Generate binomial matrix and column-normalize
Company: Google
Role: Data Scientist
Category: Data Manipulation (SQL/Python)
Difficulty: Medium
Interview Round: Technical Screen
Using Python with NumPy, generate a 100×100 matrix of Binomial(n = 10, p = 0.3) draws with a fixed random seed, then normalize each column so it sums to 1. Ensure vectorized code, guard against any all-zero column by leaving it as all zeros or replacing with a uniform distribution (state your choice), and verify numerically that column sums are 1 within floating-point tolerance. Provide time and space complexity and a brief unit test.
Quick Answer: This question evaluates a candidate's ability to perform vectorized data manipulation and numerical validation with Python/NumPy, covering random matrix generation, column normalization, handling edge cases like all-zero columns, and producing unit tests plus time and space complexity analysis.