The 60-second answer
Reject immediately if total_sum is not divisible by k or the largest value exceeds target=total_sum/k. Sort descending and backtrack by placing each value into a bucket without exceeding target.
Build the answer in this order
1
Clarify constraints
Reject immediately if total_sum is not divisible by k or the largest value exceeds target=total_sum/k.
2
Choose the approach
Sort descending and backtrack by placing each value into a bucket without exceeding target.
3
Prove complexity
Prune symmetric bucket states—especially identical empty/equal buckets—to avoid repeated equivalent work.
4
Test edge cases
Worst-case complexity is exponential; memoized used-mask formulations can trade memory for stronger pruning.
A useful interview mental model
This is the shape of a strong answer—not a script to memorize.
01Clarify
02Approach
03Implement
04Test
05Complexity
Senior-level signal
- Explain state-compression and symmetry-pruning correctness, not just the code.
- Discuss when pseudo-polynomial DP is feasible based on n and value bounds.
What the interviewer is really testing
Problem decomposition, correctness, data-structure choice, complexity reasoning, and clean implementation under pressure.
Likely follow-up questions
Can you improve the time or space complexity?
Which edge case is most likely to break this solution?
How would you test this under interview time pressure?
Common weak-answer patterns
- Starting to code before constraints are clear.
- Giving complexity without explaining why it is correct.
- Skipping adversarial and boundary cases.