Amazon·Software Engineer·Technical Phone Screen·Intermediate

Intermediate

Jun 2026

Summary

Amazon SWE coding round, one question about grid traversal and robot coverage. Pretty standard algorithmic problem but the details matter more than you'd think.

Questions Asked (1)

You're given a 2D grid representing a factory floor. Some cells are blocked, others contain robots. Can the robots collectively reach every unblocked cell? Robots move in four directions and can't pass through blocked cells.

Algorithms & Data Structures

Author's notes

My first instinct was multi-source BFS starting from every robot simultaneously, which is the right move.

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AI HintsAI Generated

Suggested Approach

Model the factory floor as a graph where unblocked cells are nodes and adjacent unblocked cells are edges. The robots can collectively reach every unblocked cell if and only if all robots and all unblocked cells belong to the same connected component. Use BFS/DFS from any robot to check if all unblocked cells are visited.

Pro tip: Clarify edge cases upfront: what if there are no robots? What if there are no unblocked cells? Also, mention that if the grid is large, you can optimize by only exploring from one robot and counting visited cells against total unblocked cells.

1. Clarify the problem

Confirm that robots can move independently and that 'collectively reach' means every unblocked cell is reachable by at least one robot. Ask about grid size, robot count, and whether robots can occupy the same cell.

2. Model as a graph

Treat each unblocked cell as a node, with edges between adjacent unblocked cells (up, down, left, right). The problem reduces to checking if all unblocked cells are in a single connected component that contains at least one robot.

3. Choose traversal algorithm

Use BFS or DFS starting from any robot to explore the connected component. Count the number of unblocked cells visited and compare with the total number of unblocked cells.

4. Handle edge cases

If there are no robots, return true only if there are no unblocked cells. If there are unblocked cells but no robots, return false. Also consider disconnected components with no robots.

5. Analyze complexity and optimize

Time complexity is O(m*n) for BFS/DFS, space O(m*n) for visited set. Mention that you can avoid extra space by modifying the grid in-place if allowed.

Key Points to Mention

Graph connectivity: all unblocked cells must be in one connected component.
BFS/DFS traversal from a robot to mark reachable cells.
Counting total unblocked cells and comparing with visited count.
Edge cases: no robots, no unblocked cells, multiple disconnected components.
Time and space complexity: O(m*n) time, O(m*n) space (or O(1) extra if modifying grid).
Alternative: Union-Find (Disjoint Set Union) to group connected cells, then check if all unblocked cells share the same root as a robot.

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