Nested Loop Pattern Generation (Cartesian Products)

Nested loops generate Cartesian products of choices—every combo of outer × inner—useful for brute-forcing small keyspaces, building test strings, or enumerating edit patterns.

Why this shows up in the real world

PIN brute-force demos (educational only) nest digit loops. Test data factories combine prefixes and suffixes exhaustively for QA.

Core idea (explained for students)

Python offers itertools.product instead of manual nested loops: for tup in product('ab', '12'): .... For large spaces, add pruning or random sampling instead of full enumeration.

Try this in Python

from itertools import product


def all_pairs(chars: str, digits: str) -> list[str]:
    return [a + b for a, b in product(chars, digits)]


print(all_pairs("AB", "12")[:6])

Common mistakes

• Exponential blowup—know constraints before enumerating.
• Accidentally quadratic nested loops on big inputs in production.

Key takeaways

• Replace nested loops with product or recursion with backtracking for clarity.
• Log estimated iteration counts before running brute generators.