Shortest Distance from All Buildings (BFS)
You are given a grid of 0s, 1s, and 2s. Find an empty land (0) that has the shortest total travel distance to all buildings (1s). This is a multi-source shortest path problem using BFS.
Why Interviewers Ask This
Meta evaluates candidates on their ability to optimize graph traversal in constrained environments. This problem tests if you can handle multi-source BFS efficiently without redundant calculations, ensuring the solution scales with grid size while managing memory usage for distance accumulation.
How to Answer This Question
1. Clarify constraints: Ask about grid dimensions and whether buildings are reachable from all empty lands. 2. Define the core strategy: Explain that running BFS from every building is better than from every empty land to avoid repeated traversals of the same nodes. 3. Outline the algorithm: Describe iterating through each building, performing a level-order BFS to record distances to reachable empty lands, and accumulating these distances in a separate matrix. 4. Discuss optimization: Mention checking reachability (ensuring all buildings can reach a spot) and pruning paths that exceed current minimums. 5. Analyze complexity: State the time complexity as O(M*N*Buildings) and space complexity as O(M*N) for storing distances and visited states. 6. Validate edge cases: Address scenarios with no valid empty land or unreachable buildings.
Key Points to Cover
- Running BFS from each building is more efficient than from each empty land
- Using a visit count matrix to verify all buildings can reach a specific location
- Accumulating distances in a separate matrix during traversal to avoid re-computation
- Handling edge cases where no valid meeting point exists or buildings are isolated
- Explicitly stating time and space complexity relative to grid dimensions
Sample Answer
To solve this, I would first clarify the input constraints, specifically the maximum grid size and whether we assume connectivity. My approach involves a reverse BFS strategy. Instead of starting from every empty land, w…
Common Mistakes to Avoid
- Attempting to run BFS from every empty land, leading to Time Limit Exceeded errors on large grids
- Failing to track which buildings have reached a specific cell, resulting in invalid solutions
- Ignoring obstacles (2s) during BFS traversal, causing incorrect path calculations
- Not handling the case where multiple buildings exist but cannot reach any common empty land
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