Math & Numbers

Python Program for Factorial (Recursion & Iteration)

Calculate the factorial of a non-negative integer (n!) using both recursive and iterative paradigms, handling base cases safely.

Python Source Code

Editable code sample with line numbers

Python

Expected Output

When this program is compiled and executed, the terminal outputs:

0! = 1 (recursive match: True)
1! = 1 (recursive match: True)
5! = 120 (recursive match: True)
7! = 5040 (recursive match: True)
10! = 3628800 (recursive match: True)

How the Code Works

Factorial n! is the product of all positive integers less than or equal to n, with 0! = 1. The iterative version loops from 2 to n, multiplying into an accumulator. The recursive version uses the recurrence relation fact(n) = n * fact(n-1) until reaching the base case fact(0) or fact(1) = 1.

Time Complexity

O(N)

Space Complexity

O(1) iterative, O(N) recursive call stack

Key Takeaways & Best Practices

0! is mathematically defined as 1.
Iterative approach avoids recursion depth limit (sys.getrecursionlimit()).
Python automatically promotes large integers to arbitrary precision without overflow.

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