← Pinterest Interview Insights
Model the grid as a graph where each cell is a node and edges connect to its 8 neighbors if they are not obstacles. Run a BFS or DFS from each robot's starting cell to find all reachable cells, then take the union of the two sets. Return the count or the set of unique cells.
Pro tip: Clarify whether the robots can occupy the same cell and whether obstacles are static; this shows attention to detail and avoids incorrect assumptions. Also, mention that using a single visited set for both BFS runs can save memory and time.
Ask about grid size, obstacle representation, robot starting positions, and whether movement is simultaneous or independent. Confirm that reachability is independent for each robot.
Select BFS or DFS for reachability. BFS is often preferred for shortest path but either works for reachability; mention trade-offs like recursion depth for DFS.
Use a queue (BFS) or stack (DFS) and a visited set to avoid revisiting cells. For each robot, start from its initial cell and explore all 8 directions, skipping obstacles and out-of-bounds cells.
After both traversals, combine the visited sets (e.g., using set union) to get all reachable cells. Return the count or the set itself as required.
State time complexity O(R*C) and space O(R*C) for visited set. Suggest optimizations like early termination if one robot covers all cells or using a single visited set for both robots.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
This is where things went sideways for me.
Model the environment as a graph, compute reachable cells via BFS, then formulate the multi-robot coverage problem as an optimization over partitions and schedules. For minimum total moves, minimize the sum of individual path lengths; for minimum makespan, minimize the maximum individual path length. Discuss how the objective changes the partitioning strategy and coordination.
Pro tip: Mention that minimizing total moves often leads to unbalanced partitions (one robot does most work) while minimizing makespan requires balancing the load, and that the latter is generally harder (NP-hard) but can be approximated with heuristics like binary search on makespan.
Represent the environment as a graph where nodes are cells and edges are valid moves. Identify all reachable cells from the robots' start positions using BFS or DFS.
Clearly define total moves as the sum of moves made by both robots, and makespan as the maximum of the two robots' move counts. Explain that these metrics lead to different optimization goals.
For minimum total moves, assign cells to robots to minimize the sum of path lengths, possibly using a greedy or dynamic programming approach. For minimum makespan, balance the workload by partitioning cells into two sets with roughly equal coverage times, using binary search on the makespan and checking feasibility.
Plan paths that avoid collisions and redundant coverage. For makespan, synchronize movements so both robots finish simultaneously; for total moves, allow one robot to idle if it reduces overall moves.
Discuss the computational complexity: minimum total moves can be solved optimally for small instances but is NP-hard in general; minimum makespan is also NP-hard but can be approximated. Mention that the choice depends on the application's priority.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.