Two Sigma·Data Scientist·Technical Phone Screen·Intermediate

Intermediate

Jun 2026

Summary

Two Sigma Data Scientist round, algorithmic coding question focused on assignment optimization. Clean problem statement but the O(n log n) constraint is what makes or breaks you here.

Questions Asked (1)

You have 2n workers and two tasks. Each worker has a time cost for task A and a different time cost for task B. You must assign exactly n workers to each task. Return the minimum total hours across all workers.

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

My first instinct was brute force and I basically said that out loud before catching myself.

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AI HintsAI Generated

Suggested Approach

First, clarify the problem: we need to choose exactly n workers for task A and the remaining n for task B, minimizing the sum of their respective costs. A greedy approach works: sort workers by the difference (costA - costB), assign the first n to task A and the rest to task B. Prove optimality via an exchange argument.

Pro tip: Mention that this is a classic scheduling problem solvable in O(n log n) time, and emphasize that the greedy choice is optimal because any swap that moves a worker from B to A and another from A to B cannot reduce the total cost when the list is sorted by the difference.

1. Understand the problem

Restate the problem: given 2n workers with costs (a_i, b_i), assign exactly n to task A and n to task B to minimize total cost. Confirm that each worker must be assigned to exactly one task.

2. Identify the greedy strategy

Compute the difference d_i = a_i - b_i for each worker. Sort workers by d_i in ascending order. Assign the first n workers to task A and the remaining n to task B.

3. Prove optimality

Use an exchange argument: if there is an optimal assignment that differs, swapping a worker assigned to B with one assigned to A (where the B worker has a smaller d) does not increase the total cost. Thus the sorted greedy assignment is optimal.

4. Analyze complexity

Sorting takes O(n log n) time, and computing the total cost takes O(n) time. Space complexity is O(n) for storing the differences or O(1) extra if sorting in place.

5. Discuss edge cases and extensions

Consider cases where costs are equal, or when n=1. Also mention that the same approach works if we need to assign exactly k workers to A and 2n-k to B, by sorting and picking the k smallest differences.

Key Points to Mention

Greedy algorithm based on sorting by cost difference (a_i - b_i).
Exchange argument for proof of optimality.
Time complexity O(n log n) due to sorting.
Space complexity O(n) or O(1) extra.
Handling ties in differences arbitrarily.
Generalization to assigning k workers to task A.

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