Interactive Python Lab

Factorial (Iterative)

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Samjhein

Line 1

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

Yeh approach kyun?

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

n! = n x (n-1) x ... x 1. Yaar, ye combinatorics ka base hai — permutations calculate karne mein kaam aata hai.

Analogy

Jaise 5 logo ko line mein arrange karo — 5! = 120 tariqe hain.

Step-by-step

0! = 1 (base case)
1 se n tak multiply karo
Ya recursion: factorial(n) = n * factorial(n-1)
math.factorial() built-in use karo production mein

Visual

def factorial(n): result = 1 for i in range(1, n+1): result *= i return result factorial(5) # 120

Common mistakes

Negative numbers ke liye factorial undefined hai
0! = 1 bhool jaana
Large numbers mein stack overflow — iterative use karo

Practice questions

Recursive aur iterative dono se banao
nCr (combinations) factorial se calculate karo

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

N = 8 pe

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

Challenge

Factorial iteratively implement karo. Verify karo: 0!=1, 5!=120, 10!=3628800.

Hint

product=1 se start karo, 1 se n tak har number se multiply karo. n=0 ko special case handle karo.

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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