Point72·Data Scientist·Technical Phone Screen·Intermediate

Intermediate

Jul 2026

Summary

Point72 data scientist interview with a geometry-heavy coding problem that felt more like a competitive programming round than anything I expected from a finance firm. The problem was well-scoped but the edge case handling is where they really pushed.

Questions Asked (1)

Given an array of circle pairs where each circle is defined by (x, y, r), classify each pair as IDENTICAL, CONCENTRIC, TOUCHING_EXTERNALLY, TOUCHING_INTERNALLY, INTERSECTING, or DISJOINT. Coordinates and radii are integers up to 1e9, and N can be up to 2e5. You must avoid floating-point errors, handle degenerate cases like r=0, and explain your time and space complexity.

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

My first instinct was to just compute Euclidean distance and compare, which the interviewer immediately flagged.

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AI HintsAI Generated

Suggested Approach

Start by clarifying the classification rules and edge cases, then propose an integer-based distance comparison to avoid floating-point errors. Explain how to compute squared distances and compare them to squared radii sums/differences, and outline the O(N) time and O(1) extra space complexity.

Pro tip: Mention that for large coordinates (up to 1e9), squared distances can be up to 4e18, which fits in a 64-bit signed integer (max ~9.22e18), so using 64-bit integers is safe. Also, explicitly handle r=0 as a point circle and note that identical circles must have the same center and radius.

1. Clarify definitions and edge cases

Confirm the exact conditions for each classification, especially for degenerate cases like r=0, and ensure you understand that 'identical' requires both same center and same radius.

2. Use squared distances to avoid floating-point

Compute the squared distance between centers (dx^2 + dy^2) and compare it to squared sums/differences of radii. This avoids sqrt and floating-point precision issues.

3. Derive integer-based conditions

For each pair, compute d2 = dx^2 + dy^2, r_sum = r1 + r2, r_diff = |r1 - r2|. Then classify based on comparisons: d2 == 0 and r1 == r2 (identical), d2 == 0 and r1 != r2 (concentric), d2 == r_sum^2 (touching externally), d2 == r_diff^2 (touching internally), r_diff^2 < d2 < r_sum^2 (intersecting), else disjoint.

4. Handle degenerate cases explicitly

If either radius is 0, treat it as a point. For example, a point inside a circle is not intersecting; it's either internally touching (if on boundary) or disjoint (if inside).

5. Analyze complexity and scalability

State that the algorithm processes each pair in O(1) time, leading to O(N) total time and O(1) extra space (or O(N) if storing results). Emphasize that integer arithmetic handles up to 1e9 coordinates without overflow in 64-bit integers.

Key Points to Mention

Use of squared distances to avoid floating-point errors and sqrt.
Integer overflow considerations: coordinates up to 1e9, squared distances up to 4e18, which fits in 64-bit signed integers.
Explicit handling of degenerate cases: r=0, identical centers, and zero-distance scenarios.
Correct classification conditions using comparisons of d2 with (r1+r2)^2 and (r1-r2)^2.
Time complexity O(N) and space complexity O(1) extra (or O(N) for output).
Importance of testing edge cases like concentric circles with different radii, internally touching when one circle is inside another, and disjoint when one is completely inside without touching.

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