Tesla·Machine Learning Engineer·Technical Phone Screen·Senior

Senior

May 2026

Summary

Tesla ML engineer interview, technical phone screen that went deep fast. One question, very algorithmic, felt more like a geometry/CS fundamentals test than anything ML-specific.

Questions Asked (1)

Given a polyline defined by N 2D coordinates, a list of M step distances, and a threshold t, simulate walking along the polyline by advancing each step distance from the current position. After each step, find the nearest vertex within t miles and return its index (or None). Implement this efficiently using NumPy, avoiding naive O(N*M) scanning, and handle edge cases like zero-length segments, repeated points, d=0, and empty input. Discuss time and space complexity.

Algorithms & Data StructuresTechnical Trade-offsSystem Design

Author's notes

This one took me a minute to even parse.

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AI HintsAI Generated

Suggested Approach

First, preprocess the polyline by computing cumulative arc lengths and segment vectors, then for each step, advance the current arc length and use vectorized NumPy operations to find the nearest vertex within threshold t. To avoid O(N*M), build a spatial index (e.g., KD-tree) or use broadcasting with chunking for efficient nearest neighbor queries, and handle edge cases by validating inputs and using epsilon tolerances.

Pro tip: Mention that for Tesla-scale data, you'd use a spatial index like a KD-tree or ball tree from scipy.spatial, and consider parallelizing across steps with NumPy's vectorization or even GPU acceleration, but always start with a correct baseline and profile before optimizing.

1. Clarify and Validate Inputs

Confirm the problem details: polyline as array of shape (N,2), steps as array of M distances, threshold t. Check for empty inputs, zero-length segments, repeated points, and d=0, and decide on behavior (e.g., return None if no vertex within t).

2. Preprocess Polyline

Compute segment vectors, segment lengths, and cumulative arc lengths. Handle zero-length segments by skipping or merging them. Use NumPy for vectorized computation.

3. Simulate Walking and Find Nearest Vertex

For each step, update the current arc length, then find the nearest vertex within t. Use a spatial index (e.g., KD-tree) built on vertices for efficient queries, or vectorized distance computation with broadcasting if N is small.

4. Handle Edge Cases and Return Results

Ensure d=0 returns the current nearest vertex, empty inputs return empty list, and no vertex within t returns None. Use epsilon for floating-point comparisons.

5. Analyze Complexity and Optimize

Discuss time and space complexity: preprocessing O(N), each step O(log N) with KD-tree, total O(N + M log N). Space O(N). Mention trade-offs and potential optimizations like batch queries or GPU.

Key Points to Mention

Use cumulative arc length to map step distances to positions on the polyline.
Leverage NumPy vectorization for distance computations and avoid Python loops.
Build a spatial index (KD-tree) for efficient nearest neighbor queries, reducing complexity from O(N*M) to O(N + M log N).
Handle zero-length segments and repeated points by filtering or using epsilon tolerances.
For d=0, return the nearest vertex to the current position without advancing.
Discuss time and space complexity, and mention potential parallelization or GPU acceleration for large-scale data.

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