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Factorial – Solution & Complexity

Interview solutions
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Factorial

1. Understand the Definition

  • Factorial means multiplying all positive integers from 1 through n.
  • By definition, 0! equals 1.
  • The input is non-negative, so we do not need to handle negative numbers.

2. Recursive Idea

  • Factorial has a direct recursive definition: n! = n * (n - 1)!.
  • The base case is 0! = 1 or 1! = 1.
  • This works, but an iterative loop avoids recursion depth concerns.
def factorial(n):
    if n <= 1:
        return 1
    return n * factorial(n - 1)

3. Iterative Accumulation

  • Start with result = 1.
  • Multiply by each number from 2 through n.
  • If n is 0 or 1, the loop does not run and the answer remains 1.

4. Build the Loop

  • Use range(2, n + 1) so the final multiplier n is included.
  • Update the running product each iteration.
  • Return the product after all factors have been applied.
def factorial(n):
    result = 1
    for value in range(2, n + 1):
        result *= value
    return result

5. Final Solution and Complexity

  • The solution directly follows the mathematical definition.
  • Time complexity is O(n).
  • Space complexity is O(1) because it uses one accumulator.
def factorial(n: int) -> int:
    result = 1
    for value in range(2, n + 1):
        result *= value
    return result

FAQ

See also:

Practice Factorial online (run code in the browser)Climbing Stairs solution (easy)Fibonacci Number solution (easy)FizzBuzz solution (easy)Palindrome Number solution (easy)All coding interview problems
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