Microsoft·Software Engineer·Technical Phone Screen·Intermediate

IntermediatePrefer not to say

Jun 2026

Summary

Microsoft coding interview, grid path problem that sounds straightforward until you realize brute force won't cut it. Came away feeling okay about my solution but not totally sure I nailed the explanation.

Questions Asked (1)

Given an m x n grid of integers, find a path from the top-left to the bottom-right corner (moving in any of the four directions) such that the minimum value along the path is as large as possible. Return that maximized minimum value.

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

My first instinct was pure BFS and I started coding before really thinking it through.

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AI HintsAI Generated

Suggested Approach

Reframe the problem as finding the maximum threshold T such that there exists a path from start to end where all cells have value >= T. Use binary search on T and for each T, check connectivity via BFS/DFS. Alternatively, use a max-heap (Dijkstra-like) to greedily expand the path with the highest minimum value so far.

Pro tip: Mention that the binary search approach is O(mn log(maxVal)) and the heap approach is O(mn log(mn)); both are acceptable, but the heap approach is more efficient when values are large. Also, clarify that the path can revisit cells, but optimal paths never need to.

1. Clarify the problem and constraints

Confirm that movement is allowed in all four directions, that the path can be any length, and that we want to maximize the minimum value along the path. Ask about grid size and value range to choose the best algorithm.

2. Identify the core algorithmic pattern

Recognize this as a 'maximin' path problem, which can be solved by binary search on the answer or by a modified Dijkstra using a max-heap. Explain that both approaches are valid and discuss trade-offs.

3. Outline the chosen approach

For binary search: define low and high bounds, and for each mid, run BFS/DFS to check if a path exists using only cells >= mid. For heap: initialize a max-heap with the start cell, and repeatedly pop the cell with the largest minimum value, updating neighbors.

4. Analyze complexity and edge cases

State time and space complexity for your approach. Discuss edge cases: 1x1 grid, all equal values, negative values, and unreachable destination (though always reachable in a grid).

5. Test with a small example

Walk through a small grid (e.g., 3x3) to demonstrate how the algorithm works and verify correctness. Mention that you would write unit tests for edge cases.

Key Points to Mention

Binary search on the answer combined with BFS/DFS for connectivity check.
Max-heap (priority queue) approach similar to Dijkstra's algorithm, where the priority is the minimum value along the path so far.
Time complexity: O(mn log(maxVal)) for binary search, O(mn log(mn)) for heap approach.
Space complexity: O(mn) for visited set and queue/heap.
Edge cases: single cell, negative values, all cells same value.
Optimization: early termination when start or end value is less than current threshold.

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