Google·Software Engineer·Technical Phone Screen·Intermediate

Intermediate

Apr 2026

Summary

Google SWE interview that focused on a graph problem I thought I'd already solved, then immediately asked me to re-solve it a different way. The follow-up felt like a gut check on whether I actually understood the first solution or just memorized it.

Questions Asked (1)

Given the minimax path problem (find a path from the top-left to bottom-right of a grid that minimizes the maximum cell height along the path), can you solve it using DFS instead of Dijkstra? Walk through a binary search approach where you pick a threshold T and run DFS/BFS to check reachability, then analyze the time complexity versus the Dijkstra approach and discuss the trade-offs.

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

I knew the Dijkstra version cold, so I figured this would be easy.

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AI HintsAI Generated

Suggested Approach

Confirm that DFS/BFS can be used with binary search on the threshold T to solve the minimax path problem, then walk through the binary search + DFS approach step by step. Finally, compare its time complexity with Dijkstra's and discuss trade-offs such as simplicity, constant factors, and applicability.

Pro tip: Mention that the binary search + DFS approach is often preferred in practice for grid problems due to its simplicity and cache-friendly BFS, but Dijkstra is more general for weighted graphs. Also, note that the threshold T can be binary searched over the sorted unique heights to reduce the search space.

1. Clarify the problem and approach

Restate the minimax path problem and confirm that the goal is to minimize the maximum cell height along a path. Explain that binary search on T combined with DFS/BFS reachability can solve it.

2. Binary search on threshold T

Describe how to binary search over the possible height values (or sorted unique heights) to find the smallest T such that there exists a path from start to end where all cells have height ≤ T.

3. Reachability check with DFS/BFS

For a given T, run DFS or BFS from the start cell, only moving to adjacent cells with height ≤ T. If the end cell is reached, T is feasible.

4. Analyze time complexity

Binary search takes O(log H) iterations, where H is the number of unique heights. Each DFS/BFS takes O(V+E) = O(mn) for an m×n grid. Total: O(mn log H). Dijkstra with a priority queue takes O(mn log(mn)).

5. Discuss trade-offs

Compare: binary search + DFS is simpler to implement, uses less memory (no priority queue), and can be faster in practice due to lower constant factors. Dijkstra is more general (handles weighted edges) and may be preferred when edge weights vary or when the graph is not a grid.

Key Points to Mention

Binary search over the threshold T (or sorted unique heights) to find the minimum possible maximum height.
DFS/BFS reachability check for a given T: only traverse cells with height ≤ T.
Time complexity: O(mn log H) for binary search + DFS vs O(mn log(mn)) for Dijkstra.
Space complexity: DFS/BFS uses O(mn) for visited set, Dijkstra uses O(mn) for distance array and priority queue.
Trade-offs: simplicity, constant factors, memory usage, and generality (Dijkstra works for weighted graphs).
Optimization: binary search over sorted unique heights reduces log factor; early termination in DFS/BFS when end is reached.

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