GE HealthCare·Software Engineer·Technical Phone Screen·Intermediate

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Apr 2026

Summary

Got a grid-based algorithm question at GE HealthCare, which felt more like a competitive programming problem than anything I'd expect from a healthtech company. The question had layers to it and they wanted you to walk through both the naive and optimized approaches, which caught me a bit flat-footed.

Questions Asked (1)

Given an M x N grid of 0s and 1s where 1 represents a CVS store location, compute the distance from every cell to its nearest store, then find the placement of stores that minimizes the total sum of all those distances. Walk through a brute-force approach and an optimized solution and explain the trade-offs.

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

I started with brute force, BFS from every cell independently to find its nearest 1.

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AI HintsAI Generated

Suggested Approach

Start by clarifying the problem: the first part is computing distances to nearest stores, which is a classic multi-source BFS. The second part is an optimization problem: choosing store placements to minimize total distance. For the optimization, discuss brute-force (try all combinations) and then optimized approaches like dynamic programming or greedy heuristics, highlighting trade-offs in time and optimality.

Pro tip: Mention that the optimization problem is NP-hard in general (like k-median), so for large grids, exact solutions are infeasible; instead, discuss approximation algorithms or heuristics, and relate to real-world constraints like store placement costs.

1. Clarify the problem

Restate the problem to ensure understanding: given a grid with some cells as stores, compute distance from each cell to nearest store, then find store placements minimizing total distance. Ask if the number of stores is fixed or variable, and if stores can be placed anywhere.

2. Solve distance computation

Explain that for a fixed set of stores, distances can be computed efficiently using multi-source BFS from all stores simultaneously, giving O(MN) time. This is optimal for grid distances.

3. Brute-force optimization

For choosing store placements, brute-force would try all possible combinations of k stores among MN cells, compute total distance for each, and pick the minimum. This is O(C(MN, k) * MN), which is exponential and only feasible for very small grids.

4. Optimized approaches

Discuss that the problem is NP-hard (k-median on grid). For exact solutions, use dynamic programming for 1D or small grids; for larger, use approximation algorithms like greedy (repeatedly add store that reduces total distance most) or local search. Mention that multi-source BFS can be reused to evaluate each candidate set quickly.

5. Trade-offs and conclusion

Compare brute-force (exact but infeasible for large inputs) vs. optimized (heuristic/approximate but scalable). Emphasize that in practice, constraints dictate the approach, and discuss potential improvements like using k-d trees or clustering.

Key Points to Mention

Multi-source BFS for computing distances from all cells to nearest store in O(MN) time.
Brute-force combinatorial explosion: number of ways to place k stores is C(MN, k), infeasible for large grids.
The optimization problem is equivalent to the k-median problem on a grid, which is NP-hard.
Greedy heuristic: iteratively place stores where they reduce total distance the most; not optimal but efficient.
Dynamic programming for 1D or small grids: can find optimal placement by considering intervals.
Trade-offs: exact vs. approximate, time vs. optimality, and scalability for real-world applications.

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