Microsoft·Software Engineer·Technical Phone Screen·Intermediate

Intermediate

May 2026

Summary

Microsoft SWE interview with a grid traversal problem that looks like BFS but has a twist that'll trip you up if you're not careful. One question, fairly well-defined, but the edge cases pile up fast.

Questions Asked (1)

Given an m x n grid of open and blocked cells, find the minimum number of moves to travel from a start cell to a target cell, where each move lets you travel 1 to k cells in a straight cardinal direction as long as every cell along the path is open and within bounds. Return -1 if the target is unreachable.

Algorithms & Data Structures

Author's notes

My first instinct was plain BFS and I started coding before fully thinking through what 'move' meant here.

Create a free account to read the full note

AI HintsAI Generated

Suggested Approach

Model the grid as a graph where each cell is a node, and edges exist between cells that can be reached in one move (up to k steps in a cardinal direction through open cells). Use BFS to find the shortest path from start to target, as BFS guarantees minimum moves in an unweighted graph. Optimize neighbor generation by scanning in each direction until blocked or out of bounds, and consider pruning visited cells to avoid redundant exploration.

Pro tip: Mention that while BFS is standard, you can optimize by using a priority queue (Dijkstra) if moves have different costs, but here all moves cost 1 so BFS is optimal. Also, discuss how to handle large k efficiently by stopping early when hitting a blocked cell or boundary, and consider using a visited set to skip already processed cells.

1. Clarify problem constraints and edge cases

Ask about grid size limits, k value, whether start and target are guaranteed open, and if moves can be zero (start equals target). Confirm that moves are only cardinal and cannot jump over blocked cells.

2. Choose BFS as the core algorithm

Explain that BFS is ideal for finding the shortest path in an unweighted graph. Each cell is a node, and from a cell you can move up to k steps in four directions if all intermediate cells are open.

3. Design efficient neighbor generation

For each direction, iterate step by step up to k, checking bounds and openness. Stop early if a blocked cell is encountered. Use a queue to process cells level by level, tracking distance.

4. Handle visited states and termination

Mark cells as visited when enqueued to avoid reprocessing. If the target is reached, return the current distance. If the queue empties without reaching target, return -1.

5. Analyze complexity and potential optimizations

Time complexity is O(m*n*k) in worst case, but can be improved by skipping visited cells during scanning. Space complexity is O(m*n) for the queue and visited set. Mention possible optimizations like bidirectional BFS or A* if heuristic available.

Key Points to Mention

BFS guarantees shortest path in unweighted graphs, making it suitable for this problem.
Neighbor generation must check all cells along the path up to k steps, stopping at blocked cells or boundaries.
Use a visited set to avoid cycles and redundant work, marking cells when enqueued.
Edge cases: start equals target (return 0), unreachable target (return -1), and k larger than grid dimensions.
Complexity analysis: O(m*n*k) time, O(m*n) space, with potential to optimize by skipping visited cells during scanning.
Alternative approaches like Dijkstra with priority queue are unnecessary since all moves have equal cost.

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