Factorial of a Number

📌 Definition:

📖 Detailed Explanation:

Iterative multiplication is O(n) and safest; recursion (n * factorial(n-1), base case n <= 1) is elegant and often requested. Reject negatives. Results overflow fixed-width integers quickly (13! exceeds int, 21! exceeds long), so use big integers for large n.

💻 Solutions:

• Java
• JavaScript
• Python

public static long factorial(int n) {
    if (n < 0) throw new IllegalArgumentException("n >= 0");
    long r = 1;
    for (int i = 2; i <= n; i++) r *= i;
    return r;
}

function factorial(n) {
  if (n < 0) throw new Error('n >= 0');
  let r = 1n;                 // BigInt for large n
  for (let i = 2; i <= n; i++) r *= BigInt(i);
  return r;
}

def factorial(n):
    if n < 0:
        raise ValueError('n >= 0')
    r = 1
    for i in range(2, n + 1):
        r *= i
    return r

🔑 Key Points:

• 0! = 1; reject negatives
• Iterative O(n), no stack risk
• Recursion needs a clear base case
• Overflows int at 13!, long at 21!

🌍 Real-World Example: