Meta·Machine Learning Engineer·Technical Phone Screen·Senior

Senior

Jun 2026

Summary

Meta MLE interview with a greedy optimization problem involving resource allocation between two agents. Pretty clean problem once you see the right framing, but the constraint on k makes it trickier than it first looks.

Questions Asked (1)

Given n types of cheese and two mice, where mouse 1 eats exactly k types and mouse 2 eats the rest, and each cheese has a separate reward value per mouse, find the assignment that maximizes total reward.

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

The naive approach is to try all combinations which obviously blows up.

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AI HintsAI Generated

Suggested Approach

First, clarify the problem: we need to select exactly k types for mouse 1, and the rest go to mouse 2, maximizing the sum of rewards. This is equivalent to choosing k items to assign to mouse 1, where the gain of assigning item i to mouse 1 instead of mouse 2 is (reward1[i] - reward2[i]). Then sort these gains and pick the top k.

Pro tip: Mention that this greedy approach works because the objective is linear and the constraint is a simple cardinality constraint; also note that if k is not fixed, the problem becomes trivial (assign each cheese to the mouse with higher reward).

1. Understand the problem and constraints

Restate the problem: n cheeses, two mice, mouse 1 must eat exactly k types, mouse 2 eats the rest. Each cheese has a reward for each mouse. Goal: maximize total reward.

2. Transform to a selection problem

Define the baseline where all cheeses go to mouse 2. Then, assigning cheese i to mouse 1 changes the total reward by delta_i = reward1[i] - reward2[i].

3. Solve with greedy sorting

Sort the deltas in descending order and pick the top k cheeses to assign to mouse 1. The total reward is sum(reward2) + sum of top k deltas.

4. Analyze complexity and edge cases

Time complexity: O(n log n) due to sorting. Space: O(n) for deltas. Handle edge cases: k=0 (all to mouse 2), k=n (all to mouse 1), and ties in deltas.

5. Discuss alternative approaches and trade-offs

Mention that dynamic programming is unnecessary but could be used if constraints were different (e.g., if mouse 1 had a capacity constraint). Greedy is optimal here due to matroid structure or exchange argument.

Key Points to Mention

The problem reduces to selecting k items with the largest difference in rewards.
Greedy algorithm is optimal because the objective is linear and the feasible sets form a uniform matroid.
Time complexity O(n log n) and space O(n).
Edge cases: k=0, k=n, and negative deltas (if all deltas are negative, we still must pick k, so pick the least negative).
Proof of optimality via exchange argument: if an optimal solution doesn't include the item with the highest delta, swapping it in improves or maintains the total reward.
If k is not fixed, the problem is trivial: assign each cheese to the mouse with higher reward.

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