Microsoft·Software Engineer·Technical Phone Screen·Intermediate

IntermediatePrefer not to say

May 2026

Summary

Microsoft coding interview, one problem the whole session, geometry-flavored but really just a hashing exercise once you see it. Walked away feeling okay about it but not great.

Questions Asked (1)

Given a set of points in the 2D plane, find the minimum area of any axis-aligned rectangle whose four corners all appear in the set. Return 0 if none exists.

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

Started with brute force because I panicked a little seeing the geometry angle.

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AI HintsAI Generated

Suggested Approach

Clarify the problem constraints and edge cases, then propose an efficient algorithm such as grouping points by x-coordinate and checking pairs of x-values for matching y-coordinates. Analyze time and space complexity, and discuss potential optimizations or trade-offs.

Pro tip: Mention that sorting points and using a hash set for quick lookups can reduce the time complexity, and always consider the possibility of multiple rectangles with the same area.

1. Clarify the problem

Ask about input size, coordinate ranges, duplicates, and whether the rectangle must have positive area. Confirm that corners must be exactly from the set.

2. Brute-force baseline

Explain a naive O(n^4) approach: iterate over all pairs of points as diagonal corners and check if the other two corners exist. This shows understanding but is inefficient.

3. Optimized approach

Group points by x-coordinate. For each pair of x-values, find common y-values and compute areas. Use a hash set for O(1) lookups to check if corners exist.

4. Complexity analysis

Analyze time and space complexity of the optimized approach. Discuss worst-case and average-case scenarios, and compare with brute-force.

5. Edge cases and trade-offs

Handle cases with no rectangle, duplicate points, collinear points, and large inputs. Discuss trade-offs between time and space, and possible further optimizations.

Key Points to Mention

Time and space complexity of the proposed solution
Use of hash sets for O(1) lookups
Grouping points by x-coordinate to reduce search space
Handling edge cases: no rectangle, duplicates, collinear points
Trade-offs between different approaches (e.g., sorting vs. hashing)
Potential optimizations like early termination or pruning

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.