Why is any comparison-based sort Omega(n log n) in the worst case?
PICTURE THIS: GIT FLOW
Simple meaning
There are n!
WHY — Sorting instead of guessing?
Why interviewers care about Sorting:
on Sorting.
the situation, the default choice, and one exception - that reads as experience.
Name the idea, why it exists, then one short example.
End with when you use it and one common pitfall.
STEPS — What happens step by step?
Before you speak the answer, walk the interviewer through these steps:
- 1Define it
There are n!
- 2possible orders, and each
comparison has two outcomes, so a decision tree must have height at least log2(n!), which is Theta(n log n) by Stirling.
- 3That is why merge/heap
sort are optimal among comparison sorts.
- 4Counting and radix sort
beat this by using integer structure, not comparisons.
- 5Common mistake
What juniors usually get wrong.
- 6Close
When you pick this over the alternative.
EXAMPLE — See it in action
Here's a short line you can speak, broken into clear beats:
Note: Adapt this scaffold to your own project — keep it under 60–90 seconds.
Key takeaway
There are n! possible orders, and each comparison has two outcomes, so a decision tree must have height at least log2(n!), which is Theta(n log n) by Stirling.