Pure Storage·Software Engineer·Technical Phone Screen·Intermediate

IntermediatePrefer not to say

Apr 2026

Summary

Pure Storage coding round, one problem the whole session. The question was a geometry/hashing thing that looked deceptively clean but had some annoying edge cases around integer arithmetic.

Questions Asked (1)

Given a set of distinct points on a 2D plane, count how many squares can be formed using exactly four of those points as vertices. Squares can be axis-aligned or rotated at any angle.

Algorithms & Data Structures

Author's notes

The key insight I kept circling around was treating each pair of points as a diagonal rather than a side.

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AI HintsAI Generated

Suggested Approach

Clarify the problem constraints (e.g., number of points, coordinate ranges) and discuss the trade-offs between brute force and optimized approaches. Present an O(n^2) algorithm using hashing: for each pair of points, compute the two possible squares they could form and check if the other two vertices exist in a hash set. Emphasize handling both axis-aligned and rotated squares by using vector rotation.

Pro tip: Mention that you would use a hash set for O(1) lookups and that you can avoid double-counting by only considering each square once (e.g., by processing pairs in a consistent order or using a set of squares). This shows attention to efficiency and correctness.

1. Clarify requirements and constraints

Ask about the input size, coordinate ranges, and whether points are distinct. This determines the acceptable time complexity and data structures.

2. Choose an approach

Decide between brute force O(n^4) and optimized O(n^2) using hashing. Explain why O(n^2) is preferable for large inputs.

3. Derive square vertices from a pair

Given two points, compute the other two vertices of the square using vector rotation (90 degrees). Show the formulas for both possible squares.

4. Check existence and count

Use a hash set to check if the computed vertices exist. Count each square once by ensuring a consistent ordering (e.g., only count when the pair is the leftmost-bottom edge or by storing squares in a set).

5. Analyze complexity and edge cases

State time complexity O(n^2) and space O(n). Discuss edge cases like duplicate points, collinear points, and large coordinates.

Key Points to Mention

Hash set for O(1) point lookup
Vector rotation to find other vertices: (x, y) rotated 90° becomes (-y, x)
Avoiding double-counting by processing each square once
Time complexity O(n^2) and space O(n)
Handling both axis-aligned and rotated squares uniformly
Edge cases: duplicate points, collinear points, integer overflow

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