How do you find the median of a stream of integers as numbers arrive?
PICTURE THIS: 1, 2, 2, 8
Simple meaning
Keep a max-heap of the lower half and a min-heap of the upper half, rebalancing so sizes differ by at most one.
WHY — Heap instead of guessing?
Why interviewers care about Heap:
question about Heap.
trade-offs, and what you would actually do on a DSA project - not buzzwords.
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:
- 1Keep a max-heap of
the lower half and a min-heap of the upper half, rebalancing so sizes differ by at most one.
- 2Why it exists
Insert is O(log n)
- 3median is O(1) from
one root or the average of both.
- 4Give an example
Space is O(n).
- 5Sorting each query would
be too slow.
- 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
Keep a max-heap of the lower half and a min-heap of the upper half, rebalancing so sizes differ by at most one. Insert is O(log n)