Interactive Python Lab

Factorial (Iterative)

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Explain

Line 1

Computing 5! = 5 × 4 × 3 × 2 × 1 = 120.

Why this approach?

We choose 5 as a demonstration because it's small enough to trace fully but large enough to show how the result grows. The mathematical definition: n! = n × (n-1) × ... × 2 × 1.

Structured Explanation

Overview

Factorial n! = n × (n-1) × ... × 1 for n≥1; 0! = 1 by convention.

Analogy

Counting arrangements of n cards: n choices for first, n-1 for second, and so on.

Step-by-step

Check base case: if n == 0: return 1.
Otherwise: return n * factorial(n-1).
Iterative version: start result=1, multiply 1..n.

Visual

4! = 4×3×2×1 = 24

Common mistakes

Not handling n=0 (should be 1).
Stack overflow for large n in recursive version (use iterative or math.factorial).

Practice questions

Compute 10! manually then verify with math.factorial.
Find how many trailing zeros 100! has (hint: count factors of 5).

Time

O(n)

Space

O(n) recursive (stack), O(1) iterative

Complexity

Time

O(n)

Space

O(1)

Complexity Overview

O(1)space

O(log n)

O(n)time

O(n log n)

O(n²)

n = 8range 1-20

AT N = 8

Complexity	Operations
O(1)	1
O(log n)	3
O(n)	8
O(n log n)	24
O(n²)	64

Challenge

Implement factorial iteratively. Then verify: 0! = 1, 5! = 120, 10! = 3628800.

Hint

Start product=1, multiply by each number from 1 to n. Handle n=0 as a special case.

Code Studio

Factorial (Iterative)

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Real-World Applications

1

Understanding mathematical accumulation

2

Debugging recursive call stacks (Stack overflow)

3

Permutation logic

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