * 3 * 2 * 1 = 120

Input: n = 4
Output: 24
Explanation: 4! = 4 * 3 * 2 * 1 = 24

Iterative Solution - O(n) Time and O(1) Space

Factorial is computed by multiplying all integers from 1 to n using a loop. We initialize a variable ans as 1 and update it in each iteration by multiplying with the current number. This approach avoids recursion and uses constant extra space.

Step-by-step execution:

For n = 4

• Initialize : ans = 1
• i = 1, ans = 1 * 1 = 1
• i = 2, ans = 1 * 2 = 2
• i = 3, ans = 2 * 3 = 6
• i = 4, ans = 6 * 4 = 24

Final factorial = 24

#include <iostream>
using namespace std;

int factorial(int n) {
    
        // Calculating factorial of number
        int ans = 1;
        for (int i = 2; i <= n; i++) {
            ans = ans * i;
        }
        return ans;
    }

int main()
{
    int num = 5;
    cout <<  factorial(num) << endl;
    return 0;
}

#include <stdio.h>

int factorial(int n)
{
    
    // Calculating factorial of number
    int ans = 1, i;
    for (i = 2; i <= n; i++)
        ans *= i;
    return ans;
}

int main()
{
    int num = 5;
    printf("%d\n", factorial(num));
    return 0;
}

class GfG {

    public static int factorial(int n) {
        
        // Calculating factorial of number
        int ans = 1;
        for (int i = 2; i <= n; i++) {
            ans = ans * i;
        }
        return ans;
    }

    public static void main(String[] args)
    {
        int num = 5;
        System.out.println( factorial(5));
    }
}

def factorial(n):
    ans = 1
    i = 2
    
    #Calculating factorial of number
    while (i <= n):
        ans *= i
        i += 1
    return ans

if __name__ == "__main__":
    num = 5
    print(factorial(num))

using System;

class GFG {

    public static int factorial(int n) {
        
        // Calculating factorial of number
        int ans = 1;
        for (int i = 2; i <= n; i++) {
            ans = ans * i;
        }
        return ans;
    }

    public static void Main()
    {
        int n = 5;
        Console.WriteLine(factorial(n));
    }
}

function factorial(n) {
    
    // Calculating factorial of number
    let ans = 1;
    for (let i = 2; i <= n; i++) {
        ans = ans * i;
    }
    return ans;
}

// Driver method
let num = 5;
console.log(factorial(5));

120

Recursive Solution - O(n) Time and O(n) Space

Factorial is defined recursively as n! = n × (n - 1)!. We define a base case where if n equals 0 or 1, the function returns 1. Otherwise, the function calls itself with n minus 1, breaking the problem into smaller subproblems until reaching the base case.

#include <iostream>
using namespace std;

int factorial(int n)
{

    // Calculating factorial of number
    if (n == 0 || n == 1)
        return 1;
    return n * factorial(n - 1);
}

int main()
{
    int num = 5;
    cout << factorial(num) << endl;
    return 0;
}

#include <stdio.h>

int factorial(int n)
{
    // Calculating factorial of number
    if (n == 0)
        return 1;
    return n * factorial(n - 1);
}

int main()
{
    int num = 5;
    printf("%d\n", factorial(num));
    return 0;
}

class GFG {

    static int factorial(int n)
    {
        // Calculating factorial of number
        if (n == 0 || n == 1)
            return 1;
        return n * factorial(n - 1);
    }

    public static void main(String[] args)
    {
        int num = 5;
        System.out.println(factorial(num));
    }
}

def factorial(n):

   # Calculating factorial of number
    if n == 0:
        return 1

    return n * factorial(n - 1)


if __name__ == "__main__":

    num = 5
    print(factorial(num))

using System;

class GFG {

    static int factorial(int n)
    {
        // Calculating factorial of number
        if (n == 0)
            return 1;

        return n * factorial(n - 1);
    }

    public static void Main()
    {
        int n = 5;
        Console.WriteLine(factorial(n));
    }
}

function factorial(n)
{

    // Calculating factorial of number
    if (n == 0)
        return 1;
    return n * factorial(n - 1);
}

// Driver Code
let num = 5;
console.log(factorial(num));

120