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Factorial – Solution & Complexity

Interview solutions
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Factorial

Solution Walkthrough

  1. Step 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. Step 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. Step 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. Step 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. Step 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)Add Two Numbers solution (medium)Balanced Binary Tree solution (easy)Binary Tree Inorder Traversal solution (easy)Binary Tree Postorder Traversal solution (easy)All coding interview problems
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