Python Factorial Function | Dataford Interview Questions

In an Alten Nederland engineering tool, implement a reusable function that computes the factorial of a non-negative integer. The function must avoid Python's built-in factorial implementation and must support large values without relying on recursion depth.

For an integer n, factorial is defined as n! = 1 * 2 * ... * n, with 0! = 1. If an optional positive modulo is provided, return n! % modulo instead of the exact factorial.

Formal Specification

Implement factorial(n, modulo=None).

Input: n, a non-negative integer, and optional modulo, a positive integer or None.
Output: An integer containing either the exact value of n! or its remainder modulo modulo.
Do not use math.factorial or recursion in the primary solution.

Constraints

0 <= n <= 100000
modulo is None or an integer from 1 through 1000000007
Inputs are valid integers

Function Signature

def factorial(n, modulo=None):

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