How do you find the two numbers that appear once when every other number appears twice?
PICTURE THIS: HASH MAP
Key"user_id"
Hashslot 17
Valuethe record
Simple meaning
XOR everything
WHY — Bit Manipulation instead of guessing?
Why interviewers care about Bit Manipulation:
This is a process
question about Bit Manipulation.
Panels listen for order,
trade-offs, and what you would actually do on a DSA project - not buzzwords.
Stay structured
Name the idea, why it exists, then one short example.
Close cleanly
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
XOR everything
- 2the result is a
XOR b.
- 3Isolate a bit that
differs (xor & -xor), partition numbers by that bit, and XOR each group to recover a and b.
- 4Time is O(n) and
space is O(1).
- 5A hash map of
counts is O(n) space and weaker in interviews.
- 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:
Say this line
“Time is O(n) and space is O(1).”
Break into beats
TimeisOnandspace
Speaking order
2987408337471632900
Note: Adapt this scaffold to your own project — keep it under 60–90 seconds.
Key takeaway
XOR everything the result is a XOR b.