Problem 7: Factorial

Hey everyone! 👋

Today, we're tackling a classic mathematical problem: Calculating the Factorial.

The Problem

The goal is to write a function that calculates the factorial of a number.
The factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n.

Formula: n! = n × (n-1) × (n-2) × ... × 1
Special Case: 0! = 1

Example:

• factorial(5) should return 120 (because 5 × 4 × 3 × 2 × 1 = 120)
• factorial(0) should return 1

The Solution

Here is the Python implementation using a loop:

def factorial(n):
    """
    Calculates the factorial of a number using a loop.
    """
    # Base case: 0! and 1! are both 1
    if n == 0 or n == 1:
        return 1
    else:
        result = 1
        # Loop from 2 up to n
        for i in range(2, n + 1):
            result *= i
        return result

# Test cases
print(factorial(5))
# Output: 120
print(factorial(0))
# Output: 1
print(factorial(7))
# Output: 5040

Code Breakdown

Let's walk through the code line by line:

1. def factorial(n):

   • Defines a function named factorial that takes one parameter n (the number to calculate the factorial for).

2. if n == 0 or n == 1: return 1

   • Base case: If n is 0 or 1, we return 1 immediately.
   • This is because 0! is defined as 1, and 1! is obviously 1.

3. else: result = 1

   • If n is greater than 1, we initialize a variable result to 1.
   • 1 is the multiplicative identity (multiplying by 1 doesn't change the value), making it a safe starting point.

4. for i in range(2, n + 1):

   • We start a loop that iterates from 2 up to n.
   • range(2, n + 1) generates numbers starting from 2 and stopping before n + 1, which means it includes n.

5. result *= i

   • In each iteration, we multiply the current result by the loop variable i.
   • This accumulates the product (1 * 2 * 3 * ... * n).

6. return result

   • After the loop finishes, we return the final computed factorial value.

Example Walkthrough with factorial(5)

Let's trace what happens when we call factorial(5):

1. Check: Is 5 equal to 0 or 1? No.
2. Initialize: result starts at 1.
3. Loop: i will take values 2, 3, 4, 5.
   • i = 2: result = 1 * 2 = 2
   • i = 3: result = 2 * 3 = 6
   • i = 4: result = 6 * 4 = 24
   • i = 5: result = 24 * 5 = 120
4. Return: The loop ends, and the function returns 120.

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Happy coding! 💻