Shortest Distance from All Buildings
You want to build a house on an empty land that is closest to all the buildings. Find the shortest total travel distance to all buildings. Use BFS starting from each building.
Why Interviewers Ask This
Salesforce asks this to evaluate a candidate's ability to handle complex graph traversal problems with multiple constraints. They specifically test if you can optimize for space and time when performing Breadth-First Search from multiple sources, ensuring the solution scales efficiently without redundant calculations or memory overflows.
How to Answer This Question
1. Clarify Constraints: Immediately ask about grid dimensions, movement rules (4-directional), and whether buildings are passable obstacles. Salesforce values clarity before coding.
2. Define Strategy: Propose running BFS from each building separately rather than trying to solve it in one pass. Explain that you will accumulate distances and reachability counts for every empty land cell.
3. Data Structure Selection: Detail how you will use a 2D array to store total distance and another to track how many buildings reached each cell. Mention using a queue for the BFS layers.
4. Optimization Check: Discuss pruning invalid cells early if an empty land cannot reach all buildings, saving computation time.
5. Implementation Plan: Outline the loop structure: iterate through buildings, run BFS, update global grids, then find the minimum valid distance at the end.
Key Points to Cover
- Explicitly state the decision to run BFS from each building individually
- Mention the use of two matrices: one for total distance and one for reachability counts
- Explain how to filter out empty lands that cannot reach all buildings
- Clearly articulate the Time Complexity as O(Buildings * GridSize)
- Demonstrate awareness of edge cases like disconnected components
Sample Answer
To solve the 'Shortest Distance from All Buildings' problem, I would first clarify the grid constraints, such as maximum size and whether diagonal movement is allowed. My approach involves treating each building as a source node for a Breadth-First Search. Instead of attempting a complex multi-source search, I will iterate through every building in the grid. For each building, I will perform a standard BFS to calculate the shortest distance to all reachable empty lands, accumulating these distances in a separate result matrix. Simultaneously, I will maintain a visitation count matrix to ensure a specific empty land is reachable from every single building. Once all buildings have been processed, I will scan the result matrix to find the empty land cell where the visitation count equals the total number of buildings and the accumulated distance is minimized. This approach ensures we only consider valid locations. In terms of complexity, if there are B buildings and an MxN grid, the time complexity is O(B * M * N) because we traverse the grid once per building. Space complexity is also O(M * N) for our auxiliary matrices. This method aligns well with Salesforce's focus on scalable, efficient algorithms for large datasets, ensuring we don't waste resources on unreachable paths.
Common Mistakes to Avoid
- Attempting a single BFS from a hypothetical center point which fails to account for varying building locations
- Forgetting to track which buildings have visited each cell, leading to incorrect distance sums
- Ignoring the constraint that walls block movement, causing infinite loops or wrong path calculations
- Failing to check if the optimal location is actually reachable from every single building
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