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Pitchbook·Software Engineer·Technical Phone Screen·Intermediate

Intermediate
May 2026

Summary

Pitchbook software engineer interview with a coding round focused on computational geometry and nearest neighbor search. Two related problems, both building on each other, which felt reasonable in isolation but the second one had some gotchas around tie-breaking that I almost missed.

Questions Asked (2)

Q1

Write a function that computes the Euclidean distance between two points in n-dimensional space, where each point is a list of floats.

Algorithms & Data Structures
Author's notes

Pretty standard warmup.

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AI HintsAI Generated

Suggested Approach

Start by clarifying assumptions (e.g., points are lists of floats, same length, non-empty) and then describe the algorithm: compute the sum of squared differences across dimensions, then take the square root. Walk through a simple example and discuss edge cases and complexity.

Pro tip: Mention that for very large dimensions or many distance computations, you can avoid the square root if only comparing distances, and consider using a numerically stable approach like math.hypot for 2D or scaling for high dimensions.

1. Clarify requirements and assumptions

Confirm that both points are lists of floats of equal length, and decide how to handle edge cases like empty lists or mismatched dimensions (e.g., raise an error).

2. Explain the algorithm

Describe the Euclidean distance formula: sqrt(sum((a_i - b_i)^2 for i in range(n))). Emphasize iterating over dimensions, computing squared differences, summing, and taking the square root.

3. Write the code

Implement the function in a clean, readable way, using a loop or a generator expression with sum. Include input validation if appropriate.

4. Test with examples

Walk through a simple test case (e.g., 2D points) to verify correctness, and mention testing edge cases like identical points (distance 0) and high dimensions.

5. Discuss complexity and optimizations

State time complexity O(n) and space O(1). Mention potential optimizations like using math.hypot for 2D, avoiding sqrt when comparing distances, or using NumPy for performance.

Key Points to Mention

  • Input validation: ensure both points have the same length and are non-empty.
  • Algorithm: sum of squared differences followed by square root.
  • Time complexity O(n) and space complexity O(1).
  • Edge cases: identical points (distance 0), zero-dimensional points, mismatched dimensions.
  • Numerical stability: use math.hypot for 2D or scaling for very large/small values.
  • Optimization: avoid sqrt if only comparing distances; use NumPy for large-scale computations.

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

Q2

Using the distance function you just wrote, implement a k-nearest neighbors lookup that takes a query point, an integer k, and a dataset, and returns the indices of the k closest points sorted by increasing distance. Break ties by smaller index.

Algorithms & Data Structures
Author's notes

The tie-breaking rule is where I almost fumbled.

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AI HintsAI Generated

Suggested Approach

Start by clarifying the problem constraints (e.g., dataset size, dimensionality, whether k is small relative to n) and then propose a solution using a max-heap of size k to efficiently track the k nearest neighbors. For each point, compute the distance using the provided function, and maintain the heap with a tie-breaking rule that favors smaller indices. Finally, extract the indices from the heap and sort them by increasing distance (and index for ties) to return the result.

Pro tip: Mention that you would use a max-heap of size k to achieve O(n log k) time, which is optimal when k is much smaller than n, and discuss how to handle ties consistently by comparing indices when distances are equal.

1. Clarify requirements and constraints

Ask about dataset size, dimensionality, whether k can be larger than the dataset, and if the distance function returns a numeric value. Confirm that ties should be broken by smaller index.

2. Choose the right data structure

Decide between a max-heap of size k (for efficiency when k << n) or sorting all points (for simplicity when n is small). Explain the trade-offs.

3. Implement the heap-based selection

Iterate through the dataset, compute distance for each point, and maintain a max-heap of size k. For ties, compare indices to ensure the heap keeps the k smallest distances with smaller indices preferred.

4. Extract and sort the results

After processing all points, extract the indices from the heap and sort them by increasing distance, breaking ties by smaller index. Return the sorted list.

5. Analyze complexity and edge cases

State the time complexity O(n log k) and space O(k). Discuss edge cases: k=0, k > n, duplicate points, and negative distances (if applicable).

Key Points to Mention

  • Use a max-heap of size k to efficiently find the k smallest distances.
  • Tie-breaking: when distances are equal, the point with the smaller index should be considered closer.
  • Time complexity: O(n log k) for heap approach, which is optimal for large n and small k.
  • Space complexity: O(k) for the heap, plus O(k) for the result.
  • Edge cases: handle k=0, k >= n, and ensure the distance function is called correctly.
  • Alternative approaches: sorting all points O(n log n) or quickselect O(n) average, but heap is simpler and efficient for small k.

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