Google·Data Scientist·Technical Phone Screen·Senior

Senior

Jun 2026

Summary

Google data scientist technical screen, basically one meaty coding problem that touched NumPy, probability, and numerical correctness all at once. More involved than I expected for a phone round.

Questions Asked (1)

Using Python and NumPy, generate a 100x100 matrix of binomial draws (n=10, p=0.3) with a fixed random seed, then normalize each column to sum to 1. Handle any all-zero columns explicitly, verify column sums within floating-point tolerance, and provide time/space complexity plus a unit test.

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

This question has a lot of layers and I underestimated it at first.

Create a free account to read the full note

AI HintsAI Generated

Suggested Approach

Start by clarifying the requirements and edge cases, then outline a vectorized NumPy solution that uses a fixed seed, handles all-zero columns by setting them to uniform or zero, and verifies column sums with np.allclose. Finally, analyze time and space complexity and provide a unit test using pytest or unittest.

Pro tip: Mention that using a fixed seed ensures reproducibility, but also discuss the trade-off between reproducibility and randomness in production; for all-zero columns, explicitly state your handling strategy (e.g., uniform distribution) and justify it.

1. Clarify requirements and edge cases

Confirm the parameters (n=10, p=0.3, shape 100x100), the meaning of normalization (sum to 1 per column), and how to handle all-zero columns (e.g., set to uniform or leave as zeros).

2. Implement the solution with NumPy

Use np.random.seed for reproducibility, generate the matrix with np.random.binomial, compute column sums, and normalize by dividing each column by its sum, handling zero sums explicitly.

3. Verify correctness

Check that all column sums are approximately 1 using np.allclose with a tolerance, and ensure no division by zero occurs.

4. Analyze complexity

State that time complexity is O(m*n) for generating and normalizing (m=100, n=100), and space complexity is O(m*n) for storing the matrix.

5. Write a unit test

Create a test that checks the shape, column sums, and reproducibility with the same seed, and verifies that all-zero columns are handled as specified.

Key Points to Mention

Use of np.random.seed for reproducibility and its implications.
Vectorized operations for efficiency (avoid loops).
Handling all-zero columns: set to uniform distribution or zeros, with justification.
Verification with np.allclose and appropriate tolerance (e.g., 1e-9).
Time and space complexity analysis (O(m*n)).
Unit testing with pytest or unittest, including edge cases.

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