Tubitv·Machine Learning Engineer·Technical Phone Screen·Intermediate

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Jun 2026Remote

Summary

Interviewed for an ML Engineer role at Tubitv and got a probability/sampling problem that looked deceptively simple at first glance. The core challenge was implementing weighted random sampling efficiently, which ended up being more of an algorithms question than anything ML-specific.

Questions Asked (1)

Design and implement a class that takes an array of positive integer weights and supports a method that returns a random index with probability proportional to its weight, with O(n) construction time and O(log n) per query.

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

My first instinct was to just expand the weights into a big array and sample uniformly, which works but blows up memory if weights are huge.

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AI HintsAI Generated

Suggested Approach

Start by clarifying the requirements and constraints, then propose using prefix sums and binary search to achieve O(n) construction and O(log n) query. Explain the algorithm step-by-step, analyze time and space complexity, and discuss potential pitfalls like floating-point precision and edge cases.

Pro tip: Mention that you can avoid floating-point issues by using integer prefix sums and binary search on a random integer in [0, totalWeight). Also, note that if weights are updated frequently, a Fenwick tree could support O(log n) updates, but for static weights, prefix sums are simpler and faster.

1. Clarify requirements and constraints

Confirm that weights are positive integers, the array is static (no updates), and queries should be independent. Ask about expected input size and performance requirements.

2. Design the data structure

Propose storing prefix sums of weights in an array, where prefix[i] = sum of weights[0..i]. This allows O(n) construction and O(log n) queries via binary search.

3. Explain the query algorithm

Generate a random integer r uniformly in [0, totalWeight). Use binary search to find the smallest index i such that prefix[i] > r. Return i.

4. Analyze complexity and edge cases

State that construction is O(n) time and O(n) space, and each query is O(log n) time. Discuss handling of zero weights (if allowed) and large sums causing overflow.

5. Implement and test

Write clean code for the class, including constructor and method. Test with small examples, edge cases (single element, all equal weights), and verify probabilities empirically.

Key Points to Mention

Prefix sums enable O(1) range sum queries, which are essential for weighted random selection.
Binary search on prefix sums gives O(log n) query time, meeting the requirement.
Use integer arithmetic to avoid floating-point precision issues; generate a random integer in [0, totalWeight).
The algorithm is equivalent to inverse transform sampling for discrete distributions.
Space complexity is O(n) for storing prefix sums, which is optimal for this problem.
If weights can be updated, consider a Fenwick tree (Binary Indexed Tree) for O(log n) updates and queries.

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